Subgroups — C₁₃×#62592 #15748931

Order 3328.

1790 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3329	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3326	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3325	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3322	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3171	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3171	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3140	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	C₂²	1	1	yes	characteristic
19	C₁₃×#556	—	2	1	no	—
20	C₁₃×#556	C₂²	1	1	yes	characteristic
21	C₁₃×#555	—	2	1	no	—
22	C₁₃×#555	C₂²	1	2	yes	—
23	C₁₃×#554	C₂²	1	2	yes	complemented
24	C₁₃×#553	C₂²	1	4	yes	complemented
25	C₁₃×#551	—	2	2	no	—
26	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#548	—	2	2	no	—
28	C₁₃×#548	C₂²	1	2	yes	—
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#546	—	2	1	no	—
31	C₁₃×#546	C₂²	1	2	yes	—
32	D₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#542	—	2	1	no	—
34	C₁₃×#542	—	2	2	no	—
35	C₁₃×#538	—	2	2	no	—
36	C₁₃×#537	—	2	1	no	—
37	C₁₃×#533	C₂²	1	2	yes	complemented
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	2	yes	complemented
40	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#529	C₂²	1	1	yes	characteristic
43	C₁₃×#529	C₂²	1	2	yes	—
44	C₂×C₁₃×#124	C₂²	1	2	yes	—
45	C₁₃×#520	—	2	1	no	—
46	C₁₃×#518	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	2	yes	complemented
49	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#496	C₂²	1	1	yes	characteristic
51	C₁₃×#496	C₂²	1	2	yes	complemented
52	C₁₃×#490	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#489	C₂²	1	1	yes	characteristic
54	C₁₃×#489	C₂²	1	2	yes	—
55	C₁₃×#489	C₂²	1	2	yes	complemented
56	C₁₃×#489	C₂²	1	2	yes	complemented
57	C₁₃×#489	C₂²	1	2	yes	complemented
58	C₁₃×#488	C₂²	1	4	yes	—
59	C₁₃×#488	C₂²	1	4	yes	complemented
60	C₁₃×#487	C₂²	1	2	yes	complemented
61	C₁₃×#486	C₂²	1	2	yes	—
62	C₁₃×#485	C₂²	1	4	yes	complemented
63	C₁₃×#483	C₂²	1	2	yes	complemented
64	C₁₃×#482	C₂²	1	4	yes	—
65	C₁₃×#480	C₂²	1	2	yes	—
66	C₁₃×#479	C₂²	1	4	yes	complemented
67	C₁₃×#478	C₂²	1	4	yes	complemented
68	C₁₃×#477	C₂²	1	2	yes	complemented
69	C₁₃×#476	C₂²	1	2	yes	—
70	C₁₃×#469	C₂²	1	2	yes	—
71	C₁₃×#469	C₂²	1	4	yes	—
72	C₁₃×#468	C₂²	1	4	yes	complemented
73	C₁₃×#468	C₂²	1	2	yes	complemented
74	C₁₃×#463	C₂²	1	4	yes	—
75	C₁₃×#463	C₂²	1	4	yes	complemented
76	C₁₃×#461	C₂²	1	2	yes	complemented
77	C₁₃×#459	C₂²	1	2	yes	—
78	C₁₃×#449	C₂²	1	4	yes	complemented
79	C₁₃×#448	C₂²	1	4	yes	complemented
80	C₁₃×#447	C₂²	1	4	yes	—
81	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
82	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
84	C₄×C₁₃×D₈	C₂²	1	2	yes	—
85	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
86	C₁₃×#436	C₂²	1	2	yes	—
87	C₁₃×#436	C₂²	1	4	yes	complemented
88	C₁₃×#432	C₂²	1	2	yes	complemented
89	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#419	C₂²	1	4	yes	complemented
91	C₁₃×#418	C₂²	1	4	yes	—
92	C₁₃×#417	C₂²	1	4	yes	complemented
93	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
94	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
