Subgroups — C₁₃×#62107 #15748446

Order 3328.

1958 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3384	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3354	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3343	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3330	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3306	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3239	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3115	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3079	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
19	C₁₃×#556	C₂²	1	1	yes	characteristic
20	C₁₃×#555	C₂²	1	1	yes	characteristic
21	C₁₃×#554	C₂²	1	1	yes	characteristic
22	C₁₃×#553	—	2	1	no	—
23	C₁₃×#552	—	2	1	no	—
24	C₁₃×#552	C₂²	1	2	yes	—
25	C₁₃×#551	—	2	2	no	—
26	D₄×Q₈×C₁₃	—	2	1	no	—
27	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
28	C₁₃×#547	—	2	2	no	—
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#547	C₂²	1	1	yes	characteristic
31	C₁₃×#547	C₂²	1	4	yes	—
32	C₁₃×#547	C₂²	1	2	yes	complemented
33	C₁₃×#546	C₂²	1	2	yes	—
34	C₁₃×#536	—	2	1	no	—
35	C₁₃×#536	—	2	2	no	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#532	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	2	yes	complemented
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
41	C₁₃×#529	—	2	2	no	—
42	C₁₃×#529	C₂²	1	2	yes	—
43	C₁₃×#525	—	2	1	no	—
44	C₄×C₁₃×#41	C₂²	1	2	yes	—
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#117	—	2	1	no	—
48	C₁₃×#501	C₂²	1	4	yes	complemented
49	C₁₃×#498	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	4	yes	—
51	C₁₃×#487	C₂²	1	2	yes	complemented
52	C₁₃×#484	C₂²	1	4	yes	complemented
53	C₁₃×#483	C₂²	1	4	yes	—
54	C₁₃×#482	C₂²	1	4	yes	complemented
55	C₁₃×#481	C₂²	1	4	yes	—
56	C₁₃×#480	C₂²	1	2	yes	—
57	C₁₃×#478	C₂²	1	4	yes	complemented
58	C₁₃×#477	C₂²	1	4	yes	complemented
59	C₁₃×#476	C₂²	1	4	yes	—
60	C₁₃×#476	C₂²	1	2	yes	complemented
61	C₁₃×#475	C₂²	1	2	yes	complemented
62	C₁₃×#475	C₂²	1	2	yes	complemented
63	C₁₃×#475	C₂²	1	2	yes	complemented
64	C₁₃×#474	C₂²	1	2	yes	—
65	C₁₃×#474	C₂²	1	2	yes	—
66	C₁₃×#474	C₂²	1	2	yes	—
67	C₁₃×#474	C₂²	1	2	yes	—
68	C₁₃×#474	C₂²	1	1	yes	characteristic
69	C₁₃×#474	C₂²	1	1	yes	characteristic
70	C₁₃×#469	C₂²	1	4	yes	—
71	C₁₃×#468	C₂²	1	4	yes	complemented
72	C₁₃×#465	C₂²	1	4	yes	—
73	C₁₃×#463	C₂²	1	4	yes	—
74	C₁₃×#461	C₂²	1	2	yes	complemented
75	C₁₃×#460	C₂²	1	2	yes	complemented
76	C₁₃×#459	C₂²	1	1	yes	characteristic
77	C₁₃×#459	C₂²	1	1	yes	characteristic
78	C₁₃×#449	C₂²	1	4	yes	—
79	C₁₃×#447	C₂²	1	2	yes	—
80	C₁₃×#446	C₂²	1	2	yes	complemented
81	C₁₃×#442	C₂²	1	4	yes	—
82	C₁₃×#440	C₂²	1	4	yes	complemented
83	C₄×C₁₃×D₈	C₂²	1	2	yes	—
84	C₄×C₁₃×D₈	C₂²	1	2	yes	—
85	C₁₃×#436	C₂²	1	2	yes	complemented
86	C₁₃×#435	C₂²	1	4	yes	—
87	C₁₃×#432	C₂²	1	2	yes	complemented
88	C₁₃×#431	C₂²	1	1	yes	characteristic
89	C₁₃×#428	C₂²	1	4	yes	complemented
90	C₂×C₁₃×#107	C₂²	1	2	yes	—
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	C₁₃×#417	C₂²	1	4	yes	—
94	C₂×C₁₃×#102	C₂²	1	2	yes	—
95	C₁₃×2₋¹⁺⁴	—	4	8	no	—
96	C₂×C₁₃×#41	—	2	4	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	—	2	1	no	—
99	C₂×C₁₃×#41	—	2	2	no	—
