Subgroups — C₁₃×#61658 #15747997

Order 3328.

2110 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3323	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3282	C₂	1	2	yes	maximal, complemented
11	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3275	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3204	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3201	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3009	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
25	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
26	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
28	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
29	C₁₃×#562	—	2	2	no	—
30	C₁₃×#555	—	2	1	no	—
31	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#553	—	2	1	no	—
34	C₁₃×#552	C₂²	1	2	yes	complemented
35	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#548	C₂²	1	2	yes	complemented
37	C₁₃×#547	—	2	1	no	—
38	C₁₃×#547	C₂²	1	1	yes	characteristic
39	C₁₃×#547	C₂²	1	1	yes	characteristic
40	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#546	—	2	2	no	—
42	C₁₃×#546	C₂²	1	2	yes	—
43	C₁₃×#546	C₂²	1	2	yes	—
44	D₄²×C₁₃	—	2	1	no	—
45	D₄²×C₁₃	C₂²	1	1	yes	characteristic
46	D₄²×C₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#544	—	2	1	no	—
48	C₁₃×#542	—	2	2	no	—
49	C₁₃×#540	—	2	1	no	—
50	C₁₃×#537	C₂²	1	2	yes	—
51	C₁₃×#537	C₂²	1	2	yes	complemented
52	C₁₃×#536	C₂²	1	2	yes	complemented
53	C₁₃×#534	—	2	2	no	—
54	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#532	C₂²	1	1	yes	characteristic
56	C₁₃×#532	C₂²	1	1	yes	characteristic
57	C₁₃×#529	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₁₃×#121	—	2	1	no	—
59	C₂×C₁₃×#121	—	2	1	no	—
60	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
61	C₁₃×#495	C₂²	1	2	yes	complemented
62	C₁₃×#494	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×#484	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#483	C₂²	1	2	yes	complemented
70	C₁₃×#483	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	2	yes	complemented
72	C₁₃×#481	C₂²	1	2	yes	complemented
73	C₁₃×#481	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#470	C₂²	1	2	yes	complemented
79	C₁₃×#470	C₂²	1	2	yes	complemented
80	C₁₃×#469	C₂²	1	2	yes	complemented
81	C₁₃×#468	C₂²	1	2	yes	complemented
82	C₁₃×#467	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	2	yes	complemented
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#460	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	2	yes	complemented
98	C₁₃×#452	C₂²	1	2	yes	complemented
99	C₁₃×#452	C₂²	1	2	yes	complemented
100	C₁₃×#452	C₂²	1	2	yes	complemented
101	C₁₃×#452	C₂²	1	2	yes	complemented
102	C₁₃×#452	C₂²	1	2	yes	complemented
103	C₁₃×#451	C₂²	1	2	yes	complemented
104	C₁₃×#450	C₂²	1	1	yes	characteristic
105	C₁₃×#450	C₂²	1	2	yes	—
106	C₁₃×#450	C₂²	1	2	yes	complemented
107	C₁₃×#450	C₂²	1	2	yes	complemented
108	C₁₃×#450	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	1	yes	characteristic
114	C₁₃×#447	C₂²	1	2	yes	complemented
115	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
116	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
119	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₃×#436	C₂²	1	2	yes	complemented
123	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
125	C₈×D₄×C₁₃	C₂²	1	2	yes	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×#418	C₂²	1	2	yes	complemented
130	C₁₃×#417	C₂²	1	2	yes	complemented
131	C₁₃×#416	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
133	C₁₃×#408	C₂²	1	2	yes	complemented
134	C₁₃×#408	C₂²	1	2	yes	complemented
135	C₁₃×H(5,𝔽₂)	—	4	4	no	—
136	C₁₃×H(5,𝔽₂)	—	4	4	no	—
137	C₂×C₁₃×#41	—	2	2	no	—
138	C₂×C₁₃×#41	C₂³	1	2	yes	—
139	C₂×C₁₃×#41	C₂³	1	2	yes	—
140	C₂×C₁₃×#41	C₂³	1	2	yes	—
141	C₂×C₁₃×#41	C₂³	1	2	yes	—
142	C₂×C₁₃×#41	C₂³	1	2	yes	—
143	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₁₃	—	2	2	no	—
145	C₂²×D₄×C₁₃	—	2	2	no	—
146	C₂²×D₄×C₁₃	—	2	2	no	—
147	C₂²×D₄×C₁₃	—	2	1	no	—
148	C₂²×D₄×C₁₃	—	2	1	no	—
149	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
151	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
152	C₂³×C₄×C₁₃	—	2	1	no	—
153	C₁₃×#137	—	4	4	no	—
154	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
155	C₁₃×#135	—	4	4	no	—
156	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
158	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
159	C₂×C₁₃×SD₁₆	—	4	4	no	—
160	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
162	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
163	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
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×SD₁₆	C₂³	1	2	yes	—
168	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×D₈	C₂³	1	2	yes	—
171	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
172	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
