Subgroups — C₁₃×#62611 #15748950

Order 3328.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3552	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3328	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3327	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3313	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3242	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3177	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#563	—	2	2	no	—
25	C₁₃×#563	—	2	2	no	—
26	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#557	—	2	1	no	—
28	C₁₃×#557	C₂²	1	1	yes	characteristic
29	C₁₃×#557	C₂²	1	1	yes	characteristic
30	C₁₃×#556	—	2	1	no	—
31	C₁₃×#556	C₂²	1	1	yes	characteristic
32	C₁₃×#556	C₂²	1	1	yes	characteristic
33	C₁₃×#556	C₂²	1	2	yes	—
34	C₁₃×#554	—	2	1	no	—
35	C₁₃×#554	C₂²	1	1	yes	characteristic
36	C₁₃×#553	—	2	1	no	—
37	C₁₃×#552	C₂²	1	2	yes	—
38	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
40	C₁₃×#548	C₂²	1	2	yes	—
41	C₁₃×#547	C₂²	1	1	yes	characteristic
42	C₁₃×#544	—	2	1	no	—
43	C₁₃×#544	C₂²	1	2	yes	—
44	C₁₃×#542	—	2	1	no	—
45	C₁₃×#542	—	2	1	no	—
46	C₁₃×#541	—	2	2	no	—
47	C₁₃×#541	—	2	1	no	—
48	C₁₃×#541	C₂²	1	2	yes	—
49	C₁₃×#541	C₂²	1	2	yes	—
50	C₁₃×#539	—	2	2	no	—
51	C₁₃×#536	C₂²	1	2	yes	—
52	C₁₃×#533	C₂²	1	1	yes	characteristic
53	C₁₃×#533	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
55	C₁₃×#529	C₂²	1	1	yes	characteristic
56	C₁₃×#529	C₂²	1	1	yes	characteristic
57	C₁₃×#501	C₂²	1	1	yes	characteristic
58	C₁₃×#499	C₂²	1	2	yes	—
59	C₁₃×#497	C₂²	1	1	yes	characteristic
60	C₁₃×#494	C₂²	1	2	yes	—
61	C₁₃×#491	C₂²	1	2	yes	—
62	C₁₃×#491	C₂²	1	2	yes	—
63	C₁₃×#491	C₂²	1	2	yes	—
64	C₁₃×#491	C₂²	1	1	yes	characteristic
65	C₁₃×#489	C₂²	1	2	yes	—
66	C₁₃×#489	C₂²	1	1	yes	characteristic
67	C₁₃×#488	C₂²	1	2	yes	—
68	C₁₃×#488	C₂²	1	2	yes	—
69	C₁₃×#487	C₂²	1	1	yes	characteristic
70	C₁₃×#487	C₂²	1	1	yes	characteristic
71	C₁₃×#487	C₂²	1	2	yes	—
72	C₁₃×#487	C₂²	1	1	yes	characteristic
73	C₁₃×#487	C₂²	1	1	yes	characteristic
74	C₁₃×#487	C₂²	1	2	yes	—
75	C₁₃×#485	C₂²	1	2	yes	—
76	C₁₃×#485	C₂²	1	2	yes	—
77	C₁₃×#485	C₂²	1	2	yes	—
78	C₁₃×#484	C₂²	1	2	yes	—
79	C₁₃×#483	C₂²	1	2	yes	—
80	C₁₃×#482	C₂²	1	2	yes	—
81	C₁₃×#479	C₂²	1	2	yes	—
82	C₁₃×#479	C₂²	1	2	yes	—
83	C₁₃×#477	C₂²	1	1	yes	characteristic
84	C₁₃×#477	C₂²	1	2	yes	—
85	C₁₃×#476	C₂²	1	1	yes	characteristic
86	C₁₃×#475	C₂²	1	2	yes	—
87	C₁₃×#475	C₂²	1	1	yes	characteristic
88	C₁₃×#474	C₂²	1	1	yes	characteristic
89	C₁₃×#470	C₂²	1	1	yes	characteristic
90	C₁₃×#470	C₂²	1	2	yes	—
91	C₁₃×#470	C₂²	1	1	yes	characteristic
92	C₁₃×#470	C₂²	1	2	yes	—
93	C₁₃×#468	C₂²	1	1	yes	characteristic
94	C₁₃×#468	C₂²	1	1	yes	characteristic
95	C₁₃×#467	C₂²	1	2	yes	—
96	C₁₃×#467	C₂²	1	2	yes	—
97	C₁₃×#464	C₂²	1	2	yes	—
98	C₁₃×#464	C₂²	1	2	yes	—
99	C₁₃×#462	C₂²	1	1	yes	characteristic
100	C₁₃×#462	C₂²	1	1	yes	characteristic
101	C₁₃×#462	C₂²	1	2	yes	—
102	C₁₃×#462	C₂²	1	1	yes	characteristic
103	C₁₃×#462	C₂²	1	2	yes	—
104	C₁₃×#462	C₂²	1	1	yes	characteristic
105	C₁₃×#452	C₂²	1	2	yes	—
106	C₁₃×#452	C₂²	1	2	yes	—
107	C₁₃×#451	C₂²	1	2	yes	—
108	C₁₃×#451	C₂²	1	2	yes	—
109	C₁₃×#451	C₂²	1	2	yes	—
110	C₁₃×#451	C₂²	1	2	yes	—
111	C₁₃×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
113	C₁₃×#441	C₂²	1	2	yes	—
114	C₁₃×#441	C₂²	1	2	yes	—
115	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
116	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
