Subgroups — C₁₃×#61340 #15747679

Order 3328.

1792 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3372	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3042	C₂	1	2	yes	maximal
14	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2949	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₁₃×#557	C₂²	1	2	yes	complemented
21	C₁₃×#557	C₂²	1	2	yes	complemented
22	C₁₃×#556	C₂²	1	2	yes	complemented
23	C₁₃×#556	C₂²	1	2	yes	complemented
24	C₁₃×#554	—	2	1	no	—
25	C₁₃×#554	—	2	2	no	—
26	C₁₃×#554	C₂²	1	2	yes	—
27	C₁₃×#554	C₂²	1	4	yes	—
28	C₁₃×#552	—	2	2	no	—
29	C₁₃×#552	—	2	2	no	—
30	D₄×Q₈×C₁₃	—	2	1	no	—
31	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#544	C₂²	1	2	yes	—
33	C₁₃×#543	—	2	2	no	—
34	C₁₃×#541	—	2	2	no	—
35	C₁₃×#536	C₂²	1	2	yes	—
36	C₁₃×#533	—	2	1	no	—
37	C₁₃×#533	—	2	1	no	—
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
42	C₁₃×#519	C₂²	1	2	yes	—
43	C₁₃×#518	C₂²	1	2	yes	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
46	C₁₃×#491	C₂²	1	4	yes	complemented
47	C₁₃×#491	C₂²	1	4	yes	complemented
48	C₁₃×#489	C₂²	1	4	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	complemented
50	C₁₃×#487	C₂²	1	2	yes	complemented
51	C₁₃×#487	C₂²	1	4	yes	complemented
52	C₁₃×#487	C₂²	1	2	yes	complemented
53	C₁₃×#479	C₂²	1	2	yes	complemented
54	C₁₃×#479	C₂²	1	4	yes	complemented
55	C₁₃×#479	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	2	yes	complemented
57	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#477	C₂²	1	4	yes	complemented
59	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#475	C₂²	1	4	yes	complemented
62	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#463	C₂²	1	4	yes	—
64	C₁₃×#463	C₂²	1	4	yes	—
65	C₁₃×#461	C₂²	1	2	yes	—
66	C₁₃×#461	C₂²	1	2	yes	—
67	C₁₃×#461	C₂²	1	4	yes	—
68	C₁₃×#461	C₂²	1	4	yes	—
69	C₁₃×#461	C₂²	1	4	yes	—
70	C₁₃×#446	C₂²	1	2	yes	complemented
71	C₁₃×#446	C₂²	1	4	yes	complemented
72	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
73	C₁₃×#442	C₂²	1	2	yes	—
74	C₁₃×#440	C₂²	1	4	yes	—
75	C₁₃×#440	C₂²	1	2	yes	—
76	C₁₃×#440	C₂²	1	4	yes	—
77	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
78	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
79	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
80	C₄×C₁₃×D₈	C₂²	1	2	yes	—
81	C₁₃×#428	C₂²	1	1	yes	characteristic
82	C₁₃×#427	C₂²	1	2	yes	—
83	C₁₃×#424	C₂²	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₁₃×#419	C₂²	1	2	yes	—
86	C₁₃×#419	C₂²	1	2	yes	—
87	C₁₃×#418	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	2	yes	—
90	C₂×C₁₃×#103	C₂²	1	2	yes	—
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₁₃	—	2	2	no	—
95	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	—	2	1	no	—
98	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
99	C₂×C₁₃×SD₁₆	—	2	8	no	—
100	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×D₈	C₂³	1	2	yes	—
104	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	—	2	2	no	—
122	C₁₃×#125	—	2	4	no	—
123	C₁₃×#125	—	2	4	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	D₄	1	2	yes	—
126	C₁₃×#125	C₂³	1	2	yes	—
127	C₁₃×#125	C₂³	1	4	yes	—
128	C₁₃×#124	C₂³	1	4	yes	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	2	no	—
131	C₁₃×C₂²⋊Q₈	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	—	2	4	no	—
144	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	2	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
154	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×D₄×C₁₃	—	2	1	no	—