100	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	—	2	2	no	—
103	C₂²×Q₈×C₁₃	—	2	1	no	—
104	C₂²×Q₈×C₁₃	—	2	2	no	—
105	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	—	2	1	no	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×D₈	C₂³	1	2	yes	—
109	C₂×C₁₃×D₈	C₂³	1	2	yes	—
110	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
111	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	—	2	2	no	—
115	C₁₃×C₄⋊Q₈	—	2	2	no	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₁₃×#127	C₂³	1	1	yes	characteristic
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	—	2	1	no	—
128	C₁₃×#125	C₂³	1	2	yes	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	C₂³	1	2	yes	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	4	no	—
138	C₁₃×#123	—	2	4	no	—
139	C₁₃×#123	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	4	no	—
146	C₁₃×C₂²⋊Q₈	—	2	4	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₁₃×#121	—	2	1	no	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	C₂³	1	2	yes	—
156	C₁₃×#121	C₂³	1	4	yes	—
157	C₁₃×#121	C₂³	1	2	yes	—
158	C₁₃×#120	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	1	no	—
160	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
163	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
164	C₄×D₄×C₁₃	—	2	2	no	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	2	no	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	D₄	1	2	yes	—
172	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
173	C₄×D₄×C₁₃	C₂³	1	2	yes	—
174	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₁₃	C₂³	1	4	yes	—
177	C₄×D₄×C₁₃	C₂³	1	2	yes	—
178	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
182	C₁₃×#117	—	2	1	no	—
183	C₁₃×#117	—	2	1	no	—
184	C₁₃×#117	—	2	1	no	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	2	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	D₄	1	1	yes	characteristic
189	C₁₃×#117	D₄	1	2	yes	—
190	C₁₃×#117	C₂³	1	2	yes	—
191	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₄²×C₁₃	—	2	2	no	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#107	C₂³	1	2	yes	—
206	C₁₃×#107	C₂³	1	2	yes	—
207	C₁₃×#106	C₂³	1	4	yes	—
208	C₁₃×#106	C₂³	1	4	yes	—
209	C₁₃×#106	C₂³	1	4	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₁₃×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	#62107	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂⁴×C₁₃	—	2	1	no	—
231	C₁₃×#41	—	2	4	no	—
232	C₁₃×#41	—	2	4	no	—
233	C₁₃×#41	—	4	2	no	—
234	C₁₃×#41	—	4	8	no	—
235	C₁₃×#41	—	4	16	no	—
236	C₁₃×#41	—	4	8	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₂×Q₈×C₁₃	—	2	4	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	1	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	1	no	—
243	C₂×Q₈×C₁₃	—	4	8	no	—
244	C₂×Q₈×C₁₃	—	4	8	no	—
245	C₂×Q₈×C₁₃	—	4	4	no	—
246	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	4	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	1	no	—
254	C₂×D₄×C₁₃	—	2	1	no	—
255	C₂×D₄×C₁₃	—	2	1	no	—
256	C₂×D₄×C₁₃	—	4	1	no	—
257	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	4	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	4	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	2	no	—
273	C₂²×C₄×C₁₃	—	4	4	no	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₁₃×SD₁₆	—	4	4	no	—