173	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
174	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
175	C₁₃×C₄⋊Q₈	—	2	2	no	—
176	C₁₃×C₄⋊Q₈	—	2	1	no	—
177	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
178	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	C₁₃×#127	D₄	1	1	yes	characteristic
182	C₁₃×#127	C₂³	1	1	yes	characteristic
183	C₁₃×#126	—	2	2	no	—
184	C₁₃×#126	—	2	1	no	—
185	C₁₃×#125	—	2	2	no	—
186	C₁₃×#125	—	2	1	no	—
187	C₁₃×#125	—	2	1	no	—
188	C₁₃×#125	C₂³	1	1	yes	characteristic
189	C₁₃×#124	—	2	2	no	—
190	C₁₃×#124	—	2	2	no	—
191	C₁₃×#124	—	2	2	no	—
192	C₁₃×#124	D₄	1	2	yes	—
193	C₁₃×#124	C₂³	1	1	yes	characteristic
194	C₁₃×#124	C₂³	1	2	yes	—
195	C₁₃×#123	—	2	2	no	—
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	1	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×#123	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	2	no	—
206	C₁₃×C₂²⋊Q₈	—	2	1	no	—
207	C₁₃×C₂²⋊Q₈	—	2	2	no	—
208	C₁₃×C₂²⋊Q₈	—	2	2	no	—
209	C₁₃×C₂²⋊Q₈	—	2	2	no	—
210	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
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	—	2	2	no	—
224	C₁₃×#121	—	2	2	no	—
225	C₁₃×#121	—	2	1	no	—
226	C₁₃×#121	—	2	2	no	—
227	C₁₃×#121	—	2	1	no	—
228	C₁₃×#121	—	2	1	no	—
229	C₁₃×#121	—	2	1	no	—
230	C₁₃×#121	—	2	1	no	—
231	C₁₃×#121	—	2	1	no	—
232	C₁₃×#121	—	2	2	no	—
233	C₁₃×#121	—	2	2	no	—
234	C₁₃×#121	D₄	1	1	yes	characteristic
235	C₁₃×#121	D₄	1	1	yes	characteristic
236	C₁₃×#121	D₄	1	2	yes	—
237	C₁₃×#121	C₂³	1	1	yes	characteristic
238	C₁₃×#121	C₂³	1	2	yes	—
239	C₁₃×#121	C₂³	1	2	yes	—
240	C₁₃×#121	C₂³	1	2	yes	—
241	C₁₃×#120	—	2	2	no	—
242	C₁₃×#120	—	2	2	no	—
243	C₁₃×#120	—	2	2	no	—
244	C₁₃×#120	—	2	2	no	—
245	C₄×Q₈×C₁₃	—	2	1	no	—
246	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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	2	no	—
252	C₄×D₄×C₁₃	—	2	1	no	—
253	C₄×D₄×C₁₃	—	2	1	no	—
254	C₄×D₄×C₁₃	—	2	1	no	—
255	C₄×D₄×C₁₃	—	2	1	no	—
256	C₄×D₄×C₁₃	C₂³	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	1	yes	characteristic
261	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₁₃	C₂³	1	2	yes	—
264	C₁₃×#117	—	2	1	no	—
265	C₁₃×#117	—	2	1	no	—
266	C₁₃×#117	—	2	2	no	—
267	C₁₃×#117	—	2	1	no	—
268	C₁₃×#117	C₂³	1	2	yes	—
269	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
278	C₁₃×#107	C₂³	1	1	yes	characteristic
279	C₁₃×#107	C₂³	1	1	yes	characteristic
280	C₁₃×#106	C₂³	1	2	yes	—
281	C₁₃×#106	C₂³	1	1	yes	characteristic
282	C₁₃×#106	C₂³	1	2	yes	—
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	2	yes	—
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×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	1	yes	characteristic
304	C₁₃×#102	C₂³	1	2	yes	—
305	C₁₃×#102	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	1	yes	characteristic
307	C₁₃×#102	C₂³	1	1	yes	characteristic
308	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	#61658	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂⁴×C₁₃	—	2	1	no	—
320	C₂⁴×C₁₃	—	2	2	no	—
321	C₂⁴×C₁₃	—	2	2	no	—
322	C₁₃×#41	—	2	4	no	—
323	C₁₃×#41	—	2	4	no	—
324	C₁₃×#41	—	4	2	no	—
325	C₁₃×#41	—	4	2	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	2	no	—
331	C₁₃×#41	—	4	2	no	—
332	C₁₃×#41	—	4	8	no	—
333	C₂×Q₈×C₁₃	—	2	1	no	—
334	C₂×Q₈×C₁₃	—	2	2	no	—
335	C₂×Q₈×C₁₃	—	4	2	no	—
336	C₂×Q₈×C₁₃	—	4	2	no	—
337	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
338	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
339	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
341	C₂×D₄×C₁₃	—	2	2	no	—
342	C₂×D₄×C₁₃	—	2	2	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	1	no	—
354	C₂×D₄×C₁₃	—	2	1	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	—	4	2	no	—
359	C₂×D₄×C₁₃	—	4	2	no	—
360	C₂×D₄×C₁₃	—	4	8	no	—
361	C₂×D₄×C₁₃	—	4	8	no	—
362	C₂×D₄×C₁₃	—	4	8	no	—
363	C₂×D₄×C₁₃	—	8	2	no	—
364	C₂×D₄×C₁₃	—	8	2	no	—
365	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
372	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₁₃	—	2	1	no	—
376	C₂²×C₄×C₁₃	—	2	2	no	—
377	C₂²×C₄×C₁₃	—	2	2	no	—
378	C₂²×C₄×C₁₃	—	2	2	no	—
379	C₂²×C₄×C₁₃	—	2	2	no	—
380	C₂²×C₄×C₁₃	—	2	1	no	—
381	C₂²×C₄×C₁₃	—	2	1	no	—
382	C₂²×C₄×C₁₃	—	2	1	no	—
383	C₂²×C₄×C₁₃	—	2	2	no	—
384	C₂²×C₄×C₁₃	—	2	1	no	—
385	C₂²×C₄×C₁₃	—	2	1	no	—
386	C₂²×C₄×C₁₃	—	2	2	no	—
387	C₂²×C₄×C₁₃	—	8	2	no	—
388	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
392	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
393	C₁₃×Q₁₆	—	4	2	no	—
394	C₁₃×Q₁₆	—	4	2	no	—
395	C₁₃×Q₁₆	—	4	2	no	—
396	C₁₃×SD₁₆	—	2	2	no	—
397	C₁₃×SD₁₆	—	2	4	no	—
398	C₁₃×SD₁₆	—	2	4	no	—
399	C₁₃×SD₁₆	—	2	2	no	—
400	C₁₃×SD₁₆	—	4	2	no	—
401	C₁₃×SD₁₆	—	4	2	no	—
402	C₁₃×SD₁₆	—	4	2	no	—
403	C₁₃×SD₁₆	—	4	2	no	—
404	C₁₃×D₈	—	2	2	no	—
405	C₁₃×D₈	—	2	2	no	—
406	C₁₃×D₈	—	4	2	no	—
407	C₁₃×M₁₆	—	4	2	no	—
408	C₁₃×M₁₆	—	4	2	no	—
409	C₂×C₈×C₁₃	—	4	2	no	—
410	C₂×C₈×C₁₃	—	4	2	no	—