159	C₄×D₄×C₁₃	—	2	1	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	1	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₁₃	C₂³	1	2	yes	—
166	C₄×D₄×C₁₃	C₂³	1	4	yes	—
167	C₄×D₄×C₁₃	C₂³	1	4	yes	—
168	C₄×D₄×C₁₃	C₂³	1	2	yes	—
169	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
170	C₁₃×#117	—	2	2	no	—
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	—	2	4	no	—
173	C₁₃×#117	—	2	1	no	—
174	C₁₃×#117	C₂³	1	2	yes	—
175	C₁₃×#117	C₂³	1	1	yes	characteristic
176	C₁₃×#117	C₂³	1	2	yes	—
177	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₂×C₄²×C₁₃	—	2	1	no	—
185	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₁₃×#107	C₂³	1	2	yes	—
187	C₁₃×#107	C₂³	1	2	yes	—
188	C₁₃×#107	C₂³	1	2	yes	—
189	C₁₃×#106	C₂³	1	2	yes	—
190	C₁₃×#106	C₂³	1	2	yes	—
191	C₁₃×#106	C₂³	1	2	yes	—
192	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
196	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
197	C₁₃×#103	C₂³	1	4	yes	—
198	C₁₃×#103	C₂³	1	4	yes	—
199	C₁₃×#103	C₂³	1	2	yes	—
200	C₁₃×#103	C₂³	1	2	yes	—
201	C₁₃×#103	C₂³	1	2	yes	—
202	C₁₃×#103	C₂³	1	4	yes	—
203	C₁₃×#103	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#103	C₂³	1	4	yes	—
206	C₁₃×#102	C₂³	1	2	yes	—
207	C₁₃×#102	C₂³	1	2	yes	—
208	C₁₃×#102	C₂³	1	2	yes	—
209	C₁₃×#102	C₂³	1	2	yes	—
210	C₁₃×#102	C₂³	1	2	yes	—
211	C₁₃×#97	C₂³	1	2	yes	—
212	C₁₃×#97	C₂³	1	4	yes	—
213	C₄×C₈×C₁₃	C₂³	1	2	yes	—
214	C₄×C₈×C₁₃	C₂³	1	4	yes	—
215	#61340	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂⁴×C₁₃	—	2	1	no	—
217	C₁₃×#41	—	2	2	no	—
218	C₁₃×#41	—	2	2	no	—
219	C₂×Q₈×C₁₃	—	2	2	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	4	no	—
223	C₂×Q₈×C₁₃	—	2	4	no	—
224	C₂×Q₈×C₁₃	—	2	4	no	—
225	C₂×Q₈×C₁₃	—	8	4	no	—
226	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
229	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	#41	1	4	yes	—
234	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	—	2	2	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	2	no	—
242	C₂²×C₄×C₁₃	—	2	4	no	—
243	C₂²×C₄×C₁₃	—	2	4	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	8	2	no	—
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₁₃×SD₁₆	—	2	8	no	—
250	C₁₃×SD₁₆	—	2	8	no	—
251	C₁₃×SD₁₆	—	2	4	no	—
252	C₁₃×D₈	—	2	4	no	—
253	C₁₃×M₁₆	—	2	2	no	—
254	C₁₃×M₁₆	—	2	2	no	—
255	C₂×C₈×C₁₃	—	2	4	no	—
256	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
258	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
259	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
260	C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	—	2	2	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
285	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	1	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	2	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₁₃×C₂²⋊C₄	—	2	1	no	—
296	C₁₃×C₂²⋊C₄	—	2	1	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	2	4	no	—
299	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
300	C₄²×C₁₃	—	2	1	no	—
301	C₄²×C₁₃	—	2	1	no	—
302	C₄²×C₁₃	—	2	1	no	—
303	C₄²×C₁₃	—	2	4	no	—
304	C₄²×C₁₃	—	2	4	no	—
305	C₄²×C₁₃	—	2	2	no	—
306	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₄²×C₁₃	C₂⁴	1	4	yes	—
310	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
311	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#3376	C₂×C₁₃	1	4	yes	complemented
314	#3372	C₂×C₁₃	1	2	yes	complemented
315	#3372	C₂×C₁₃	1	4	yes	complemented
316	#3367	C₂×C₁₃	1	2	yes	complemented
317	#3360	C₂×C₁₃	1	2	yes	complemented
318	#3359	C₂×C₁₃	1	2	yes	complemented