281	C₁₃×D₈	—	2	4	no	—
282	C₁₃×D₈	—	4	2	no	—
283	C₁₃×M₁₆	—	4	4	no	—
284	C₂×C₈×C₁₃	—	4	2	no	—
285	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	1	no	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	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	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	1	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
331	C₄²×C₁₃	—	2	2	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	C₂×D₄	1	2	yes	—
335	C₄²×C₁₃	C₂×D₄	1	2	yes	—
336	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₁₃	C₂⁴	1	2	yes	—
340	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
341	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3475	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#3384	C₂×C₁₃	1	2	yes	complemented
344	#3367	C₂×C₁₃	1	2	yes	complemented
345	#3354	C₂×C₁₃	1	2	yes	complemented
346	#3343	C₂×C₁₃	1	4	yes	complemented
347	#3330	C₂×C₁₃	1	2	yes	complemented
348	#3306	C₂×C₁₃	1	4	yes	complemented
349	#3251	C₂×C₁₃	1	2	yes	complemented
350	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3239	C₂×C₁₃	1	2	yes	complemented
352	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3115	C₂×C₁₃	1	2	yes	complemented
354	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3079	C₂×C₁₃	1	2	yes	complemented
356	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	—	2	1	no	—
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	4	2	no	—
362	C₂³×C₁₃	—	4	2	no	—
363	C₂³×C₁₃	—	8	1	no	—
364	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
365	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	2	no	—
369	Q₈×C₁₃	—	4	8	no	—
370	Q₈×C₁₃	—	4	2	no	—
371	Q₈×C₁₃	—	4	4	no	—
372	Q₈×C₁₃	—	4	4	no	—
373	Q₈×C₁₃	—	8	1	no	—
374	D₄×C₁₃	—	2	4	no	—
375	D₄×C₁₃	—	2	2	no	—
376	D₄×C₁₃	—	2	2	no	—
377	D₄×C₁₃	—	2	1	no	—
378	D₄×C₁₃	—	2	1	no	—
379	D₄×C₁₃	—	2	1	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	4	2	no	—
382	D₄×C₁₃	—	4	2	no	—
383	D₄×C₁₃	—	4	4	no	—
384	D₄×C₁₃	—	4	8	no	—
385	D₄×C₁₃	—	4	4	no	—
386	D₄×C₁₃	—	4	2	no	—
387	D₄×C₁₃	—	8	2	no	—
388	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	complemented
389	C₂×C₄×C₁₃	—	2	4	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	4	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	4	2	no	—
401	C₂×C₄×C₁₃	—	4	1	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	4	8	no	—
404	C₂×C₄×C₁₃	—	4	8	no	—
405	C₂×C₄×C₁₃	—	4	2	no	—
406	C₂×C₄×C₁₃	—	4	4	no	—
407	C₂×C₄×C₁₃	—	4	2	no	—
408	C₂×C₄×C₁₃	—	4	2	no	—
409	C₂×C₄×C₁₃	—	4	2	no	—
410	C₂×C₄×C₁₃	—	4	2	no	—
411	C₂×C₄×C₁₃	—	4	4	no	—
412	C₂×C₄×C₁₃	—	8	2	no	—
413	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
414	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
423	C₈×C₁₃	—	2	2	no	—
424	C₈×C₁₃	—	2	4	no	—
425	C₈×C₁₃	—	2	2	no	—
426	C₂×2₋¹⁺⁴	—	2	1	no	—
427	#556	C₂²×C₁₃	1	1	yes	characteristic
428	#555	C₂²×C₁₃	1	1	yes	characteristic
429	#554	C₂²×C₁₃	1	1	yes	characteristic
430	#553	—	2	1	no	—
431	#552	—	2	1	no	—
432	#552	C₂²×C₁₃	1	2	yes	—
433	#551	—	2	2	no	—
434	D₄×Q₈	—	2	1	no	—
435	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
436	#547	—	2	2	no	—
437	#547	—	2	1	no	—
438	#547	C₂²×C₁₃	1	1	yes	characteristic
439	#547	C₂²×C₁₃	1	4	yes	—