411	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
415	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
416	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
417	C₁₃×C₄⋊C₄	—	2	1	no	—
418	C₁₃×C₄⋊C₄	—	2	1	no	—
419	C₁₃×C₄⋊C₄	—	2	2	no	—
420	C₁₃×C₄⋊C₄	—	2	2	no	—
421	C₁₃×C₄⋊C₄	—	2	2	no	—
422	C₁₃×C₄⋊C₄	—	2	1	no	—
423	C₁₃×C₄⋊C₄	—	2	2	no	—
424	C₁₃×C₄⋊C₄	—	2	1	no	—
425	C₁₃×C₄⋊C₄	—	2	1	no	—
426	C₁₃×C₄⋊C₄	—	2	2	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	2	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	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	2	no	—
446	C₁₃×C₂²⋊C₄	—	2	2	no	—
447	C₁₃×C₂²⋊C₄	—	2	2	no	—
448	C₁₃×C₂²⋊C₄	—	2	2	no	—
449	C₁₃×C₂²⋊C₄	—	2	2	no	—
450	C₁₃×C₂²⋊C₄	—	2	1	no	—
451	C₁₃×C₂²⋊C₄	—	2	2	no	—
452	C₁₃×C₂²⋊C₄	—	2	1	no	—
453	C₁₃×C₂²⋊C₄	—	2	1	no	—
454	C₁₃×C₂²⋊C₄	—	2	1	no	—
455	C₁₃×C₂²⋊C₄	—	2	1	no	—
456	C₁₃×C₂²⋊C₄	—	2	2	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	1	no	—
462	C₁₃×C₂²⋊C₄	—	2	2	no	—
463	C₁₃×C₂²⋊C₄	—	2	1	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	2	no	—
469	C₄²×C₁₃	—	2	2	no	—
470	C₄²×C₁₃	—	2	1	no	—
471	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
474	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
475	#3547	C₂×C₁₃	1	1	yes	characteristic, complemented
476	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
477	#3331	C₂×C₁₃	1	1	yes	characteristic, complemented
478	#3325	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#3323	C₂×C₁₃	1	2	yes	complemented
480	#3303	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#3296	C₂×C₁₃	1	2	yes	complemented
482	#3295	C₂×C₁₃	1	1	yes	characteristic, complemented
483	#3283	C₂×C₁₃	1	1	yes	characteristic, complemented
484	#3282	C₂×C₁₃	1	2	yes	complemented
485	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
486	#3276	C₂×C₁₃	1	1	yes	characteristic, complemented
487	#3275	C₂×C₁₃	1	2	yes	complemented
488	#3272	C₂×C₁₃	1	1	yes	characteristic, complemented
489	#3212	C₂×C₁₃	1	1	yes	characteristic, complemented
490	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
491	#3204	C₂×C₁₃	1	2	yes	complemented
492	#3201	C₂×C₁₃	1	2	yes	complemented
493	#3105	C₂×C₁₃	1	1	yes	characteristic, complemented
494	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
495	#3012	C₂×C₁₃	1	2	yes	complemented
496	#3009	C₂×C₁₃	1	2	yes	complemented
497	#2979	C₂×C₁₃	1	1	yes	characteristic, complemented
498	C₂³×C₁₃	—	2	4	no	—
499	C₂³×C₁₃	—	2	1	no	—
500	C₂³×C₁₃	—	2	1	no	—
501	C₂³×C₁₃	—	2	1	no	—
502	C₂³×C₁₃	—	2	2	no	—
503	C₂³×C₁₃	—	4	4	no	—
504	C₂³×C₁₃	—	4	4	no	—
505	C₂³×C₁₃	—	8	1	no	—
506	C₂³×C₁₃	—	8	1	no	—
507	C₂³×C₁₃	—	8	2	no	—
508	C₂³×C₁₃	—	8	2	no	—
509	C₂³×C₁₃	—	8	2	no	—
510	C₂³×C₁₃	—	8	2	no	—
511	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
512	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
513	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
514	Q₈×C₁₃	—	2	1	no	—
515	Q₈×C₁₃	—	2	2	no	—
516	Q₈×C₁₃	—	2	2	no	—
517	Q₈×C₁₃	—	2	1	no	—
518	Q₈×C₁₃	—	2	2	no	—
519	Q₈×C₁₃	—	2	2	no	—
520	Q₈×C₁₃	—	4	2	no	—
521	Q₈×C₁₃	—	8	1	no	—
522	Q₈×C₁₃	—	8	2	no	—
523	D₄×C₁₃	—	2	4	no	—
524	D₄×C₁₃	—	2	2	no	—
525	D₄×C₁₃	—	2	2	no	—
526	D₄×C₁₃	—	2	1	no	—
527	D₄×C₁₃	—	2	1	no	—
528	D₄×C₁₃	—	2	1	no	—
529	D₄×C₁₃	—	2	1	no	—
530	D₄×C₁₃	—	2	2	no	—
531	D₄×C₁₃	—	2	2	no	—
532	D₄×C₁₃	—	4	2	no	—
533	D₄×C₁₃	—	4	2	no	—
534	D₄×C₁₃	—	4	2	no	—
535	D₄×C₁₃	—	4	2	no	—
536	D₄×C₁₃	—	4	4	no	—
537	D₄×C₁₃	—	4	4	no	—
538	D₄×C₁₃	—	4	4	no	—
539	D₄×C₁₃	—	4	4	no	—
540	D₄×C₁₃	—	4	4	no	—
541	D₄×C₁₃	—	4	2	no	—
542	D₄×C₁₃	—	8	1	no	—
543	D₄×C₁₃	—	8	1	no	—
544	D₄×C₁₃	—	8	2	no	—
545	D₄×C₁₃	—	8	2	no	—
546	D₄×C₁₃	—	8	2	no	—
547	D₄×C₁₃	—	8	2	no	—
548	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
549	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
550	C₂×C₄×C₁₃	—	2	2	no	—
551	C₂×C₄×C₁₃	—	2	2	no	—
552	C₂×C₄×C₁₃	—	2	2	no	—
553	C₂×C₄×C₁₃	—	2	2	no	—
554	C₂×C₄×C₁₃	—	2	2	no	—
555	C₂×C₄×C₁₃	—	2	1	no	—
556	C₂×C₄×C₁₃	—	2	1	no	—
557	C₂×C₄×C₁₃	—	2	1	no	—
558	C₂×C₄×C₁₃	—	2	2	no	—
559	C₂×C₄×C₁₃	—	2	1	no	—
560	C₂×C₄×C₁₃	—	2	1	no	—
561	C₂×C₄×C₁₃	—	2	2	no	—
562	C₂×C₄×C₁₃	—	2	1	no	—
563	C₂×C₄×C₁₃	—	2	1	no	—
564	C₂×C₄×C₁₃	—	2	2	no	—
565	C₂×C₄×C₁₃	—	4	1	no	—
566	C₂×C₄×C₁₃	—	4	4	no	—
567	C₂×C₄×C₁₃	—	4	4	no	—
568	C₂×C₄×C₁₃	—	4	4	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	—	8	1	no	—
573	C₂×C₄×C₁₃	—	8	1	no	—
574	C₂×C₄×C₁₃	—	8	2	no	—
575	C₂×C₄×C₁₃	—	8	2	no	—
576	C₂×C₄×C₁₃	—	8	1	no	—
577	C₂×C₄×C₁₃	—	8	2	no	—
578	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
580	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
584	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
586	C₈×C₁₃	—	2	1	no	—
587	C₈×C₁₃	—	2	1	no	—
588	C₈×C₁₃	—	2	2	no	—
589	C₈×C₁₃	—	2	1	no	—
590	C₈×C₁₃	—	2	2	no	—
591	C₈×C₁₃	—	2	1	no	—
592	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
593	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