319	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#3137	C₂×C₁₃	1	2	yes	complemented
321	#3082	C₂×C₁₃	1	2	yes	complemented
322	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#3042	C₂×C₁₃	1	2	yes	—
324	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#2949	C₂×C₁₃	1	2	yes	complemented
327	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	2	4	no	—
330	C₂³×C₁₃	—	2	1	no	—
331	C₂³×C₁₃	—	8	1	no	—
332	C₂³×C₁₃	—	8	1	no	—
333	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
334	Q₈×C₁₃	—	2	4	no	—
335	Q₈×C₁₃	—	2	4	no	—
336	Q₈×C₁₃	—	2	1	no	—
337	Q₈×C₁₃	—	2	4	no	—
338	Q₈×C₁₃	—	2	1	no	—
339	Q₈×C₁₃	—	4	2	no	—
340	Q₈×C₁₃	—	4	4	no	—
341	Q₈×C₁₃	—	4	2	no	—
342	Q₈×C₁₃	—	8	1	no	—
343	Q₈×C₁₃	—	8	4	no	—
344	D₄×C₁₃	—	2	4	no	—
345	D₄×C₁₃	—	2	1	no	—
346	D₄×C₁₃	—	2	2	no	—
347	D₄×C₁₃	—	2	1	no	—
348	D₄×C₁₃	—	4	2	no	—
349	D₄×C₁₃	C₂×#41	1	4	yes	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	4	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	4	1	no	—
359	C₂×C₄×C₁₃	—	4	2	no	—
360	C₂×C₄×C₁₃	—	4	4	no	—
361	C₂×C₄×C₁₃	—	4	2	no	—
362	C₂×C₄×C₁₃	—	4	2	no	—
363	C₂×C₄×C₁₃	—	4	4	no	—
364	C₂×C₄×C₁₃	—	8	4	no	—
365	C₂×C₄×C₁₃	—	8	2	no	—
366	C₂×C₄×C₁₃	—	8	4	no	—
367	C₂×C₄×C₁₃	—	8	1	no	—
368	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
376	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
377	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
378	C₈×C₁₃	—	2	2	no	—
379	C₈×C₁₃	—	2	2	no	—
380	C₈×C₁₃	—	2	2	no	—
381	C₈×C₁₃	—	2	2	no	—
382	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
383	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
384	#557	C₂²×C₁₃	1	2	yes	complemented
385	#557	C₂²×C₁₃	1	2	yes	complemented
386	#556	C₂²×C₁₃	1	2	yes	complemented
387	#556	C₂²×C₁₃	1	2	yes	complemented
388	#554	—	2	1	no	—
389	#554	—	2	2	no	—
390	#554	C₂²×C₁₃	1	2	yes	—
391	#554	C₂²×C₁₃	1	4	yes	—
392	#552	—	2	2	no	—
393	#552	—	2	2	no	—
394	D₄×Q₈	—	2	1	no	—
395	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
396	#544	C₂²×C₁₃	1	2	yes	—
397	#543	—	2	2	no	—
398	#541	—	2	2	no	—
399	#536	C₂²×C₁₃	1	2	yes	—
400	#533	—	2	1	no	—
401	#533	—	2	1	no	—
402	#533	C₂²×C₁₃	1	1	yes	characteristic
403	#533	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	—	2	2	no	—
406	#519	C₂²×C₁₃	1	2	yes	—
407	#518	C₂²×C₁₃	1	2	yes	—
408	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
410	#491	C₂²×C₁₃	1	4	yes	complemented
411	#491	C₂²×C₁₃	1	4	yes	complemented
412	#489	C₂²×C₁₃	1	4	yes	complemented
413	#488	C₂²×C₁₃	1	4	yes	complemented
414	#487	C₂²×C₁₃	1	2	yes	complemented
415	#487	C₂²×C₁₃	1	4	yes	complemented
416	#487	C₂²×C₁₃	1	2	yes	complemented
417	#479	C₂²×C₁₃	1	2	yes	complemented
418	#479	C₂²×C₁₃	1	4	yes	complemented
419	#479	C₂²×C₁₃	1	4	yes	complemented
420	#478	C₂²×C₁₃	1	2	yes	complemented
421	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
422	#477	C₂²×C₁₃	1	4	yes	complemented
423	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
424	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	#475	C₂²×C₁₃	1	4	yes	complemented
426	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	#463	C₂²×C₁₃	1	4	yes	—
428	#463	C₂²×C₁₃	1	4	yes	—
429	#461	C₂²×C₁₃	1	2	yes	—
430	#461	C₂²×C₁₃	1	4	yes	—
431	#461	C₂²×C₁₃	1	2	yes	—
432	#461	C₂²×C₁₃	1	4	yes	—
433	#461	C₂²×C₁₃	1	4	yes	—
434	#446	C₂²×C₁₃	1	2	yes	complemented
435	#446	C₂²×C₁₃	1	4	yes	complemented
436	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
437	#442	C₂²×C₁₃	1	2	yes	—
438	#440	C₂²×C₁₃	1	4	yes	—
439	#440	C₂²×C₁₃	1	2	yes	—
440	#440	C₂²×C₁₃	1	4	yes	—
