Subgroups — C₁₃×#61175 #15747514

Order 3328.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3325	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3324	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3323	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3322	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3319	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3318	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3311	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3310	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#556	—	2	1	no	—
32	C₁₃×#556	C₂²	1	2	yes	complemented
33	C₁₃×#555	—	2	1	no	—
34	C₁₃×#555	C₂²	1	2	yes	complemented
35	C₁₃×#553	—	2	1	no	—
36	C₁₃×#553	C₂²	1	2	yes	complemented
37	C₁₃×#552	—	2	1	no	—
38	C₁₃×#552	C₂²	1	2	yes	complemented
39	C₁₃×#546	—	2	1	no	—
40	C₁₃×#546	—	2	1	no	—
41	C₁₃×#546	C₂²	1	2	yes	—
42	C₁₃×#546	C₂²	1	2	yes	—
43	D₄²×C₁₃	—	2	1	no	—
44	D₄²×C₁₃	—	2	1	no	—
45	D₄²×C₁₃	C₂²	1	2	yes	—
46	D₄²×C₁₃	C₂²	1	2	yes	—
47	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#538	—	2	2	no	—
49	C₁₃×#537	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#535	C₂²	1	1	yes	characteristic
51	C₁₃×#535	C₂²	1	1	yes	characteristic
52	C₁₃×#534	—	2	2	no	—
53	C₁₃×#529	—	2	2	no	—
54	C₁₃×#525	C₂²	1	1	yes	characteristic
55	C₁₃×#525	C₂²	1	1	yes	characteristic
56	C₁₃×#525	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₁₃×#120	—	2	2	no	—
58	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#518	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#490	C₂²	1	2	yes	complemented
63	C₁₃×#489	C₂²	1	2	yes	complemented
64	C₁₃×#488	C₂²	1	2	yes	complemented
65	C₁₃×#486	C₂²	1	2	yes	complemented
66	C₁₃×#485	C₂²	1	2	yes	complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#482	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	complemented
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	2	yes	complemented
72	C₁₃×#481	C₂²	1	2	yes	complemented
73	C₁₃×#480	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	complemented
75	C₁₃×#478	C₂²	1	2	yes	complemented
76	C₁₃×#476	C₂²	1	2	yes	complemented
77	C₁₃×#474	C₂²	1	2	yes	complemented
78	C₁₃×#470	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#470	C₂²	1	1	yes	characteristic, complemented
80	C₁₃×#469	C₂²	1	2	yes	complemented
81	C₁₃×#469	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#469	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#468	C₂²	1	2	yes	complemented
84	C₁₃×#468	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#468	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#468	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#468	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#466	C₂²	1	2	yes	complemented
89	C₁₃×#465	C₂²	1	2	yes	complemented
90	C₁₃×#464	C₂²	1	2	yes	complemented
91	C₁₃×#463	C₂²	1	2	yes	complemented
92	C₁₃×#460	C₂²	1	2	yes	complemented
93	C₁₃×#459	C₂²	1	2	yes	complemented
94	C₁₃×#452	C₂²	1	2	yes	complemented
95	C₁₃×#450	C₂²	1	2	yes	complemented
96	C₁₃×#450	C₂²	1	2	yes	complemented
97	C₁₃×#450	C₂²	1	2	yes	complemented
98	C₁₃×#449	C₂²	1	2	yes	complemented
99	C₁₃×#447	C₂²	1	2	yes	complemented
100	C₁₃×#447	C₂²	1	2	yes	complemented
101	C₁₃×#447	C₂²	1	2	yes	complemented
102	C₁₃×#442	C₂²	1	2	yes	complemented
103	C₁₃×#440	C₂²	1	2	yes	complemented
104	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
105	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
106	C₁₃×#436	C₂²	1	2	yes	complemented
107	C₁₃×#436	C₂²	1	2	yes	complemented
108	C₁₃×#435	C₂²	1	2	yes	complemented
109	C₁₃×#435	C₂²	1	2	yes	complemented
110	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
111	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
112	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
113	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
114	C₁₃×#418	C₂²	1	1	yes	characteristic
115	C₁₃×#418	C₂²	1	2	yes	complemented
116	C₁₃×#418	C₂²	1	2	yes	complemented
117	C₁₃×#418	C₂²	1	2	yes	complemented
118	C₁₃×#418	C₂²	1	2	yes	complemented
119	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
120	C₁₃×#418	C₂²	1	2	yes	complemented
121	C₁₃×#417	C₂²	1	2	yes	complemented
122	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
124	C₁₃×#416	C₂²	1	2	yes	complemented
125	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
126	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
128	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
129	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
132	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
134	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂⁵×C₁₃	—	2	1	no	—
136	C₁₃×H(5,𝔽₂)	—	2	4	no	—
137	C₁₃×H(5,𝔽₂)	—	4	2	no	—
138	C₂×C₁₃×#41	—	2	1	no	—
139	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×#41	C₂³	1	2	yes	—
142	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₁₃	—	2	4	no	—
144	C₂²×D₄×C₁₃	—	2	2	no	—
145	C₂²×D₄×C₁₃	—	2	1	no	—
146	C₂²×D₄×C₁₃	—	2	2	no	—
147	C₂²×D₄×C₁₃	—	2	2	no	—
148	C₂²×D₄×C₁₃	—	2	1	no	—
149	C₂²×D₄×C₁₃	—	2	1	no	—
150	C₂²×D₄×C₁₃	—	2	1	no	—
151	C₂²×D₄×C₁₃	—	4	2	no	—
152	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
153	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
154	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
155	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
156	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
158	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
159	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
160	C₁₃×#135	—	4	2	no	—
161	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic, complemented
162	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
163	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic, complemented
165	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic, complemented
166	C₂×C₁₃×D₈	C₂³	1	2	yes	—
167	C₂×C₁₃×D₈	C₂³	1	2	yes	—
168	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic, complemented
169	C₁₃×#131	—	4	2	no	—
170	C₂×C₁₃×M₁₆	—	4	2	no	—