117	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
118	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
121	C₁₃×#436	C₂²	1	2	yes	—
122	C₁₃×#436	C₂²	1	1	yes	characteristic
123	C₁₃×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
125	C₁₃×#433	C₂²	1	2	yes	—
126	C₁₃×#431	C₂²	1	1	yes	characteristic
127	C₁₃×#419	C₂²	1	2	yes	—
128	C₁₃×#419	C₂²	1	2	yes	—
129	C₁₃×#419	C₂²	1	2	yes	—
130	C₁₃×#417	C₂²	1	2	yes	—
131	C₁₃×#416	C₂²	1	2	yes	—
132	C₂×C₁₃×#103	C₂²	1	2	yes	—
133	C₁₃×#405	C₂²	1	2	yes	—
134	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	C₂³	1	2	yes	—
136	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
137	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
138	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
143	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
149	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
150	C₁₃×C₄⋊Q₈	—	2	1	no	—
151	C₁₃×C₄⋊Q₈	—	2	2	no	—
152	C₁₃×C₄⋊Q₈	—	2	1	no	—
153	C₁₃×C₄⋊Q₈	—	2	1	no	—
154	C₁₃×C₄⋊Q₈	—	2	2	no	—
155	C₁₃×C₄⋊Q₈	—	2	2	no	—
156	C₁₃×C₄⋊Q₈	—	2	1	no	—
157	C₁₃×C₄⋊Q₈	—	2	1	no	—
158	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#126	—	2	2	no	—
172	C₁₃×#126	—	2	2	no	—
173	C₁₃×#126	—	2	2	no	—
174	C₁₃×#126	—	2	2	no	—
175	C₁₃×#126	—	2	2	no	—
176	C₁₃×#126	—	2	1	no	—
177	C₁₃×#126	D₄	1	2	yes	—
178	C₁₃×#125	—	2	2	no	—
179	C₁₃×#125	—	2	2	no	—
180	C₁₃×#125	—	2	2	no	—
181	C₁₃×#125	—	2	2	no	—
182	C₁₃×#125	—	2	2	no	—
183	C₁₃×#125	—	2	1	no	—
184	C₁₃×#125	—	2	2	no	—
185	C₁₃×#125	—	2	2	no	—
186	C₁₃×#125	—	2	2	no	—
187	C₁₃×#125	—	2	1	no	—
188	C₁₃×#125	—	2	1	no	—
189	C₁₃×#125	D₄	1	1	yes	characteristic
190	C₁₃×#125	C₂³	1	2	yes	—
191	C₁₃×#125	C₂³	1	2	yes	—
192	C₁₃×#125	C₂³	1	1	yes	characteristic
193	C₁₃×#124	—	2	1	no	—
194	C₁₃×#124	—	2	2	no	—
195	C₁₃×#124	—	2	2	no	—
196	C₁₃×#124	D₄	1	1	yes	characteristic
197	C₁₃×#124	C₂³	1	2	yes	—
198	C₁₃×#124	C₂³	1	1	yes	characteristic
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	1	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×#123	—	2	2	no	—
204	C₁₃×#123	D₄	1	2	yes	—
205	C₁₃×C₂²⋊Q₈	—	2	1	no	—
206	C₁₃×C₂²⋊Q₈	—	2	1	no	—
207	C₁₃×C₂²⋊Q₈	—	2	1	no	—
208	C₁₃×C₂²⋊Q₈	—	2	1	no	—
209	C₁₃×C₂²⋊Q₈	—	2	2	no	—
210	C₁₃×C₂²⋊Q₈	—	2	2	no	—
211	C₁₃×C₂²⋊Q₈	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	—	2	2	no	—
213	C₁₃×C₂²⋊Q₈	—	2	2	no	—
214	C₁₃×C₂²⋊Q₈	—	2	2	no	—
215	C₁₃×C₂²⋊Q₈	—	2	2	no	—
216	C₁₃×C₂²⋊Q₈	—	2	2	no	—
217	C₁₃×C₂²⋊Q₈	—	2	2	no	—
218	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
219	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₁₃×#121	—	2	2	no	—
227	C₁₃×#121	—	2	1	no	—
228	C₁₃×#121	D₄	1	1	yes	characteristic
229	C₁₃×#121	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₁₃	—	2	1	no	—
231	C₄×Q₈×C₁₃	—	2	1	no	—
232	C₄×Q₈×C₁₃	—	2	2	no	—
233	C₄×Q₈×C₁₃	—	2	1	no	—
234	C₄×Q₈×C₁₃	—	2	1	no	—
235	C₄×Q₈×C₁₃	—	2	1	no	—
236	C₄×Q₈×C₁₃	—	2	1	no	—
237	C₄×Q₈×C₁₃	—	2	1	no	—
238	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
243	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
244	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
245	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	2	no	—
251	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₃	C₂³	1	2	yes	—
254	C₁₃×#117	—	2	1	no	—
255	C₁₃×#117	—	2	1	no	—
256	C₁₃×#117	—	2	2	no	—
257	C₁₃×#117	—	2	1	no	—
258	C₁₃×#117	C₂³	1	2	yes	—
259	C₁₃×#117	C₂³	1	2	yes	—
260	C₁₃×#117	C₂³	1	2	yes	—
