Subgroups — C₁₃×#62603 #15748942

Order 3328.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3376	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3321	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3316	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3306	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3298	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3244	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3181	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3173	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#563	—	2	2	no	—
21	C₁₃×#563	—	2	1	no	—
22	C₁₃×#562	—	2	1	no	—
23	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#556	C₂²	1	2	yes	—
25	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#552	—	2	1	no	—
29	C₁₃×#552	C₂²	1	2	yes	—
30	C₁₃×#551	—	2	2	no	—
31	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#548	C₂²	1	2	yes	—
33	C₁₃×#547	—	2	1	no	—
34	C₁₃×#547	C₂²	1	2	yes	—
35	C₁₃×#546	C₂²	1	2	yes	—
36	C₁₃×#544	—	2	1	no	—
37	C₁₃×#544	C₂²	1	2	yes	complemented
38	C₁₃×#543	—	2	1	no	—
39	C₁₃×#542	—	2	2	no	—
40	C₁₃×#542	—	2	1	no	—
41	C₁₃×#542	C₂²	1	2	yes	—
42	C₁₃×#542	C₂²	1	2	yes	complemented
43	C₁₃×#538	—	2	1	no	—
44	C₁₃×#536	—	2	2	no	—
45	C₁₃×#536	C₂²	1	2	yes	—
46	C₁₃×#533	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
48	C₁₃×#529	C₂²	1	1	yes	characteristic
49	C₁₃×#529	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#498	C₂²	1	2	yes	complemented
53	C₁₃×#497	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#495	C₂²	1	2	yes	—
55	C₁₃×#491	C₂²	1	2	yes	complemented
56	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#489	C₂²	1	2	yes	—
58	C₁₃×#489	C₂²	1	2	yes	—
59	C₁₃×#489	C₂²	1	2	yes	—
60	C₁₃×#489	C₂²	1	2	yes	—
61	C₁₃×#489	C₂²	1	2	yes	—
62	C₁₃×#489	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#488	C₂²	1	2	yes	—
64	C₁₃×#488	C₂²	1	2	yes	—
65	C₁₃×#487	C₂²	1	2	yes	complemented
66	C₁₃×#487	C₂²	1	2	yes	complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#483	C₂²	1	2	yes	—
69	C₁₃×#483	C₂²	1	2	yes	—
70	C₁₃×#483	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	2	yes	—
72	C₁₃×#481	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	—
75	C₁₃×#476	C₂²	1	2	yes	—
76	C₁₃×#475	C₂²	1	2	yes	complemented
77	C₁₃×#475	C₂²	1	2	yes	complemented
78	C₁₃×#475	C₂²	1	2	yes	complemented
79	C₁₃×#470	C₂²	1	2	yes	complemented
80	C₁₃×#469	C₂²	1	2	yes	—
81	C₁₃×#467	C₂²	1	2	yes	—
82	C₁₃×#465	C₂²	1	2	yes	—
83	C₁₃×#465	C₂²	1	2	yes	—
84	C₁₃×#465	C₂²	1	2	yes	complemented
85	C₁₃×#464	C₂²	1	2	yes	—
86	C₁₃×#464	C₂²	1	2	yes	—
87	C₁₃×#463	C₂²	1	2	yes	—
88	C₁₃×#463	C₂²	1	2	yes	—
89	C₁₃×#462	C₂²	1	2	yes	complemented
90	C₁₃×#461	C₂²	1	2	yes	complemented
91	C₁₃×#452	C₂²	1	2	yes	—
92	C₁₃×#451	C₂²	1	1	yes	characteristic
93	C₁₃×#451	C₂²	1	2	yes	complemented
94	C₁₃×#450	C₂²	1	1	yes	characteristic
95	C₁₃×#449	C₂²	1	2	yes	—
96	C₁₃×#448	C₂²	1	1	yes	characteristic
97	C₁₃×#448	C₂²	1	2	yes	complemented
98	C₁₃×#447	C₂²	1	1	yes	characteristic
99	C₁₃×#446	C₂²	1	2	yes	complemented
100	C₁₃×#442	C₂²	1	2	yes	—
101	C₁₃×#441	C₂²	1	2	yes	complemented
102	C₁₃×#441	C₂²	1	2	yes	complemented
103	C₁₃×#440	C₂²	1	2	yes	complemented
104	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
105	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
106	C₁₃×#435	C₂²	1	2	yes	—
107	C₁₃×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₁₃	C₂²	1	2	yes	—
109	C₁₃×#433	C₂²	1	2	yes	complemented
110	C₁₃×#431	C₂²	1	1	yes	characteristic
111	C₁₃×#419	C₂²	1	2	yes	complemented
112	C₁₃×#417	C₂²	1	2	yes	—
113	C₁₃×#416	C₂²	1	2	yes	—
114	C₂×C₁₃×#103	C₂²	1	2	yes	—
115	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
116	C₂×C₁₃×#102	C₂²	1	2	yes	—
117	C₁₃×#405	C₂²	1	2	yes	complemented
118	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	—	2	2	no	—