98	C₂×C₁₃×#41	C₂³	1	2	yes	—
99	C₂²×Q₈×C₁₃	—	2	1	no	—
100	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×D₈	C₂³	1	2	yes	—
106	C₂×C₁₃×D₈	C₂³	1	4	yes	—
107	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	—	2	1	no	—
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×#127	C₂³	1	1	yes	characteristic
117	C₁₃×#127	C₂³	1	1	yes	characteristic
118	C₁₃×#126	—	2	2	no	—
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#126	—	2	2	no	—
121	C₁₃×#126	—	2	1	no	—
122	C₁₃×#125	C₂³	1	4	yes	—
123	C₁₃×#125	C₂³	1	1	yes	characteristic
124	C₁₃×#124	—	2	1	no	—
125	C₁₃×#124	—	2	2	no	—
126	C₁₃×#124	—	2	4	no	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	1	no	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	C₂³	1	2	yes	—
132	C₁₃×#124	C₂³	1	2	yes	—
133	C₁₃×#124	C₂³	1	1	yes	characteristic
134	C₁₃×#124	C₂³	1	2	yes	—
135	C₁₃×#123	—	2	1	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	4	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	4	no	—
151	C₁₃×#121	—	2	2	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	C₂³	1	4	yes	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#121	C₂³	1	1	yes	characteristic
161	C₁₃×#121	C₂³	1	2	yes	—
162	C₁₃×#120	—	2	2	no	—
163	C₁₃×#120	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	—	2	2	no	—
166	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	4	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
181	C₄×D₄×C₁₃	D₄	1	2	yes	—
182	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	4	yes	—
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₁₃×#117	—	2	1	no	—
189	C₁₃×#117	—	2	2	no	—
190	C₁₃×#117	—	2	1	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	D₄	1	1	yes	characteristic
193	C₁₃×#117	D₄	1	2	yes	—
194	C₁₃×#117	C₂³	1	4	yes	—
195	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₁₃×#107	C₂³	1	2	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#106	C₂³	1	4	yes	—
206	C₁₃×#106	C₂³	1	2	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×#103	C₂³	1	4	yes	—
210	C₁₃×#103	C₂³	1	4	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#102	C₂³	1	4	yes	—
215	C₁₃×#102	C₂³	1	4	yes	—
216	C₁₃×#102	C₂³	1	2	yes	—
217	C₁₃×#102	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	2	yes	—
220	C₁₃×#102	C₂³	1	2	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
222	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₁₃×#97	C₂³	1	1	yes	characteristic
224	C₁₃×#97	C₂³	1	2	yes	—
225	C₁₃×#97	C₂³	1	1	yes	characteristic
226	C₄×C₈×C₁₃	C₂³	1	2	yes	—
227	C₄×C₈×C₁₃	C₂³	1	4	yes	—
228	#62592	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	2	no	—
230	C₁₃×#41	—	4	2	no	—
231	C₁₃×#41	—	4	4	no	—
232	C₁₃×#41	—	4	4	no	—
233	C₁₃×#41	—	8	4	no	—
234	C₂×Q₈×C₁₃	—	2	1	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	4	4	no	—
239	C₂×Q₈×C₁₃	—	8	2	no	—
240	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	4	4	no	—
254	C₂×D₄×C₁₃	—	4	4	no	—
255	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	4	no	—
267	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₁₃×SD₁₆	—	4	2	no	—
274	C₁₃×SD₁₆	—	4	4	no	—
275	C₁₃×D₈	—	4	4	no	—
276	C₁₃×D₈	—	4	2	no	—
277	C₁₃×M₁₆	—	4	4	no	—
278	C₁₃×M₁₆	—	4	2	no	—