441	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
442	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
443	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
444	C₄×D₈	C₂²×C₁₃	1	2	yes	—
445	#428	C₂²×C₁₃	1	1	yes	characteristic
446	#427	C₂²×C₁₃	1	2	yes	—
447	#424	C₂²×C₁₃	1	2	yes	—
448	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
449	#419	C₂²×C₁₃	1	2	yes	—
450	#419	C₂²×C₁₃	1	2	yes	—
451	#418	C₂²×C₁₃	1	1	yes	characteristic
452	#417	C₂²×C₁₃	1	1	yes	characteristic
453	#416	C₂²×C₁₃	1	2	yes	—
454	C₂×#103	C₂²×C₁₃	1	2	yes	—
455	#405	C₂²×C₁₃	1	2	yes	—
456	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
457	C₂²×C₁₃	—	2	1	no	—
458	C₂²×C₁₃	—	2	1	no	—
459	C₂²×C₁₃	—	2	4	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	1	no	—
464	C₂²×C₁₃	—	4	1	no	—
465	C₂²×C₁₃	—	8	4	no	—
466	C₂²×C₁₃	#548	1	2	yes	—
467	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	2	1	no	—
470	C₄×C₁₃	—	2	4	no	—
471	C₄×C₁₃	—	2	1	no	—
472	C₄×C₁₃	—	2	4	no	—
473	C₄×C₁₃	—	4	1	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	1	no	—
476	C₄×C₁₃	—	4	4	no	—
477	C₄×C₁₃	—	4	1	no	—
478	C₄×C₁₃	—	4	2	no	—
479	C₄×C₁₃	—	4	2	no	—
480	C₄×C₁₃	#548	1	2	yes	—
481	C₄×C₁₃	#577	1	2	yes	—
482	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
483	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
484	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×Q₈	—	2	2	no	—
486	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
487	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂³×C₄	—	2	1	no	—
489	AGL(1,ℤ/8)	—	2	4	no	—
490	C₂×SD₁₆	—	2	8	no	—
491	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
492	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
493	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
494	C₂×D₈	C₂³×C₁₃	1	2	yes	—
495	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
496	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	—	2	1	no	—
501	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
502	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
505	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
506	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
509	#126	—	2	4	no	—
510	#126	—	2	4	no	—
511	#125	—	2	2	no	—
512	#125	—	2	2	no	—
513	#125	—	2	4	no	—
514	#125	—	2	4	no	—
515	#125	—	2	2	no	—
516	#125	D₄×C₁₃	1	2	yes	—
517	#125	C₂³×C₁₃	1	2	yes	—
518	#125	C₂³×C₁₃	1	4	yes	—
519	#124	C₂³×C₁₃	1	4	yes	—
520	#123	—	2	4	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	2	1	no	—
526	C₂²⋊Q₈	—	2	1	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
536	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
544	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
545	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
546	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
547	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
548	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	C₂³×C₁₃	1	2	yes	—
556	C₄×D₄	C₂³×C₁₃	1	2	yes	—
557	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
559	C₄×D₄	C₂³×C₁₃	1	4	yes	—
560	C₄×D₄	C₂³×C₁₃	1	4	yes	—
561	#117	—	2	2	no	—
562	#117	—	2	2	no	—
563	#117	—	2	4	no	—
564	#117	—	2	1	no	—
565	#117	C₂³×C₁₃	1	1	yes	characteristic
566	#117	C₂³×C₁₃	1	2	yes	—
567	#117	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	4	no	—
571	C₂×C₄⋊C₄	—	2	2	no	—
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	4	no	—
575	C₂×C₄²	—	2	1	no	—
576	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
577	#107	C₂³×C₁₃	1	2	yes	—
578	#107	C₂³×C₁₃	1	2	yes	—