120	C₂×C₁₃×#41	C₂³	1	2	yes	—
121	C₂²×Q₈×C₁₃	—	2	1	no	—
122	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
130	C₂×C₁₃×D₈	C₂³	1	2	yes	—
131	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
132	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
133	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
134	C₁₃×C₄⋊Q₈	—	2	2	no	—
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	—	2	2	no	—
137	C₁₃×C₄⋊Q₈	—	2	1	no	—
138	C₁₃×C₄⋊Q₈	—	2	1	no	—
139	C₁₃×C₄⋊Q₈	—	2	1	no	—
140	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
145	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
147	C₁₃×#126	—	2	2	no	—
148	C₁₃×#126	—	2	2	no	—
149	C₁₃×#126	—	2	2	no	—
150	C₁₃×#126	—	2	2	no	—
151	C₁₃×#126	—	2	2	no	—
152	C₁₃×#126	—	2	1	no	—
153	C₁₃×#126	D₄	1	2	yes	—
154	C₁₃×#125	—	2	1	no	—
155	C₁₃×#125	—	2	2	no	—
156	C₁₃×#125	—	2	2	no	—
157	C₁₃×#125	—	2	1	no	—
158	C₁₃×#125	D₄	1	1	yes	characteristic
159	C₁₃×#125	C₂³	1	2	yes	—
160	C₁₃×#125	C₂³	1	1	yes	characteristic
161	C₁₃×#124	—	2	2	no	—
162	C₁₃×#124	—	2	2	no	—
163	C₁₃×#124	—	2	2	no	—
164	C₁₃×#124	—	2	2	no	—
165	C₁₃×#124	—	2	1	no	—
166	C₁₃×#124	—	2	1	no	—
167	C₁₃×#124	D₄	1	1	yes	characteristic
168	C₁₃×#124	C₂³	1	2	yes	—
169	C₁₃×#124	C₂³	1	2	yes	—
170	C₁₃×#124	C₂³	1	2	yes	—
171	C₁₃×#124	C₂³	1	1	yes	characteristic
172	C₁₃×#123	—	2	2	no	—
173	C₁₃×#123	—	2	1	no	—
174	C₁₃×#123	—	2	2	no	—
175	C₁₃×#123	—	2	2	no	—
176	C₁₃×#123	—	2	2	no	—
177	C₁₃×#123	—	2	2	no	—
178	C₁₃×#123	—	2	2	no	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	D₄	1	2	yes	—
182	C₁₃×C₂²⋊Q₈	—	2	1	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	1	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
198	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
199	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	1	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	D₄	1	1	yes	characteristic
206	C₁₃×#121	C₂³	1	1	yes	characteristic
207	C₁₃×#121	C₂³	1	2	yes	—
208	C₁₃×#121	C₂³	1	2	yes	—
209	C₁₃×#120	—	2	2	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₁₃	—	2	2	no	—
218	C₄×D₄×C₁₃	—	2	1	no	—
219	C₄×D₄×C₁₃	—	2	1	no	—
220	C₄×D₄×C₁₃	—	2	2	no	—
221	C₄×D₄×C₁₃	C₂³	1	2	yes	—
222	C₄×D₄×C₁₃	C₂³	1	2	yes	—
223	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₁₃	C₂³	1	2	yes	—
225	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
226	C₁₃×#117	—	2	1	no	—
227	C₁₃×#117	—	2	2	no	—
228	C₁₃×#117	—	2	1	no	—
229	C₁₃×#117	—	2	2	no	—
230	C₁₃×#117	—	2	1	no	—
231	C₁₃×#117	C₂³	1	2	yes	—
232	C₁₃×#117	C₂³	1	2	yes	—
233	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
236	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
239	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#106	C₂³	1	2	yes	—
243	C₁₃×#106	C₂³	1	2	yes	—
244	C₁₃×#106	C₂³	1	2	yes	—
245	C₁₃×#106	C₂³	1	2	yes	—
246	C₁₃×#106	C₂³	1	2	yes	—
247	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
248	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₁₃×#103	C₂³	1	2	yes	—
251	C₁₃×#103	C₂³	1	2	yes	—
252	C₁₃×#103	C₂³	1	2	yes	—
253	C₁₃×#103	C₂³	1	2	yes	—
254	C₁₃×#103	C₂³	1	2	yes	—
255	C₁₃×#103	C₂³	1	2	yes	—
256	C₁₃×#103	C₂³	1	2	yes	—
257	C₁₃×#103	C₂³	1	2	yes	—
258	C₁₃×#103	C₂³	1	2	yes	—
259	C₁₃×#103	C₂³	1	2	yes	—
260	C₁₃×#103	C₂³	1	2	yes	—
261	C₁₃×#103	C₂³	1	2	yes	—
262	C₁₃×#103	C₂³	1	2	yes	—
263	C₁₃×#102	C₂³	1	2	yes	—
264	C₁₃×#102	C₂³	1	2	yes	—
265	C₁₃×#102	C₂³	1	2	yes	—
266	C₁₃×#102	C₂³	1	2	yes	—
267	C₁₃×#102	C₂³	1	2	yes	—
268	C₁₃×#102	C₂³	1	2	yes	—
269	C₁₃×#102	C₂³	1	2	yes	—
270	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₁₃×#97	C₂³	1	1	yes	characteristic
275	C₁₃×#97	C₂³	1	1	yes	characteristic
276	C₁₃×#97	C₂³	1	2	yes	—
277	C₁₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₁₃	C₂³	1	2	yes	—