171	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
177	C₂×C₁₃×M₁₆	C₂³	1	2	yes	complemented
178	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
179	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₁₃	C₂³	1	2	yes	complemented
181	C₁₃×C₄⋊Q₈	—	2	1	no	—
182	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
183	C₁₃×#127	—	2	1	no	—
184	C₁₃×#127	C₂³	1	2	yes	—
185	C₁₃×#126	—	2	2	no	—
186	C₁₃×#126	—	2	2	no	—
187	C₁₃×#126	—	2	2	no	—
188	C₁₃×#126	—	2	2	no	—
189	C₁₃×#125	—	2	2	no	—
190	C₁₃×#125	—	2	1	no	—
191	C₁₃×#125	C₂³	1	2	yes	complemented
192	C₁₃×#124	—	2	1	no	—
193	C₁₃×#124	—	2	2	no	—
194	C₁₃×#124	—	2	2	no	—
195	C₁₃×#124	—	2	2	no	—
196	C₁₃×#124	C₂³	1	2	yes	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	1	no	—
199	C₁₃×#123	—	2	1	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×#123	D₄	1	2	yes	—
204	C₁₃×C₂²⋊Q₈	—	2	1	no	—
205	C₁₃×C₂²⋊Q₈	—	2	2	no	—
206	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
209	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
213	C₁₃×#121	—	2	2	no	—
214	C₁₃×#121	—	2	1	no	—
215	C₁₃×#121	—	2	2	no	—
216	C₁₃×#121	—	2	2	no	—
217	C₁₃×#121	—	2	2	no	—
218	C₁₃×#121	—	2	2	no	—
219	C₁₃×#121	—	2	1	no	—
220	C₁₃×#121	—	2	1	no	—
221	C₁₃×#121	—	2	2	no	—
222	C₁₃×#121	—	2	2	no	—
223	C₁₃×#121	D₄	1	1	yes	characteristic
224	C₁₃×#121	D₄	1	1	yes	characteristic
225	C₁₃×#121	C₂³	1	1	yes	characteristic
226	C₁₃×#121	C₂³	1	1	yes	characteristic
227	C₁₃×#121	C₂³	1	2	yes	—
228	C₁₃×#121	C₂³	1	2	yes	—
229	C₁₃×#121	C₂³	1	1	yes	characteristic
230	C₁₃×#121	C₂³	1	1	yes	characteristic
231	C₁₃×#121	C₂³	1	2	yes	complemented
232	C₁₃×#120	—	2	1	no	—
233	C₁₃×#120	—	2	1	no	—
234	C₁₃×#120	—	2	2	no	—
235	C₁₃×#120	—	2	2	no	—
236	C₁₃×#120	—	2	2	no	—
237	C₁₃×#120	—	2	2	no	—
238	C₁₃×#120	—	2	2	no	—
239	C₁₃×#120	—	2	2	no	—
240	C₁₃×#120	—	2	2	no	—
241	C₁₃×#120	—	2	2	no	—
242	C₁₃×#120	D₄	1	2	yes	—
243	C₄×Q₈×C₁₃	—	2	1	no	—
244	C₄×Q₈×C₁₃	—	2	2	no	—
245	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
246	C₄×D₄×C₁₃	—	2	2	no	—
247	C₄×D₄×C₁₃	—	2	1	no	—
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	1	no	—
250	C₄×D₄×C₁₃	—	2	1	no	—
251	C₄×D₄×C₁₃	—	2	1	no	—
252	C₄×D₄×C₁₃	—	2	1	no	—
253	C₄×D₄×C₁₃	—	2	1	no	—
254	C₄×D₄×C₁₃	—	2	2	no	—
255	C₄×D₄×C₁₃	—	2	2	no	—
256	C₄×D₄×C₁₃	C₂³	1	2	yes	—
257	C₄×D₄×C₁₃	C₂³	1	2	yes	—
258	C₄×D₄×C₁₃	C₂³	1	2	yes	—
259	C₄×D₄×C₁₃	C₂³	1	2	yes	—
260	C₄×D₄×C₁₃	C₂³	1	2	yes	complemented
261	C₁₃×#117	—	2	1	no	—
262	C₁₃×#117	—	2	1	no	—
263	C₁₃×#117	—	2	1	no	—
264	C₁₃×#117	—	2	2	no	—
265	C₁₃×#117	—	2	2	no	—
266	C₁₃×#117	C₂³	1	1	yes	characteristic
267	C₁₃×#117	C₂³	1	1	yes	characteristic
268	C₁₃×#117	C₂³	1	2	yes	—
269	C₁₃×#117	C₂³	1	2	yes	—
270	C₁₃×#117	C₂³	1	1	yes	characteristic
271	C₁₃×#117	C₂³	1	2	yes	complemented
272	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
276	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²×C₁₃	—	2	1	no	—
281	C₁₃×#107	C₂³	1	1	yes	characteristic, complemented
282	C₁₃×#107	C₂³	1	1	yes	characteristic, complemented
283	C₁₃×#107	C₂³	1	2	yes	complemented
284	C₁₃×#107	C₂³	1	2	yes	complemented
285	C₁₃×#106	C₂³	1	1	yes	characteristic, complemented
286	C₁₃×#106	C₂³	1	1	yes	characteristic, complemented
287	C₁₃×#106	C₂³	1	2	yes	complemented
288	C₁₃×#106	C₂³	1	2	yes	complemented
289	C₁₃×C₄⋊C₈	C₂³	1	2	yes	complemented
290	C₁₃×C₄⋊C₈	C₂³	1	2	yes	complemented
291	C₁₃×#103	C₂³	1	1	yes	characteristic, complemented
292	C₁₃×#103	C₂³	1	2	yes	complemented
293	C₁₃×#103	C₂³	1	1	yes	characteristic, complemented
294	C₁₃×#103	C₂³	1	1	yes	characteristic, complemented
295	C₁₃×#103	C₂³	1	1	yes	characteristic, complemented
296	C₁₃×#103	C₂³	1	2	yes	complemented
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×#102	C₂³	1	2	yes	—
305	C₁₃×#102	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×#102	C₂³	1	2	yes	—
308	C₁₃×#102	C₂³	1	2	yes	—
309	C₁₃×#102	C₂³	1	1	yes	characteristic, complemented
310	C₁₃×#102	C₂³	1	2	yes	complemented
311	C₁₃×#102	C₂³	1	1	yes	characteristic, complemented
312	C₁₃×#102	C₂³	1	1	yes	characteristic, complemented
313	C₁₃×#102	C₂³	1	1	yes	characteristic, complemented
314	C₁₃×#102	C₂³	1	2	yes	complemented
315	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	complemented
318	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	complemented
319	C₁₃×#97	C₂³	1	2	yes	complemented
320	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
321	#61175	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂⁴×C₁₃	—	2	1	no	—
323	C₂⁴×C₁₃	—	2	2	no	—
324	C₂⁴×C₁₃	—	2	2	no	—
325	C₂⁴×C₁₃	—	2	1	no	—
326	C₂⁴×C₁₃	—	2	2	no	—
327	C₂⁴×C₁₃	—	4	4	no	—
328	C₂⁴×C₁₃	—	8	2	no	—
329	C₂⁴×C₁₃	—	8	2	no	—
330	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₁₃×#41	—	2	2	no	—
332	C₁₃×#41	—	2	2	no	—
333	C₁₃×#41	—	2	4	no	—
334	C₁₃×#41	—	2	2	no	—
335	C₁₃×#41	—	2	2	no	—
336	C₁₃×#41	—	2	2	no	—
337	C₁₃×#41	—	2	2	no	—
338	C₁₃×#41	—	4	2	no	—
339	C₁₃×#41	—	4	4	no	—
340	C₂×Q₈×C₁₃	—	2	2	no	—
341	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
342	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₁₃	—	2	4	no	—
345	C₂×D₄×C₁₃	—	2	4	no	—
346	C₂×D₄×C₁₃	—	2	4	no	—
347	C₂×D₄×C₁₃	—	2	1	no	—
348	C₂×D₄×C₁₃	—	2	1	no	—
349	C₂×D₄×C₁₃	—	2	1	no	—
350	C₂×D₄×C₁₃	—	2	1	no	—
351	C₂×D₄×C₁₃	—	2	2	no	—
352	C₂×D₄×C₁₃	—	2	1	no	—
353	C₂×D₄×C₁₃	—	2	1	no	—
354	C₂×D₄×C₁₃	—	2	2	no	—
355	C₂×D₄×C₁₃	—	2	2	no	—
356	C₂×D₄×C₁₃	—	2	2	no	—
357	C₂×D₄×C₁₃	—	2	1	no	—
358	C₂×D₄×C₁₃	—	2	2	no	—
359	C₂×D₄×C₁₃	—	2	2	no	—
360	C₂×D₄×C₁₃	—	2	2	no	—
361	C₂×D₄×C₁₃	—	2	1	no	—
362	C₂×D₄×C₁₃	—	2	2	no	—
363	C₂×D₄×C₁₃	—	2	2	no	—
364	C₂×D₄×C₁₃	—	2	2	no	—
365	C₂×D₄×C₁₃	—	2	2	no	—
366	C₂×D₄×C₁₃	—	2	2	no	—
367	C₂×D₄×C₁₃	—	4	2	no	—
368	C₂×D₄×C₁₃	—	4	2	no	—
369	C₂×D₄×C₁₃	—	4	2	no	—
370	C₂×D₄×C₁₃	—	4	4	no	—
371	C₂×D₄×C₁₃	—	4	4	no	—
372	C₂×D₄×C₁₃	—	4	4	no	—
373	C₂×D₄×C₁₃	—	4	4	no	—
374	C₂×D₄×C₁₃	—	4	8	no	—
375	C₂×D₄×C₁₃	—	8	4	no	—
376	C₂×D₄×C₁₃	—	8	4	no	—
377	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
378	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
379	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