594	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
595	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
596	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
597	#562	—	2	2	no	—
598	#555	—	2	1	no	—
599	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
600	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
601	#553	—	2	1	no	—
602	#552	C₂²×C₁₃	1	2	yes	complemented
603	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
604	#548	C₂²×C₁₃	1	2	yes	complemented
605	#547	—	2	1	no	—
606	#547	C₂²×C₁₃	1	1	yes	characteristic
607	#547	C₂²×C₁₃	1	1	yes	characteristic
608	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
609	#546	—	2	2	no	—
610	#546	C₂²×C₁₃	1	2	yes	—
611	#546	C₂²×C₁₃	1	2	yes	—
612	D₄²	—	2	1	no	—
613	D₄²	C₂²×C₁₃	1	1	yes	characteristic
614	D₄²	C₂²×C₁₃	1	1	yes	characteristic
615	#544	—	2	1	no	—
616	#542	—	2	2	no	—
617	#540	—	2	1	no	—
618	#537	C₂²×C₁₃	1	2	yes	—
619	#537	C₂²×C₁₃	1	2	yes	complemented
620	#536	C₂²×C₁₃	1	2	yes	complemented
621	#534	—	2	2	no	—
622	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
623	#532	C₂²×C₁₃	1	1	yes	characteristic
624	#532	C₂²×C₁₃	1	1	yes	characteristic
625	#529	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	C₂×#121	—	2	1	no	—
627	C₂×#121	—	2	1	no	—
628	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
629	#495	C₂²×C₁₃	1	2	yes	complemented
630	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	#488	C₂²×C₁₃	1	2	yes	complemented
633	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
634	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#485	C₂²×C₁₃	1	2	yes	complemented
636	#484	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	#483	C₂²×C₁₃	1	2	yes	complemented
638	#483	C₂²×C₁₃	1	2	yes	complemented
639	#482	C₂²×C₁₃	1	2	yes	complemented
640	#481	C₂²×C₁₃	1	1	yes	characteristic, complemented
641	#481	C₂²×C₁₃	1	2	yes	complemented
642	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
644	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
645	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
646	#470	C₂²×C₁₃	1	2	yes	complemented
647	#470	C₂²×C₁₃	1	2	yes	complemented
648	#469	C₂²×C₁₃	1	2	yes	complemented
649	#468	C₂²×C₁₃	1	2	yes	complemented
650	#467	C₂²×C₁₃	1	2	yes	complemented
651	#465	C₂²×C₁₃	1	2	yes	complemented
652	#465	C₂²×C₁₃	1	2	yes	complemented
653	#465	C₂²×C₁₃	1	2	yes	complemented
654	#464	C₂²×C₁₃	1	2	yes	complemented
655	#464	C₂²×C₁₃	1	2	yes	complemented
656	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
658	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
659	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
660	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
663	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
664	#452	C₂²×C₁₃	1	2	yes	complemented
665	#452	C₂²×C₁₃	1	2	yes	complemented
666	#452	C₂²×C₁₃	1	2	yes	complemented
667	#452	C₂²×C₁₃	1	2	yes	complemented
668	#452	C₂²×C₁₃	1	2	yes	complemented
669	#452	C₂²×C₁₃	1	2	yes	complemented
670	#452	C₂²×C₁₃	1	2	yes	complemented
671	#451	C₂²×C₁₃	1	2	yes	complemented
672	#450	C₂²×C₁₃	1	2	yes	—
673	#450	C₂²×C₁₃	1	1	yes	characteristic
674	#450	C₂²×C₁₃	1	2	yes	complemented
675	#450	C₂²×C₁₃	1	2	yes	complemented
676	#450	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	#448	C₂²×C₁₃	1	2	yes	complemented
681	#447	C₂²×C₁₃	1	1	yes	characteristic
682	#447	C₂²×C₁₃	1	2	yes	complemented
683	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
684	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
685	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
686	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
687	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
688	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
689	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
690	#436	C₂²×C₁₃	1	2	yes	complemented
691	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
692	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
693	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
694	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
695	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
696	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
697	#418	C₂²×C₁₃	1	2	yes	complemented
698	#417	C₂²×C₁₃	1	2	yes	complemented
699	#416	C₂²×C₁₃	1	2	yes	complemented
700	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
701	#408	C₂²×C₁₃	1	2	yes	complemented
702	#408	C₂²×C₁₃	1	2	yes	complemented
703	C₂²×C₁₃	—	2	1	no	—
704	C₂²×C₁₃	—	2	2	no	—
705	C₂²×C₁₃	—	2	2	no	—
706	C₂²×C₁₃	—	2	2	no	—
707	C₂²×C₁₃	—	2	1	no	—
708	C₂²×C₁₃	—	2	2	no	—
709	C₂²×C₁₃	—	2	2	no	—
710	C₂²×C₁₃	—	2	2	no	—
711	C₂²×C₁₃	—	2	1	no	—
712	C₂²×C₁₃	—	2	2	no	—
713	C₂²×C₁₃	—	2	2	no	—
714	C₂²×C₁₃	—	4	1	no	—
715	C₂²×C₁₃	—	4	1	no	—
716	C₂²×C₁₃	—	4	1	no	—
717	C₂²×C₁₃	—	4	1	no	—
718	C₂²×C₁₃	—	4	1	no	—
719	C₂²×C₁₃	—	4	2	no	—
720	C₂²×C₁₃	—	4	2	no	—