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#62603	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂⁴×C₁₃	—	2	1	no	—
282	C₁₃×#41	—	4	2	no	—
283	C₁₃×#41	—	4	2	no	—
284	C₁₃×#41	—	8	4	no	—
285	C₂×Q₈×C₁₃	—	2	1	no	—
286	C₂×Q₈×C₁₃	—	2	2	no	—
287	C₂×Q₈×C₁₃	—	2	1	no	—
288	C₂×Q₈×C₁₃	—	2	1	no	—
289	C₂×Q₈×C₁₃	—	2	2	no	—
290	C₂×Q₈×C₁₃	—	2	2	no	—
291	C₂×Q₈×C₁₃	—	2	1	no	—
292	C₂×Q₈×C₁₃	—	4	2	no	—
293	C₂×Q₈×C₁₃	—	4	2	no	—
294	C₂×Q₈×C₁₃	—	4	2	no	—
295	C₂×Q₈×C₁₃	—	8	2	no	—
296	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂×D₄×C₁₃	—	2	1	no	—
301	C₂×D₄×C₁₃	—	2	2	no	—
302	C₂×D₄×C₁₃	—	2	2	no	—
303	C₂×D₄×C₁₃	—	2	2	no	—
304	C₂×D₄×C₁₃	—	2	1	no	—
305	C₂×D₄×C₁₃	—	4	2	no	—
306	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
307	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
309	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₁₃	—	2	2	no	—
311	C₂²×C₄×C₁₃	—	2	1	no	—
312	C₂²×C₄×C₁₃	—	2	2	no	—
313	C₂²×C₄×C₁₃	—	2	2	no	—
314	C₂²×C₄×C₁₃	—	2	1	no	—
315	C₂²×C₄×C₁₃	—	2	2	no	—
316	C₂²×C₄×C₁₃	—	2	2	no	—
317	C₂²×C₄×C₁₃	—	2	2	no	—
318	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
322	C₁₃×Q₁₆	—	4	2	no	—
323	C₁₃×Q₁₆	—	4	2	no	—
324	C₁₃×SD₁₆	—	4	2	no	—
325	C₁₃×SD₁₆	—	4	2	no	—
326	C₁₃×SD₁₆	—	4	2	no	—
327	C₁₃×D₈	—	4	2	no	—
328	C₁₃×M₁₆	—	4	2	no	—
329	C₂×C₈×C₁₃	—	4	2	no	—
330	C₂×C₈×C₁₃	—	4	2	no	—
331	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
332	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
333	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
334	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
335	C₁₃×C₄⋊C₄	—	2	1	no	—
336	C₁₃×C₄⋊C₄	—	2	1	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	2	no	—
344	C₁₃×C₄⋊C₄	—	2	1	no	—
345	C₁₃×C₄⋊C₄	—	2	1	no	—
346	C₁₃×C₄⋊C₄	—	2	1	no	—
347	C₁₃×C₄⋊C₄	—	2	1	no	—
348	C₁₃×C₄⋊C₄	—	2	2	no	—
349	C₁₃×C₄⋊C₄	—	2	1	no	—
350	C₁₃×C₄⋊C₄	—	2	2	no	—
351	C₁₃×C₄⋊C₄	—	2	2	no	—
352	C₁₃×C₄⋊C₄	—	2	1	no	—
353	C₁₃×C₄⋊C₄	—	2	2	no	—
354	C₁₃×C₄⋊C₄	—	2	2	no	—
355	C₁₃×C₄⋊C₄	—	2	2	no	—
356	C₁₃×C₄⋊C₄	—	2	1	no	—
357	C₁₃×C₄⋊C₄	—	2	2	no	—
358	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
359	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
360	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
361	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
366	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
368	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
369	C₁₃×C₂²⋊C₄	—	2	2	no	—
370	C₁₃×C₂²⋊C₄	—	2	1	no	—
371	C₁₃×C₂²⋊C₄	—	2	2	no	—
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	2	no	—
377	C₁₃×C₂²⋊C₄	—	2	2	no	—
378	C₁₃×C₂²⋊C₄	—	2	2	no	—
379	C₁₃×C₂²⋊C₄	—	2	2	no	—
380	C₁₃×C₂²⋊C₄	—	2	2	no	—
381	C₁₃×C₂²⋊C₄	—	2	1	no	—
382	C₁₃×C₂²⋊C₄	—	2	2	no	—
383	C₁₃×C₂²⋊C₄	—	2	1	no	—
384	C₁₃×C₂²⋊C₄	—	2	1	no	—
385	C₁₃×C₂²⋊C₄	—	2	2	no	—
386	C₁₃×C₂²⋊C₄	—	2	2	no	—
387	C₁₃×C₂²⋊C₄	—	2	1	no	—
388	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
389	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
390	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
391	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
392	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
393	C₄²×C₁₃	—	2	2	no	—
394	C₄²×C₁₃	—	2	2	no	—
395	C₄²×C₁₃	—	2	1	no	—
396	C₄²×C₁₃	—	2	2	no	—
397	C₄²×C₁₃	—	2	2	no	—
398	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
401	C₄²×C₁₃	C₂⁴	1	2	yes	—
402	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
403	#3561	C₂×C₁₃	1	1	yes	characteristic, complemented
404	#3544	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#3376	C₂×C₁₃	1	2	yes	complemented
406	#3369	C₂×C₁₃	1	2	yes	complemented
407	#3321	C₂×C₁₃	1	2	yes	complemented
408	#3316	C₂×C₁₃	1	2	yes	complemented
409	#3312	C₂×C₁₃	1	2	yes	complemented
410	#3306	C₂×C₁₃	1	2	yes	complemented
411	#3298	C₂×C₁₃	1	2	yes	complemented
412	#3296	C₂×C₁₃	1	2	yes	complemented