380	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
381	C₂×D₄×C₁₃	#41	1	4	yes	—
382	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
383	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₁₃	—	2	2	no	—
387	C₂²×C₄×C₁₃	—	2	2	no	—
388	C₂²×C₄×C₁₃	—	2	1	no	—
389	C₂²×C₄×C₁₃	—	2	1	no	—
390	C₂²×C₄×C₁₃	—	2	2	no	—
391	C₂²×C₄×C₁₃	—	2	2	no	—
392	C₂²×C₄×C₁₃	—	2	1	no	—
393	C₂²×C₄×C₁₃	—	2	1	no	—
394	C₂²×C₄×C₁₃	—	2	2	no	—
395	C₂²×C₄×C₁₃	—	2	2	no	—
396	C₂²×C₄×C₁₃	—	2	2	no	—
397	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
403	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
404	C₁₃×Q₁₆	—	4	1	no	—
405	C₁₃×SD₁₆	—	2	4	no	—
406	C₁₃×SD₁₆	—	4	2	no	—
407	C₁₃×SD₁₆	—	4	1	no	—
408	C₁₃×SD₁₆	—	4	1	no	—
409	C₁₃×D₈	—	2	4	no	—
410	C₁₃×D₈	—	4	2	no	—
411	C₁₃×D₈	—	4	1	no	—
412	C₁₃×M₁₆	—	2	2	no	—
413	C₁₃×M₁₆	—	2	2	no	—
414	C₁₃×M₁₆	—	4	1	no	—
415	C₁₃×M₁₆	—	4	1	no	—
416	C₁₃×M₁₆	—	4	1	no	—
417	C₁₃×M₁₆	—	4	1	no	—
418	C₁₃×M₁₆	—	4	2	no	—
419	C₂×C₈×C₁₃	—	2	2	no	—
420	C₂×C₈×C₁₃	—	2	2	no	—
421	C₂×C₈×C₁₃	—	4	2	no	—
422	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
423	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
424	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
426	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
428	C₁₃×C₄⋊C₄	—	2	1	no	—
429	C₁₃×C₄⋊C₄	—	2	2	no	—
430	C₁₃×C₄⋊C₄	—	2	1	no	—
431	C₁₃×C₄⋊C₄	—	2	2	no	—
432	C₁₃×C₄⋊C₄	—	2	1	no	—
433	C₁₃×C₄⋊C₄	—	2	2	no	—
434	C₁₃×C₄⋊C₄	—	2	2	no	—
435	C₁₃×C₄⋊C₄	—	2	1	no	—
436	C₁₃×C₄⋊C₄	—	2	1	no	—
437	C₁₃×C₄⋊C₄	—	2	1	no	—
438	C₁₃×C₄⋊C₄	—	2	2	no	—
439	C₁₃×C₄⋊C₄	—	2	2	no	—
440	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
443	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
444	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
445	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
446	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
450	C₁₃×C₂²⋊C₄	—	2	1	no	—
451	C₁₃×C₂²⋊C₄	—	2	1	no	—
452	C₁₃×C₂²⋊C₄	—	2	1	no	—
453	C₁₃×C₂²⋊C₄	—	2	2	no	—
454	C₁₃×C₂²⋊C₄	—	2	2	no	—
455	C₁₃×C₂²⋊C₄	—	2	2	no	—
456	C₁₃×C₂²⋊C₄	—	2	1	no	—
457	C₁₃×C₂²⋊C₄	—	2	2	no	—
458	C₁₃×C₂²⋊C₄	—	2	1	no	—
459	C₁₃×C₂²⋊C₄	—	2	1	no	—
460	C₁₃×C₂²⋊C₄	—	2	2	no	—
461	C₁₃×C₂²⋊C₄	—	2	2	no	—
462	C₁₃×C₂²⋊C₄	—	2	2	no	—
463	C₁₃×C₂²⋊C₄	—	2	2	no	—
464	C₁₃×C₂²⋊C₄	—	2	2	no	—
465	C₁₃×C₂²⋊C₄	—	2	2	no	—
466	C₁₃×C₂²⋊C₄	—	2	1	no	—
467	C₁₃×C₂²⋊C₄	—	2	2	no	—
468	C₁₃×C₂²⋊C₄	—	2	2	no	—
469	C₁₃×C₂²⋊C₄	—	2	1	no	—
470	C₁₃×C₂²⋊C₄	—	2	1	no	—
471	C₁₃×C₂²⋊C₄	—	2	1	no	—
472	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
473	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
474	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
475	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
476	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
477	C₄²×C₁₃	—	2	2	no	—
478	C₄²×C₁₃	—	2	2	no	—
479	C₄²×C₁₃	—	2	2	no	—
480	C₄²×C₁₃	—	2	2	no	—
481	C₄²×C₁₃	—	2	1	no	—
482	C₄²×C₁₃	—	2	1	no	—
483	C₄²×C₁₃	C₂⁴	1	2	yes	—
484	#3493	C₂×C₁₃	1	1	yes	characteristic, complemented
485	#3484	C₂×C₁₃	1	1	yes	characteristic, complemented
486	#3325	C₂×C₁₃	1	2	yes	complemented
487	#3324	C₂×C₁₃	1	2	yes	complemented
488	#3323	C₂×C₁₃	1	2	yes	complemented
489	#3322	C₂×C₁₃	1	2	yes	complemented
490	#3319	C₂×C₁₃	1	2	yes	complemented
491	#3318	C₂×C₁₃	1	2	yes	complemented
492	#3311	C₂×C₁₃	1	2	yes	complemented
493	#3310	C₂×C₁₃	1	2	yes	complemented
494	#3136	C₂×C₁₃	1	1	yes	characteristic, complemented
495	#3096	C₂×C₁₃	1	1	yes	characteristic, complemented
496	#3093	C₂×C₁₃	1	1	yes	characteristic, complemented
497	#3081	C₂×C₁₃	1	1	yes	characteristic, complemented
498	#3062	C₂×C₁₃	1	1	yes	characteristic, complemented
499	#3054	C₂×C₁₃	1	1	yes	characteristic, complemented
500	#3045	C₂×C₁₃	1	1	yes	characteristic, complemented
501	#3012	C₂×C₁₃	1	1	yes	characteristic, complemented
502	#3003	C₂×C₁₃	1	1	yes	characteristic, complemented
503	#2946	C₂×C₁₃	1	1	yes	characteristic, complemented
504	#2930	C₂×C₁₃	1	1	yes	characteristic, complemented
505	#2897	C₂×C₁₃	1	1	yes	characteristic, complemented
506	C₂×#418	C₂×C₁₃	1	1	yes	characteristic, complemented
507	C₂³×C₁₃	—	2	2	no	—
508	C₂³×C₁₃	—	2	2	no	—
509	C₂³×C₁₃	—	2	4	no	—
510	C₂³×C₁₃	—	2	1	no	—
511	C₂³×C₁₃	—	2	2	no	—
512	C₂³×C₁₃	—	2	1	no	—
513	C₂³×C₁₃	—	4	1	no	—
514	C₂³×C₁₃	—	4	1	no	—
515	C₂³×C₁₃	—	4	4	no	—
516	C₂³×C₁₃	—	4	4	no	—
517	C₂³×C₁₃	—	4	4	no	—
518	C₂³×C₁₃	—	4	4	no	—
519	C₂³×C₁₃	—	4	4	no	—
520	C₂³×C₁₃	—	4	2	no	—
521	C₂³×C₁₃	—	8	1	no	—
522	C₂³×C₁₃	—	8	1	no	—
523	C₂³×C₁₃	—	8	1	no	—
524	C₂³×C₁₃	—	8	1	no	—
525	C₂³×C₁₃	—	8	2	no	—
526	C₂³×C₁₃	—	8	2	no	—
527	C₂³×C₁₃	—	8	2	no	—
528	C₂³×C₁₃	—	8	2	no	—
529	C₂³×C₁₃	—	8	16	no	—
530	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
531	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
532	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
533	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
534	Q₈×C₁₃	—	2	2	no	—
535	Q₈×C₁₃	—	2	1	no	—
536	Q₈×C₁₃	—	2	1	no	—
537	Q₈×C₁₃	—	2	1	no	—
538	Q₈×C₁₃	—	2	1	no	—
539	Q₈×C₁₃	—	8	2	no	—
540	D₄×C₁₃	—	2	4	no	—
541	D₄×C₁₃	—	2	4	no	—
542	D₄×C₁₃	—	2	2	no	—
543	D₄×C₁₃	—	2	1	no	—
544	D₄×C₁₃	—	2	2	no	—
545	D₄×C₁₃	—	2	1	no	—
546	D₄×C₁₃	—	2	2	no	—
547	D₄×C₁₃	—	2	1	no	—
548	D₄×C₁₃	—	2	2	no	—
549	D₄×C₁₃	—	2	1	no	—
550	D₄×C₁₃	—	4	2	no	—
551	D₄×C₁₃	—	4	2	no	—
552	D₄×C₁₃	—	4	4	no	—
553	D₄×C₁₃	—	4	4	no	—
554	D₄×C₁₃	—	4	4	no	—
555	D₄×C₁₃	—	4	4	no	—
556	D₄×C₁₃	—	4	2	no	—
557	D₄×C₁₃	—	4	2	no	—
558	D₄×C₁₃	—	4	2	no	—
559	D₄×C₁₃	—	4	2	no	—
560	D₄×C₁₃	—	4	2	no	—
561	D₄×C₁₃	—	8	2	no	—
562	D₄×C₁₃	—	8	2	no	—
563	D₄×C₁₃	—	8	1	no	—
564	D₄×C₁₃	—	8	2	no	—
565	D₄×C₁₃	—	8	1	no	—
566	D₄×C₁₃	—	8	2	no	—
567	D₄×C₁₃	—	8	2	no	—
568	D₄×C₁₃	C₂×#41	1	4	yes	—
569	C₂×C₄×C₁₃	—	2	2	no	—
570	C₂×C₄×C₁₃	—	2	2	no	—
571	C₂×C₄×C₁₃	—	2	2	no	—
572	C₂×C₄×C₁₃	—	2	1	no	—
573	C₂×C₄×C₁₃	—	2	1	no	—
574	C₂×C₄×C₁₃	—	2	2	no	—
575	C₂×C₄×C₁₃	—	2	2	no	—
576	C₂×C₄×C₁₃	—	2	1	no	—
577	C₂×C₄×C₁₃	—	2	1	no	—
578	C₂×C₄×C₁₃	—	2	2	no	—
579	C₂×C₄×C₁₃	—	2	1	no	—
580	C₂×C₄×C₁₃	—	2	1	no	—
581	C₂×C₄×C₁₃	—	2	2	no	—
582	C₂×C₄×C₁₃	—	2	1	no	—