721	C₂²×C₁₃	—	4	1	no	—
722	C₂²×C₁₃	—	4	1	no	—
723	C₂²×C₁₃	—	4	2	no	—
724	C₂²×C₁₃	—	8	4	no	—
725	C₂²×C₁₃	—	16	4	no	—
726	C₂²×C₁₃	—	16	4	no	—
727	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
728	C₄×C₁₃	—	2	1	no	—
729	C₄×C₁₃	—	2	1	no	—
730	C₄×C₁₃	—	2	1	no	—
731	C₄×C₁₃	—	2	2	no	—
732	C₄×C₁₃	—	2	2	no	—
733	C₄×C₁₃	—	2	1	no	—
734	C₄×C₁₃	—	4	1	no	—
735	C₄×C₁₃	—	4	2	no	—
736	C₄×C₁₃	—	4	2	no	—
737	C₄×C₁₃	—	4	2	no	—
738	C₄×C₁₃	—	4	1	no	—
739	C₄×C₁₃	—	4	1	no	—
740	C₄×C₁₃	—	4	1	no	—
741	C₄×C₁₃	—	4	1	no	—
742	C₄×C₁₃	#577	1	2	yes	—
743	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
744	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
745	H(5,𝔽₂)	—	4	4	no	—
746	H(5,𝔽₂)	—	4	4	no	—
747	C₂×#41	—	2	2	no	—
748	C₂×#41	C₂³×C₁₃	1	2	yes	—
749	C₂×#41	C₂³×C₁₃	1	2	yes	—
750	C₂×#41	C₂³×C₁₃	1	2	yes	—
751	C₂×#41	C₂³×C₁₃	1	2	yes	—
752	C₂×#41	C₂³×C₁₃	1	2	yes	—
753	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
754	C₂²×D₄	—	2	2	no	—
755	C₂²×D₄	—	2	2	no	—
756	C₂²×D₄	—	2	2	no	—
757	C₂²×D₄	—	2	1	no	—
758	C₂²×D₄	—	2	1	no	—
759	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
760	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
761	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
762	C₂³×C₄	—	2	1	no	—
763	#137	—	4	4	no	—
764	AGL(1,ℤ/8)	—	4	4	no	—
765	#135	—	4	4	no	—
766	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
767	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
768	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
769	C₂×SD₁₆	—	4	4	no	—
770	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
771	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
772	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
773	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
774	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
778	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
779	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
780	C₂×D₈	C₂³×C₁₃	1	2	yes	—
781	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
782	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
783	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
784	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
785	C₄⋊Q₈	—	2	2	no	—
786	C₄⋊Q₈	—	2	1	no	—
787	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
788	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
789	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
790	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
791	#127	D₄×C₁₃	1	1	yes	characteristic
792	#127	C₂³×C₁₃	1	1	yes	characteristic
793	#126	—	2	2	no	—
794	#126	—	2	1	no	—
795	#125	—	2	2	no	—
796	#125	—	2	1	no	—
797	#125	—	2	1	no	—
798	#125	C₂³×C₁₃	1	1	yes	characteristic
799	#124	—	2	2	no	—
800	#124	—	2	2	no	—
801	#124	—	2	2	no	—
802	#124	D₄×C₁₃	1	2	yes	—
803	#124	C₂³×C₁₃	1	1	yes	characteristic
804	#124	C₂³×C₁₃	1	2	yes	—
805	#123	—	2	2	no	—
806	#123	—	2	2	no	—
807	#123	—	2	2	no	—
808	#123	—	2	1	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
821	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
822	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
823	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	1	no	—
836	#121	—	2	2	no	—
837	#121	—	2	1	no	—
838	#121	—	2	1	no	—
839	#121	—	2	1	no	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	D₄×C₁₃	1	1	yes	characteristic
845	#121	D₄×C₁₃	1	1	yes	characteristic
846	#121	D₄×C₁₃	1	2	yes	—
847	#121	C₂³×C₁₃	1	1	yes	characteristic
848	#121	C₂³×C₁₃	1	2	yes	—
849	#121	C₂³×C₁₃	1	2	yes	—
850	#121	C₂³×C₁₃	1	2	yes	—
851	#120	—	2	2	no	—
852	#120	—	2	2	no	—
853	#120	—	2	2	no	—
854	#120	—	2	2	no	—
855	C₄×Q₈	—	2	1	no	—
856	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
857	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
867	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
868	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
869	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
870	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
871	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
872	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
873	C₄×D₄	C₂³×C₁₃	1	2	yes	—
874	#117	—	2	1	no	—
875	#117	—	2	1	no	—
876	#117	—	2	2	no	—
877	#117	—	2	1	no	—
878	#117	C₂³×C₁₃	1	2	yes	—
879	C₂×C₄⋊C₄	—	2	1	no	—
880	C₂×C₄⋊C₄	—	2	1	no	—
881	C₂×C₄⋊C₄	—	2	1	no	—
882	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
884	C₂×C₂²⋊C₄	—	2	1	no	—
885	C₂×C₂²⋊C₄	—	2	2	no	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
888	#107	C₂³×C₁₃	1	1	yes	characteristic
889	#107	C₂³×C₁₃	1	1	yes	characteristic
890	#106	C₂³×C₁₃	1	2	yes	—
891	#106	C₂³×C₁₃	1	1	yes	characteristic
892	#106	C₂³×C₁₃	1	2	yes	—
893	#106	C₂³×C₁₃	1	1	yes	characteristic
894	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
895	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