413	#3244	C₂×C₁₃	1	2	yes	complemented
414	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
415	#3225	C₂×C₁₃	1	2	yes	complemented
416	#3211	C₂×C₁₃	1	1	yes	characteristic, complemented
417	#3181	C₂×C₁₃	1	1	yes	characteristic, complemented
418	#3173	C₂×C₁₃	1	2	yes	complemented
419	#3137	C₂×C₁₃	1	2	yes	complemented
420	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
421	#2968	C₂×C₁₃	1	1	yes	characteristic, complemented
422	C₂³×C₁₃	—	2	1	no	—
423	C₂³×C₁₃	—	2	2	no	—
424	C₂³×C₁₃	—	4	2	no	—
425	C₂³×C₁₃	—	8	1	no	—
426	C₂³×C₁₃	—	8	1	no	—
427	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
428	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	Q₈×C₁₃	—	2	2	no	—
430	Q₈×C₁₃	—	2	2	no	—
431	Q₈×C₁₃	—	2	2	no	—
432	Q₈×C₁₃	—	2	2	no	—
433	Q₈×C₁₃	—	2	2	no	—
434	Q₈×C₁₃	—	4	1	no	—
435	Q₈×C₁₃	—	8	1	no	—
436	Q₈×C₁₃	—	8	2	no	—
437	Q₈×C₁₃	—	8	1	no	—
438	Q₈×C₁₃	—	8	1	no	—
439	Q₈×C₁₃	—	8	2	no	—
440	Q₈×C₁₃	—	8	1	no	—
441	Q₈×C₁₃	—	8	2	no	—
442	D₄×C₁₃	—	2	4	no	—
443	D₄×C₁₃	—	2	2	no	—
444	D₄×C₁₃	—	2	2	no	—
445	D₄×C₁₃	—	2	2	no	—
446	D₄×C₁₃	—	4	1	no	—
447	D₄×C₁₃	—	4	2	no	—
448	D₄×C₁₃	—	8	1	no	—
449	D₄×C₁₃	—	8	2	no	—
450	D₄×C₁₃	—	8	2	no	—
451	D₄×C₁₃	—	8	2	no	—
452	C₂×C₄×C₁₃	—	2	2	no	—
453	C₂×C₄×C₁₃	—	2	2	no	—
454	C₂×C₄×C₁₃	—	2	2	no	—
455	C₂×C₄×C₁₃	—	2	2	no	—
456	C₂×C₄×C₁₃	—	2	1	no	—
457	C₂×C₄×C₁₃	—	2	1	no	—
458	C₂×C₄×C₁₃	—	2	2	no	—
459	C₂×C₄×C₁₃	—	2	2	no	—
460	C₂×C₄×C₁₃	—	2	2	no	—
461	C₂×C₄×C₁₃	—	2	2	no	—
462	C₂×C₄×C₁₃	—	2	1	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	4	1	no	—
465	C₂×C₄×C₁₃	—	4	2	no	—
466	C₂×C₄×C₁₃	—	4	4	no	—
467	C₂×C₄×C₁₃	—	8	2	no	—
468	C₂×C₄×C₁₃	—	8	2	no	—
469	C₂×C₄×C₁₃	—	8	2	no	—
470	C₂×C₄×C₁₃	—	8	2	no	—
471	C₂×C₄×C₁₃	—	8	1	no	—
472	C₂×C₄×C₁₃	—	8	2	no	—
473	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
482	C₈×C₁₃	—	2	2	no	—
483	C₈×C₁₃	—	2	2	no	—
484	C₈×C₁₃	—	2	2	no	—
485	C₈×C₁₃	—	2	2	no	—
486	#563	—	2	2	no	—
487	#563	—	2	1	no	—
488	#562	—	2	1	no	—
489	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#556	C₂²×C₁₃	1	2	yes	—
491	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	#552	—	2	1	no	—
495	#552	C₂²×C₁₃	1	2	yes	—
496	#551	—	2	2	no	—
497	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
498	#548	C₂²×C₁₃	1	2	yes	—
499	#547	—	2	1	no	—
500	#547	C₂²×C₁₃	1	2	yes	—
501	#546	C₂²×C₁₃	1	2	yes	—
502	#544	—	2	1	no	—
503	#544	C₂²×C₁₃	1	2	yes	complemented
504	#543	—	2	1	no	—
505	#542	—	2	2	no	—
506	#542	—	2	1	no	—
507	#542	C₂²×C₁₃	1	2	yes	—
508	#542	C₂²×C₁₃	1	2	yes	complemented
509	#538	—	2	1	no	—
510	#536	—	2	2	no	—
511	#536	C₂²×C₁₃	1	2	yes	—
512	#533	C₂²×C₁₃	1	1	yes	characteristic
513	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
514	#529	C₂²×C₁₃	1	1	yes	characteristic
515	#529	C₂²×C₁₃	1	1	yes	characteristic
516	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
517	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
518	#498	C₂²×C₁₃	1	2	yes	complemented
519	#497	C₂²×C₁₃	1	1	yes	characteristic, complemented
520	#495	C₂²×C₁₃	1	2	yes	—
521	#491	C₂²×C₁₃	1	2	yes	complemented
522	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
523	#489	C₂²×C₁₃	1	2	yes	—
524	#489	C₂²×C₁₃	1	2	yes	—
525	#489	C₂²×C₁₃	1	2	yes	—
526	#489	C₂²×C₁₃	1	2	yes	—
527	#489	C₂²×C₁₃	1	2	yes	—
528	#489	C₂²×C₁₃	1	1	yes	characteristic, complemented
529	#488	C₂²×C₁₃	1	2	yes	—
530	#488	C₂²×C₁₃	1	2	yes	—
531	#487	C₂²×C₁₃	1	2	yes	complemented
532	#487	C₂²×C₁₃	1	2	yes	complemented
533	#485	C₂²×C₁₃	1	2	yes	complemented
534	#483	C₂²×C₁₃	1	2	yes	—
535	#483	C₂²×C₁₃	1	2	yes	—
536	#483	C₂²×C₁₃	1	2	yes	complemented
537	#482	C₂²×C₁₃	1	2	yes	—
538	#481	C₂²×C₁₃	1	2	yes	—
539	#479	C₂²×C₁₃	1	2	yes	complemented
540	#478	C₂²×C₁₃	1	2	yes	—
541	#476	C₂²×C₁₃	1	2	yes	—
542	#475	C₂²×C₁₃	1	2	yes	complemented
543	#475	C₂²×C₁₃	1	2	yes	complemented
544	#475	C₂²×C₁₃	1	2	yes	complemented