583	C₂×C₄×C₁₃	—	2	1	no	—
584	C₂×C₄×C₁₃	—	2	1	no	—
585	C₂×C₄×C₁₃	—	2	1	no	—
586	C₂×C₄×C₁₃	—	4	4	no	—
587	C₂×C₄×C₁₃	—	4	2	no	—
588	C₂×C₄×C₁₃	—	4	2	no	—
589	C₂×C₄×C₁₃	—	8	2	no	—
590	C₂×C₄×C₁₃	—	8	2	no	—
591	C₂×C₄×C₁₃	—	8	2	no	—
592	C₂×C₄×C₁₃	—	8	1	no	—
593	C₂×C₄×C₁₃	—	8	2	no	—
594	C₂×C₄×C₁₃	—	8	1	no	—
595	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
597	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
598	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
599	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
600	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
602	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
603	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
604	C₈×C₁₃	—	2	2	no	—
605	C₈×C₁₃	—	2	1	no	—
606	C₈×C₁₃	—	2	1	no	—
607	C₈×C₁₃	—	2	1	no	—
608	C₈×C₁₃	—	2	1	no	—
609	C₈×C₁₃	—	2	2	no	—
610	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
611	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
612	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
613	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic, complemented
614	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
617	#556	—	2	1	no	—
618	#556	C₂²×C₁₃	1	2	yes	complemented
619	#555	—	2	1	no	—
620	#555	C₂²×C₁₃	1	2	yes	complemented
621	#553	—	2	1	no	—
622	#553	C₂²×C₁₃	1	2	yes	complemented
623	#552	—	2	1	no	—
624	#552	C₂²×C₁₃	1	2	yes	complemented
625	#546	—	2	1	no	—
626	#546	—	2	1	no	—
627	#546	C₂²×C₁₃	1	2	yes	—
628	#546	C₂²×C₁₃	1	2	yes	—
629	D₄²	—	2	1	no	—
630	D₄²	—	2	1	no	—
631	D₄²	C₂²×C₁₃	1	2	yes	—
632	D₄²	C₂²×C₁₃	1	2	yes	—
633	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
634	#538	—	2	2	no	—
635	#537	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	#535	C₂²×C₁₃	1	1	yes	characteristic
637	#535	C₂²×C₁₃	1	1	yes	characteristic
638	#534	—	2	2	no	—
639	#529	—	2	2	no	—
640	#525	C₂²×C₁₃	1	1	yes	characteristic
641	#525	C₂²×C₁₃	1	1	yes	characteristic
642	#525	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	C₂×#120	—	2	2	no	—
644	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
645	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
646	#518	C₂²×C₁₃	1	1	yes	characteristic
647	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
648	#490	C₂²×C₁₃	1	2	yes	complemented
649	#489	C₂²×C₁₃	1	2	yes	complemented
650	#488	C₂²×C₁₃	1	2	yes	complemented
651	#486	C₂²×C₁₃	1	2	yes	complemented
652	#485	C₂²×C₁₃	1	2	yes	complemented
653	#485	C₂²×C₁₃	1	2	yes	complemented
654	#482	C₂²×C₁₃	1	2	yes	complemented
655	#482	C₂²×C₁₃	1	2	yes	complemented
656	#482	C₂²×C₁₃	1	2	yes	complemented
657	#482	C₂²×C₁₃	1	2	yes	complemented
658	#481	C₂²×C₁₃	1	2	yes	complemented
659	#480	C₂²×C₁₃	1	2	yes	complemented
660	#478	C₂²×C₁₃	1	2	yes	complemented
661	#478	C₂²×C₁₃	1	2	yes	complemented
662	#476	C₂²×C₁₃	1	2	yes	complemented
663	#474	C₂²×C₁₃	1	2	yes	complemented
664	#470	C₂²×C₁₃	1	1	yes	characteristic, complemented
665	#470	C₂²×C₁₃	1	1	yes	characteristic, complemented
666	#469	C₂²×C₁₃	1	2	yes	complemented
667	#469	C₂²×C₁₃	1	1	yes	characteristic, complemented
668	#469	C₂²×C₁₃	1	1	yes	characteristic, complemented
669	#468	C₂²×C₁₃	1	2	yes	complemented
670	#468	C₂²×C₁₃	1	1	yes	characteristic, complemented
671	#468	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	#468	C₂²×C₁₃	1	1	yes	characteristic, complemented
673	#468	C₂²×C₁₃	1	1	yes	characteristic, complemented
674	#466	C₂²×C₁₃	1	2	yes	complemented
675	#465	C₂²×C₁₃	1	2	yes	complemented
676	#464	C₂²×C₁₃	1	2	yes	complemented
677	#463	C₂²×C₁₃	1	2	yes	complemented
678	#460	C₂²×C₁₃	1	2	yes	complemented
679	#459	C₂²×C₁₃	1	2	yes	complemented
680	#452	C₂²×C₁₃	1	2	yes	complemented
681	#450	C₂²×C₁₃	1	2	yes	complemented
682	#450	C₂²×C₁₃	1	2	yes	complemented
683	#450	C₂²×C₁₃	1	2	yes	complemented
684	#449	C₂²×C₁₃	1	2	yes	complemented
685	#447	C₂²×C₁₃	1	2	yes	complemented
686	#447	C₂²×C₁₃	1	2	yes	complemented
687	#447	C₂²×C₁₃	1	2	yes	complemented
688	#442	C₂²×C₁₃	1	2	yes	complemented
689	#440	C₂²×C₁₃	1	2	yes	complemented
690	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
691	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
692	#436	C₂²×C₁₃	1	2	yes	complemented
693	#436	C₂²×C₁₃	1	2	yes	complemented
694	#435	C₂²×C₁₃	1	2	yes	complemented
695	#435	C₂²×C₁₃	1	2	yes	complemented
696	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
697	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
698	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
699	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
700	#418	C₂²×C₁₃	1	1	yes	characteristic
701	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
702	#418	C₂²×C₁₃	1	2	yes	complemented
703	#418	C₂²×C₁₃	1	2	yes	complemented
704	#418	C₂²×C₁₃	1	2	yes	complemented
705	#418	C₂²×C₁₃	1	2	yes	complemented
706	#418	C₂²×C₁₃	1	2	yes	complemented
707	#417	C₂²×C₁₃	1	2	yes	complemented
708	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
709	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
710	#416	C₂²×C₁₃	1	2	yes	complemented
711	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
712	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
713	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
714	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
715	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
716	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
717	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
718	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
719	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
720	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
721	C₂²×C₁₃	—	2	1	no	—
722	C₂²×C₁₃	—	2	1	no	—
723	C₂²×C₁₃	—	2	2	no	—
724	C₂²×C₁₃	—	2	1	no	—
725	C₂²×C₁₃	—	2	1	no	—
726	C₂²×C₁₃	—	2	2	no	—
727	C₂²×C₁₃	—	2	1	no	—
728	C₂²×C₁₃	—	2	1	no	—
729	C₂²×C₁₃	—	2	1	no	—
730	C₂²×C₁₃	—	2	1	no	—
731	C₂²×C₁₃	—	2	2	no	—
732	C₂²×C₁₃	—	2	4	no	—
733	C₂²×C₁₃	—	4	4	no	—
734	C₂²×C₁₃	—	4	2	no	—
735	C₂²×C₁₃	—	4	2	no	—
736	C₂²×C₁₃	—	4	1	no	—
737	C₂²×C₁₃	—	4	1	no	—