896	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
897	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
898	#103	C₂³×C₁₃	1	2	yes	—
899	#103	C₂³×C₁₃	1	2	yes	—
900	#103	C₂³×C₁₃	1	2	yes	—
901	#103	C₂³×C₁₃	1	2	yes	—
902	#103	C₂³×C₁₃	1	1	yes	characteristic
903	#103	C₂³×C₁₃	1	2	yes	—
904	#103	C₂³×C₁₃	1	2	yes	—
905	#103	C₂³×C₁₃	1	1	yes	characteristic
906	#102	C₂³×C₁₃	1	1	yes	characteristic
907	#102	C₂³×C₁₃	1	2	yes	—
908	#102	C₂³×C₁₃	1	2	yes	—
909	#102	C₂³×C₁₃	1	2	yes	—
910	#102	C₂³×C₁₃	1	1	yes	characteristic
911	#102	C₂³×C₁₃	1	1	yes	characteristic
912	#102	C₂³×C₁₃	1	2	yes	—
913	#102	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
918	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
919	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
920	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
921	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
922	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
923	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
924	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
925	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
926	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
927	C₄×C₈	C₂³×C₁₃	1	2	yes	—
928	C₂×C₁₃	—	4	1	no	—
929	C₂×C₁₃	—	4	2	no	—
930	C₂×C₁₃	—	4	2	no	—
931	C₂×C₁₃	—	4	2	no	—
932	C₂×C₁₃	—	4	2	no	—
933	C₂×C₁₃	—	8	1	no	—
934	C₂×C₁₃	—	8	2	no	—
935	C₂×C₁₃	#3484	1	1	yes	characteristic
936	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
937	C₂×C₁₃	#3584	1	1	yes	characteristic
938	C₂⁴	—	2	1	no	—
939	C₂⁴	—	2	2	no	—
940	C₂⁴	—	2	2	no	—
941	#41	—	2	4	no	—
942	#41	—	2	4	no	—
943	#41	—	4	2	no	—
944	#41	—	4	2	no	—
945	#41	—	4	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	2	no	—
949	#41	—	4	2	no	—
950	#41	—	4	2	no	—
951	#41	—	4	8	no	—
952	C₂×Q₈	—	2	1	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	4	2	no	—
955	C₂×Q₈	—	4	2	no	—
956	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
957	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
958	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
959	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	4	no	—
963	C₂×D₄	—	2	4	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	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	1	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	2	no	—
979	C₂×D₄	—	4	8	no	—
980	C₂×D₄	—	4	8	no	—
981	C₂×D₄	—	4	8	no	—
982	C₂×D₄	—	8	2	no	—
983	C₂×D₄	—	8	2	no	—
984	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
985	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
986	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
987	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
988	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
989	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
990	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
991	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
992	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
993	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	8	2	no	—
1007	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1011	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1012	Q₁₆	—	4	2	no	—
1013	Q₁₆	—	4	2	no	—
1014	Q₁₆	—	4	2	no	—
1015	SD₁₆	—	2	2	no	—
1016	SD₁₆	—	2	4	no	—
1017	SD₁₆	—	2	4	no	—
1018	SD₁₆	—	2	2	no	—
1019	SD₁₆	—	4	2	no	—
1020	SD₁₆	—	4	2	no	—
1021	SD₁₆	—	4	2	no	—
1022	SD₁₆	—	4	2	no	—
1023	D₈	—	2	2	no	—
1024	D₈	—	2	2	no	—
1025	D₈	—	4	2	no	—
1026	M₁₆	—	4	2	no	—
1027	M₁₆	—	4	2	no	—
1028	C₂×C₈	—	4	2	no	—
1029	C₂×C₈	—	4	2	no	—
1030	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1031	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1032	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1033	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1034	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1035	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1055	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1056	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1057	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1058	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1059	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1060	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1061	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
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	1	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	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1084	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1085	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1086	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	1	no	—
1090	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1091	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1092	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1093	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1094	C₁₃	#61658	1	1	yes	characteristic, direct product factor, Sylow
