Subgroups — C₁₃×#61567 #15747906

Order 3328.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3301	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3297	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3282	C₂	1	2	yes	maximal, complemented
12	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3280	C₂	1	2	yes	maximal, complemented
14	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3191	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3188	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3002	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₃×#449	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
27	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
28	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
29	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#554	C₂²	1	1	yes	characteristic
31	C₁₃×#553	—	2	1	no	—
32	C₁₃×#553	C₂²	1	2	yes	complemented
33	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#548	C₂²	1	2	yes	complemented
37	C₁₃×#547	—	2	1	no	—
38	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#546	—	2	2	no	—
40	C₁₃×#546	—	2	2	no	—
41	C₁₃×#546	C₂²	1	2	yes	complemented
42	C₁₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₁₃	—	2	1	no	—
44	D₄²×C₁₃	—	2	1	no	—
45	D₄²×C₁₃	C₂²	1	1	yes	characteristic
46	D₄²×C₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#540	—	2	1	no	—
48	C₁₃×#538	—	2	2	no	—
49	C₁₃×#532	—	2	1	no	—
50	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#529	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#525	—	2	2	no	—
54	C₁₃×#525	C₂²	1	2	yes	complemented
55	C₁₃×#525	C₂²	1	2	yes	complemented
56	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
57	C₁₃×#518	—	2	1	no	—
58	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×D₄×C₁₃	—	2	1	no	—
60	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
61	C₁₃×#495	C₂²	1	2	yes	complemented
62	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#488	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#484	C₂²	1	2	yes	complemented
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#482	C₂²	1	2	yes	complemented
73	C₁₃×#481	C₂²	1	2	yes	complemented
74	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#467	C₂²	1	2	yes	complemented
79	C₁₃×#466	C₂²	1	2	yes	complemented
80	C₁₃×#466	C₂²	1	2	yes	complemented
81	C₁₃×#466	C₂²	1	2	yes	complemented
82	C₁₃×#465	C₂²	1	2	yes	complemented
83	C₁₃×#465	C₂²	1	2	yes	complemented
84	C₁₃×#465	C₂²	1	2	yes	complemented
85	C₁₃×#465	C₂²	1	2	yes	complemented
86	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#463	C₂²	1	2	yes	complemented
89	C₁₃×#463	C₂²	1	2	yes	complemented
90	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#452	C₂²	1	2	yes	complemented
97	C₁₃×#452	C₂²	1	1	yes	characteristic, complemented
98	C₁₃×#452	C₂²	1	2	yes	complemented
99	C₁₃×#451	C₂²	1	2	yes	complemented
100	C₁₃×#450	C₂²	1	2	yes	complemented
101	C₁₃×#450	C₂²	1	2	yes	complemented
102	C₁₃×#449	C₂²	1	1	yes	characteristic
103	C₁₃×#449	C₂²	1	2	yes	complemented
104	C₁₃×#449	C₂²	1	2	yes	complemented
105	C₁₃×#449	C₂²	1	2	yes	complemented
106	C₁₃×#449	C₂²	1	2	yes	complemented
107	C₁₃×#449	C₂²	1	2	yes	complemented
108	C₁₃×#449	C₂²	1	2	yes	complemented
109	C₁₃×#449	C₂²	1	2	yes	complemented
110	C₁₃×#449	C₂²	1	2	yes	complemented
111	C₁₃×#449	C₂²	1	2	yes	complemented
112	C₁₃×#448	C₂²	1	2	yes	complemented
113	C₁₃×#447	C₂²	1	2	yes	complemented
114	C₁₃×#447	C₂²	1	2	yes	complemented
115	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
121	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
125	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
128	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₁₃×#416	C₂²	1	2	yes	complemented
130	C₁₃×#416	C₂²	1	2	yes	complemented
131	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
133	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
134	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	2	no	—
136	C₂×C₁₃×#41	—	2	2	no	—
137	C₂×C₁₃×#41	—	2	1	no	—
138	C₂×C₁₃×#41	—	4	4	no	—
139	C₂×C₁₃×#41	—	4	4	no	—
140	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×#41	C₂³	1	2	yes	—
142	C₂×C₁₃×#41	C₂³	1	2	yes	—
143	C₂×C₁₃×#41	C₂³	1	2	yes	—
144	C₂×C₁₃×#41	C₂³	1	2	yes	—
145	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
151	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
152	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
153	C₂³×C₄×C₁₃	—	2	2	no	—
154	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
155	C₁₃×#135	—	4	4	no	—
156	C₁₃×#135	—	4	4	no	—
157	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
159	C₂×C₁₃×SD₁₆	—	4	4	no	—
160	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₁₃×D₈	—	4	4	no	—
168	C₂×C₁₃×D₈	C₂³	1	2	yes	—
169	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×D₈	C₂³	1	2	yes	—
171	C₂×C₁₃×D₈	C₂³	1	2	yes	—
172	C₂×C₁₃×D₈	C₂³	1	2	yes	—
173	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
174	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
175	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
176	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
177	C₁₃×C₄⋊Q₈	—	2	1	no	—