738	C₂²×C₁₃	—	4	1	no	—
739	C₂²×C₁₃	—	4	1	no	—
740	C₂²×C₁₃	—	4	2	no	—
741	C₂²×C₁₃	—	4	2	no	—
742	C₂²×C₁₃	—	4	1	no	—
743	C₂²×C₁₃	—	4	1	no	—
744	C₂²×C₁₃	—	4	2	no	—
745	C₂²×C₁₃	—	8	4	no	—
746	C₂²×C₁₃	—	8	4	no	—
747	C₂²×C₁₃	—	8	8	no	—
748	C₂²×C₁₃	—	8	8	no	—
749	C₂²×C₁₃	—	16	4	no	—
750	C₂²×C₁₃	#546	1	2	yes	—
751	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
752	C₄×C₁₃	—	2	2	no	—
753	C₄×C₁₃	—	2	2	no	—
754	C₄×C₁₃	—	2	1	no	—
755	C₄×C₁₃	—	2	1	no	—
756	C₄×C₁₃	—	2	2	no	—
757	C₄×C₁₃	—	4	2	no	—
758	C₄×C₁₃	—	4	1	no	—
759	C₄×C₁₃	—	4	1	no	—
760	C₄×C₁₃	—	4	1	no	—
761	C₄×C₁₃	—	4	2	no	—
762	C₄×C₁₃	—	4	1	no	—
763	C₄×C₁₃	—	4	1	no	—
764	C₄×C₁₃	—	4	1	no	—
765	C₄×C₁₃	#546	1	2	yes	—
766	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
767	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
768	C₂⁵	—	2	1	no	—
769	H(5,𝔽₂)	—	2	4	no	—
770	H(5,𝔽₂)	—	4	2	no	—
771	C₂×#41	—	2	1	no	—
772	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
773	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
774	C₂×#41	C₂³×C₁₃	1	2	yes	—
775	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
776	C₂²×D₄	—	2	4	no	—
777	C₂²×D₄	—	2	2	no	—
778	C₂²×D₄	—	2	1	no	—
779	C₂²×D₄	—	2	2	no	—
780	C₂²×D₄	—	2	2	no	—
781	C₂²×D₄	—	2	1	no	—
782	C₂²×D₄	—	2	1	no	—
783	C₂²×D₄	—	2	1	no	—
784	C₂²×D₄	—	4	2	no	—
785	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
786	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
787	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
788	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
789	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
790	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
791	AGL(1,ℤ/8)	—	2	4	no	—
792	AGL(1,ℤ/8)	—	4	2	no	—
793	#135	—	4	2	no	—
794	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic, complemented
795	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
796	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
797	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic, complemented
798	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic, complemented
799	C₂×D₈	C₂³×C₁₃	1	2	yes	—
800	C₂×D₈	C₂³×C₁₃	1	2	yes	—
801	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
802	#131	—	4	2	no	—
803	C₂×M₁₆	—	4	2	no	—
804	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
805	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
806	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
807	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
808	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
809	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
810	C₂×M₁₆	C₂³×C₁₃	1	2	yes	complemented
811	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
812	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
813	C₂²×C₈	C₂³×C₁₃	1	2	yes	complemented
814	C₄⋊Q₈	—	2	1	no	—
815	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
816	#127	—	2	1	no	—
817	#127	C₂³×C₁₃	1	2	yes	—
818	#126	—	2	2	no	—
819	#126	—	2	2	no	—
820	#126	—	2	2	no	—
821	#126	—	2	2	no	—
822	#125	—	2	2	no	—
823	#125	—	2	1	no	—
824	#125	C₂³×C₁₃	1	2	yes	complemented
825	#124	—	2	1	no	—
826	#124	—	2	2	no	—
827	#124	—	2	2	no	—
828	#124	—	2	2	no	—
829	#124	C₂³×C₁₃	1	2	yes	—
830	#123	—	2	2	no	—
831	#123	—	2	1	no	—
832	#123	—	2	1	no	—
833	#123	—	2	2	no	—
834	#123	—	2	2	no	—
835	#123	—	2	2	no	—
836	#123	D₄×C₁₃	1	2	yes	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	2	no	—
839	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
840	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
843	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
844	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
845	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
846	#121	—	2	2	no	—
847	#121	—	2	1	no	—
848	#121	—	2	2	no	—
849	#121	—	2	2	no	—
850	#121	—	2	2	no	—
851	#121	—	2	2	no	—
852	#121	—	2	1	no	—
853	#121	—	2	1	no	—
854	#121	—	2	2	no	—
855	#121	—	2	2	no	—
856	#121	D₄×C₁₃	1	1	yes	characteristic
857	#121	D₄×C₁₃	1	1	yes	characteristic
858	#121	C₂³×C₁₃	1	1	yes	characteristic
859	#121	C₂³×C₁₃	1	1	yes	characteristic
860	#121	C₂³×C₁₃	1	1	yes	characteristic
861	#121	C₂³×C₁₃	1	1	yes	characteristic
862	#121	C₂³×C₁₃	1	2	yes	—
863	#121	C₂³×C₁₃	1	2	yes	—
864	#121	C₂³×C₁₃	1	2	yes	complemented
865	#120	—	2	1	no	—
866	#120	—	2	1	no	—
867	#120	—	2	2	no	—
868	#120	—	2	2	no	—
869	#120	—	2	2	no	—
870	#120	—	2	2	no	—
871	#120	—	2	2	no	—
872	#120	—	2	2	no	—
873	#120	—	2	2	no	—
874	#120	—	2	2	no	—
875	#120	D₄×C₁₃	1	2	yes	—
876	C₄×Q₈	—	2	1	no	—
877	C₄×Q₈	—	2	2	no	—
878	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
879	C₄×D₄	—	2	2	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	2	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	C₂³×C₁₃	1	2	yes	—
890	C₄×D₄	C₂³×C₁₃	1	2	yes	—
891	C₄×D₄	C₂³×C₁₃	1	2	yes	—
892	C₄×D₄	C₂³×C₁₃	1	2	yes	—
893	C₄×D₄	C₂³×C₁₃	1	2	yes	complemented
894	#117	—	2	1	no	—
895	#117	—	2	1	no	—
896	#117	—	2	1	no	—
897	#117	—	2	2	no	—
898	#117	—	2	2	no	—
899	#117	C₂³×C₁₃	1	2	yes	—
900	#117	C₂³×C₁₃	1	2	yes	—
901	#117	C₂³×C₁₃	1	1	yes	characteristic
902	#117	C₂³×C₁₃	1	1	yes	characteristic
903	#117	C₂³×C₁₃	1	1	yes	characteristic
904	#117	C₂³×C₁₃	1	2	yes	complemented
905	C₂×C₄⋊C₄	—	2	1	no	—
906	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
907	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
908	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
909	C₂×C₂²⋊C₄	—	2	1	no	—
910	C₂×C₂²⋊C₄	—	2	2	no	—
911	C₂×C₂²⋊C₄	—	2	2	no	—
912	C₂×C₂²⋊C₄	—	2	2	no	—
913	C₂×C₄²	—	2	1	no	—
914	#107	C₂³×C₁₃	1	1	yes	characteristic, complemented
915	#107	C₂³×C₁₃	1	1	yes	characteristic, complemented
916	#107	C₂³×C₁₃	1	2	yes	complemented
917	#107	C₂³×C₁₃	1	2	yes	complemented
918	#106	C₂³×C₁₃	1	1	yes	characteristic, complemented
919	#106	C₂³×C₁₃	1	1	yes	characteristic, complemented
920	#106	C₂³×C₁₃	1	2	yes	complemented
921	#106	C₂³×C₁₃	1	2	yes	complemented
922	C₄⋊C₈	C₂³×C₁₃	1	2	yes	complemented
923	C₄⋊C₈	C₂³×C₁₃	1	2	yes	complemented
924	#103	C₂³×C₁₃	1	1	yes	characteristic, complemented