279	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
280	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
281	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	4	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
297	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₁₃×C₂²⋊C₄	—	2	4	no	—
306	C₁₃×C₂²⋊C₄	—	2	1	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	1	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	1	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
324	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
325	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	4	no	—
328	C₄²×C₁₃	—	2	1	no	—
329	C₄²×C₁₃	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂×D₄	1	2	yes	—
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
336	#3514	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3361	C₂×C₁₃	1	2	yes	complemented
339	#3360	C₂×C₁₃	1	2	yes	complemented
340	#3329	C₂×C₁₃	1	2	yes	complemented
341	#3326	C₂×C₁₃	1	4	yes	complemented
342	#3325	C₂×C₁₃	1	2	yes	complemented
343	#3322	C₂×C₁₃	1	4	yes	complemented
344	#3240	C₂×C₁₃	1	2	yes	complemented
345	#3238	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3214	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3213	C₂×C₁₃	1	2	yes	complemented
348	#3171	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3171	C₂×C₁₃	1	2	yes	complemented
350	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3140	C₂×C₁₃	1	2	yes	complemented
352	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₂³×C₁₃	—	2	1	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	4	4	no	—
357	C₂³×C₁₃	—	8	2	no	—
358	C₂³×C₁₃	—	8	2	no	—
359	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
360	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	4	no	—
364	Q₈×C₁₃	—	4	4	no	—
365	Q₈×C₁₃	—	4	2	no	—
366	Q₈×C₁₃	—	8	2	no	—
367	Q₈×C₁₃	—	8	2	no	—
368	D₄×C₁₃	—	2	2	no	—
369	D₄×C₁₃	—	2	2	no	—
370	D₄×C₁₃	—	2	2	no	—
371	D₄×C₁₃	—	2	2	no	—
372	D₄×C₁₃	—	2	4	no	—
373	D₄×C₁₃	—	4	2	no	—
374	D₄×C₁₃	—	4	2	no	—
375	D₄×C₁₃	—	4	2	no	—
376	D₄×C₁₃	—	4	4	no	—
377	D₄×C₁₃	—	4	4	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	8	1	no	—
380	D₄×C₁₃	—	8	2	no	—
381	D₄×C₁₃	—	8	1	no	—
382	D₄×C₁₃	—	8	2	no	—
383	D₄×C₁₃	—	8	4	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	4	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	4	no	—
393	C₂×C₄×C₁₃	—	4	1	no	—
394	C₂×C₄×C₁₃	—	4	2	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	—	4	2	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	8	2	no	—
399	C₂×C₄×C₁₃	—	8	2	no	—
400	C₂×C₄×C₁₃	—	8	4	no	—
401	C₂×C₄×C₁₃	—	8	2	no	—
402	C₂×C₄×C₁₃	—	8	2	no	—
403	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
412	C₈×C₁₃	—	2	2	no	—
413	C₈×C₁₃	—	2	2	no	—
414	C₈×C₁₃	—	2	4	no	—
415	#559	C₂²×C₁₃	1	1	yes	characteristic
416	#556	—	2	1	no	—
417	#556	C₂²×C₁₃	1	1	yes	characteristic
418	#555	—	2	1	no	—
419	#555	C₂²×C₁₃	1	2	yes	—
420	#554	C₂²×C₁₃	1	2	yes	complemented
421	#553	C₂²×C₁₃	1	4	yes	complemented
422	#551	—	2	2	no	—
423	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
424	#548	—	2	2	no	—
425	#548	C₂²×C₁₃	1	2	yes	—
426	#547	—	2	1	no	—
427	#546	—	2	1	no	—
428	#546	C₂²×C₁₃	1	2	yes	—