178	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₁₃×#127	—	2	1	no	—
181	C₁₃×#127	—	2	1	no	—
182	C₁₃×#127	C₂³	1	1	yes	characteristic
183	C₁₃×#127	C₂³	1	1	yes	characteristic
184	C₁₃×#126	—	2	2	no	—
185	C₁₃×#126	—	2	1	no	—
186	C₁₃×#125	—	2	1	no	—
187	C₁₃×#125	C₂³	1	1	yes	characteristic
188	C₁₃×#124	—	2	2	no	—
189	C₁₃×#124	—	2	2	no	—
190	C₁₃×#124	—	2	1	no	—
191	C₁₃×#124	C₂³	1	2	yes	—
192	C₁₃×#124	C₂³	1	1	yes	characteristic
193	C₁₃×#123	—	2	2	no	—
194	C₁₃×#123	—	2	2	no	—
195	C₁₃×#123	—	2	1	no	—
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×C₂²⋊Q₈	—	2	2	no	—
201	C₁₃×C₂²⋊Q₈	—	2	2	no	—
202	C₁₃×C₂²⋊Q₈	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
206	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	—	2	1	no	—
209	C₁₃×#121	—	2	2	no	—
210	C₁₃×#121	—	2	1	no	—
211	C₁₃×#121	—	2	2	no	—
212	C₁₃×#121	—	2	2	no	—
213	C₁₃×#121	—	2	1	no	—
214	C₁₃×#121	—	2	1	no	—
215	C₁₃×#121	—	2	1	no	—
216	C₁₃×#121	—	2	1	no	—
217	C₁₃×#121	—	2	1	no	—
218	C₁₃×#121	—	2	2	no	—
219	C₁₃×#121	—	2	2	no	—
220	C₁₃×#121	—	2	2	no	—
221	C₁₃×#121	—	2	2	no	—
222	C₁₃×#121	C₂³	1	2	yes	—
223	C₁₃×#121	C₂³	1	2	yes	—
224	C₁₃×#121	C₂³	1	1	yes	characteristic
225	C₁₃×#121	C₂³	1	2	yes	—
226	C₁₃×#121	C₂³	1	2	yes	—
227	C₁₃×#121	C₂³	1	2	yes	—
228	C₁₃×#121	C₂³	1	2	yes	—
229	C₁₃×#120	—	2	2	no	—
230	C₁₃×#120	—	2	2	no	—
231	C₁₃×#120	—	2	2	no	—
232	C₁₃×#120	—	2	2	no	—
233	C₁₃×#120	—	2	2	no	—
234	C₁₃×#120	—	2	2	no	—
235	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₁₃	—	2	1	no	—
239	C₄×D₄×C₁₃	—	2	1	no	—
240	C₄×D₄×C₁₃	—	2	2	no	—
241	C₄×D₄×C₁₃	—	2	1	no	—
242	C₄×D₄×C₁₃	—	2	1	no	—
243	C₄×D₄×C₁₃	—	2	2	no	—
244	C₄×D₄×C₁₃	—	2	2	no	—
245	C₄×D₄×C₁₃	—	2	2	no	—
246	C₄×D₄×C₁₃	—	2	1	no	—
247	C₄×D₄×C₁₃	—	2	1	no	—
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	2	no	—
250	C₄×D₄×C₁₃	—	2	2	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	D₄	1	1	yes	characteristic
255	C₄×D₄×C₁₃	D₄	1	2	yes	—
256	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
257	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₁₃	C₂³	1	2	yes	—
261	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₁₃	C₂³	1	2	yes	—
263	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
264	C₁₃×#117	—	2	1	no	—
265	C₁₃×#117	—	2	1	no	—
266	C₁₃×#117	—	2	1	no	—
267	C₁₃×#117	C₂³	1	2	yes	—
268	C₁₃×#117	C₂³	1	1	yes	characteristic
269	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
271	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
276	C₂×C₄²×C₁₃	—	2	1	no	—
277	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
278	C₁₃×#107	C₂³	1	1	yes	characteristic
279	C₁₃×#107	C₂³	1	2	yes	—
280	C₁₃×#107	C₂³	1	1	yes	characteristic
281	C₁₃×#106	C₂³	1	2	yes	—
282	C₁₃×#106	C₂³	1	1	yes	characteristic
283	C₁₃×#106	C₂³	1	1	yes	characteristic
284	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	1	yes	characteristic
296	C₁₃×#103	C₂³	1	1	yes	characteristic
297	C₁₃×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×#102	C₂³	1	1	yes	characteristic
305	C₁₃×#102	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×#102	C₂³	1	1	yes	characteristic
308	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₁₃	C₂³	1	2	yes	—
318	#61567	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂⁴×C₁₃	—	2	2	no	—
320	C₂⁴×C₁₃	—	2	2	no	—
321	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
322	C₁₃×#41	—	2	2	no	—
323	C₁₃×#41	—	2	2	no	—
324	C₁₃×#41	—	2	4	no	—
325	C₁₃×#41	—	2	4	no	—
326	C₁₃×#41	—	4	2	no	—
327	C₁₃×#41	—	4	2	no	—
328	C₁₃×#41	—	4	2	no	—
329	C₁₃×#41	—	4	2	no	—
330	C₁₃×#41	—	4	8	no	—
331	C₁₃×#41	—	4	2	no	—
332	C₁₃×#41	—	4	2	no	—
333	C₁₃×#41	—	4	8	no	—
334	C₁₃×#41	—	8	2	no	—
335	C₂×Q₈×C₁₃	—	2	2	no	—
336	C₂×Q₈×C₁₃	—	2	1	no	—
337	C₂×Q₈×C₁₃	—	2	4	no	—
338	C₂×Q₈×C₁₃	—	4	2	no	—
339	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
340	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₁₃	—	2	1	no	—
343	C₂×D₄×C₁₃	—	2	4	no	—
344	C₂×D₄×C₁₃	—	2	4	no	—
345	C₂×D₄×C₁₃	—	2	2	no	—
346	C₂×D₄×C₁₃	—	2	2	no	—
347	C₂×D₄×C₁₃	—	2	2	no	—
348	C₂×D₄×C₁₃	—	2	1	no	—
349	C₂×D₄×C₁₃	—	2	2	no	—
350	C₂×D₄×C₁₃	—	2	2	no	—
351	C₂×D₄×C₁₃	—	2	2	no	—
352	C₂×D₄×C₁₃	—	2	2	no	—
353	C₂×D₄×C₁₃	—	2	2	no	—
354	C₂×D₄×C₁₃	—	2	2	no	—
355	C₂×D₄×C₁₃	—	2	2	no	—
356	C₂×D₄×C₁₃	—	2	1	no	—
357	C₂×D₄×C₁₃	—	2	1	no	—
358	C₂×D₄×C₁₃	—	2	2	no	—
359	C₂×D₄×C₁₃	—	2	1	no	—
360	C₂×D₄×C₁₃	—	2	1	no	—
361	C₂×D₄×C₁₃	—	2	2	no	—
362	C₂×D₄×C₁₃	—	4	2	no	—
363	C₂×D₄×C₁₃	—	4	2	no	—
364	C₂×D₄×C₁₃	—	4	2	no	—
365	C₂×D₄×C₁₃	—	4	8	no	—
366	C₂×D₄×C₁₃	—	4	4	no	—
367	C₂×D₄×C₁₃	—	4	4	no	—
368	C₂×D₄×C₁₃	—	8	4	no	—
369	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
373	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
375	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₁₃	—	2	1	no	—
377	C₂²×C₄×C₁₃	—	2	2	no	—
378	C₂²×C₄×C₁₃	—	2	2	no	—
379	C₂²×C₄×C₁₃	—	2	1	no	—
380	C₂²×C₄×C₁₃	—	2	2	no	—
381	C₂²×C₄×C₁₃	—	2	1	no	—
382	C₂²×C₄×C₁₃	—	2	2	no	—
383	C₂²×C₄×C₁₃	—	2	2	no	—
384	C₂²×C₄×C₁₃	—	2	1	no	—
385	C₂²×C₄×C₁₃	—	2	2	no	—
386	C₂²×C₄×C₁₃	—	2	2	no	—
387	C₂²×C₄×C₁₃	—	4	2	no	—
388	C₂²×C₄×C₁₃	—	4	2	no	—
389	C₂²×C₄×C₁₃	—	4	8	no	—
390	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
393	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