579	#107	C₂³×C₁₃	1	2	yes	—
580	#106	C₂³×C₁₃	1	2	yes	—
581	#106	C₂³×C₁₃	1	2	yes	—
582	#106	C₂³×C₁₃	1	2	yes	—
583	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
584	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
586	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
587	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
588	#103	C₂³×C₁₃	1	4	yes	—
589	#103	C₂³×C₁₃	1	4	yes	—
590	#103	C₂³×C₁₃	1	2	yes	—
591	#103	C₂³×C₁₃	1	2	yes	—
592	#103	C₂³×C₁₃	1	2	yes	—
593	#103	C₂³×C₁₃	1	4	yes	—
594	#103	C₂³×C₁₃	1	4	yes	—
595	#103	C₂³×C₁₃	1	4	yes	—
596	#103	C₂³×C₁₃	1	4	yes	—
597	#102	C₂³×C₁₃	1	2	yes	—
598	#102	C₂³×C₁₃	1	2	yes	—
599	#102	C₂³×C₁₃	1	2	yes	—
600	#102	C₂³×C₁₃	1	2	yes	—
601	#102	C₂³×C₁₃	1	2	yes	—
602	#97	C₂³×C₁₃	1	2	yes	—
603	#97	C₂³×C₁₃	1	4	yes	—
604	C₄×C₈	C₂³×C₁₃	1	2	yes	—
605	C₄×C₈	C₂³×C₁₃	1	4	yes	—
606	C₂×C₁₃	—	2	2	no	—
607	C₂×C₁₃	—	4	4	no	—
608	C₂×C₁₃	—	8	1	no	—
609	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
610	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
611	C₂×C₁₃	#3586	1	1	yes	characteristic
612	C₂⁴	—	2	1	no	—
613	#41	—	2	2	no	—
614	#41	—	2	2	no	—
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	4	no	—
619	C₂×Q₈	—	2	4	no	—
620	C₂×Q₈	—	2	4	no	—
621	C₂×Q₈	—	8	4	no	—
622	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
623	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
624	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
625	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	C₁₃×#41	1	4	yes	—
630	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
631	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	8	2	no	—
642	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
645	SD₁₆	—	2	8	no	—
646	SD₁₆	—	2	8	no	—
647	SD₁₆	—	2	4	no	—
648	D₈	—	2	4	no	—
649	M₁₆	—	2	2	no	—
650	M₁₆	—	2	2	no	—
651	C₂×C₈	—	2	4	no	—
652	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
653	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
654	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
655	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
676	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
677	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
679	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
680	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
681	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
682	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
705	C₄²	C₂⁴×C₁₃	1	4	yes	—
706	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
707	C₁₃	#61340	1	1	yes	characteristic, direct product factor, Sylow
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	8	1	no	—
712	C₂³	—	8	1	no	—
713	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
714	Q₈	—	2	4	no	—
715	Q₈	—	2	4	no	—
716	Q₈	—	2	1	no	—
717	Q₈	—	2	4	no	—
718	Q₈	—	2	1	no	—
719	Q₈	—	4	2	no	—
720	Q₈	—	4	4	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	8	4	no	—
723	Q₈	—	8	1	no	—
724	D₄	—	2	4	no	—
725	D₄	—	2	1	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	1	no	—
728	D₄	—	4	2	no	—
729	D₄	C₂×C₁₃×#41	1	4	yes	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	8	2	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	—	8	4	no	—
747	C₂×C₄	—	8	1	no	—
748	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
750	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
751	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
755	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
756	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