261	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
265	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
266	C₁₃×#107	C₂³	1	2	yes	—
267	C₁₃×#107	C₂³	1	2	yes	—
268	C₁₃×#107	C₂³	1	1	yes	characteristic
269	C₁₃×#107	C₂³	1	1	yes	characteristic
270	C₁₃×#106	C₂³	1	1	yes	characteristic
271	C₁₃×#106	C₂³	1	1	yes	characteristic
272	C₁₃×#106	C₂³	1	2	yes	—
273	C₁₃×#106	C₂³	1	2	yes	—
274	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
277	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₁₃×#103	C₂³	1	1	yes	characteristic
279	C₁₃×#103	C₂³	1	2	yes	—
280	C₁₃×#103	C₂³	1	2	yes	—
281	C₁₃×#103	C₂³	1	2	yes	—
282	C₁₃×#103	C₂³	1	2	yes	—
283	C₁₃×#103	C₂³	1	2	yes	—
284	C₁₃×#103	C₂³	1	2	yes	—
285	C₁₃×#103	C₂³	1	2	yes	—
286	C₁₃×#103	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	2	yes	—
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	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	1	yes	characteristic
295	C₁₃×#103	C₂³	1	1	yes	characteristic
296	C₁₃×#103	C₂³	1	1	yes	characteristic
297	C₁₃×#103	C₂³	1	1	yes	characteristic
298	C₁₃×#102	C₂³	1	1	yes	characteristic
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×#97	C₂³	1	1	yes	characteristic
306	C₁₃×#97	C₂³	1	1	yes	characteristic
307	C₁₃×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₃	C₂³	1	2	yes	—
311	C₄×C₈×C₁₃	C₂³	1	2	yes	—
312	#62611	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃×#41	—	4	2	no	—
314	C₁₃×#41	—	4	2	no	—
315	C₂×Q₈×C₁₃	—	2	1	no	—
316	C₂×Q₈×C₁₃	—	2	1	no	—
317	C₂×Q₈×C₁₃	—	2	1	no	—
318	C₂×Q₈×C₁₃	—	2	2	no	—
319	C₂×Q₈×C₁₃	—	2	2	no	—
320	C₂×Q₈×C₁₃	—	2	2	no	—
321	C₂×Q₈×C₁₃	—	4	2	no	—
322	C₂×Q₈×C₁₃	—	4	2	no	—
323	C₂×Q₈×C₁₃	—	4	2	no	—
324	C₂×Q₈×C₁₃	—	4	2	no	—
325	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₁₃	—	2	1	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₁₃	—	2	2	no	—
337	C₂²×C₄×C₁₃	—	2	2	no	—
338	C₂²×C₄×C₁₃	—	2	2	no	—
339	C₂²×C₄×C₁₃	—	2	1	no	—
340	C₂²×C₄×C₁₃	—	2	2	no	—
341	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
345	C₁₃×Q₁₆	—	4	2	no	—
346	C₁₃×Q₁₆	—	4	2	no	—
347	C₁₃×Q₁₆	—	4	1	no	—
348	C₁₃×Q₁₆	—	4	1	no	—
349	C₁₃×Q₁₆	—	4	2	no	—
350	C₁₃×Q₁₆	—	4	2	no	—
351	C₁₃×SD₁₆	—	4	1	no	—
352	C₁₃×SD₁₆	—	4	1	no	—
353	C₁₃×M₁₆	—	4	1	no	—
354	C₁₃×M₁₆	—	4	1	no	—
355	C₁₃×M₁₆	—	4	2	no	—
356	C₂×C₈×C₁₃	—	4	2	no	—
357	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
359	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
361	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
363	C₁₃×C₄⋊C₄	—	2	1	no	—
364	C₁₃×C₄⋊C₄	—	2	1	no	—
365	C₁₃×C₄⋊C₄	—	2	1	no	—
366	C₁₃×C₄⋊C₄	—	2	2	no	—
367	C₁₃×C₄⋊C₄	—	2	2	no	—
368	C₁₃×C₄⋊C₄	—	2	2	no	—
369	C₁₃×C₄⋊C₄	—	2	1	no	—
370	C₁₃×C₄⋊C₄	—	2	2	no	—
371	C₁₃×C₄⋊C₄	—	2	1	no	—
372	C₁₃×C₄⋊C₄	—	2	1	no	—
373	C₁₃×C₄⋊C₄	—	2	1	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	—	2	1	no	—
376	C₁₃×C₄⋊C₄	—	2	1	no	—
377	C₁₃×C₄⋊C₄	—	2	1	no	—
378	C₁₃×C₄⋊C₄	—	2	2	no	—
379	C₁₃×C₄⋊C₄	—	2	2	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	2	no	—
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	1	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	2	no	—
391	C₁₃×C₄⋊C₄	—	2	2	no	—
392	C₁₃×C₄⋊C₄	—	2	1	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	1	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	—	2	2	no	—
398	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
406	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₂²⋊C₄	—	2	1	no	—
411	C₁₃×C₂²⋊C₄	—	2	1	no	—