394	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
395	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
398	C₁₃×Q₁₆	—	2	2	no	—
399	C₁₃×Q₁₆	—	4	2	no	—
400	C₁₃×SD₁₆	—	2	2	no	—
401	C₁₃×SD₁₆	—	2	4	no	—
402	C₁₃×SD₁₆	—	2	2	no	—
403	C₁₃×SD₁₆	—	4	2	no	—
404	C₁₃×SD₁₆	—	4	2	no	—
405	C₁₃×SD₁₆	—	4	2	no	—
406	C₁₃×SD₁₆	—	4	2	no	—
407	C₁₃×D₈	—	2	2	no	—
408	C₁₃×D₈	—	2	4	no	—
409	C₁₃×D₈	—	4	2	no	—
410	C₁₃×D₈	—	4	2	no	—
411	C₁₃×D₈	—	4	2	no	—
412	C₂×C₈×C₁₃	—	4	2	no	—
413	C₂×C₈×C₁₃	—	4	2	no	—
414	C₂×C₈×C₁₃	—	4	2	no	—
415	C₂×C₈×C₁₃	—	4	2	no	—
416	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
419	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
420	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
421	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
422	C₁₃×C₄⋊C₄	—	2	1	no	—
423	C₁₃×C₄⋊C₄	—	2	2	no	—
424	C₁₃×C₄⋊C₄	—	2	2	no	—
425	C₁₃×C₄⋊C₄	—	2	1	no	—
426	C₁₃×C₄⋊C₄	—	2	1	no	—
427	C₁₃×C₄⋊C₄	—	2	1	no	—
428	C₁₃×C₄⋊C₄	—	2	1	no	—
429	C₁₃×C₄⋊C₄	—	2	1	no	—
430	C₁₃×C₄⋊C₄	—	2	1	no	—
431	C₁₃×C₄⋊C₄	—	2	1	no	—
432	C₁₃×C₄⋊C₄	—	2	2	no	—
433	C₁₃×C₄⋊C₄	—	2	2	no	—
434	C₁₃×C₄⋊C₄	—	2	1	no	—
435	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
436	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
437	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
438	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
440	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
441	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
442	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
443	C₁₃×C₂²⋊C₄	—	2	2	no	—
444	C₁₃×C₂²⋊C₄	—	2	2	no	—
445	C₁₃×C₂²⋊C₄	—	2	1	no	—
446	C₁₃×C₂²⋊C₄	—	2	2	no	—
447	C₁₃×C₂²⋊C₄	—	2	1	no	—
448	C₁₃×C₂²⋊C₄	—	2	2	no	—
449	C₁₃×C₂²⋊C₄	—	2	1	no	—
450	C₁₃×C₂²⋊C₄	—	2	1	no	—
451	C₁₃×C₂²⋊C₄	—	2	2	no	—
452	C₁₃×C₂²⋊C₄	—	2	2	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	1	no	—
458	C₁₃×C₂²⋊C₄	—	2	1	no	—
459	C₁₃×C₂²⋊C₄	—	2	2	no	—
460	C₁₃×C₂²⋊C₄	—	2	2	no	—
461	C₁₃×C₂²⋊C₄	—	2	2	no	—
462	C₁₃×C₂²⋊C₄	—	2	1	no	—
463	C₁₃×C₂²⋊C₄	—	2	2	no	—
464	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
465	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
466	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
467	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
468	C₄²×C₁₃	—	2	1	no	—
469	C₄²×C₁₃	—	2	1	no	—
470	C₄²×C₁₃	—	2	1	no	—
471	C₄²×C₁₃	—	2	2	no	—
472	C₄²×C₁₃	—	2	1	no	—
473	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
474	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
476	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
477	#3519	C₂×C₁₃	1	1	yes	characteristic, complemented
478	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#3305	C₂×C₁₃	1	1	yes	characteristic, complemented
480	#3303	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#3301	C₂×C₁₃	1	2	yes	complemented
482	#3299	C₂×C₁₃	1	1	yes	characteristic, complemented
483	#3297	C₂×C₁₃	1	2	yes	complemented
484	#3295	C₂×C₁₃	1	1	yes	characteristic, complemented
485	#3287	C₂×C₁₃	1	1	yes	characteristic, complemented
486	#3284	C₂×C₁₃	1	1	yes	characteristic, complemented
487	#3282	C₂×C₁₃	1	2	yes	complemented
488	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
489	#3280	C₂×C₁₃	1	2	yes	complemented
490	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
491	#3212	C₂×C₁₃	1	1	yes	characteristic, complemented
492	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
493	#3191	C₂×C₁₃	1	2	yes	complemented
494	#3188	C₂×C₁₃	1	2	yes	complemented
495	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
496	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
497	#3002	C₂×C₁₃	1	2	yes	complemented
498	C₂×#449	C₂×C₁₃	1	2	yes	complemented
499	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
500	C₂³×C₁₃	—	2	1	no	—
501	C₂³×C₁₃	—	2	4	no	—
502	C₂³×C₁₃	—	2	1	no	—
503	C₂³×C₁₃	—	2	2	no	—
504	C₂³×C₁₃	—	2	2	no	—
505	C₂³×C₁₃	—	4	2	no	—
506	C₂³×C₁₃	—	4	2	no	—
507	C₂³×C₁₃	—	4	4	no	—
508	C₂³×C₁₃	—	4	4	no	—
509	C₂³×C₁₃	—	4	4	no	—
510	C₂³×C₁₃	—	8	2	no	—
511	C₂³×C₁₃	—	8	2	no	—
512	C₂³×C₁₃	—	8	2	no	—
513	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
514	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
515	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
516	Q₈×C₁₃	—	2	1	no	—
517	Q₈×C₁₃	—	2	1	no	—
518	Q₈×C₁₃	—	2	1	no	—
519	Q₈×C₁₃	—	2	2	no	—
520	Q₈×C₁₃	—	2	2	no	—
521	Q₈×C₁₃	—	4	4	no	—
522	Q₈×C₁₃	—	8	1	no	—
523	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
524	D₄×C₁₃	—	2	4	no	—
525	D₄×C₁₃	—	2	4	no	—
526	D₄×C₁₃	—	2	2	no	—
527	D₄×C₁₃	—	2	1	no	—
528	D₄×C₁₃	—	2	1	no	—
529	D₄×C₁₃	—	2	2	no	—
530	D₄×C₁₃	—	2	2	no	—
531	D₄×C₁₃	—	2	2	no	—
532	D₄×C₁₃	—	2	2	no	—
533	D₄×C₁₃	—	2	1	no	—
534	D₄×C₁₃	—	4	4	no	—
535	D₄×C₁₃	—	4	4	no	—
536	D₄×C₁₃	—	4	4	no	—
537	D₄×C₁₃	—	4	4	no	—
538	D₄×C₁₃	—	4	2	no	—
539	D₄×C₁₃	—	4	4	no	—
540	D₄×C₁₃	—	4	4	no	—
541	D₄×C₁₃	—	4	4	no	—
542	D₄×C₁₃	—	4	2	no	—
543	D₄×C₁₃	—	4	2	no	—
544	D₄×C₁₃	—	8	1	no	—
545	D₄×C₁₃	—	8	2	no	—
546	D₄×C₁₃	—	8	1	no	—
547	D₄×C₁₃	—	8	2	no	—
548	D₄×C₁₃	—	8	2	no	—
549	D₄×C₁₃	—	8	2	no	—
550	D₄×C₁₃	—	8	2	no	—
551	D₄×C₁₃	#135	1	4	yes	complemented
552	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