545	#470	C₂²×C₁₃	1	2	yes	complemented
546	#469	C₂²×C₁₃	1	2	yes	—
547	#467	C₂²×C₁₃	1	2	yes	—
548	#465	C₂²×C₁₃	1	2	yes	—
549	#465	C₂²×C₁₃	1	2	yes	—
550	#465	C₂²×C₁₃	1	2	yes	complemented
551	#464	C₂²×C₁₃	1	2	yes	—
552	#464	C₂²×C₁₃	1	2	yes	—
553	#463	C₂²×C₁₃	1	2	yes	—
554	#463	C₂²×C₁₃	1	2	yes	—
555	#462	C₂²×C₁₃	1	2	yes	complemented
556	#461	C₂²×C₁₃	1	2	yes	complemented
557	#452	C₂²×C₁₃	1	2	yes	—
558	#451	C₂²×C₁₃	1	1	yes	characteristic
559	#451	C₂²×C₁₃	1	2	yes	complemented
560	#450	C₂²×C₁₃	1	1	yes	characteristic
561	#449	C₂²×C₁₃	1	2	yes	—
562	#448	C₂²×C₁₃	1	1	yes	characteristic
563	#448	C₂²×C₁₃	1	2	yes	complemented
564	#447	C₂²×C₁₃	1	1	yes	characteristic
565	#446	C₂²×C₁₃	1	2	yes	complemented
566	#442	C₂²×C₁₃	1	2	yes	—
567	#441	C₂²×C₁₃	1	2	yes	complemented
568	#441	C₂²×C₁₃	1	2	yes	complemented
569	#440	C₂²×C₁₃	1	2	yes	complemented
570	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
571	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
572	#435	C₂²×C₁₃	1	2	yes	—
573	#435	C₂²×C₁₃	1	2	yes	complemented
574	C₈×D₄	C₂²×C₁₃	1	2	yes	—
575	#433	C₂²×C₁₃	1	2	yes	complemented
576	#431	C₂²×C₁₃	1	1	yes	characteristic
577	#419	C₂²×C₁₃	1	2	yes	complemented
578	#417	C₂²×C₁₃	1	2	yes	—
579	#416	C₂²×C₁₃	1	2	yes	—
580	C₂×#103	C₂²×C₁₃	1	2	yes	—
581	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
582	C₂×#102	C₂²×C₁₃	1	2	yes	—
583	#405	C₂²×C₁₃	1	2	yes	complemented
584	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
585	C₂²×C₁₃	—	2	1	no	—
586	C₂²×C₁₃	—	2	1	no	—
587	C₂²×C₁₃	—	2	2	no	—
588	C₂²×C₁₃	—	2	2	no	—
589	C₂²×C₁₃	—	2	2	no	—
590	C₂²×C₁₃	—	4	1	no	—
591	C₂²×C₁₃	—	4	2	no	—
592	C₂²×C₁₃	—	4	2	no	—
593	C₂²×C₁₃	—	4	1	no	—
594	C₂²×C₁₃	—	4	1	no	—
595	C₂²×C₁₃	—	4	2	no	—
596	C₂²×C₁₃	—	16	2	no	—
597	C₂²×C₁₃	#577	1	2	yes	—
598	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
599	C₄×C₁₃	—	2	1	no	—
600	C₄×C₁₃	—	2	1	no	—
601	C₄×C₁₃	—	2	2	no	—
602	C₄×C₁₃	—	2	2	no	—
603	C₄×C₁₃	—	2	1	no	—
604	C₄×C₁₃	—	2	1	no	—
605	C₄×C₁₃	—	2	1	no	—
606	C₄×C₁₃	—	2	2	no	—
607	C₄×C₁₃	—	4	1	no	—
608	C₄×C₁₃	—	4	2	no	—
609	C₄×C₁₃	—	4	2	no	—
610	C₄×C₁₃	—	4	2	no	—
611	C₄×C₁₃	—	4	1	no	—
612	C₄×C₁₃	—	4	2	no	—
613	C₄×C₁₃	—	4	2	no	—
614	C₄×C₁₃	—	4	1	no	—
615	C₄×C₁₃	#585	1	2	yes	—
616	C₂×#41	—	2	2	no	—
617	C₂×#41	C₂³×C₁₃	1	2	yes	—
618	C₂²×Q₈	—	2	1	no	—
619	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
620	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
621	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
623	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
624	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
625	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
626	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
627	C₂×D₈	C₂³×C₁₃	1	2	yes	—
628	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
629	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
630	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
631	C₄⋊Q₈	—	2	2	no	—
632	C₄⋊Q₈	—	2	2	no	—
633	C₄⋊Q₈	—	2	2	no	—
634	C₄⋊Q₈	—	2	1	no	—
635	C₄⋊Q₈	—	2	1	no	—
636	C₄⋊Q₈	—	2	1	no	—
637	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
638	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
639	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
640	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
641	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
642	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
644	#126	—	2	2	no	—
645	#126	—	2	2	no	—
646	#126	—	2	2	no	—
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#126	—	2	1	no	—
650	#126	D₄×C₁₃	1	2	yes	—
651	#125	—	2	1	no	—
652	#125	—	2	2	no	—
653	#125	—	2	2	no	—
654	#125	—	2	1	no	—
655	#125	D₄×C₁₃	1	1	yes	characteristic
656	#125	C₂³×C₁₃	1	1	yes	characteristic
657	#125	C₂³×C₁₃	1	2	yes	—
658	#124	—	2	2	no	—
659	#124	—	2	2	no	—