429	D₄²	C₂²×C₁₃	1	1	yes	characteristic
430	#542	—	2	1	no	—
431	#542	—	2	2	no	—
432	#538	—	2	2	no	—
433	#537	—	2	1	no	—
434	#533	C₂²×C₁₃	1	2	yes	complemented
435	#532	C₂²×C₁₃	1	1	yes	characteristic
436	#532	C₂²×C₁₃	1	2	yes	complemented
437	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#529	C₂²×C₁₃	1	1	yes	characteristic
440	#529	C₂²×C₁₃	1	2	yes	—
441	C₂×#124	C₂²×C₁₃	1	2	yes	—
442	#520	—	2	1	no	—
443	#518	—	2	1	no	—
444	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
445	#501	C₂²×C₁₃	1	2	yes	complemented
446	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	#496	C₂²×C₁₃	1	1	yes	characteristic
448	#496	C₂²×C₁₃	1	2	yes	complemented
449	#490	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	#489	C₂²×C₁₃	1	1	yes	characteristic
451	#489	C₂²×C₁₃	1	2	yes	—
452	#489	C₂²×C₁₃	1	2	yes	complemented
453	#489	C₂²×C₁₃	1	2	yes	complemented
454	#489	C₂²×C₁₃	1	2	yes	complemented
455	#488	C₂²×C₁₃	1	4	yes	—
456	#488	C₂²×C₁₃	1	4	yes	complemented
457	#487	C₂²×C₁₃	1	2	yes	complemented
458	#486	C₂²×C₁₃	1	2	yes	—
459	#485	C₂²×C₁₃	1	4	yes	complemented
460	#483	C₂²×C₁₃	1	2	yes	complemented
461	#482	C₂²×C₁₃	1	4	yes	—
462	#480	C₂²×C₁₃	1	2	yes	—
463	#479	C₂²×C₁₃	1	4	yes	complemented
464	#478	C₂²×C₁₃	1	4	yes	complemented
465	#477	C₂²×C₁₃	1	2	yes	complemented
466	#476	C₂²×C₁₃	1	2	yes	—
467	#469	C₂²×C₁₃	1	2	yes	—
468	#469	C₂²×C₁₃	1	4	yes	—
469	#468	C₂²×C₁₃	1	4	yes	complemented
470	#468	C₂²×C₁₃	1	2	yes	complemented
471	#463	C₂²×C₁₃	1	4	yes	—
472	#463	C₂²×C₁₃	1	4	yes	complemented
473	#461	C₂²×C₁₃	1	2	yes	complemented
474	#459	C₂²×C₁₃	1	2	yes	—
475	#449	C₂²×C₁₃	1	4	yes	complemented
476	#448	C₂²×C₁₃	1	4	yes	complemented
477	#447	C₂²×C₁₃	1	4	yes	—
478	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
479	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
480	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
481	C₄×D₈	C₂²×C₁₃	1	2	yes	—
482	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
483	#436	C₂²×C₁₃	1	2	yes	—
484	#436	C₂²×C₁₃	1	4	yes	complemented
485	#432	C₂²×C₁₃	1	2	yes	complemented
486	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	#419	C₂²×C₁₃	1	4	yes	complemented
488	#418	C₂²×C₁₃	1	4	yes	—
489	#417	C₂²×C₁₃	1	4	yes	complemented
490	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
491	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	C₂²×C₁₃	—	2	1	no	—
493	C₂²×C₁₃	—	2	2	no	—
494	C₂²×C₁₃	—	2	2	no	—
495	C₂²×C₁₃	—	2	1	no	—
496	C₂²×C₁₃	—	2	1	no	—
497	C₂²×C₁₃	—	2	2	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	1	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	—	4	1	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	4	1	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	16	4	no	—
508	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	1	no	—
512	C₄×C₁₃	—	2	1	no	—
513	C₄×C₁₃	—	2	2	no	—
514	C₄×C₁₃	—	2	1	no	—
515	C₄×C₁₃	—	2	2	no	—
516	C₄×C₁₃	—	4	1	no	—
517	C₄×C₁₃	—	4	4	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	1	no	—
520	C₄×C₁₃	—	4	1	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	#575	1	2	yes	—
523	C₄×C₁₃	#585	1	2	yes	—
524	C₂×#41	—	2	1	no	—
525	C₂×#41	—	2	2	no	—
526	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