553	C₂×C₄×C₁₃	—	2	4	no	—
554	C₂×C₄×C₁₃	—	2	1	no	—
555	C₂×C₄×C₁₃	—	2	2	no	—
556	C₂×C₄×C₁₃	—	2	2	no	—
557	C₂×C₄×C₁₃	—	2	2	no	—
558	C₂×C₄×C₁₃	—	2	2	no	—
559	C₂×C₄×C₁₃	—	2	2	no	—
560	C₂×C₄×C₁₃	—	2	1	no	—
561	C₂×C₄×C₁₃	—	2	1	no	—
562	C₂×C₄×C₁₃	—	2	1	no	—
563	C₂×C₄×C₁₃	—	2	1	no	—
564	C₂×C₄×C₁₃	—	2	1	no	—
565	C₂×C₄×C₁₃	—	2	1	no	—
566	C₂×C₄×C₁₃	—	2	2	no	—
567	C₂×C₄×C₁₃	—	2	1	no	—
568	C₂×C₄×C₁₃	—	2	2	no	—
569	C₂×C₄×C₁₃	—	4	2	no	—
570	C₂×C₄×C₁₃	—	4	2	no	—
571	C₂×C₄×C₁₃	—	4	2	no	—
572	C₂×C₄×C₁₃	—	4	1	no	—
573	C₂×C₄×C₁₃	—	4	4	no	—
574	C₂×C₄×C₁₃	—	4	4	no	—
575	C₂×C₄×C₁₃	—	4	4	no	—
576	C₂×C₄×C₁₃	—	4	4	no	—
577	C₂×C₄×C₁₃	—	4	2	no	—
578	C₂×C₄×C₁₃	—	4	2	no	—
579	C₂×C₄×C₁₃	—	8	1	no	—
580	C₂×C₄×C₁₃	—	8	2	no	—
581	C₂×C₄×C₁₃	—	8	2	no	—
582	C₂×C₄×C₁₃	—	8	2	no	—
583	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
586	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
589	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
591	C₈×C₁₃	—	2	1	no	—
592	C₈×C₁₃	—	2	2	no	—
593	C₈×C₁₃	—	2	1	no	—
594	C₈×C₁₃	—	2	1	no	—
595	C₈×C₁₃	—	2	2	no	—
596	C₈×C₁₃	—	2	1	no	—
597	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
598	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
599	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
600	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
601	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
602	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
603	#554	C₂²×C₁₃	1	1	yes	characteristic
604	#553	—	2	1	no	—
605	#553	C₂²×C₁₃	1	2	yes	complemented
606	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
607	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
609	#548	C₂²×C₁₃	1	2	yes	complemented
610	#547	—	2	1	no	—
611	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	#546	—	2	2	no	—
613	#546	—	2	2	no	—
614	#546	C₂²×C₁₃	1	2	yes	complemented
615	#546	C₂²×C₁₃	1	2	yes	complemented
616	D₄²	—	2	1	no	—
617	D₄²	—	2	1	no	—
618	D₄²	C₂²×C₁₃	1	1	yes	characteristic
619	D₄²	C₂²×C₁₃	1	1	yes	characteristic
620	#540	—	2	1	no	—
621	#538	—	2	2	no	—
622	#532	—	2	1	no	—
623	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
624	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
625	#529	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	#525	—	2	2	no	—
627	#525	C₂²×C₁₃	1	2	yes	complemented
628	#525	C₂²×C₁₃	1	2	yes	complemented
629	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
630	#518	—	2	1	no	—
631	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	C₂×C₄×D₄	—	2	1	no	—
633	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
634	#495	C₂²×C₁₃	1	2	yes	complemented
635	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	#488	C₂²×C₁₃	1	2	yes	complemented
638	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
639	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	#485	C₂²×C₁₃	1	1	yes	characteristic, complemented
641	#485	C₂²×C₁₃	1	2	yes	complemented
642	#484	C₂²×C₁₃	1	2	yes	complemented
643	#482	C₂²×C₁₃	1	1	yes	characteristic, complemented
644	#482	C₂²×C₁₃	1	2	yes	complemented
645	#482	C₂²×C₁₃	1	2	yes	complemented
646	#481	C₂²×C₁₃	1	2	yes	complemented
647	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
648	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	#467	C₂²×C₁₃	1	2	yes	complemented
652	#466	C₂²×C₁₃	1	2	yes	complemented
653	#466	C₂²×C₁₃	1	2	yes	complemented
654	#466	C₂²×C₁₃	1	2	yes	complemented
655	#465	C₂²×C₁₃	1	2	yes	complemented
656	#465	C₂²×C₁₃	1	2	yes	complemented
657	#465	C₂²×C₁₃	1	2	yes	complemented
658	#465	C₂²×C₁₃	1	2	yes	complemented
659	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
660	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#463	C₂²×C₁₃	1	2	yes	complemented
662	#463	C₂²×C₁₃	1	2	yes	complemented
663	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
664	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
665	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
666	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
668	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
669	#452	C₂²×C₁₃	1	1	yes	characteristic, complemented
670	#452	C₂²×C₁₃	1	2	yes	complemented
671	#452	C₂²×C₁₃	1	2	yes	complemented
672	#451	C₂²×C₁₃	1	2	yes	complemented
673	#450	C₂²×C₁₃	1	2	yes	complemented
674	#450	C₂²×C₁₃	1	2	yes	complemented
675	#449	C₂²×C₁₃	1	1	yes	characteristic
676	#449	C₂²×C₁₃	1	2	yes	complemented
677	#449	C₂²×C₁₃	1	2	yes	complemented
678	#449	C₂²×C₁₃	1	2	yes	complemented
679	#449	C₂²×C₁₃	1	2	yes	complemented
680	#449	C₂²×C₁₃	1	2	yes	complemented
681	#449	C₂²×C₁₃	1	2	yes	complemented
682	#449	C₂²×C₁₃	1	2	yes	complemented
683	#449	C₂²×C₁₃	1	2	yes	complemented
684	#449	C₂²×C₁₃	1	2	yes	complemented
685	#448	C₂²×C₁₃	1	2	yes	complemented
686	#447	C₂²×C₁₃	1	2	yes	complemented
687	#447	C₂²×C₁₃	1	2	yes	complemented
688	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
689	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
692	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
693	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
694	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
695	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