925	#103	C₂³×C₁₃	1	2	yes	complemented
926	#103	C₂³×C₁₃	1	1	yes	characteristic, complemented
927	#103	C₂³×C₁₃	1	1	yes	characteristic, complemented
928	#103	C₂³×C₁₃	1	1	yes	characteristic, complemented
929	#103	C₂³×C₁₃	1	2	yes	complemented
930	#102	C₂³×C₁₃	1	2	yes	—
931	#102	C₂³×C₁₃	1	2	yes	—
932	#102	C₂³×C₁₃	1	2	yes	—
933	#102	C₂³×C₁₃	1	2	yes	—
934	#102	C₂³×C₁₃	1	2	yes	—
935	#102	C₂³×C₁₃	1	2	yes	—
936	#102	C₂³×C₁₃	1	2	yes	—
937	#102	C₂³×C₁₃	1	2	yes	—
938	#102	C₂³×C₁₃	1	2	yes	—
939	#102	C₂³×C₁₃	1	2	yes	—
940	#102	C₂³×C₁₃	1	2	yes	—
941	#102	C₂³×C₁₃	1	2	yes	—
942	#102	C₂³×C₁₃	1	1	yes	characteristic, complemented
943	#102	C₂³×C₁₃	1	2	yes	complemented
944	#102	C₂³×C₁₃	1	1	yes	characteristic, complemented
945	#102	C₂³×C₁₃	1	1	yes	characteristic, complemented
946	#102	C₂³×C₁₃	1	1	yes	characteristic, complemented
947	#102	C₂³×C₁₃	1	2	yes	complemented
948	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
949	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
950	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	complemented
951	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	complemented
952	#97	C₂³×C₁₃	1	2	yes	complemented
953	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
954	C₂×C₁₃	—	2	2	no	—
955	C₂×C₁₃	—	4	1	no	—
956	C₂×C₁₃	—	4	1	no	—
957	C₂×C₁₃	—	4	2	no	—
958	C₂×C₁₃	—	4	4	no	—
959	C₂×C₁₃	—	8	1	no	—
960	C₂×C₁₃	—	8	2	no	—
961	C₂×C₁₃	—	8	1	no	—
962	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
963	C₂×C₁₃	#3585	1	1	yes	characteristic
964	C₂×C₁₃	#3585	1	1	yes	characteristic
965	C₂⁴	—	2	1	no	—
966	C₂⁴	—	2	2	no	—
967	C₂⁴	—	2	2	no	—
968	C₂⁴	—	2	1	no	—
969	C₂⁴	—	2	2	no	—
970	C₂⁴	—	4	4	no	—
971	C₂⁴	—	8	2	no	—
972	C₂⁴	—	8	2	no	—
973	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
974	#41	—	2	2	no	—
975	#41	—	2	2	no	—
976	#41	—	2	4	no	—
977	#41	—	2	2	no	—
978	#41	—	2	2	no	—
979	#41	—	2	2	no	—
980	#41	—	2	2	no	—
981	#41	—	4	2	no	—
982	#41	—	4	4	no	—
983	C₂×Q₈	—	2	2	no	—
984	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
985	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
986	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
987	C₂×D₄	—	2	4	no	—
988	C₂×D₄	—	2	4	no	—
989	C₂×D₄	—	2	4	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	2	no	—
1010	C₂×D₄	—	4	2	no	—
1011	C₂×D₄	—	4	2	no	—
1012	C₂×D₄	—	4	2	no	—
1013	C₂×D₄	—	4	4	no	—
1014	C₂×D₄	—	4	4	no	—
1015	C₂×D₄	—	4	4	no	—
1016	C₂×D₄	—	4	4	no	—
1017	C₂×D₄	—	4	8	no	—
1018	C₂×D₄	—	8	4	no	—
1019	C₂×D₄	—	8	4	no	—
1020	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1021	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1022	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1023	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1024	C₂×D₄	C₁₃×#41	1	4	yes	—
1025	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1026	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1027	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1028	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1029	C₂²×C₄	—	2	2	no	—
1030	C₂²×C₄	—	2	2	no	—
1031	C₂²×C₄	—	2	1	no	—
1032	C₂²×C₄	—	2	1	no	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1041	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1042	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1043	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1044	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1046	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1047	Q₁₆	—	4	1	no	—
1048	SD₁₆	—	2	4	no	—
1049	SD₁₆	—	4	2	no	—
1050	SD₁₆	—	4	1	no	—
1051	SD₁₆	—	4	1	no	—
1052	D₈	—	2	4	no	—
1053	D₈	—	4	2	no	—
1054	D₈	—	4	1	no	—
1055	M₁₆	—	2	2	no	—
1056	M₁₆	—	2	2	no	—
1057	M₁₆	—	4	1	no	—
1058	M₁₆	—	4	1	no	—
1059	M₁₆	—	4	1	no	—
1060	M₁₆	—	4	1	no	—
1061	M₁₆	—	4	2	no	—
1062	C₂×C₈	—	2	2	no	—
1063	C₂×C₈	—	2	2	no	—
1064	C₂×C₈	—	4	2	no	—
1065	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1066	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1067	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1068	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1069	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1070	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1084	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1085	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1086	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1087	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1088	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1089	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1090	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1091	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1092	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1116	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1117	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1118	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1119	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1120	C₄²	—	2	2	no	—
1121	C₄²	—	2	2	no	—
1122	C₄²	—	2	2	no	—
1123	C₄²	—	2	2	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	C₂⁴×C₁₃	1	2	yes	—
1127	C₁₃	#61175	1	1	yes	characteristic, direct product factor, Sylow
1128	C₂³	—	2	2	no	—
1129	C₂³	—	2	2	no	—
1130	C₂³	—	2	4	no	—
1131	C₂³	—	2	1	no	—
1132	C₂³	—	2	2	no	—
1133	C₂³	—	2	1	no	—
1134	C₂³	—	4	1	no	—
1135	C₂³	—	4	1	no	—
1136	C₂³	—	4	4	no	—
1137	C₂³	—	4	4	no	—
1138	C₂³	—	4	4	no	—
1139	C₂³	—	4	4	no	—
1140	C₂³	—	4	4	no	—
1141	C₂³	—	4	2	no	—
1142	C₂³	—	8	1	no	—
1143	C₂³	—	8	1	no	—
1144	C₂³	—	8	1	no	—
1145	C₂³	—	8	1	no	—
1146	C₂³	—	8	2	no	—
1147	C₂³	—	8	2	no	—
1148	C₂³	—	8	2	no	—
1149	C₂³	—	8	2	no	—
1150	C₂³	—	8	16	no	—
1151	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1152	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1153	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1154	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1155	Q₈	—	2	2	no	—
1156	Q₈	—	2	1	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	2	1	no	—
1160	Q₈	—	8	2	no	—