440	#547	C₂²×C₁₃	1	2	yes	complemented
441	#546	C₂²×C₁₃	1	2	yes	—
442	#536	—	2	1	no	—
443	#536	—	2	2	no	—
444	#533	C₂²×C₁₃	1	1	yes	characteristic
445	#532	C₂²×C₁₃	1	1	yes	characteristic
446	#532	C₂²×C₁₃	1	2	yes	complemented
447	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
449	#529	—	2	2	no	—
450	#529	C₂²×C₁₃	1	2	yes	—
451	#525	—	2	1	no	—
452	C₄×#41	C₂²×C₁₃	1	2	yes	—
453	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×#117	—	2	1	no	—
456	#501	C₂²×C₁₃	1	4	yes	complemented
457	#498	C₂²×C₁₃	1	2	yes	complemented
458	#489	C₂²×C₁₃	1	4	yes	—
459	#487	C₂²×C₁₃	1	2	yes	complemented
460	#484	C₂²×C₁₃	1	4	yes	complemented
461	#483	C₂²×C₁₃	1	4	yes	—
462	#482	C₂²×C₁₃	1	4	yes	complemented
463	#481	C₂²×C₁₃	1	4	yes	—
464	#480	C₂²×C₁₃	1	2	yes	—
465	#478	C₂²×C₁₃	1	4	yes	complemented
466	#477	C₂²×C₁₃	1	4	yes	complemented
467	#476	C₂²×C₁₃	1	4	yes	—
468	#476	C₂²×C₁₃	1	2	yes	complemented
469	#475	C₂²×C₁₃	1	2	yes	complemented
470	#475	C₂²×C₁₃	1	2	yes	complemented
471	#475	C₂²×C₁₃	1	2	yes	complemented
472	#474	C₂²×C₁₃	1	2	yes	—
473	#474	C₂²×C₁₃	1	1	yes	characteristic
474	#474	C₂²×C₁₃	1	2	yes	—
475	#474	C₂²×C₁₃	1	2	yes	—
476	#474	C₂²×C₁₃	1	1	yes	characteristic
477	#474	C₂²×C₁₃	1	2	yes	—
478	#469	C₂²×C₁₃	1	4	yes	—
479	#468	C₂²×C₁₃	1	4	yes	complemented
480	#465	C₂²×C₁₃	1	4	yes	—
481	#463	C₂²×C₁₃	1	4	yes	—
482	#461	C₂²×C₁₃	1	2	yes	complemented
483	#460	C₂²×C₁₃	1	2	yes	complemented
484	#459	C₂²×C₁₃	1	1	yes	characteristic
485	#459	C₂²×C₁₃	1	1	yes	characteristic
486	#449	C₂²×C₁₃	1	4	yes	—
487	#447	C₂²×C₁₃	1	2	yes	—
488	#446	C₂²×C₁₃	1	2	yes	complemented
489	#442	C₂²×C₁₃	1	4	yes	—
490	#440	C₂²×C₁₃	1	4	yes	complemented
491	C₄×D₈	C₂²×C₁₃	1	2	yes	—
492	C₄×D₈	C₂²×C₁₃	1	2	yes	—
493	#436	C₂²×C₁₃	1	2	yes	complemented
494	#435	C₂²×C₁₃	1	4	yes	—
495	#432	C₂²×C₁₃	1	2	yes	complemented
496	#431	C₂²×C₁₃	1	1	yes	characteristic
497	#428	C₂²×C₁₃	1	4	yes	complemented
498	C₂×#107	C₂²×C₁₃	1	2	yes	—
499	#423	C₂²×C₁₃	1	2	yes	complemented
500	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
501	#417	C₂²×C₁₃	1	4	yes	—
502	C₂×#102	C₂²×C₁₃	1	2	yes	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	2	2	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	1	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	—	4	1	no	—
513	C₂²×C₁₃	—	4	1	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	—	4	1	no	—
517	C₂²×C₁₃	—	8	4	no	—
518	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
519	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	2	1	no	—
523	C₄×C₁₃	—	2	2	no	—
524	C₄×C₁₃	—	2	1	no	—
525	C₄×C₁₃	—	2	2	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	1	no	—
529	C₄×C₁₃	—	4	1	no	—
530	C₄×C₁₃	—	4	4	no	—
531	C₄×C₁₃	—	4	2	no	—
532	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
533	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
534	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	C₄×C₁₃	#585	1	1	yes	characteristic
536	2₋¹⁺⁴	—	4	8	no	—
537	C₂×#41	—	2	4	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	—	2	1	no	—
540	C₂×#41	—	2	2	no	—
541	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
542	C₂×#41	C₂³×C₁₃	1	2	yes	—
543	C₂²×Q₈	—	2	2	no	—
544	C₂²×Q₈	—	2	1	no	—
545	C₂²×Q₈	—	2	2	no	—