696	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
697	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
698	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
699	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
700	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
701	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
702	#416	C₂²×C₁₃	1	2	yes	complemented
703	#416	C₂²×C₁₃	1	2	yes	complemented
704	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
705	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
706	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
707	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
708	C₂²×C₁₃	—	2	2	no	—
709	C₂²×C₁₃	—	2	2	no	—
710	C₂²×C₁₃	—	2	1	no	—
711	C₂²×C₁₃	—	2	2	no	—
712	C₂²×C₁₃	—	2	1	no	—
713	C₂²×C₁₃	—	2	2	no	—
714	C₂²×C₁₃	—	2	2	no	—
715	C₂²×C₁₃	—	2	1	no	—
716	C₂²×C₁₃	—	2	2	no	—
717	C₂²×C₁₃	—	4	1	no	—
718	C₂²×C₁₃	—	4	1	no	—
719	C₂²×C₁₃	—	4	2	no	—
720	C₂²×C₁₃	—	4	1	no	—
721	C₂²×C₁₃	—	4	2	no	—
722	C₂²×C₁₃	—	4	2	no	—
723	C₂²×C₁₃	—	4	2	no	—
724	C₂²×C₁₃	—	4	1	no	—
725	C₂²×C₁₃	—	4	1	no	—
726	C₂²×C₁₃	—	4	2	no	—
727	C₂²×C₁₃	—	4	2	no	—
728	C₂²×C₁₃	—	8	4	no	—
729	C₂²×C₁₃	—	8	8	no	—
730	C₂²×C₁₃	—	16	4	no	—
731	C₂²×C₁₃	C₂×#135	1	4	yes	—
732	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
733	C₄×C₁₃	—	2	1	no	—
734	C₄×C₁₃	—	2	1	no	—
735	C₄×C₁₃	—	2	1	no	—
736	C₄×C₁₃	—	2	2	no	—
737	C₄×C₁₃	—	2	2	no	—
738	C₄×C₁₃	—	2	2	no	—
739	C₄×C₁₃	—	2	1	no	—
740	C₄×C₁₃	—	4	1	no	—
741	C₄×C₁₃	—	4	2	no	—
742	C₄×C₁₃	—	4	1	no	—
743	C₄×C₁₃	—	4	2	no	—
744	C₄×C₁₃	—	4	1	no	—
745	C₄×C₁₃	—	4	1	no	—
746	C₄×C₁₃	—	4	1	no	—
747	C₄×C₁₃	C₂×#135	1	2	yes	—
748	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
749	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
750	C₂×#41	—	2	2	no	—
751	C₂×#41	—	2	2	no	—
752	C₂×#41	—	2	1	no	—
753	C₂×#41	—	4	4	no	—
754	C₂×#41	—	4	4	no	—
755	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
756	C₂×#41	C₂³×C₁₃	1	2	yes	—
757	C₂×#41	C₂³×C₁₃	1	2	yes	—
758	C₂×#41	C₂³×C₁₃	1	2	yes	—
759	C₂×#41	C₂³×C₁₃	1	2	yes	—
760	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
761	C₂²×D₄	—	2	2	no	—
762	C₂²×D₄	—	2	2	no	—
763	C₂²×D₄	—	2	1	no	—
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
766	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
767	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
768	C₂³×C₄	—	2	2	no	—
769	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
770	#135	—	4	4	no	—
771	#135	—	4	4	no	—
772	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
773	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
774	C₂×SD₁₆	—	4	4	no	—
775	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
778	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
781	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
782	C₂×D₈	—	4	4	no	—
783	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
784	C₂×D₈	C₂³×C₁₃	1	2	yes	—
785	C₂×D₈	C₂³×C₁₃	1	2	yes	—
786	C₂×D₈	C₂³×C₁₃	1	2	yes	—
787	C₂×D₈	C₂³×C₁₃	1	2	yes	—
788	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
789	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
790	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
791	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
792	C₄⋊Q₈	—	2	1	no	—
793	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
794	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
795	#127	—	2	1	no	—
796	#127	—	2	1	no	—
797	#127	C₂³×C₁₃	1	1	yes	characteristic
798	#127	C₂³×C₁₃	1	1	yes	characteristic
799	#126	—	2	2	no	—
800	#126	—	2	1	no	—
801	#125	—	2	1	no	—
802	#125	C₂³×C₁₃	1	1	yes	characteristic
803	#124	—	2	2	no	—
804	#124	—	2	2	no	—
805	#124	—	2	1	no	—
806	#124	C₂³×C₁₃	1	1	yes	characteristic
807	#124	C₂³×C₁₃	1	2	yes	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	1	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
819	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
820	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
821	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
822	#121	—	2	2	no	—
823	#121	—	2	1	no	—
824	#121	—	2	2	no	—
825	#121	—	2	1	no	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	C₂³×C₁₃	1	1	yes	characteristic
838	#121	C₂³×C₁₃	1	2	yes	—
839	#121	C₂³×C₁₃	1	2	yes	—
840	#121	C₂³×C₁₃	1	2	yes	—
841	#121	C₂³×C₁₃	1	2	yes	—
842	#121	C₂³×C₁₃	1	2	yes	—
843	#121	C₂³×C₁₃	1	2	yes	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	#120	—	2	2	no	—
847	#120	—	2	2	no	—
848	#120	—	2	2	no	—
849	#120	—	2	2	no	—
850	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
851	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
852	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
870	C₄×D₄	D₄×C₁₃	1	2	yes	—
871	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
872	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
873	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₁₃	1	2	yes	—
876	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
877	C₄×D₄	C₂³×C₁₃	1	2	yes	—
878	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
879	#117	—	2	1	no	—
880	#117	—	2	1	no	—
881	#117	—	2	1	no	—
882	#117	C₂³×C₁₃	1	1	yes	characteristic