1095	C₂³	—	2	4	no	—
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	1	no	—
1098	C₂³	—	2	1	no	—
1099	C₂³	—	2	2	no	—
1100	C₂³	—	4	4	no	—
1101	C₂³	—	4	4	no	—
1102	C₂³	—	8	1	no	—
1103	C₂³	—	8	1	no	—
1104	C₂³	—	8	2	no	—
1105	C₂³	—	8	2	no	—
1106	C₂³	—	8	2	no	—
1107	C₂³	—	8	2	no	—
1108	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1109	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1110	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1111	Q₈	—	2	1	no	—
1112	Q₈	—	2	2	no	—
1113	Q₈	—	2	2	no	—
1114	Q₈	—	2	1	no	—
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	4	2	no	—
1118	Q₈	—	8	2	no	—
1119	Q₈	—	8	1	no	—
1120	D₄	—	2	4	no	—
1121	D₄	—	2	2	no	—
1122	D₄	—	2	2	no	—
1123	D₄	—	2	1	no	—
1124	D₄	—	2	1	no	—
1125	D₄	—	2	1	no	—
1126	D₄	—	2	1	no	—
1127	D₄	—	2	2	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	4	2	no	—
1132	D₄	—	4	2	no	—
1133	D₄	—	4	4	no	—
1134	D₄	—	4	4	no	—
1135	D₄	—	4	4	no	—
1136	D₄	—	4	4	no	—
1137	D₄	—	4	4	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	8	1	no	—
1140	D₄	—	8	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	1	no	—
1143	D₄	—	8	2	no	—
1144	D₄	—	8	2	no	—
1145	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1146	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	4	no	—
1164	C₂×C₄	—	4	4	no	—
1165	C₂×C₄	—	4	4	no	—
1166	C₂×C₄	—	4	2	no	—
1167	C₂×C₄	—	4	2	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	8	1	no	—
1170	C₂×C₄	—	8	1	no	—
1171	C₂×C₄	—	8	2	no	—
1172	C₂×C₄	—	8	1	no	—
1173	C₂×C₄	—	8	2	no	—
1174	C₂×C₄	—	8	2	no	—
1175	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1177	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1178	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1179	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1180	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1181	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1182	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1183	C₈	—	2	1	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	2	2	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	2	no	—
1188	C₈	—	2	1	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	2	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	2	no	—
1208	C₂²	—	4	2	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	8	4	no	—
1211	C₂²	—	16	4	no	—
1212	C₂²	—	16	4	no	—
1213	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1214	C₄	—	2	1	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	1	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	2	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	2	no	—
1225	C₄	—	4	2	no	—
1226	C₄	—	4	2	no	—
1227	C₄	—	4	1	no	—
1228	C₄	C₁₃×#577	1	2	yes	—
1229	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1230	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1231	C₂	—	4	1	no	—
1232	C₂	—	4	2	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	4	2	no	—
1235	C₂	—	4	2	no	—
1236	C₂	—	8	2	no	—
1237	C₂	—	8	1	no	—
1238	C₂	C₁₃×#3484	1	1	yes	characteristic
1239	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1240	C₂	C₁₃×#3584	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3547	C₂	semidirect
2. C₁₃×#3496	C₂	semidirect
3. C₁₃×#3331	C₂	semidirect
4. C₁₃×#3325	C₂	semidirect
5. C₁₃×#3323	C₂	semidirect
6. C₁₃×#3303	C₂	semidirect
7. C₁₃×#3296	C₂	semidirect
8. C₁₃×#3295	C₂	semidirect
9. C₁₃×#3283	C₂	semidirect
10. C₁₃×#3282	C₂	semidirect
11. D₄×C₁₃×SD₁₆	C₂	semidirect
12. C₁₃×#3276	C₂	semidirect
13. C₁₃×#3275	C₂	semidirect
14. C₁₃×#3272	C₂	semidirect
15. C₁₃×#3212	C₂	semidirect
16. C₁₃×#3210	C₂	semidirect
17. C₁₃×#3204	C₂	semidirect
18. C₁₃×#3201	C₂	semidirect
19. C₁₃×#3105	C₂	semidirect
20. C₁₃×#3101	C₂	semidirect
21. C₁₃×#3012	C₂	semidirect
22. C₁₃×#3009	C₂	semidirect
23. C₁₃×#2979	C₂	semidirect
25. C₂×C₁₃×#137	C₂²	semidirect
26. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₁₃×#135	C₂²	semidirect
28. C₂²×C₁₃×SD₁₆	C₂²	semidirect
31. C₁₃×#555	C₂²	semidirect
32. C₁₃×#554	C₂²	semidirect
34. C₁₃×#552	C₂²	semidirect
35. D₄×Q₈×C₁₃	C₂²	semidirect
36. C₁₃×#548	C₂²	semidirect
40. C₁₃×#547	C₂²	semidirect
51. C₁₃×#537	C₂²	semidirect
52. C₁₃×#536	C₂²	semidirect
54. C₁₃×#533	C₂²	semidirect
57. C₁₃×#529	C₂²	semidirect
61. C₁₃×#495	C₂²	semidirect
62. C₁₃×#494	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×#484	C₂²	semidirect
69. C₁₃×#483	C₂²	semidirect
70. C₁₃×#483	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#481	C₂²	semidirect
73. C₁₃×#481	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#476	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#470	C₂²	semidirect
79. C₁₃×#470	C₂²	semidirect
80. C₁₃×#469	C₂²	semidirect
81. C₁₃×#468	C₂²	semidirect
82. C₁₃×#467	C₂²	semidirect
83. C₁₃×#465	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#463	C₂²	semidirect