527	C₂×#41	C₂³×C₁₃	1	2	yes	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
533	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
534	C₂×D₈	C₂³×C₁₃	1	2	yes	—
535	C₂×D₈	C₂³×C₁₃	1	4	yes	—
536	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
537	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
543	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
544	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
545	#127	C₂³×C₁₃	1	1	yes	characteristic
546	#127	C₂³×C₁₃	1	1	yes	characteristic
547	#126	—	2	2	no	—
548	#126	—	2	4	no	—
549	#126	—	2	2	no	—
550	#126	—	2	1	no	—
551	#125	C₂³×C₁₃	1	1	yes	characteristic
552	#125	C₂³×C₁₃	1	4	yes	—
553	#124	—	2	1	no	—
554	#124	—	2	2	no	—
555	#124	—	2	4	no	—
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	—	2	1	no	—
559	#124	—	2	2	no	—
560	#124	C₂³×C₁₃	1	1	yes	characteristic
561	#124	C₂³×C₁₃	1	2	yes	—
562	#124	C₂³×C₁₃	1	2	yes	—
563	#124	C₂³×C₁₃	1	2	yes	—
564	#123	—	2	1	no	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	#123	—	2	4	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	4	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
577	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
578	#121	—	2	2	no	—
579	#121	—	2	4	no	—
580	#121	—	2	2	no	—
581	#121	—	2	1	no	—
582	#121	—	2	1	no	—
583	#121	—	2	2	no	—
584	#121	—	2	1	no	—
585	#121	—	2	1	no	—
586	#121	—	2	2	no	—
587	#121	C₂³×C₁₃	1	2	yes	—
588	#121	C₂³×C₁₃	1	1	yes	characteristic
589	#121	C₂³×C₁₃	1	2	yes	—
590	#121	C₂³×C₁₃	1	4	yes	—
591	#120	—	2	2	no	—
592	#120	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
596	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
597	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	4	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
610	C₄×D₄	D₄×C₁₃	1	2	yes	—
611	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₁₃	1	2	yes	—
613	C₄×D₄	C₂³×C₁₃	1	4	yes	—
614	C₄×D₄	C₂³×C₁₃	1	2	yes	—
615	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₁₃	1	2	yes	—
617	#117	—	2	1	no	—
618	#117	—	2	2	no	—
619	#117	—	2	1	no	—
620	#117	—	2	2	no	—
621	#117	D₄×C₁₃	1	1	yes	characteristic
622	#117	D₄×C₁₃	1	2	yes	—
623	#117	C₂³×C₁₃	1	4	yes	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	2	no	—
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
631	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
632	#107	C₂³×C₁₃	1	2	yes	—
633	#107	C₂³×C₁₃	1	4	yes	—
634	#106	C₂³×C₁₃	1	4	yes	—
635	#106	C₂³×C₁₃	1	2	yes	—
636	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
638	#103	C₂³×C₁₃	1	4	yes	—
639	#103	C₂³×C₁₃	1	4	yes	—
640	#103	C₂³×C₁₃	1	2	yes	—
641	#103	C₂³×C₁₃	1	4	yes	—
642	#103	C₂³×C₁₃	1	4	yes	—
643	#102	C₂³×C₁₃	1	4	yes	—
644	#102	C₂³×C₁₃	1	4	yes	—
645	#102	C₂³×C₁₃	1	2	yes	—
646	#102	C₂³×C₁₃	1	4	yes	—
647	#102	C₂³×C₁₃	1	4	yes	—
648	#102	C₂³×C₁₃	1	2	yes	—
649	#102	C₂³×C₁₃	1	2	yes	—
650	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
651	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
652	#97	C₂³×C₁₃	1	1	yes	characteristic
653	#97	C₂³×C₁₃	1	2	yes	—
654	#97	C₂³×C₁₃	1	1	yes	characteristic
655	C₄×C₈	C₂³×C₁₃	1	2	yes	—
656	C₄×C₈	C₂³×C₁₃	1	4	yes	—
657	C₂×C₁₃	—	4	1	no	—
658	C₂×C₁₃	—	4	2	no	—