412	C₁₃×C₂²⋊C₄	—	2	2	no	—
413	C₁₃×C₂²⋊C₄	—	2	2	no	—
414	C₁₃×C₂²⋊C₄	—	2	2	no	—
415	C₁₃×C₂²⋊C₄	—	2	1	no	—
416	C₁₃×C₂²⋊C₄	—	2	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	1	no	—
421	C₁₃×C₂²⋊C₄	—	2	1	no	—
422	C₁₃×C₂²⋊C₄	—	2	1	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	1	no	—
425	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
426	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
429	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₄²×C₁₃	—	2	2	no	—
431	C₄²×C₁₃	—	2	1	no	—
432	C₄²×C₁₃	—	2	1	no	—
433	C₄²×C₁₃	—	2	2	no	—
434	C₄²×C₁₃	—	2	1	no	—
435	C₄²×C₁₃	—	2	2	no	—
436	C₄²×C₁₃	—	2	2	no	—
437	C₄²×C₁₃	—	2	2	no	—
438	C₄²×C₁₃	—	2	2	no	—
439	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
443	C₄²×C₁₃	C₂⁴	1	2	yes	—
444	#3555	C₂×C₁₃	1	1	yes	characteristic, complemented
445	#3552	C₂×C₁₃	1	1	yes	characteristic
446	#3374	C₂×C₁₃	1	1	yes	characteristic, complemented
447	#3369	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3364	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3331	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3328	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3328	C₂×C₁₃	1	2	yes	complemented
453	#3327	C₂×C₁₃	1	2	yes	complemented
454	#3313	C₂×C₁₃	1	2	yes	complemented
455	#3312	C₂×C₁₃	1	2	yes	complemented
456	#3302	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3299	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3242	C₂×C₁₃	1	2	yes	complemented
459	#3233	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3223	C₂×C₁₃	1	2	yes	complemented
461	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3177	C₂×C₁₃	1	2	yes	complemented
463	#3172	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3137	C₂×C₁₃	1	2	yes	complemented
466	#2969	C₂×C₁₃	1	1	yes	characteristic, complemented
467	C₂³×C₁₃	—	2	1	no	—
468	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
469	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
470	Q₈×C₁₃	—	2	2	no	—
471	Q₈×C₁₃	—	2	1	no	—
472	Q₈×C₁₃	—	2	1	no	—
473	Q₈×C₁₃	—	2	1	no	—
474	Q₈×C₁₃	—	2	1	no	—
475	Q₈×C₁₃	—	2	2	no	—
476	Q₈×C₁₃	—	2	1	no	—
477	Q₈×C₁₃	—	2	1	no	—
478	Q₈×C₁₃	—	2	2	no	—
479	Q₈×C₁₃	—	2	2	no	—
480	Q₈×C₁₃	—	2	2	no	—
481	Q₈×C₁₃	—	4	2	no	—
482	Q₈×C₁₃	—	8	1	no	—
483	Q₈×C₁₃	—	8	1	no	—
484	Q₈×C₁₃	—	8	2	no	—
485	Q₈×C₁₃	—	8	2	no	—
486	Q₈×C₁₃	—	8	2	no	—
487	D₄×C₁₃	—	2	2	no	—
488	D₄×C₁₃	—	2	1	no	—
489	D₄×C₁₃	—	2	1	no	—
490	D₄×C₁₃	—	4	2	no	—
491	D₄×C₁₃	—	4	2	no	—
492	D₄×C₁₃	—	8	2	no	—
493	C₂×C₄×C₁₃	—	2	2	no	—
494	C₂×C₄×C₁₃	—	2	2	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	1	no	—
497	C₂×C₄×C₁₃	—	2	2	no	—
498	C₂×C₄×C₁₃	—	2	1	no	—
499	C₂×C₄×C₁₃	—	2	1	no	—
500	C₂×C₄×C₁₃	—	2	1	no	—
501	C₂×C₄×C₁₃	—	2	2	no	—
502	C₂×C₄×C₁₃	—	2	1	no	—
503	C₂×C₄×C₁₃	—	2	1	no	—
504	C₂×C₄×C₁₃	—	2	2	no	—
505	C₂×C₄×C₁₃	—	2	1	no	—
506	C₂×C₄×C₁₃	—	2	2	no	—
507	C₂×C₄×C₁₃	—	2	1	no	—
508	C₂×C₄×C₁₃	—	2	2	no	—
509	C₂×C₄×C₁₃	—	4	1	no	—
510	C₂×C₄×C₁₃	—	4	2	no	—
511	C₂×C₄×C₁₃	—	8	2	no	—
512	C₂×C₄×C₁₃	—	8	2	no	—
513	C₂×C₄×C₁₃	—	8	2	no	—
514	C₂×C₄×C₁₃	—	8	2	no	—
515	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
524	C₈×C₁₃	—	2	1	no	—
525	C₈×C₁₃	—	2	2	no	—
526	C₈×C₁₃	—	2	1	no	—
527	C₈×C₁₃	—	2	1	no	—
528	C₈×C₁₃	—	2	1	no	—
529	C₈×C₁₃	—	2	2	no	—
530	#563	—	2	2	no	—
531	#563	—	2	2	no	—
532	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
533	#557	—	2	1	no	—
534	#557	C₂²×C₁₃	1	1	yes	characteristic