883	#117	C₂³×C₁₃	1	2	yes	—
884	C₂×C₄⋊C₄	—	2	1	no	—
885	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
887	C₂×C₂²⋊C₄	—	2	2	no	—
888	C₂×C₂²⋊C₄	—	2	2	no	—
889	C₂×C₂²⋊C₄	—	2	2	no	—
890	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
891	C₂×C₄²	—	2	1	no	—
892	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
893	#107	C₂³×C₁₃	1	1	yes	characteristic
894	#107	C₂³×C₁₃	1	2	yes	—
895	#107	C₂³×C₁₃	1	1	yes	characteristic
896	#106	C₂³×C₁₃	1	2	yes	—
897	#106	C₂³×C₁₃	1	1	yes	characteristic
898	#106	C₂³×C₁₃	1	1	yes	characteristic
899	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
900	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
901	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
902	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
903	#103	C₂³×C₁₃	1	1	yes	characteristic
904	#103	C₂³×C₁₃	1	2	yes	—
905	#103	C₂³×C₁₃	1	2	yes	—
906	#103	C₂³×C₁₃	1	2	yes	—
907	#103	C₂³×C₁₃	1	1	yes	characteristic
908	#103	C₂³×C₁₃	1	2	yes	—
909	#103	C₂³×C₁₃	1	2	yes	—
910	#103	C₂³×C₁₃	1	1	yes	characteristic
911	#103	C₂³×C₁₃	1	1	yes	characteristic
912	#102	C₂³×C₁₃	1	1	yes	characteristic
913	#102	C₂³×C₁₃	1	2	yes	—
914	#102	C₂³×C₁₃	1	2	yes	—
915	#102	C₂³×C₁₃	1	2	yes	—
916	#102	C₂³×C₁₃	1	1	yes	characteristic
917	#102	C₂³×C₁₃	1	2	yes	—
918	#102	C₂³×C₁₃	1	2	yes	—
919	#102	C₂³×C₁₃	1	1	yes	characteristic
920	#102	C₂³×C₁₃	1	2	yes	—
921	#102	C₂³×C₁₃	1	2	yes	—
922	#102	C₂³×C₁₃	1	1	yes	characteristic
923	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
924	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
925	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
927	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
930	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
931	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
932	C₄×C₈	C₂³×C₁₃	1	2	yes	—
933	C₂×C₁₃	—	2	4	no	—
934	C₂×C₁₃	—	4	2	no	—
935	C₂×C₁₃	—	4	1	no	—
936	C₂×C₁₃	—	4	2	no	—
937	C₂×C₁₃	—	8	2	no	—
938	C₂×C₁₃	—	8	2	no	—
939	C₂×C₁₃	—	8	1	no	—
940	C₂×C₁₃	#3484	1	1	yes	characteristic
941	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
942	C₂×C₁₃	#3585	1	1	yes	characteristic
943	C₂⁴	—	2	2	no	—
944	C₂⁴	—	2	2	no	—
945	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	4	no	—
949	#41	—	2	4	no	—
950	#41	—	4	2	no	—
951	#41	—	4	2	no	—
952	#41	—	4	2	no	—
953	#41	—	4	2	no	—
954	#41	—	4	8	no	—
955	#41	—	4	2	no	—
956	#41	—	4	2	no	—
957	#41	—	4	8	no	—
958	#41	—	8	2	no	—
959	C₂×Q₈	—	2	2	no	—
960	C₂×Q₈	—	2	1	no	—
961	C₂×Q₈	—	2	4	no	—
962	C₂×Q₈	—	4	2	no	—
963	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
964	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
965	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	4	no	—
968	C₂×D₄	—	2	4	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	4	2	no	—
987	C₂×D₄	—	4	2	no	—
988	C₂×D₄	—	4	2	no	—
989	C₂×D₄	—	4	8	no	—
990	C₂×D₄	—	4	4	no	—
991	C₂×D₄	—	4	4	no	—
992	C₂×D₄	—	8	4	no	—
993	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
994	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
995	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
996	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
997	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
998	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
999	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	4	2	no	—
1012	C₂²×C₄	—	4	2	no	—
1013	C₂²×C₄	—	4	8	no	—
1014	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1017	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1018	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1019	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1021	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1022	Q₁₆	—	2	2	no	—
1023	Q₁₆	—	4	2	no	—
1024	SD₁₆	—	2	2	no	—
1025	SD₁₆	—	2	4	no	—
1026	SD₁₆	—	2	2	no	—
1027	SD₁₆	—	4	2	no	—
1028	SD₁₆	—	4	2	no	—
1029	SD₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	D₈	—	2	2	no	—
1032	D₈	—	2	4	no	—
1033	D₈	—	4	2	no	—
1034	D₈	—	4	2	no	—
1035	D₈	—	4	2	no	—
1036	C₂×C₈	—	4	2	no	—
1037	C₂×C₈	—	4	2	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	—	4	2	no	—
1040	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1041	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1043	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1044	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1045	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1060	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1062	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1063	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1064	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1065	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1089	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	2	no	—
1096	C₄²	—	2	1	no	—
1097	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1098	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1099	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1100	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1101	C₁₃	#61567	1	1	yes	characteristic, direct product factor, Sylow
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	4	no	—