659	C₂×C₁₃	—	8	2	no	—
660	C₂×C₁₃	—	8	2	no	—
661	C₂×C₁₃	—	8	1	no	—
662	C₂×C₁₃	#3500	1	1	yes	characteristic
663	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
664	C₂×C₁₃	#3585	1	1	yes	characteristic
665	C₂⁴	—	2	2	no	—
666	#41	—	4	2	no	—
667	#41	—	4	4	no	—
668	#41	—	4	4	no	—
669	#41	—	8	4	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	4	4	no	—
675	C₂×Q₈	—	8	2	no	—
676	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	4	4	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
692	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
693	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
695	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
705	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
706	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
709	SD₁₆	—	4	2	no	—
710	SD₁₆	—	4	4	no	—
711	D₈	—	4	4	no	—
712	D₈	—	4	2	no	—
713	M₁₆	—	4	4	no	—
714	M₁₆	—	4	2	no	—
715	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
716	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
717	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
760	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	1	no	—
765	C₄²	C₂×D₄×C₁₃	1	2	yes	—
766	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₁₃	1	2	yes	—
769	C₄²	C₂⁴×C₁₃	1	2	yes	—
770	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
772	C₁₃	#62592	1	1	yes	characteristic, direct product factor, Sylow
773	C₂³	—	2	1	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	8	2	no	—
778	C₂³	—	8	2	no	—
779	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
780	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
781	Q₈	—	2	2	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	4	4	no	—
785	Q₈	—	4	2	no	—
786	Q₈	—	8	2	no	—
787	Q₈	—	8	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	2	no	—
792	D₄	—	2	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	2	no	—
795	D₄	—	4	2	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	2	no	—
799	D₄	—	8	2	no	—
800	D₄	—	8	1	no	—
801	D₄	—	8	1	no	—
802	D₄	—	8	2	no	—
803	D₄	—	8	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	4	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
831	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	2	2	no	—
834	C₈	—	2	4	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	16	4	no	—
851	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	4	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	C₁₃×#575	1	2	yes	—
866	C₄	C₁₃×#585	1	2	yes	—
867	C₂	—	4	2	no	—
868	C₂	—	4	1	no	—
869	C₂	—	8	1	no	—
870	C₂	—	8	2	no	—
871	C₂	—	8	2	no	—
872	C₂	C₁₃×#3500	1	1	yes	characteristic
873	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
874	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3514	C₂	semidirect
2. C₁₃×#3511	C₂	semidirect
3. C₁₃×#3361	C₂	semidirect
4. C₁₃×#3360	C₂	semidirect
5. C₁₃×#3329	C₂	semidirect
6. C₁₃×#3326	C₂	semidirect
7. C₁₃×#3325	C₂	semidirect
8. C₁₃×#3322	C₂	semidirect
9. C₁₃×#3240	C₂	semidirect
10. C₁₃×#3238	C₂	semidirect
11. C₁₃×#3214	C₂	semidirect
12. C₁₃×#3213	C₂	semidirect
13. C₁₃×#3171	C₂	semidirect
14. C₁₃×#3171	C₂	semidirect
15. C₁₃×#3141	C₂	semidirect
16. C₁₃×#3140	C₂	semidirect