660	#124	—	2	2	no	—
661	#124	—	2	2	no	—
662	#124	—	2	1	no	—
663	#124	—	2	1	no	—
664	#124	D₄×C₁₃	1	1	yes	characteristic
665	#124	C₂³×C₁₃	1	2	yes	—
666	#124	C₂³×C₁₃	1	2	yes	—
667	#124	C₂³×C₁₃	1	1	yes	characteristic
668	#124	C₂³×C₁₃	1	2	yes	—
669	#123	—	2	2	no	—
670	#123	—	2	1	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	D₄×C₁₃	1	2	yes	—
679	C₂²⋊Q₈	—	2	1	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	1	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
695	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
696	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
697	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
698	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
699	#121	—	2	2	no	—
700	#121	—	2	1	no	—
701	#121	—	2	2	no	—
702	#121	D₄×C₁₃	1	1	yes	characteristic
703	#121	C₂³×C₁₃	1	1	yes	characteristic
704	#121	C₂³×C₁₃	1	2	yes	—
705	#121	C₂³×C₁₃	1	2	yes	—
706	#120	—	2	2	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
710	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
711	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
712	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
713	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
714	C₄×D₄	—	2	2	no	—
715	C₄×D₄	—	2	1	no	—
716	C₄×D₄	—	2	1	no	—
717	C₄×D₄	—	2	2	no	—
718	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
719	C₄×D₄	C₂³×C₁₃	1	2	yes	—
720	C₄×D₄	C₂³×C₁₃	1	2	yes	—
721	C₄×D₄	C₂³×C₁₃	1	2	yes	—
722	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
723	#117	—	2	1	no	—
724	#117	—	2	2	no	—
725	#117	—	2	1	no	—
726	#117	—	2	2	no	—
727	#117	—	2	1	no	—
728	#117	C₂³×C₁₃	1	2	yes	—
729	#117	C₂³×C₁₃	1	2	yes	—
730	C₂×C₄⋊C₄	—	2	1	no	—
731	C₂×C₄⋊C₄	—	2	1	no	—
732	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
734	C₂×C₂²⋊C₄	—	2	1	no	—
735	C₂×C₂²⋊C₄	—	2	1	no	—
736	C₂×C₂²⋊C₄	—	2	2	no	—
737	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
738	#107	C₂³×C₁₃	1	2	yes	—
739	#106	C₂³×C₁₃	1	2	yes	—
740	#106	C₂³×C₁₃	1	2	yes	—
741	#106	C₂³×C₁₃	1	2	yes	—
742	#106	C₂³×C₁₃	1	2	yes	—
743	#106	C₂³×C₁₃	1	2	yes	—
744	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
745	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
746	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
747	#103	C₂³×C₁₃	1	2	yes	—
748	#103	C₂³×C₁₃	1	2	yes	—
749	#103	C₂³×C₁₃	1	2	yes	—
750	#103	C₂³×C₁₃	1	2	yes	—
751	#103	C₂³×C₁₃	1	2	yes	—
752	#103	C₂³×C₁₃	1	2	yes	—
753	#103	C₂³×C₁₃	1	2	yes	—
754	#103	C₂³×C₁₃	1	2	yes	—
755	#103	C₂³×C₁₃	1	2	yes	—
756	#103	C₂³×C₁₃	1	2	yes	—
757	#103	C₂³×C₁₃	1	2	yes	—
758	#103	C₂³×C₁₃	1	2	yes	—
759	#103	C₂³×C₁₃	1	2	yes	—
760	#102	C₂³×C₁₃	1	2	yes	—
761	#102	C₂³×C₁₃	1	2	yes	—
762	#102	C₂³×C₁₃	1	2	yes	—
763	#102	C₂³×C₁₃	1	2	yes	—
764	#102	C₂³×C₁₃	1	2	yes	—
765	#102	C₂³×C₁₃	1	2	yes	—
766	#102	C₂³×C₁₃	1	2	yes	—
767	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
768	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
769	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
771	#97	C₂³×C₁₃	1	1	yes	characteristic
772	#97	C₂³×C₁₃	1	1	yes	characteristic
773	#97	C₂³×C₁₃	1	2	yes	—
774	#97	C₂³×C₁₃	1	2	yes	—
775	C₄×C₈	C₂³×C₁₃	1	2	yes	—
776	C₄×C₈	C₂³×C₁₃	1	2	yes	—
777	C₂×C₁₃	—	2	2	no	—
778	C₂×C₁₃	—	4	2	no	—
779	C₂×C₁₃	—	8	1	no	—
780	C₂×C₁₃	—	8	2	no	—
781	C₂×C₁₃	#3500	1	1	yes	characteristic
782	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
783	C₂×C₁₃	#3586	1	1	yes	characteristic
784	C₂⁴	—	2	1	no	—
785	#41	—	4	2	no	—
786	#41	—	4	2	no	—
787	#41	—	8	4	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	4	2	no	—
796	C₂×Q₈	—	4	2	no	—
797	C₂×Q₈	—	4	2	no	—
798	C₂×Q₈	—	8	2	no	—
799	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
800	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
801	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