1104	C₂³	—	2	1	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	4	2	no	—
1108	C₂³	—	4	2	no	—
1109	C₂³	—	4	4	no	—
1110	C₂³	—	4	4	no	—
1111	C₂³	—	4	4	no	—
1112	C₂³	—	8	2	no	—
1113	C₂³	—	8	2	no	—
1114	C₂³	—	8	2	no	—
1115	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1116	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1117	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1118	Q₈	—	2	1	no	—
1119	Q₈	—	2	1	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	2	2	no	—
1122	Q₈	—	2	2	no	—
1123	Q₈	—	4	4	no	—
1124	Q₈	—	8	1	no	—
1125	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
1126	D₄	—	2	4	no	—
1127	D₄	—	2	4	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	2	1	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	2	no	—
1132	D₄	—	2	2	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	1	no	—
1136	D₄	—	4	4	no	—
1137	D₄	—	4	4	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	4	no	—
1144	D₄	—	4	2	no	—
1145	D₄	—	4	2	no	—
1146	D₄	—	8	2	no	—
1147	D₄	—	8	1	no	—
1148	D₄	—	8	1	no	—
1149	D₄	—	8	2	no	—
1150	D₄	—	8	2	no	—
1151	D₄	—	8	2	no	—
1152	D₄	—	8	2	no	—
1153	D₄	C₁₃×#135	1	4	yes	complemented
1154	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1155	C₂×C₄	—	2	4	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	4	2	no	—
1172	C₂×C₄	—	4	2	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	4	no	—
1176	C₂×C₄	—	4	4	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	4	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	8	1	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	2	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1186	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1187	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1188	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1189	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1190	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1191	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1192	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1193	C₈	—	2	1	no	—
1194	C₈	—	2	2	no	—
1195	C₈	—	2	1	no	—
1196	C₈	—	2	1	no	—
1197	C₈	—	2	2	no	—
1198	C₈	—	2	1	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	8	4	no	—
1220	C₂²	—	8	8	no	—
1221	C₂²	—	16	4	no	—
1222	C₂²	C₂×C₁₃×#135	1	4	yes	—
1223	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1224	C₄	—	2	1	no	—
1225	C₄	—	2	1	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	2	2	no	—
1230	C₄	—	2	2	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	2	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	C₂×C₁₃×#135	1	2	yes	—
1239	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1240	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1241	C₂	—	2	4	no	—
1242	C₂	—	4	1	no	—
1243	C₂	—	4	2	no	—
1244	C₂	—	4	2	no	—
1245	C₂	—	8	2	no	—
1246	C₂	—	8	1	no	—
1247	C₂	—	8	2	no	—
1248	C₂	C₁₃×#3484	1	1	yes	characteristic
1249	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
1250	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3519	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3305	C₂	semidirect
4. C₁₃×#3303	C₂	semidirect
5. C₁₃×#3301	C₂	semidirect
6. C₁₃×#3299	C₂	semidirect
7. C₁₃×#3297	C₂	semidirect
8. C₁₃×#3295	C₂	semidirect
9. C₁₃×#3287	C₂	semidirect
10. C₁₃×#3284	C₂	semidirect
11. C₁₃×#3282	C₂	semidirect
12. D₄×C₁₃×SD₁₆	C₂	semidirect
13. C₁₃×#3280	C₂	semidirect
14. D₄×C₁₃×D₈	C₂	semidirect
15. C₁₃×#3212	C₂	semidirect
16. C₁₃×#3207	C₂	semidirect
17. C₁₃×#3191	C₂	semidirect
18. C₁₃×#3188	C₂	semidirect
19. C₁₃×#3106	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3002	C₂	semidirect
22. C₂×C₁₃×#449	C₂	semidirect
23. C₁₃×#2972	C₂	semidirect
24. C₂²×C₁₃×#41	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
26. C₂×C₁₃×#135	C₂²	semidirect
27. C₂²×C₁₃×SD₁₆	C₂²	semidirect
28. C₂²×C₁₃×D₈	C₂²	semidirect
29. C₁₃×#555	C₂²	semidirect
32. C₁₃×#553	C₂²	semidirect
33. C₁₃×#550	C₂²	semidirect
34. C₁₃×#550	C₂²	semidirect
36. C₁₃×#548	C₂²	semidirect
38. C₁₃×#547	C₂²	semidirect
41. C₁₃×#546	C₂²	semidirect
42. C₁₃×#546	C₂²	semidirect
50. C₁₃×#532	C₂²	semidirect
51. C₁₃×#532	C₂²	semidirect
52. C₁₃×#529	C₂²	semidirect
54. C₁₃×#525	C₂²	semidirect
55. C₁₃×#525	C₂²	semidirect
56. C₂×C₁₃×#121	C₂²	semidirect
58. C₄×C₁₃×#41	C₂²	semidirect
61. C₁₃×#495	C₂²	semidirect
62. C₁₃×#493	C₂²	semidirect
63. C₁₃×#492	C₂²	semidirect
64. C₁₃×#488	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#484	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#482	C₂²	semidirect
73. C₁₃×#481	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#467	C₂²	semidirect
79. C₁₃×#466	C₂²	semidirect
80. C₁₃×#466	C₂²	semidirect
81. C₁₃×#466	C₂²	semidirect
82. C₁₃×#465	C₂²	semidirect
83. C₁₃×#465	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#463	C₂²	semidirect
88. C₁₃×#463	C₂²	semidirect
89. C₁₃×#463	C₂²	semidirect
90. C₁₃×#462	C₂²	semidirect
91. C₁₃×#461	C₂²	semidirect
92. C₁₃×#460	C₂²	semidirect
93. C₁₃×#460	C₂²	semidirect
94. C₁₃×#459	C₂²	semidirect
95. C₁₃×#459	C₂²	semidirect
96. C₁₃×#452	C₂²	semidirect
97. C₁₃×#452	C₂²	semidirect
98. C₁₃×#452	C₂²	semidirect
99. C₁₃×#451	C₂²	semidirect