535	#557	C₂²×C₁₃	1	1	yes	characteristic
536	#556	—	2	1	no	—
537	#556	C₂²×C₁₃	1	1	yes	characteristic
538	#556	C₂²×C₁₃	1	1	yes	characteristic
539	#556	C₂²×C₁₃	1	2	yes	—
540	#554	—	2	1	no	—
541	#554	C₂²×C₁₃	1	1	yes	characteristic
542	#553	—	2	1	no	—
543	#552	C₂²×C₁₃	1	2	yes	—
544	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
545	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
546	#548	C₂²×C₁₃	1	2	yes	—
547	#547	C₂²×C₁₃	1	1	yes	characteristic
548	#544	—	2	1	no	—
549	#544	C₂²×C₁₃	1	2	yes	—
550	#542	—	2	1	no	—
551	#542	—	2	1	no	—
552	#541	—	2	2	no	—
553	#541	—	2	1	no	—
554	#541	C₂²×C₁₃	1	2	yes	—
555	#541	C₂²×C₁₃	1	2	yes	—
556	#539	—	2	2	no	—
557	#536	C₂²×C₁₃	1	2	yes	—
558	#533	C₂²×C₁₃	1	1	yes	characteristic
559	#533	C₂²×C₁₃	1	1	yes	characteristic
560	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
561	#529	C₂²×C₁₃	1	1	yes	characteristic
562	#529	C₂²×C₁₃	1	1	yes	characteristic
563	#501	C₂²×C₁₃	1	1	yes	characteristic
564	#499	C₂²×C₁₃	1	2	yes	—
565	#497	C₂²×C₁₃	1	1	yes	characteristic
566	#494	C₂²×C₁₃	1	2	yes	—
567	#491	C₂²×C₁₃	1	2	yes	—
568	#491	C₂²×C₁₃	1	2	yes	—
569	#491	C₂²×C₁₃	1	2	yes	—
570	#491	C₂²×C₁₃	1	1	yes	characteristic
571	#489	C₂²×C₁₃	1	2	yes	—
572	#489	C₂²×C₁₃	1	1	yes	characteristic
573	#488	C₂²×C₁₃	1	2	yes	—
574	#488	C₂²×C₁₃	1	2	yes	—
575	#487	C₂²×C₁₃	1	2	yes	—
576	#487	C₂²×C₁₃	1	1	yes	characteristic
577	#487	C₂²×C₁₃	1	1	yes	characteristic
578	#487	C₂²×C₁₃	1	1	yes	characteristic
579	#487	C₂²×C₁₃	1	1	yes	characteristic
580	#487	C₂²×C₁₃	1	2	yes	—
581	#485	C₂²×C₁₃	1	2	yes	—
582	#485	C₂²×C₁₃	1	2	yes	—
583	#485	C₂²×C₁₃	1	2	yes	—
584	#484	C₂²×C₁₃	1	2	yes	—
585	#483	C₂²×C₁₃	1	2	yes	—
586	#482	C₂²×C₁₃	1	2	yes	—
587	#479	C₂²×C₁₃	1	2	yes	—
588	#479	C₂²×C₁₃	1	2	yes	—
589	#477	C₂²×C₁₃	1	1	yes	characteristic
590	#477	C₂²×C₁₃	1	2	yes	—
591	#476	C₂²×C₁₃	1	1	yes	characteristic
592	#475	C₂²×C₁₃	1	2	yes	—
593	#475	C₂²×C₁₃	1	1	yes	characteristic
594	#474	C₂²×C₁₃	1	1	yes	characteristic
595	#470	C₂²×C₁₃	1	1	yes	characteristic
596	#470	C₂²×C₁₃	1	2	yes	—
597	#470	C₂²×C₁₃	1	2	yes	—
598	#470	C₂²×C₁₃	1	1	yes	characteristic
599	#468	C₂²×C₁₃	1	1	yes	characteristic
600	#468	C₂²×C₁₃	1	1	yes	characteristic
601	#467	C₂²×C₁₃	1	2	yes	—
602	#467	C₂²×C₁₃	1	2	yes	—
603	#464	C₂²×C₁₃	1	2	yes	—
604	#464	C₂²×C₁₃	1	2	yes	—
605	#462	C₂²×C₁₃	1	1	yes	characteristic
606	#462	C₂²×C₁₃	1	2	yes	—
607	#462	C₂²×C₁₃	1	1	yes	characteristic
608	#462	C₂²×C₁₃	1	1	yes	characteristic
609	#462	C₂²×C₁₃	1	2	yes	—
610	#462	C₂²×C₁₃	1	1	yes	characteristic
611	#452	C₂²×C₁₃	1	2	yes	—
612	#452	C₂²×C₁₃	1	2	yes	—
613	#451	C₂²×C₁₃	1	2	yes	—
614	#451	C₂²×C₁₃	1	2	yes	—
615	#451	C₂²×C₁₃	1	2	yes	—
616	#451	C₂²×C₁₃	1	2	yes	—
617	#446	C₂²×C₁₃	1	1	yes	characteristic
618	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
619	#441	C₂²×C₁₃	1	2	yes	—
620	#441	C₂²×C₁₃	1	2	yes	—
621	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
622	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
623	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
624	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
625	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
626	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
627	#436	C₂²×C₁₃	1	1	yes	characteristic
628	#436	C₂²×C₁₃	1	2	yes	—
629	#435	C₂²×C₁₃	1	2	yes	—
630	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
631	#433	C₂²×C₁₃	1	2	yes	—
632	#431	C₂²×C₁₃	1	1	yes	characteristic