1161	D₄	—	2	4	no	—
1162	D₄	—	2	4	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	1	no	—
1165	D₄	—	2	2	no	—
1166	D₄	—	2	1	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	1	no	—
1169	D₄	—	2	2	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	4	2	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	4	4	no	—
1174	D₄	—	4	4	no	—
1175	D₄	—	4	4	no	—
1176	D₄	—	4	4	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	8	2	no	—
1183	D₄	—	8	2	no	—
1184	D₄	—	8	2	no	—
1185	D₄	—	8	2	no	—
1186	D₄	—	8	1	no	—
1187	D₄	—	8	2	no	—
1188	D₄	—	8	1	no	—
1189	D₄	C₂×C₁₃×#41	1	4	yes	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	4	4	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	8	2	no	—
1211	C₂×C₄	—	8	2	no	—
1212	C₂×C₄	—	8	2	no	—
1213	C₂×C₄	—	8	1	no	—
1214	C₂×C₄	—	8	2	no	—
1215	C₂×C₄	—	8	1	no	—
1216	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1217	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1218	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1219	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1220	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1221	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1222	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1223	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1224	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1225	C₈	—	2	2	no	—
1226	C₈	—	2	1	no	—
1227	C₈	—	2	1	no	—
1228	C₈	—	2	1	no	—
1229	C₈	—	2	1	no	—
1230	C₈	—	2	2	no	—
1231	C₂²	—	2	1	no	—
1232	C₂²	—	2	1	no	—
1233	C₂²	—	2	2	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	1	no	—
1236	C₂²	—	2	2	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	2	no	—
1242	C₂²	—	2	4	no	—
1243	C₂²	—	4	4	no	—
1244	C₂²	—	4	2	no	—
1245	C₂²	—	4	2	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	2	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	8	4	no	—
1256	C₂²	—	8	4	no	—
1257	C₂²	—	8	8	no	—
1258	C₂²	—	8	8	no	—
1259	C₂²	—	16	4	no	—
1260	C₂²	C₁₃×#546	1	2	yes	—
1261	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1262	C₄	—	2	2	no	—
1263	C₄	—	2	2	no	—
1264	C₄	—	2	1	no	—
1265	C₄	—	2	1	no	—
1266	C₄	—	2	2	no	—
1267	C₄	—	4	2	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	2	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	C₁₃×#546	1	2	yes	—
1276	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1277	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1278	C₂	—	2	2	no	—
1279	C₂	—	4	1	no	—
1280	C₂	—	4	1	no	—
1281	C₂	—	4	2	no	—
1282	C₂	—	4	4	no	—
1283	C₂	—	8	2	no	—
1284	C₂	—	8	1	no	—
1285	C₂	—	8	1	no	—
1286	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
1287	C₂	C₁₃×#3585	1	1	yes	characteristic
1288	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3493	C₂	semidirect
2. C₁₃×#3484	C₂	semidirect
3. C₁₃×#3325	C₂	semidirect
4. C₁₃×#3324	C₂	semidirect
5. C₁₃×#3323	C₂	semidirect
6. C₁₃×#3322	C₂	semidirect
7. C₁₃×#3319	C₂	semidirect
8. C₁₃×#3318	C₂	semidirect
9. C₁₃×#3311	C₂	semidirect
10. C₁₃×#3310	C₂	semidirect
11. C₁₃×#3136	C₂	semidirect
12. C₁₃×#3096	C₂	semidirect
13. C₁₃×#3093	C₂	semidirect
14. C₁₃×#3081	C₂	semidirect
15. C₁₃×#3062	C₂	semidirect
16. C₁₃×#3054	C₂	semidirect
17. C₁₃×#3045	C₂	semidirect
18. C₁₃×#3012	C₂	semidirect
19. C₁₃×#3003	C₂	semidirect
20. C₁₃×#2946	C₂	semidirect
21. C₁₃×#2930	C₂	semidirect
22. C₁₃×#2897	C₂	semidirect
23. C₂×C₁₃×#418	C₂	semidirect
27. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₁₃×#135	C₂²	semidirect
29. C₂×C₁₃×#131	C₂²	semidirect
30. C₂²×C₁₃×M₁₆	C₂²	semidirect
32. C₁₃×#556	C₂²	semidirect
34. C₁₃×#555	C₂²	semidirect
36. C₁₃×#553	C₂²	semidirect
38. C₁₃×#552	C₂²	semidirect
47. C₁₃×#544	C₂²	semidirect
49. C₁₃×#537	C₂²	semidirect
56. C₁₃×#525	C₂²	semidirect
58. C₁₃×#520	C₂²	semidirect
59. C₁₃×#520	C₂²	semidirect
61. C₂×C₁₃×#117	C₂²	semidirect
62. C₁₃×#490	C₂²	semidirect
63. C₁₃×#489	C₂²	semidirect
64. C₁₃×#488	C₂²	semidirect
65. C₁₃×#486	C₂²	semidirect
66. C₁₃×#485	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#482	C₂²	semidirect
69. C₁₃×#482	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#481	C₂²	semidirect
73. C₁₃×#480	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#476	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#470	C₂²	semidirect
79. C₁₃×#470	C₂²	semidirect
80. C₁₃×#469	C₂²	semidirect
81. C₁₃×#469	C₂²	semidirect
82. C₁₃×#469	C₂²	semidirect
83. C₁₃×#468	C₂²	semidirect
84. C₁₃×#468	C₂²	semidirect
85. C₁₃×#468	C₂²	semidirect
86. C₁₃×#468	C₂²	semidirect
87. C₁₃×#468	C₂²	semidirect
88. C₁₃×#466	C₂²	semidirect
89. C₁₃×#465	C₂²	semidirect
90. C₁₃×#464	C₂²	semidirect
91. C₁₃×#463	C₂²	semidirect
92. C₁₃×#460	C₂²	semidirect
93. C₁₃×#459	C₂²	semidirect
94. C₁₃×#452	C₂²	semidirect
95. C₁₃×#450	C₂²	semidirect
96. C₁₃×#450	C₂²	semidirect
97. C₁₃×#450	C₂²	semidirect
98. C₁₃×#449	C₂²	semidirect
99. C₁₃×#447	C₂²	semidirect
100. C₁₃×#447	C₂²	semidirect
101. C₁₃×#447	C₂²	semidirect
102. C₁₃×#442	C₂²	semidirect
103. C₁₃×#440	C₂²	semidirect
104. C₄×C₁₃×SD₁₆	C₂²	semidirect
105. C₄×C₁₃×D₈	C₂²	semidirect
106. C₁₃×#436	C₂²	semidirect
107. C₁₃×#436	C₂²	semidirect
108. C₁₃×#435	C₂²	semidirect
109. C₁₃×#435	C₂²	semidirect
110. C₁₃×#428	C₂²	semidirect
111. C₁₃×#428	C₂²	semidirect
112. C₁₃×#427	C₂²	semidirect
113. C₁₃×#424	C₂²	semidirect
115. C₁₃×#418	C₂²	semidirect
116. C₁₃×#418	C₂²	semidirect
117. C₁₃×#418	C₂²	semidirect
118. C₁₃×#418	C₂²	semidirect
119. C₁₃×#418	C₂²	semidirect
120. C₁₃×#418	C₂²	semidirect
121. C₁₃×#417	C₂²	semidirect
122. C₁₃×#417	C₂²	semidirect
123. C₁₃×#417	C₂²	semidirect
124. C₁₃×#416	C₂²	semidirect
125. C₁₃×#416	C₂²	semidirect
126. C₁₃×#416	C₂²	semidirect
129. C₂×C₁₃×#102	C₂²	semidirect
130. C₂×C₁₃×#102	C₂²	semidirect
131. C₂×C₁₃×#102	C₂²	semidirect
132. C₁₃×#408	C₂²	semidirect
133. C₁₃×#407	C₂²	semidirect
134. C₁₃×#405	C₂²	semidirect
161. C₂×C₁₃×Q₁₆	C₂³	semidirect
164. C₂×C₁₃×SD₁₆	C₂³	semidirect
165. C₂×C₁₃×SD₁₆	C₂³	semidirect
168. C₂×C₁₃×D₈	C₂³	semidirect
177. C₂×C₁₃×M₁₆	C₂³	semidirect
180. C₂²×C₈×C₁₃	C₂³	semidirect