100. C₁₃×#450	C₂²	semidirect
101. C₁₃×#450	C₂²	semidirect
103. C₁₃×#449	C₂²	semidirect
104. C₁₃×#449	C₂²	semidirect
105. C₁₃×#449	C₂²	semidirect
106. C₁₃×#449	C₂²	semidirect
107. C₁₃×#449	C₂²	semidirect
108. C₁₃×#449	C₂²	semidirect
109. C₁₃×#449	C₂²	semidirect
110. C₁₃×#449	C₂²	semidirect
111. C₁₃×#449	C₂²	semidirect
112. C₁₃×#448	C₂²	semidirect
113. C₁₃×#447	C₂²	semidirect
114. C₁₃×#447	C₂²	semidirect
115. C₄×C₁₃×Q₁₆	C₂²	semidirect
116. C₄×C₁₃×SD₁₆	C₂²	semidirect
117. C₄×C₁₃×SD₁₆	C₂²	semidirect
118. C₄×C₁₃×SD₁₆	C₂²	semidirect
119. C₄×C₁₃×D₈	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
123. C₈×D₄×C₁₃	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
125. C₈×D₄×C₁₃	C₂²	semidirect
126. C₈×D₄×C₁₃	C₂²	semidirect
127. C₁₃×#431	C₂²	semidirect
128. C₁₃×#431	C₂²	semidirect
129. C₁₃×#416	C₂²	semidirect
130. C₁₃×#416	C₂²	semidirect
131. C₂×C₁₃×#103	C₂²	semidirect
132. C₂×C₁₃×#102	C₂²	semidirect
133. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
134. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
318. #61567	C₁₃	direct (N × H)
477. #3519	C₂×C₁₃	semidirect
478. D₄×#41	C₂×C₁₃	semidirect
479. #3305	C₂×C₁₃	semidirect
480. #3303	C₂×C₁₃	semidirect
481. #3301	C₂×C₁₃	semidirect
482. #3299	C₂×C₁₃	semidirect
483. #3297	C₂×C₁₃	semidirect
484. #3295	C₂×C₁₃	semidirect
485. #3287	C₂×C₁₃	semidirect
486. #3284	C₂×C₁₃	semidirect
487. #3282	C₂×C₁₃	semidirect
488. D₄×SD₁₆	C₂×C₁₃	semidirect
489. #3280	C₂×C₁₃	semidirect
490. D₄×D₈	C₂×C₁₃	semidirect
491. #3212	C₂×C₁₃	semidirect
492. #3207	C₂×C₁₃	semidirect
493. #3191	C₂×C₁₃	semidirect
494. #3188	C₂×C₁₃	semidirect
495. #3106	C₂×C₁₃	semidirect
496. #3102	C₂×C₁₃	semidirect
497. #3002	C₂×C₁₃	semidirect
498. C₂×#449	C₂×C₁₃	semidirect
499. #2972	C₂×C₁₃	semidirect
551. D₄×C₁₃	#135	semidirect
597. C₂²×#41	C₂²×C₁₃	semidirect
598. C₂×#135	C₂²×C₁₃	semidirect
599. C₂×#135	C₂²×C₁₃	semidirect
600. C₂²×SD₁₆	C₂²×C₁₃	semidirect
601. C₂²×D₈	C₂²×C₁₃	semidirect
602. #555	C₂²×C₁₃	semidirect
605. #553	C₂²×C₁₃	semidirect
606. #550	C₂²×C₁₃	semidirect
607. #550	C₂²×C₁₃	semidirect
609. #548	C₂²×C₁₃	semidirect
611. #547	C₂²×C₁₃	semidirect
614. #546	C₂²×C₁₃	semidirect
615. #546	C₂²×C₁₃	semidirect
623. #532	C₂²×C₁₃	semidirect
624. #532	C₂²×C₁₃	semidirect
625. #529	C₂²×C₁₃	semidirect
627. #525	C₂²×C₁₃	semidirect
628. #525	C₂²×C₁₃	semidirect
629. C₂×#121	C₂²×C₁₃	semidirect
631. C₄×#41	C₂²×C₁₃	semidirect
634. #495	C₂²×C₁₃	semidirect
635. #493	C₂²×C₁₃	semidirect
636. #492	C₂²×C₁₃	semidirect
637. #488	C₂²×C₁₃	semidirect
638. #487	C₂²×C₁₃	semidirect
639. #486	C₂²×C₁₃	semidirect
640. #485	C₂²×C₁₃	semidirect
641. #485	C₂²×C₁₃	semidirect
642. #484	C₂²×C₁₃	semidirect
643. #482	C₂²×C₁₃	semidirect
644. #482	C₂²×C₁₃	semidirect
645. #482	C₂²×C₁₃	semidirect
646. #481	C₂²×C₁₃	semidirect
647. #479	C₂²×C₁₃	semidirect
648. #478	C₂²×C₁₃	semidirect
649. #477	C₂²×C₁₃	semidirect
650. #476	C₂²×C₁₃	semidirect
651. #467	C₂²×C₁₃	semidirect
652. #466	C₂²×C₁₃	semidirect
653. #466	C₂²×C₁₃	semidirect
654. #466	C₂²×C₁₃	semidirect
655. #465	C₂²×C₁₃	semidirect
656. #465	C₂²×C₁₃	semidirect
657. #465	C₂²×C₁₃	semidirect
658. #465	C₂²×C₁₃	semidirect
659. #464	C₂²×C₁₃	semidirect
660. #463	C₂²×C₁₃	semidirect
661. #463	C₂²×C₁₃	semidirect
662. #463	C₂²×C₁₃	semidirect
663. #462	C₂²×C₁₃	semidirect
664. #461	C₂²×C₁₃	semidirect
665. #460	C₂²×C₁₃	semidirect
666. #460	C₂²×C₁₃	semidirect
667. #459	C₂²×C₁₃	semidirect
668. #459	C₂²×C₁₃	semidirect
669. #452	C₂²×C₁₃	semidirect
670. #452	C₂²×C₁₃	semidirect
671. #452	C₂²×C₁₃	semidirect
672. #451	C₂²×C₁₃	semidirect
673. #450	C₂²×C₁₃	semidirect
674. #450	C₂²×C₁₃	semidirect
676. #449	C₂²×C₁₃	semidirect
677. #449	C₂²×C₁₃	semidirect
678. #449	C₂²×C₁₃	semidirect
679. #449	C₂²×C₁₃	semidirect
680. #449	C₂²×C₁₃	semidirect
681. #449	C₂²×C₁₃	semidirect
682. #449	C₂²×C₁₃	semidirect
683. #449	C₂²×C₁₃	semidirect
684. #449	C₂²×C₁₃	semidirect
685. #448	C₂²×C₁₃	semidirect
686. #447	C₂²×C₁₃	semidirect
687. #447	C₂²×C₁₃	semidirect
688. C₄×Q₁₆	C₂²×C₁₃	semidirect
689. C₄×SD₁₆	C₂²×C₁₃	semidirect
690. C₄×SD₁₆	C₂²×C₁₃	semidirect
691. C₄×SD₁₆	C₂²×C₁₃	semidirect
692. C₄×D₈	C₂²×C₁₃	semidirect
693. C₄×D₈	C₂²×C₁₃	semidirect
696. C₈×D₄	C₂²×C₁₃	semidirect
697. C₈×D₄	C₂²×C₁₃	semidirect
698. C₈×D₄	C₂²×C₁₃	semidirect
699. C₈×D₄	C₂²×C₁₃	semidirect
700. #431	C₂²×C₁₃	semidirect
701. #431	C₂²×C₁₃	semidirect
702. #416	C₂²×C₁₃	semidirect
703. #416	C₂²×C₁₃	semidirect
704. C₂×#103	C₂²×C₁₃	semidirect
705. C₂×#102	C₂²×C₁₃	semidirect
706. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
707. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
1101. C₁₃	#61567	direct (N × H)
1153. D₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3519	2
D₄×C₁₃×#41	2
C₁₃×#3305	2
C₁₃×#3303	2
C₁₃×#3301	2
C₁₃×#3299	2
C₁₃×#3297	2
C₁₃×#3295	2
C₁₃×#3287	2
C₁₃×#3284	2
C₁₃×#3282	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3280	2
D₄×C₁₃×D₈	2
C₁₃×#3212	2
C₁₃×#3207	2
C₁₃×#3191	2
C₁₃×#3188	2
C₁₃×#3106	2
C₁₃×#3102	2
C₁₃×#3002	2
C₂×C₁₃×#449	2
C₁₃×#2972	2
#61567	13

Subgroups — C13×#61567 #15747906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61567 #15747906