802	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	1	no	—
808	C₂×D₄	—	4	2	no	—
809	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
810	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
811	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
812	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
822	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
825	Q₁₆	—	4	2	no	—
826	Q₁₆	—	4	2	no	—
827	SD₁₆	—	4	2	no	—
828	SD₁₆	—	4	2	no	—
829	SD₁₆	—	4	2	no	—
830	D₈	—	4	2	no	—
831	M₁₆	—	4	2	no	—
832	C₂×C₈	—	4	2	no	—
833	C₂×C₈	—	4	2	no	—
834	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
835	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
836	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
837	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
838	C₄⋊C₄	—	2	1	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	1	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
862	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
863	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
864	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
867	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
869	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
870	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	1	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	1	no	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
892	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
893	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
894	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	1	no	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	2	no	—
901	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
902	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
903	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
904	C₄²	C₂⁴×C₁₃	1	2	yes	—
905	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
906	C₁₃	#62603	1	1	yes	characteristic, direct product factor, Sylow
907	C₂³	—	2	1	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	4	2	no	—
910	C₂³	—	8	1	no	—
911	C₂³	—	8	1	no	—
912	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
913	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
914	Q₈	—	2	2	no	—
915	Q₈	—	2	2	no	—
916	Q₈	—	2	2	no	—
917	Q₈	—	2	2	no	—
918	Q₈	—	2	2	no	—
919	Q₈	—	4	1	no	—
920	Q₈	—	8	2	no	—
921	Q₈	—	8	1	no	—
922	Q₈	—	8	1	no	—
923	Q₈	—	8	2	no	—
924	Q₈	—	8	1	no	—
925	Q₈	—	8	2	no	—
926	Q₈	—	8	1	no	—
927	D₄	—	2	4	no	—
928	D₄	—	2	2	no	—
929	D₄	—	2	2	no	—
930	D₄	—	2	2	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	2	no	—
933	D₄	—	8	1	no	—
934	D₄	—	8	2	no	—
935	D₄	—	8	2	no	—
936	D₄	—	8	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	4	1	no	—
950	C₂×C₄	—	4	2	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	—	8	2	no	—
955	C₂×C₄	—	8	2	no	—
956	C₂×C₄	—	8	1	no	—
957	C₂×C₄	—	8	2	no	—
958	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
961	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
962	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
963	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
966	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
967	C₈	—	2	2	no	—
968	C₈	—	2	2	no	—
969	C₈	—	2	2	no	—
970	C₈	—	2	2	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	4	1	no	—
982	C₂²	—	16	2	no	—
983	C₂²	C₁₃×#577	1	2	yes	—
984	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	2	no	—
991	C₄	—	2	2	no	—
992	C₄	—	2	1	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	2	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	1	no	—
1001	C₄	C₁₃×#585	1	2	yes	—
1002	C₂	—	2	2	no	—
1003	C₂	—	4	2	no	—
1004	C₂	—	8	2	no	—
1005	C₂	—	8	1	no	—
1006	C₂	C₁₃×#3500	1	1	yes	characteristic