89. C₁₃×#463	C₂²	semidirect
90. C₁₃×#462	C₂²	semidirect
91. C₁₃×#461	C₂²	semidirect
92. C₁₃×#461	C₂²	semidirect
93. C₁₃×#461	C₂²	semidirect
94. C₁₃×#460	C₂²	semidirect
95. C₁₃×#459	C₂²	semidirect
96. C₁₃×#452	C₂²	semidirect
97. C₁₃×#452	C₂²	semidirect
98. C₁₃×#452	C₂²	semidirect
99. C₁₃×#452	C₂²	semidirect
100. C₁₃×#452	C₂²	semidirect
101. C₁₃×#452	C₂²	semidirect
102. C₁₃×#452	C₂²	semidirect
103. C₁₃×#451	C₂²	semidirect
106. C₁₃×#450	C₂²	semidirect
107. C₁₃×#450	C₂²	semidirect
108. C₁₃×#450	C₂²	semidirect
109. C₁₃×#449	C₂²	semidirect
110. C₁₃×#449	C₂²	semidirect
111. C₁₃×#449	C₂²	semidirect
112. C₁₃×#448	C₂²	semidirect
114. C₁₃×#447	C₂²	semidirect
115. C₄×C₁₃×SD₁₆	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
121. C₁₃×#436	C₂²	semidirect
122. C₁₃×#436	C₂²	semidirect
123. C₁₃×#436	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×#418	C₂²	semidirect
130. C₁₃×#417	C₂²	semidirect
131. C₁₃×#416	C₂²	semidirect
132. C₂×C₁₃×#102	C₂²	semidirect
133. C₁₃×#408	C₂²	semidirect
134. C₁₃×#408	C₂²	semidirect
318. #61658	C₁₃	direct (N × H)
475. #3547	C₂×C₁₃	semidirect
476. #3496	C₂×C₁₃	semidirect
477. #3331	C₂×C₁₃	semidirect
478. #3325	C₂×C₁₃	semidirect
479. #3323	C₂×C₁₃	semidirect
480. #3303	C₂×C₁₃	semidirect
481. #3296	C₂×C₁₃	semidirect
482. #3295	C₂×C₁₃	semidirect
483. #3283	C₂×C₁₃	semidirect
484. #3282	C₂×C₁₃	semidirect
485. D₄×SD₁₆	C₂×C₁₃	semidirect
486. #3276	C₂×C₁₃	semidirect
487. #3275	C₂×C₁₃	semidirect
488. #3272	C₂×C₁₃	semidirect
489. #3212	C₂×C₁₃	semidirect
490. #3210	C₂×C₁₃	semidirect
491. #3204	C₂×C₁₃	semidirect
492. #3201	C₂×C₁₃	semidirect
493. #3105	C₂×C₁₃	semidirect
494. #3101	C₂×C₁₃	semidirect
495. #3012	C₂×C₁₃	semidirect
496. #3009	C₂×C₁₃	semidirect
497. #2979	C₂×C₁₃	semidirect
593. C₂×#137	C₂²×C₁₃	semidirect
594. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
595. C₂×#135	C₂²×C₁₃	semidirect
596. C₂²×SD₁₆	C₂²×C₁₃	semidirect
599. #555	C₂²×C₁₃	semidirect
600. #554	C₂²×C₁₃	semidirect
602. #552	C₂²×C₁₃	semidirect
603. D₄×Q₈	C₂²×C₁₃	semidirect
604. #548	C₂²×C₁₃	semidirect
608. #547	C₂²×C₁₃	semidirect
619. #537	C₂²×C₁₃	semidirect
620. #536	C₂²×C₁₃	semidirect
622. #533	C₂²×C₁₃	semidirect
625. #529	C₂²×C₁₃	semidirect
629. #495	C₂²×C₁₃	semidirect
630. #494	C₂²×C₁₃	semidirect
631. #492	C₂²×C₁₃	semidirect
632. #488	C₂²×C₁₃	semidirect
633. #487	C₂²×C₁₃	semidirect
634. #486	C₂²×C₁₃	semidirect
635. #485	C₂²×C₁₃	semidirect
636. #484	C₂²×C₁₃	semidirect
637. #483	C₂²×C₁₃	semidirect
638. #483	C₂²×C₁₃	semidirect
639. #482	C₂²×C₁₃	semidirect
640. #481	C₂²×C₁₃	semidirect
641. #481	C₂²×C₁₃	semidirect
642. #478	C₂²×C₁₃	semidirect
643. #478	C₂²×C₁₃	semidirect
644. #476	C₂²×C₁₃	semidirect
645. #476	C₂²×C₁₃	semidirect
646. #470	C₂²×C₁₃	semidirect
647. #470	C₂²×C₁₃	semidirect
648. #469	C₂²×C₁₃	semidirect
649. #468	C₂²×C₁₃	semidirect
650. #467	C₂²×C₁₃	semidirect
651. #465	C₂²×C₁₃	semidirect
652. #465	C₂²×C₁₃	semidirect
653. #465	C₂²×C₁₃	semidirect
654. #464	C₂²×C₁₃	semidirect
655. #464	C₂²×C₁₃	semidirect
656. #463	C₂²×C₁₃	semidirect
657. #463	C₂²×C₁₃	semidirect
658. #462	C₂²×C₁₃	semidirect
659. #461	C₂²×C₁₃	semidirect
660. #461	C₂²×C₁₃	semidirect
661. #461	C₂²×C₁₃	semidirect
662. #460	C₂²×C₁₃	semidirect
663. #459	C₂²×C₁₃	semidirect
664. #452	C₂²×C₁₃	semidirect
665. #452	C₂²×C₁₃	semidirect
666. #452	C₂²×C₁₃	semidirect
667. #452	C₂²×C₁₃	semidirect
668. #452	C₂²×C₁₃	semidirect
669. #452	C₂²×C₁₃	semidirect
670. #452	C₂²×C₁₃	semidirect
671. #451	C₂²×C₁₃	semidirect
674. #450	C₂²×C₁₃	semidirect
675. #450	C₂²×C₁₃	semidirect
676. #450	C₂²×C₁₃	semidirect
677. #449	C₂²×C₁₃	semidirect
678. #449	C₂²×C₁₃	semidirect
679. #449	C₂²×C₁₃	semidirect
680. #448	C₂²×C₁₃	semidirect
682. #447	C₂²×C₁₃	semidirect
683. C₄×SD₁₆	C₂²×C₁₃	semidirect
684. C₄×SD₁₆	C₂²×C₁₃	semidirect
685. C₄×SD₁₆	C₂²×C₁₃	semidirect
686. C₄×SD₁₆	C₂²×C₁₃	semidirect
687. C₄×D₈	C₂²×C₁₃	semidirect
688. C₄×D₈	C₂²×C₁₃	semidirect
689. #436	C₂²×C₁₃	semidirect
690. #436	C₂²×C₁₃	semidirect
691. #436	C₂²×C₁₃	semidirect
692. C₈×D₄	C₂²×C₁₃	semidirect
693. C₈×D₄	C₂²×C₁₃	semidirect
694. C₈×D₄	C₂²×C₁₃	semidirect
695. #431	C₂²×C₁₃	semidirect
696. #431	C₂²×C₁₃	semidirect
697. #418	C₂²×C₁₃	semidirect
698. #417	C₂²×C₁₃	semidirect
699. #416	C₂²×C₁₃	semidirect
700. C₂×#102	C₂²×C₁₃	semidirect
701. #408	C₂²×C₁₃	semidirect
702. #408	C₂²×C₁₃	semidirect
1094. C₁₃	#61658	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×#3547	2
C₁₃×#3496	2
C₁₃×#3331	2
C₁₃×#3325	2
C₁₃×#3323	2
C₁₃×#3303	2
C₁₃×#3296	2
C₁₃×#3295	2
C₁₃×#3283	2
C₁₃×#3282	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3276	2
C₁₃×#3275	2
C₁₃×#3272	2
C₁₃×#3212	2
C₁₃×#3210	2
C₁₃×#3204	2
C₁₃×#3201	2
C₁₃×#3105	2
C₁₃×#3101	2
C₁₃×#3012	2
C₁₃×#3009	2
C₁₃×#2979	2
#61658	13

Subgroups — C13×#61658 #15747997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61658 #15747997