546	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂³×C₄	—	2	1	no	—
548	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
549	C₂×D₈	C₂³×C₁₃	1	2	yes	—
550	C₂×D₈	C₂³×C₁₃	1	2	yes	—
551	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
552	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	—	2	1	no	—
555	C₄⋊Q₈	—	2	2	no	—
556	C₄⋊Q₈	—	2	2	no	—
557	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
559	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
562	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
563	#127	C₂³×C₁₃	1	1	yes	characteristic
564	#126	—	2	2	no	—
565	#126	—	2	2	no	—
566	#126	—	2	2	no	—
567	#125	—	2	2	no	—
568	#125	—	2	1	no	—
569	#125	C₂³×C₁₃	1	2	yes	—
570	#124	—	2	2	no	—
571	#124	—	2	1	no	—
572	#124	—	2	2	no	—
573	#124	C₂³×C₁₃	1	2	yes	—
574	#123	—	2	2	no	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	4	no	—
579	#123	—	2	4	no	—
580	#123	—	2	4	no	—
581	C₂²⋊Q₈	—	2	1	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	4	no	—
587	C₂²⋊Q₈	—	2	4	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
590	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
591	#121	—	2	1	no	—
592	#121	—	2	1	no	—
593	#121	—	2	1	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	C₂³×C₁₃	1	2	yes	—
597	#121	C₂³×C₁₃	1	2	yes	—
598	#121	C₂³×C₁₃	1	4	yes	—
599	#120	—	2	2	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
603	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
604	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	D₄×C₁₃	1	2	yes	—
613	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₁₃	1	2	yes	—
619	C₄×D₄	C₂³×C₁₃	1	2	yes	—
620	C₄×D₄	C₂³×C₁₃	1	4	yes	—
621	C₄×D₄	C₂³×C₁₃	1	2	yes	—
622	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
623	#117	—	2	1	no	—
624	#117	—	2	1	no	—
625	#117	—	2	1	no	—
626	#117	—	2	2	no	—
627	#117	—	2	2	no	—
628	#117	—	2	2	no	—
629	#117	D₄×C₁₃	1	1	yes	characteristic
630	#117	D₄×C₁₃	1	2	yes	—
631	#117	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	2	no	—
641	C₂×C₄²	—	2	2	no	—
642	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
644	#107	C₂³×C₁₃	1	4	yes	—
645	#107	C₂³×C₁₃	1	4	yes	—
646	#107	C₂³×C₁₃	1	2	yes	—
647	#107	C₂³×C₁₃	1	2	yes	—
648	#106	C₂³×C₁₃	1	4	yes	—
649	#106	C₂³×C₁₃	1	4	yes	—
650	#106	C₂³×C₁₃	1	4	yes	—
651	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
652	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
653	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
654	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
655	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
656	#103	C₂³×C₁₃	1	4	yes	—
657	#103	C₂³×C₁₃	1	4	yes	—
658	#103	C₂³×C₁₃	1	4	yes	—
659	#102	C₂³×C₁₃	1	4	yes	—
660	#102	C₂³×C₁₃	1	4	yes	—
661	#102	C₂³×C₁₃	1	2	yes	—
662	#102	C₂³×C₁₃	1	2	yes	—
663	#102	C₂³×C₁₃	1	2	yes	—
664	#102	C₂³×C₁₃	1	2	yes	—
665	#102	C₂³×C₁₃	1	4	yes	—
666	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
668	#97	C₂³×C₁₃	1	4	yes	—
669	C₄×C₈	C₂³×C₁₃	1	2	yes	—
670	C₂×C₁₃	—	2	2	no	—
671	C₂×C₁₃	—	4	2	no	—
672	C₂×C₁₃	—	4	2	no	—
673	C₂×C₁₃	—	8	2	no	—
674	C₂×C₁₃	—	8	1	no	—
675	C₂×C₁₃	#3489	1	1	yes	characteristic
676	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
677	C₂×C₁₃	#3586	1	1	yes	characteristic