17. C₁₃×#2971	C₂	semidirect
23. C₁₃×#554	C₂²	semidirect
24. C₁₃×#553	C₂²	semidirect
37. C₁₃×#533	C₂²	semidirect
39. C₁₃×#532	C₂²	semidirect
40. C₁₃×#532	C₂²	semidirect
41. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#501	C₂²	semidirect
51. C₁₃×#496	C₂²	semidirect
52. C₁₃×#490	C₂²	semidirect
55. C₁₃×#489	C₂²	semidirect
56. C₁₃×#489	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
59. C₁₃×#488	C₂²	semidirect
60. C₁₃×#487	C₂²	semidirect
62. C₁₃×#485	C₂²	semidirect
63. C₁₃×#483	C₂²	semidirect
66. C₁₃×#479	C₂²	semidirect
67. C₁₃×#478	C₂²	semidirect
68. C₁₃×#477	C₂²	semidirect
72. C₁₃×#468	C₂²	semidirect
73. C₁₃×#468	C₂²	semidirect
75. C₁₃×#463	C₂²	semidirect
76. C₁₃×#461	C₂²	semidirect
78. C₁₃×#449	C₂²	semidirect
79. C₁₃×#448	C₂²	semidirect
81. C₈×Q₈×C₁₃	C₂²	semidirect
82. C₄×C₁₃×SD₁₆	C₂²	semidirect
83. C₄×C₁₃×SD₁₆	C₂²	semidirect
85. C₄×C₁₃×D₈	C₂²	semidirect
87. C₁₃×#436	C₂²	semidirect
88. C₁₃×#432	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
90. C₁₃×#419	C₂²	semidirect
92. C₁₃×#417	C₂²	semidirect
93. C₄×C₁₃×M₁₆	C₂²	semidirect
94. C₄×C₁₃×M₁₆	C₂²	semidirect
228. #62592	C₁₃	direct (N × H)
336. #3514	C₂×C₁₃	semidirect
337. #3511	C₂×C₁₃	semidirect
338. #3361	C₂×C₁₃	semidirect
339. #3360	C₂×C₁₃	semidirect
340. #3329	C₂×C₁₃	semidirect
341. #3326	C₂×C₁₃	semidirect
342. #3325	C₂×C₁₃	semidirect
343. #3322	C₂×C₁₃	semidirect
344. #3240	C₂×C₁₃	semidirect
345. #3238	C₂×C₁₃	semidirect
346. #3214	C₂×C₁₃	semidirect
347. #3213	C₂×C₁₃	semidirect
348. #3171	C₂×C₁₃	semidirect
349. #3171	C₂×C₁₃	semidirect
350. #3141	C₂×C₁₃	semidirect
351. #3140	C₂×C₁₃	semidirect
352. #2971	C₂×C₁₃	semidirect
420. #554	C₂²×C₁₃	semidirect
421. #553	C₂²×C₁₃	semidirect
434. #533	C₂²×C₁₃	semidirect
436. #532	C₂²×C₁₃	semidirect
437. #532	C₂²×C₁₃	semidirect
438. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
445. #501	C₂²×C₁₃	semidirect
446. #501	C₂²×C₁₃	semidirect
448. #496	C₂²×C₁₃	semidirect
449. #490	C₂²×C₁₃	semidirect
452. #489	C₂²×C₁₃	semidirect
453. #489	C₂²×C₁₃	semidirect
454. #489	C₂²×C₁₃	semidirect
456. #488	C₂²×C₁₃	semidirect
457. #487	C₂²×C₁₃	semidirect
459. #485	C₂²×C₁₃	semidirect
460. #483	C₂²×C₁₃	semidirect
463. #479	C₂²×C₁₃	semidirect
464. #478	C₂²×C₁₃	semidirect
465. #477	C₂²×C₁₃	semidirect
469. #468	C₂²×C₁₃	semidirect
470. #468	C₂²×C₁₃	semidirect
472. #463	C₂²×C₁₃	semidirect
473. #461	C₂²×C₁₃	semidirect
475. #449	C₂²×C₁₃	semidirect
476. #448	C₂²×C₁₃	semidirect
478. C₈×Q₈	C₂²×C₁₃	semidirect
479. C₄×SD₁₆	C₂²×C₁₃	semidirect
480. C₄×SD₁₆	C₂²×C₁₃	semidirect
482. C₄×D₈	C₂²×C₁₃	semidirect
484. #436	C₂²×C₁₃	semidirect
485. #432	C₂²×C₁₃	semidirect
486. #432	C₂²×C₁₃	semidirect
487. #419	C₂²×C₁₃	semidirect
489. #417	C₂²×C₁₃	semidirect
490. C₄×M₁₆	C₂²×C₁₃	semidirect
491. C₄×M₁₆	C₂²×C₁₃	semidirect
772. C₁₃	#62592	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×#3514	2
C₁₃×#3511	2
C₁₃×#3361	2
C₁₃×#3360	2
C₁₃×#3329	2
C₁₃×#3326	2
C₁₃×#3325	2
C₁₃×#3322	2
C₁₃×#3240	2
C₁₃×#3238	2
C₁₃×#3214	2
C₁₃×#3213	2
C₁₃×#3171	2
C₁₃×#3141	2
C₁₃×#3140	2
C₁₃×#2971	2
#62592	13

Subgroups — C13×#62592 #15748931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62592 #15748931