182. C₁₃×C₄⋊Q₈	C₂³	semidirect
191. C₁₃×#125	C₂³	semidirect
212. C₁₃×C₂²⋊Q₈	C₂³	semidirect
231. C₁₃×#121	C₂³	semidirect
245. C₄×Q₈×C₁₃	C₂³	semidirect
260. C₄×D₄×C₁₃	C₂³	semidirect
271. C₁₃×#117	C₂³	semidirect
275. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
281. C₁₃×#107	C₂³	semidirect
282. C₁₃×#107	C₂³	semidirect
283. C₁₃×#107	C₂³	semidirect
284. C₁₃×#107	C₂³	semidirect
285. C₁₃×#106	C₂³	semidirect
286. C₁₃×#106	C₂³	semidirect
287. C₁₃×#106	C₂³	semidirect
288. C₁₃×#106	C₂³	semidirect
289. C₁₃×C₄⋊C₈	C₂³	semidirect
290. C₁₃×C₄⋊C₈	C₂³	semidirect
291. C₁₃×#103	C₂³	semidirect
292. C₁₃×#103	C₂³	semidirect
293. C₁₃×#103	C₂³	semidirect
294. C₁₃×#103	C₂³	semidirect
295. C₁₃×#103	C₂³	semidirect
296. C₁₃×#103	C₂³	semidirect
309. C₁₃×#102	C₂³	semidirect
310. C₁₃×#102	C₂³	semidirect
311. C₁₃×#102	C₂³	semidirect
312. C₁₃×#102	C₂³	semidirect
313. C₁₃×#102	C₂³	semidirect
314. C₁₃×#102	C₂³	semidirect
317. C₁₃×C₂²⋊C₈	C₂³	semidirect
318. C₁₃×C₂²⋊C₈	C₂³	semidirect
319. C₁₃×#97	C₂³	semidirect
320. C₄×C₈×C₁₃	C₂³	semidirect
321. #61175	C₁₃	direct (N × H)
484. #3493	C₂×C₁₃	semidirect
485. #3484	C₂×C₁₃	semidirect
486. #3325	C₂×C₁₃	semidirect
487. #3324	C₂×C₁₃	semidirect
488. #3323	C₂×C₁₃	semidirect
489. #3322	C₂×C₁₃	semidirect
490. #3319	C₂×C₁₃	semidirect
491. #3318	C₂×C₁₃	semidirect
492. #3311	C₂×C₁₃	semidirect
493. #3310	C₂×C₁₃	semidirect
494. #3136	C₂×C₁₃	semidirect
495. #3096	C₂×C₁₃	semidirect
496. #3093	C₂×C₁₃	semidirect
497. #3081	C₂×C₁₃	semidirect
498. #3062	C₂×C₁₃	semidirect
499. #3054	C₂×C₁₃	semidirect
500. #3045	C₂×C₁₃	semidirect
501. #3012	C₂×C₁₃	semidirect
502. #3003	C₂×C₁₃	semidirect
503. #2946	C₂×C₁₃	semidirect
504. #2930	C₂×C₁₃	semidirect
505. #2897	C₂×C₁₃	semidirect
506. C₂×#418	C₂×C₁₃	semidirect
613. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
614. C₂×#135	C₂²×C₁₃	semidirect
615. C₂×#131	C₂²×C₁₃	semidirect
616. C₂²×M₁₆	C₂²×C₁₃	semidirect
618. #556	C₂²×C₁₃	semidirect
620. #555	C₂²×C₁₃	semidirect
622. #553	C₂²×C₁₃	semidirect
624. #552	C₂²×C₁₃	semidirect
633. #544	C₂²×C₁₃	semidirect
635. #537	C₂²×C₁₃	semidirect
642. #525	C₂²×C₁₃	semidirect
644. #520	C₂²×C₁₃	semidirect
645. #520	C₂²×C₁₃	semidirect
647. C₂×#117	C₂²×C₁₃	semidirect
648. #490	C₂²×C₁₃	semidirect
649. #489	C₂²×C₁₃	semidirect
650. #488	C₂²×C₁₃	semidirect
651. #486	C₂²×C₁₃	semidirect
652. #485	C₂²×C₁₃	semidirect
653. #485	C₂²×C₁₃	semidirect
654. #482	C₂²×C₁₃	semidirect
655. #482	C₂²×C₁₃	semidirect
656. #482	C₂²×C₁₃	semidirect
657. #482	C₂²×C₁₃	semidirect
658. #481	C₂²×C₁₃	semidirect
659. #480	C₂²×C₁₃	semidirect
660. #478	C₂²×C₁₃	semidirect
661. #478	C₂²×C₁₃	semidirect
662. #476	C₂²×C₁₃	semidirect
663. #474	C₂²×C₁₃	semidirect
664. #470	C₂²×C₁₃	semidirect
665. #470	C₂²×C₁₃	semidirect
666. #469	C₂²×C₁₃	semidirect
667. #469	C₂²×C₁₃	semidirect
668. #469	C₂²×C₁₃	semidirect
669. #468	C₂²×C₁₃	semidirect
670. #468	C₂²×C₁₃	semidirect
671. #468	C₂²×C₁₃	semidirect
672. #468	C₂²×C₁₃	semidirect
673. #468	C₂²×C₁₃	semidirect
674. #466	C₂²×C₁₃	semidirect
675. #465	C₂²×C₁₃	semidirect
676. #464	C₂²×C₁₃	semidirect
677. #463	C₂²×C₁₃	semidirect
678. #460	C₂²×C₁₃	semidirect
679. #459	C₂²×C₁₃	semidirect
680. #452	C₂²×C₁₃	semidirect
681. #450	C₂²×C₁₃	semidirect
682. #450	C₂²×C₁₃	semidirect
683. #450	C₂²×C₁₃	semidirect
684. #449	C₂²×C₁₃	semidirect
685. #447	C₂²×C₁₃	semidirect
686. #447	C₂²×C₁₃	semidirect
687. #447	C₂²×C₁₃	semidirect
688. #442	C₂²×C₁₃	semidirect
689. #440	C₂²×C₁₃	semidirect
690. C₄×SD₁₆	C₂²×C₁₃	semidirect
691. C₄×D₈	C₂²×C₁₃	semidirect
692. #436	C₂²×C₁₃	semidirect
693. #436	C₂²×C₁₃	semidirect
694. #435	C₂²×C₁₃	semidirect
695. #435	C₂²×C₁₃	semidirect
696. #428	C₂²×C₁₃	semidirect
697. #428	C₂²×C₁₃	semidirect
698. #427	C₂²×C₁₃	semidirect
699. #424	C₂²×C₁₃	semidirect
701. #418	C₂²×C₁₃	semidirect
702. #418	C₂²×C₁₃	semidirect
703. #418	C₂²×C₁₃	semidirect
704. #418	C₂²×C₁₃	semidirect
705. #418	C₂²×C₁₃	semidirect
706. #418	C₂²×C₁₃	semidirect
707. #417	C₂²×C₁₃	semidirect
708. #417	C₂²×C₁₃	semidirect
709. #417	C₂²×C₁₃	semidirect
710. #416	C₂²×C₁₃	semidirect
711. #416	C₂²×C₁₃	semidirect
712. #416	C₂²×C₁₃	semidirect
715. C₂×#102	C₂²×C₁₃	semidirect
716. C₂×#102	C₂²×C₁₃	semidirect
717. C₂×#102	C₂²×C₁₃	semidirect
718. #408	C₂²×C₁₃	semidirect
719. #407	C₂²×C₁₃	semidirect
720. #405	C₂²×C₁₃	semidirect
794. C₂×Q₁₆	C₂³×C₁₃	semidirect
797. C₂×SD₁₆	C₂³×C₁₃	semidirect
798. C₂×SD₁₆	C₂³×C₁₃	semidirect
801. C₂×D₈	C₂³×C₁₃	semidirect
810. C₂×M₁₆	C₂³×C₁₃	semidirect
813. C₂²×C₈	C₂³×C₁₃	semidirect
815. C₄⋊Q₈	C₂³×C₁₃	semidirect
824. #125	C₂³×C₁₃	semidirect
845. C₂²⋊Q₈	C₂³×C₁₃	semidirect
864. #121	C₂³×C₁₃	semidirect
878. C₄×Q₈	C₂³×C₁₃	semidirect
893. C₄×D₄	C₂³×C₁₃	semidirect
904. #117	C₂³×C₁₃	semidirect
908. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
914. #107	C₂³×C₁₃	semidirect
915. #107	C₂³×C₁₃	semidirect
916. #107	C₂³×C₁₃	semidirect
917. #107	C₂³×C₁₃	semidirect
918. #106	C₂³×C₁₃	semidirect
919. #106	C₂³×C₁₃	semidirect
920. #106	C₂³×C₁₃	semidirect
921. #106	C₂³×C₁₃	semidirect
922. C₄⋊C₈	C₂³×C₁₃	semidirect
923. C₄⋊C₈	C₂³×C₁₃	semidirect
924. #103	C₂³×C₁₃	semidirect
925. #103	C₂³×C₁₃	semidirect
926. #103	C₂³×C₁₃	semidirect
927. #103	C₂³×C₁₃	semidirect
928. #103	C₂³×C₁₃	semidirect
929. #103	C₂³×C₁₃	semidirect
942. #102	C₂³×C₁₃	semidirect
943. #102	C₂³×C₁₃	semidirect
944. #102	C₂³×C₁₃	semidirect
945. #102	C₂³×C₁₃	semidirect
946. #102	C₂³×C₁₃	semidirect
947. #102	C₂³×C₁₃	semidirect
950. C₂²⋊C₈	C₂³×C₁₃	semidirect
951. C₂²⋊C₈	C₂³×C₁₃	semidirect
952. #97	C₂³×C₁₃	semidirect
953. C₄×C₈	C₂³×C₁₃	semidirect
1127. C₁₃	#61175	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3493	2
C₁₃×#3484	2
C₁₃×#3325	2
C₁₃×#3324	2
C₁₃×#3323	2
C₁₃×#3322	2
C₁₃×#3319	2
C₁₃×#3318	2
C₁₃×#3311	2
C₁₃×#3310	2
C₁₃×#3136	2
C₁₃×#3096	2
C₁₃×#3093	2
C₁₃×#3081	2
C₁₃×#3062	2
C₁₃×#3054	2
C₁₃×#3045	2
C₁₃×#3012	2
C₁₃×#3003	2
C₁₃×#2946	2
C₁₃×#2930	2
C₁₃×#2897	2
C₂×C₁₃×#418	2
#61175	13

Subgroups — C13×#61175 #15747514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61175 #15747514