678	C₂⁴	—	2	1	no	—
679	#41	—	2	4	no	—
680	#41	—	2	4	no	—
681	#41	—	4	2	no	—
682	#41	—	4	8	no	—
683	#41	—	4	16	no	—
684	#41	—	4	8	no	—
685	#41	—	4	4	no	—
686	C₂×Q₈	—	2	4	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	4	8	no	—
692	C₂×Q₈	—	4	8	no	—
693	C₂×Q₈	—	4	4	no	—
694	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
695	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	4	1	no	—
705	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
707	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
708	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
709	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	4	4	no	—
722	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
728	SD₁₆	—	4	4	no	—
729	D₈	—	2	4	no	—
730	D₈	—	4	2	no	—
731	M₁₆	—	4	4	no	—
732	C₂×C₈	—	4	2	no	—
733	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
734	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
735	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
756	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
757	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
759	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
760	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
777	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	C₂×D₄×C₁₃	1	2	yes	—
783	C₄²	C₂×D₄×C₁₃	1	2	yes	—
784	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
785	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
786	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
787	C₄²	C₂⁴×C₁₃	1	2	yes	—
788	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
789	C₁₃	#62107	1	1	yes	characteristic, direct product factor, Sylow
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	4	2	no	—
794	C₂³	—	4	2	no	—
795	C₂³	—	8	1	no	—
796	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
797	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
798	Q₈	—	2	2	no	—
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	4	8	no	—
802	Q₈	—	4	2	no	—
803	Q₈	—	4	4	no	—
804	Q₈	—	4	4	no	—
805	Q₈	—	8	1	no	—
806	D₄	—	2	4	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	1	no	—
810	D₄	—	2	1	no	—
811	D₄	—	2	1	no	—
812	D₄	—	2	2	no	—
813	D₄	—	4	2	no	—
814	D₄	—	4	2	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	8	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	2	no	—
819	D₄	—	8	2	no	—
820	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	complemented
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	8	2	no	—
845	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
846	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
854	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
855	C₈	—	2	2	no	—
856	C₈	—	2	4	no	—
857	C₈	—	2	2	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	8	4	no	—
873	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
874	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
875	C₄	—	2	2	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	4	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	2	no	—
887	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
888	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
889	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