633	#419	C₂²×C₁₃	1	2	yes	—
634	#419	C₂²×C₁₃	1	2	yes	—
635	#419	C₂²×C₁₃	1	2	yes	—
636	#417	C₂²×C₁₃	1	2	yes	—
637	#416	C₂²×C₁₃	1	2	yes	—
638	C₂×#103	C₂²×C₁₃	1	2	yes	—
639	#405	C₂²×C₁₃	1	2	yes	—
640	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
641	C₂²×C₁₃	—	2	1	no	—
642	C₂²×C₁₃	—	2	2	no	—
643	C₂²×C₁₃	—	2	1	no	—
644	C₂²×C₁₃	—	2	2	no	—
645	C₂²×C₁₃	—	2	1	no	—
646	C₂²×C₁₃	—	2	2	no	—
647	C₂²×C₁₃	—	4	1	no	—
648	C₂²×C₁₃	—	4	1	no	—
649	C₂²×C₁₃	—	4	1	no	—
650	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
651	C₄×C₁₃	—	2	1	no	—
652	C₄×C₁₃	—	2	1	no	—
653	C₄×C₁₃	—	2	2	no	—
654	C₄×C₁₃	—	2	2	no	—
655	C₄×C₁₃	—	2	1	no	—
656	C₄×C₁₃	—	2	1	no	—
657	C₄×C₁₃	—	2	2	no	—
658	C₄×C₁₃	—	4	1	no	—
659	C₄×C₁₃	—	4	2	no	—
660	C₄×C₁₃	—	4	1	no	—
661	C₄×C₁₃	—	4	1	no	—
662	C₄×C₁₃	—	4	2	no	—
663	C₄×C₁₃	—	4	1	no	—
664	C₄×C₁₃	—	4	2	no	—
665	C₄×C₁₃	—	4	1	no	—
666	C₄×C₁₃	—	4	1	no	—
667	C₄×C₁₃	—	4	1	no	—
668	C₄×C₁₃	—	4	2	no	—
669	C₄×C₁₃	#578	1	2	yes	—
670	C₄×C₁₃	#585	1	1	yes	characteristic
671	C₄×C₁₃	#585	1	1	yes	characteristic
672	C₂×#41	C₂³×C₁₃	1	2	yes	—
673	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
674	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
675	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
676	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
677	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
678	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
679	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
680	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
681	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
682	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
685	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
686	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
687	C₄⋊Q₈	—	2	1	no	—
688	C₄⋊Q₈	—	2	2	no	—
689	C₄⋊Q₈	—	2	1	no	—
690	C₄⋊Q₈	—	2	1	no	—
691	C₄⋊Q₈	—	2	2	no	—
692	C₄⋊Q₈	—	2	2	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
696	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	1	no	—
714	#126	D₄×C₁₃	1	2	yes	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	1	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	1	no	—
725	#125	—	2	1	no	—
726	#125	D₄×C₁₃	1	1	yes	characteristic
727	#125	C₂³×C₁₃	1	1	yes	characteristic
728	#125	C₂³×C₁₃	1	2	yes	—
729	#125	C₂³×C₁₃	1	2	yes	—
730	#124	—	2	1	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	D₄×C₁₃	1	1	yes	characteristic
734	#124	C₂³×C₁₃	1	1	yes	characteristic
735	#124	C₂³×C₁₃	1	2	yes	—
736	#123	—	2	2	no	—
737	#123	—	2	1	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	D₄×C₁₃	1	2	yes	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
756	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
757	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
763	#121	—	2	2	no	—
764	#121	—	2	1	no	—
765	#121	D₄×C₁₃	1	1	yes	characteristic
766	#121	C₂³×C₁₃	1	1	yes	characteristic
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
779	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
780	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
781	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
782	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₁₃	1	2	yes	—
791	#117	—	2	1	no	—
792	#117	—	2	1	no	—
793	#117	—	2	2	no	—
794	#117	—	2	1	no	—
795	#117	C₂³×C₁₃	1	2	yes	—
796	#117	C₂³×C₁₃	1	2	yes	—
797	#117	C₂³×C₁₃	1	2	yes	—
798	C₂×C₄⋊C₄	—	2	1	no	—
799	C₂×C₄⋊C₄	—	2	1	no	—