1007	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1008	C₂	C₁₃×#3586	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3561	C₂	semidirect
2. C₁₃×#3544	C₂	semidirect
3. C₁₃×#3376	C₂	semidirect
4. C₁₃×#3369	C₂	semidirect
5. C₁₃×#3321	C₂	semidirect
6. C₁₃×#3316	C₂	semidirect
7. C₁₃×#3312	C₂	semidirect
8. C₁₃×#3306	C₂	semidirect
9. C₁₃×#3298	C₂	semidirect
10. C₁₃×#3296	C₂	semidirect
11. C₁₃×#3244	C₂	semidirect
12. C₁₃×#3229	C₂	semidirect
13. C₁₃×#3225	C₂	semidirect
14. C₁₃×#3211	C₂	semidirect
15. C₁₃×#3181	C₂	semidirect
16. C₁₃×#3173	C₂	semidirect
17. C₁₃×#3137	C₂	semidirect
18. C₂×C₁₃×#489	C₂	semidirect
19. C₁₃×#2968	C₂	semidirect
23. Q₈²×C₁₃	C₂²	semidirect
25. C₁₃×#555	C₂²	semidirect
26. C₁₃×#554	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
37. C₁₃×#544	C₂²	semidirect
42. C₁₃×#542	C₂²	semidirect
51. C₁₃×#501	C₂²	semidirect
52. C₁₃×#498	C₂²	semidirect
53. C₁₃×#497	C₂²	semidirect
55. C₁₃×#491	C₂²	semidirect
56. C₁₃×#491	C₂²	semidirect
62. C₁₃×#489	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#487	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
70. C₁₃×#483	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
76. C₁₃×#475	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
78. C₁₃×#475	C₂²	semidirect
79. C₁₃×#470	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
89. C₁₃×#462	C₂²	semidirect
90. C₁₃×#461	C₂²	semidirect
93. C₁₃×#451	C₂²	semidirect
97. C₁₃×#448	C₂²	semidirect
99. C₁₃×#446	C₂²	semidirect
101. C₁₃×#441	C₂²	semidirect
102. C₁₃×#441	C₂²	semidirect
103. C₁₃×#440	C₂²	semidirect
105. C₄×C₁₃×SD₁₆	C₂²	semidirect
107. C₁₃×#435	C₂²	semidirect
109. C₁₃×#433	C₂²	semidirect
111. C₁₃×#419	C₂²	semidirect
115. C₂×C₁₃×#103	C₂²	semidirect
117. C₁₃×#405	C₂²	semidirect
280. #62603	C₁₃	direct (N × H)
403. #3561	C₂×C₁₃	semidirect
404. #3544	C₂×C₁₃	semidirect
405. #3376	C₂×C₁₃	semidirect
406. #3369	C₂×C₁₃	semidirect
407. #3321	C₂×C₁₃	semidirect
408. #3316	C₂×C₁₃	semidirect
409. #3312	C₂×C₁₃	semidirect
410. #3306	C₂×C₁₃	semidirect
411. #3298	C₂×C₁₃	semidirect
412. #3296	C₂×C₁₃	semidirect
413. #3244	C₂×C₁₃	semidirect
414. #3229	C₂×C₁₃	semidirect
415. #3225	C₂×C₁₃	semidirect
416. #3211	C₂×C₁₃	semidirect
417. #3181	C₂×C₁₃	semidirect
418. #3173	C₂×C₁₃	semidirect
419. #3137	C₂×C₁₃	semidirect
420. C₂×#489	C₂×C₁₃	semidirect
421. #2968	C₂×C₁₃	semidirect
489. Q₈²	C₂²×C₁₃	semidirect
491. #555	C₂²×C₁₃	semidirect
492. #554	C₂²×C₁₃	semidirect
493. #554	C₂²×C₁₃	semidirect
503. #544	C₂²×C₁₃	semidirect
508. #542	C₂²×C₁₃	semidirect
517. #501	C₂²×C₁₃	semidirect
518. #498	C₂²×C₁₃	semidirect
519. #497	C₂²×C₁₃	semidirect
521. #491	C₂²×C₁₃	semidirect
522. #491	C₂²×C₁₃	semidirect
528. #489	C₂²×C₁₃	semidirect
531. #487	C₂²×C₁₃	semidirect
532. #487	C₂²×C₁₃	semidirect
533. #485	C₂²×C₁₃	semidirect
536. #483	C₂²×C₁₃	semidirect
539. #479	C₂²×C₁₃	semidirect
542. #475	C₂²×C₁₃	semidirect
543. #475	C₂²×C₁₃	semidirect
544. #475	C₂²×C₁₃	semidirect
545. #470	C₂²×C₁₃	semidirect
550. #465	C₂²×C₁₃	semidirect
555. #462	C₂²×C₁₃	semidirect
556. #461	C₂²×C₁₃	semidirect
559. #451	C₂²×C₁₃	semidirect
563. #448	C₂²×C₁₃	semidirect
565. #446	C₂²×C₁₃	semidirect
567. #441	C₂²×C₁₃	semidirect
568. #441	C₂²×C₁₃	semidirect
569. #440	C₂²×C₁₃	semidirect
571. C₄×SD₁₆	C₂²×C₁₃	semidirect
573. #435	C₂²×C₁₃	semidirect
575. #433	C₂²×C₁₃	semidirect
577. #419	C₂²×C₁₃	semidirect
581. C₂×#103	C₂²×C₁₃	semidirect
583. #405	C₂²×C₁₃	semidirect
906. C₁₃	#62603	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×#3561	2
C₁₃×#3544	2
C₁₃×#3376	2
C₁₃×#3369	2
C₁₃×#3321	2
C₁₃×#3316	2
C₁₃×#3312	2
C₁₃×#3306	2
C₁₃×#3298	2
C₁₃×#3296	2
C₁₃×#3244	2
C₁₃×#3229	2
C₁₃×#3225	2
C₁₃×#3211	2
C₁₃×#3181	2
C₁₃×#3173	2
C₁₃×#3137	2
C₂×C₁₃×#489	2
C₁₃×#2968	2
#62603	13

Subgroups — C13×#62603 #15748942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62603 #15748942