890	C₄	C₁₃×#585	1	1	yes	characteristic
891	C₂	—	2	2	no	—
892	C₂	—	4	2	no	—
893	C₂	—	4	2	no	—
894	C₂	—	8	1	no	—
895	C₂	—	8	2	no	—
896	C₂	C₁₃×#3489	1	1	yes	characteristic
897	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
898	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3499	C₂	semidirect
2. C₁₃×#3475	C₂	semidirect
3. C₁₃×#3384	C₂	semidirect
4. C₁₃×#3367	C₂	semidirect
5. C₁₃×#3354	C₂	semidirect
6. C₁₃×#3343	C₂	semidirect
7. C₁₃×#3330	C₂	semidirect
8. C₁₃×#3306	C₂	semidirect
9. C₁₃×#3251	C₂	semidirect
10. C₁₃×#3246	C₂	semidirect
11. C₁₃×#3239	C₂	semidirect
12. C₁₃×#3229	C₂	semidirect
13. C₁₃×#3115	C₂	semidirect
14. C₁₃×#3100	C₂	semidirect
15. C₁₃×#3079	C₂	semidirect
16. C₂×C₁₃×#474	C₂	semidirect
17. C₁₃×#2989	C₂	semidirect
27. D₄×Q₈×C₁₃	C₂²	semidirect
32. C₁₃×#547	C₂²	semidirect
38. C₁₃×#532	C₂²	semidirect
40. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#498	C₂²	semidirect
51. C₁₃×#487	C₂²	semidirect
52. C₁₃×#484	C₂²	semidirect
54. C₁₃×#482	C₂²	semidirect
57. C₁₃×#478	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
60. C₁₃×#476	C₂²	semidirect
61. C₁₃×#475	C₂²	semidirect
62. C₁₃×#475	C₂²	semidirect
63. C₁₃×#475	C₂²	semidirect
71. C₁₃×#468	C₂²	semidirect
74. C₁₃×#461	C₂²	semidirect
75. C₁₃×#460	C₂²	semidirect
80. C₁₃×#446	C₂²	semidirect
82. C₁₃×#440	C₂²	semidirect
85. C₁₃×#436	C₂²	semidirect
87. C₁₃×#432	C₂²	semidirect
89. C₁₃×#428	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
229. #62107	C₁₃	direct (N × H)
341. #3499	C₂×C₁₃	semidirect
342. #3475	C₂×C₁₃	semidirect
343. #3384	C₂×C₁₃	semidirect
344. #3367	C₂×C₁₃	semidirect
345. #3354	C₂×C₁₃	semidirect
346. #3343	C₂×C₁₃	semidirect
347. #3330	C₂×C₁₃	semidirect
348. #3306	C₂×C₁₃	semidirect
349. #3251	C₂×C₁₃	semidirect
350. #3246	C₂×C₁₃	semidirect
351. #3239	C₂×C₁₃	semidirect
352. #3229	C₂×C₁₃	semidirect
353. #3115	C₂×C₁₃	semidirect
354. #3100	C₂×C₁₃	semidirect
355. #3079	C₂×C₁₃	semidirect
356. C₂×#474	C₂×C₁₃	semidirect
357. #2989	C₂×C₁₃	semidirect
388. D₄×C₁₃	2₋¹⁺⁴	semidirect
435. D₄×Q₈	C₂²×C₁₃	semidirect
440. #547	C₂²×C₁₃	semidirect
446. #532	C₂²×C₁₃	semidirect
448. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
456. #501	C₂²×C₁₃	semidirect
457. #498	C₂²×C₁₃	semidirect
459. #487	C₂²×C₁₃	semidirect
460. #484	C₂²×C₁₃	semidirect
462. #482	C₂²×C₁₃	semidirect
465. #478	C₂²×C₁₃	semidirect
466. #477	C₂²×C₁₃	semidirect
468. #476	C₂²×C₁₃	semidirect
469. #475	C₂²×C₁₃	semidirect
470. #475	C₂²×C₁₃	semidirect
471. #475	C₂²×C₁₃	semidirect
479. #468	C₂²×C₁₃	semidirect
482. #461	C₂²×C₁₃	semidirect
483. #460	C₂²×C₁₃	semidirect
488. #446	C₂²×C₁₃	semidirect
490. #440	C₂²×C₁₃	semidirect
493. #436	C₂²×C₁₃	semidirect
495. #432	C₂²×C₁₃	semidirect
497. #428	C₂²×C₁₃	semidirect
499. #423	C₂²×C₁₃	semidirect
789. C₁₃	#62107	direct (N × H)
820. D₄	C₁₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3499	2
C₁₃×#3475	2
C₁₃×#3384	2
C₁₃×#3367	2
C₁₃×#3354	2
C₁₃×#3343	2
C₁₃×#3330	2
C₁₃×#3306	2
C₁₃×#3251	2
C₁₃×#3246	2
C₁₃×#3239	2
C₁₃×#3229	2
C₁₃×#3115	2
C₁₃×#3100	2
C₁₃×#3079	2
C₂×C₁₃×#474	2
C₁₃×#2989	2
#62107	13

Subgroups — C13×#62107 #15748446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62107 #15748446