757	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
758	C₈	—	2	2	no	—
759	C₈	—	2	2	no	—
760	C₈	—	2	2	no	—
761	C₈	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	8	4	no	—
771	C₂²	C₁₃×#548	1	2	yes	—
772	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
773	C₄	—	2	1	no	—
774	C₄	—	2	4	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	4	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	4	no	—
785	C₄	C₁₃×#548	1	2	yes	—
786	C₄	C₁₃×#577	1	2	yes	—
787	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
788	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
789	C₂	—	2	2	no	—
790	C₂	—	4	4	no	—
791	C₂	—	8	1	no	—
792	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
793	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
794	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	C₂×C₁₃×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3509	C₂	semidirect
2. C₁₃×#3501	C₂	semidirect
3. C₁₃×#3376	C₂	semidirect
4. C₁₃×#3372	C₂	semidirect
5. C₁₃×#3372	C₂	semidirect
6. C₁₃×#3367	C₂	semidirect
7. C₁₃×#3360	C₂	semidirect
8. C₁₃×#3359	C₂	semidirect
9. C₁₃×#3139	C₂	semidirect
10. C₁₃×#3137	C₂	semidirect
11. C₁₃×#3082	C₂	semidirect
12. C₁₃×#3076	C₂	semidirect
14. C₂×C₁₃×#461	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
16. C₁₃×#2949	C₂	semidirect
20. C₁₃×#557	C₂²	semidirect
21. C₁₃×#557	C₂²	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
46. C₁₃×#491	C₂²	semidirect
47. C₁₃×#491	C₂²	semidirect
48. C₁₃×#489	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#487	C₂²	semidirect
51. C₁₃×#487	C₂²	semidirect
52. C₁₃×#487	C₂²	semidirect
53. C₁₃×#479	C₂²	semidirect
54. C₁₃×#479	C₂²	semidirect
55. C₁₃×#479	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#475	C₂²	semidirect
62. C₁₃×#474	C₂²	semidirect
70. C₁₃×#446	C₂²	semidirect
71. C₁₃×#446	C₂²	semidirect
72. C₈×Q₈×C₁₃	C₂²	semidirect
215. #61340	C₁₃	direct (N × H)
311. #3509	C₂×C₁₃	semidirect
312. #3501	C₂×C₁₃	semidirect
313. #3376	C₂×C₁₃	semidirect
314. #3372	C₂×C₁₃	semidirect
315. #3372	C₂×C₁₃	semidirect
316. #3367	C₂×C₁₃	semidirect
317. #3360	C₂×C₁₃	semidirect
318. #3359	C₂×C₁₃	semidirect
319. #3139	C₂×C₁₃	semidirect
320. #3137	C₂×C₁₃	semidirect
321. #3082	C₂×C₁₃	semidirect
322. #3076	C₂×C₁₃	semidirect
324. C₂×#461	C₂×C₁₃	semidirect
325. #2962	C₂×C₁₃	semidirect
326. #2949	C₂×C₁₃	semidirect
384. #557	C₂²×C₁₃	semidirect
385. #557	C₂²×C₁₃	semidirect
386. #556	C₂²×C₁₃	semidirect
387. #556	C₂²×C₁₃	semidirect
410. #491	C₂²×C₁₃	semidirect
411. #491	C₂²×C₁₃	semidirect
412. #489	C₂²×C₁₃	semidirect
413. #488	C₂²×C₁₃	semidirect
414. #487	C₂²×C₁₃	semidirect
415. #487	C₂²×C₁₃	semidirect
416. #487	C₂²×C₁₃	semidirect
417. #479	C₂²×C₁₃	semidirect
418. #479	C₂²×C₁₃	semidirect
419. #479	C₂²×C₁₃	semidirect
420. #478	C₂²×C₁₃	semidirect
421. #477	C₂²×C₁₃	semidirect
422. #477	C₂²×C₁₃	semidirect
423. #476	C₂²×C₁₃	semidirect
424. #475	C₂²×C₁₃	semidirect
425. #475	C₂²×C₁₃	semidirect
426. #474	C₂²×C₁₃	semidirect
434. #446	C₂²×C₁₃	semidirect
435. #446	C₂²×C₁₃	semidirect
436. C₈×Q₈	C₂²×C₁₃	semidirect
707. C₁₃	#61340	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×#3509	2
C₁₃×#3501	2
C₁₃×#3376	2
C₁₃×#3372	2
C₁₃×#3367	2
C₁₃×#3360	2
C₁₃×#3359	2
C₁₃×#3139	2
C₁₃×#3137	2
C₁₃×#3082	2
C₁₃×#3076	2
C₁₃×#3042	2
C₂×C₁₃×#461	2
C₁₃×#2962	2
C₁₃×#2949	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61340	13

Subgroups — C13×#61340 #15747679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61340 #15747679