800	C₂×C₄⋊C₄	—	2	1	no	—
801	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
802	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
803	#107	C₂³×C₁₃	1	2	yes	—
804	#107	C₂³×C₁₃	1	2	yes	—
805	#107	C₂³×C₁₃	1	1	yes	characteristic
806	#107	C₂³×C₁₃	1	1	yes	characteristic
807	#106	C₂³×C₁₃	1	1	yes	characteristic
808	#106	C₂³×C₁₃	1	1	yes	characteristic
809	#106	C₂³×C₁₃	1	2	yes	—
810	#106	C₂³×C₁₃	1	2	yes	—
811	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
814	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
815	#103	C₂³×C₁₃	1	1	yes	characteristic
816	#103	C₂³×C₁₃	1	2	yes	—
817	#103	C₂³×C₁₃	1	2	yes	—
818	#103	C₂³×C₁₃	1	2	yes	—
819	#103	C₂³×C₁₃	1	2	yes	—
820	#103	C₂³×C₁₃	1	2	yes	—
821	#103	C₂³×C₁₃	1	2	yes	—
822	#103	C₂³×C₁₃	1	2	yes	—
823	#103	C₂³×C₁₃	1	1	yes	characteristic
824	#103	C₂³×C₁₃	1	2	yes	—
825	#103	C₂³×C₁₃	1	2	yes	—
826	#103	C₂³×C₁₃	1	2	yes	—
827	#103	C₂³×C₁₃	1	2	yes	—
828	#103	C₂³×C₁₃	1	2	yes	—
829	#103	C₂³×C₁₃	1	2	yes	—
830	#103	C₂³×C₁₃	1	2	yes	—
831	#103	C₂³×C₁₃	1	1	yes	characteristic
832	#103	C₂³×C₁₃	1	1	yes	characteristic
833	#103	C₂³×C₁₃	1	1	yes	characteristic
834	#103	C₂³×C₁₃	1	1	yes	characteristic
835	#102	C₂³×C₁₃	1	1	yes	characteristic
836	#102	C₂³×C₁₃	1	2	yes	—
837	#102	C₂³×C₁₃	1	1	yes	characteristic
838	#102	C₂³×C₁₃	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
840	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
842	#97	C₂³×C₁₃	1	1	yes	characteristic
843	#97	C₂³×C₁₃	1	1	yes	characteristic
844	#97	C₂³×C₁₃	1	2	yes	—
845	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
846	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
847	C₄×C₈	C₂³×C₁₃	1	2	yes	—
848	C₄×C₈	C₂³×C₁₃	1	2	yes	—
849	C₂×C₁₃	—	4	1	no	—
850	C₂×C₁₃	—	4	2	no	—
851	C₂×C₁₃	—	8	1	no	—
852	C₂×C₁₃	#3500	1	1	yes	characteristic
853	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
854	C₂×C₁₃	#3586	1	1	yes	characteristic
855	#41	—	4	2	no	—
856	#41	—	4	2	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	4	2	no	—
864	C₂×Q₈	—	4	2	no	—
865	C₂×Q₈	—	4	2	no	—
866	C₂×Q₈	—	4	2	no	—
867	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
869	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
870	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
871	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
872	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	—	2	2	no	—
875	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
876	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
877	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
884	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
887	Q₁₆	—	4	2	no	—
888	Q₁₆	—	4	2	no	—
889	Q₁₆	—	4	1	no	—
890	Q₁₆	—	4	1	no	—
891	Q₁₆	—	4	2	no	—
892	Q₁₆	—	4	2	no	—
893	SD₁₆	—	4	1	no	—
894	SD₁₆	—	4	1	no	—
895	M₁₆	—	4	1	no	—
896	M₁₆	—	4	1	no	—
897	M₁₆	—	4	2	no	—
898	C₂×C₈	—	4	2	no	—
899	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
900	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
901	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
903	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
948	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
968	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
969	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
970	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
971	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
982	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
983	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
984	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
985	C₄²	C₂⁴×C₁₃	1	2	yes	—
986	C₁₃	#62611	1	1	yes	characteristic, direct product factor, Sylow
987	C₂³	—	2	1	no	—
988	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
989	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
990	Q₈	—	2	2	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	1	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	2	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	2	2	no	—
1000	Q₈	—	2	2	no	—
1001	Q₈	—	4	2	no	—
1002	Q₈	—	8	2	no	—
1003	Q₈	—	8	2	no	—
1004	Q₈	—	8	1	no	—
1005	Q₈	—	8	1	no	—
1006	Q₈	—	8	2	no	—
1007	D₄	—	2	2	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	4	2	no	—
1011	D₄	—	4	2	no	—
1012	D₄	—	8	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	4	1	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1040	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1042	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1043	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1044	C₈	—	2	1	no	—
1045	C₈	—	2	2	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1060	C₄	—	2	1	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	C₁₃×#578	1	2	yes	—
1079	C₄	C₁₃×#585	1	1	yes	characteristic
1080	C₄	C₁₃×#585	1	1	yes	characteristic
1081	C₂	—	4	1	no	—
1082	C₂	—	4	2	no	—
1083	C₂	—	8	1	no	—
1084	C₂	C₁₃×#3500	1	1	yes	characteristic
1085	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1086	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3552	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3555	C₂	semidirect
3. C₁₃×#3374	C₂	semidirect
4. C₁₃×#3369	C₂	semidirect
5. C₁₃×#3364	C₂	semidirect
6. C₁₃×#3363	C₂	semidirect
7. C₁₃×#3331	C₂	semidirect
8. C₁₃×#3328	C₂	semidirect
9. C₁₃×#3328	C₂	semidirect
10. C₁₃×#3327	C₂	semidirect
11. C₁₃×#3313	C₂	semidirect
12. C₁₃×#3312	C₂	semidirect
13. C₁₃×#3302	C₂	semidirect
14. C₁₃×#3299	C₂	semidirect
15. C₁₃×#3242	C₂	semidirect
16. C₁₃×#3233	C₂	semidirect
17. C₁₃×#3223	C₂	semidirect
18. C₁₃×#3209	C₂	semidirect
19. C₁₃×#3177	C₂	semidirect
20. C₁₃×#3172	C₂	semidirect
21. C₁₃×#3139	C₂	semidirect
22. C₁₃×#3137	C₂	semidirect
23. C₁₃×#2969	C₂	semidirect
312. #62611	C₁₃	direct (N × H)
444. #3555	C₂×C₁₃	semidirect
446. #3374	C₂×C₁₃	semidirect
447. #3369	C₂×C₁₃	semidirect
448. #3364	C₂×C₁₃	semidirect
449. #3363	C₂×C₁₃	semidirect
450. #3331	C₂×C₁₃	semidirect
451. #3328	C₂×C₁₃	semidirect
452. #3328	C₂×C₁₃	semidirect
453. #3327	C₂×C₁₃	semidirect
454. #3313	C₂×C₁₃	semidirect
455. #3312	C₂×C₁₃	semidirect
456. #3302	C₂×C₁₃	semidirect
457. #3299	C₂×C₁₃	semidirect
458. #3242	C₂×C₁₃	semidirect
459. #3233	C₂×C₁₃	semidirect
460. #3223	C₂×C₁₃	semidirect
461. #3209	C₂×C₁₃	semidirect
462. #3177	C₂×C₁₃	semidirect
463. #3172	C₂×C₁₃	semidirect
464. #3139	C₂×C₁₃	semidirect
465. #3137	C₂×C₁₃	semidirect
466. #2969	C₂×C₁₃	semidirect
986. C₁₃	#62611	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×#3555	2
C₁₃×#3552	2
C₁₃×#3374	2
C₁₃×#3369	2
C₁₃×#3364	2
C₁₃×#3363	2
C₁₃×#3331	2
C₁₃×#3328	2
C₁₃×#3327	2
C₁₃×#3313	2
C₁₃×#3312	2
C₁₃×#3302	2
C₁₃×#3299	2
C₁₃×#3242	2
C₁₃×#3233	2
C₁₃×#3223	2
C₁₃×#3209	2
C₁₃×#3177	2
C₁₃×#3172	2
C₁₃×#3139	2
C₁₃×#3137	2
C₁₃×#2969	2
#62611	13

Subgroups — C13×#62611 #15748950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62611 #15748950