Subgroups — C₁₃×#62131 #15748470

Order 3328.

1736 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3344	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3335	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3316	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3248	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3239	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3113	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#475	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₁₃	C₂²	1	2	yes	—
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	C₂²	1	1	yes	characteristic
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	C₂²	1	1	yes	characteristic
23	C₁₃×#554	C₂²	1	2	yes	—
24	C₁₃×#554	C₂²	1	4	yes	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#552	C₂²	1	2	yes	—
27	D₄×Q₈×C₁₃	—	2	1	no	—
28	D₄×Q₈×C₁₃	—	2	2	no	—
29	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#548	C₂²	1	2	yes	—
31	C₁₃×#547	—	2	1	no	—
32	C₁₃×#547	C₂²	1	1	yes	characteristic
33	C₁₃×#544	—	2	2	no	—
34	C₁₃×#544	—	2	1	no	—
35	C₁₃×#533	—	2	1	no	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	2	yes	—
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₃×#529	—	2	2	no	—
42	C₁₃×#529	C₂²	1	2	yes	—
43	C₁₃×#520	—	2	1	no	—
44	C₄×C₁₃×#41	—	2	1	no	—
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
48	C₁₃×#501	C₂²	1	4	yes	—
49	C₁₃×#498	C₂²	1	2	yes	—
50	C₁₃×#489	C₂²	1	4	yes	—
51	C₁₃×#487	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	2	yes	—
53	C₁₃×#484	C₂²	1	4	yes	—
54	C₁₃×#483	C₂²	1	4	yes	—
55	C₁₃×#483	C₂²	1	4	yes	—
56	C₁₃×#481	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#477	C₂²	1	2	yes	—
59	C₁₃×#476	C₂²	1	2	yes	—
60	C₁₃×#475	C₂²	1	4	yes	—
61	C₁₃×#475	C₂²	1	1	yes	characteristic
62	C₁₃×#475	C₂²	1	2	yes	—
63	C₁₃×#475	C₂²	1	4	yes	—
64	C₁₃×#475	C₂²	1	2	yes	—
65	C₁₃×#475	C₂²	1	2	yes	—
66	C₁₃×#475	C₂²	1	2	yes	—
67	C₁₃×#475	C₂²	1	2	yes	—
68	C₁₃×#474	C₂²	1	2	yes	—
69	C₁₃×#474	C₂²	1	1	yes	characteristic
70	C₁₃×#470	C₂²	1	4	yes	—
71	C₁₃×#467	C₂²	1	4	yes	—
72	C₁₃×#465	C₂²	1	4	yes	—
73	C₁₃×#464	C₂²	1	4	yes	—
74	C₁₃×#462	C₂²	1	2	yes	—
75	C₁₃×#462	C₂²	1	1	yes	characteristic
76	C₁₃×#462	C₂²	1	2	yes	—
77	C₁₃×#461	C₂²	1	1	yes	characteristic
78	C₁₃×#452	C₂²	1	2	yes	—
79	C₁₃×#451	C₂²	1	4	yes	—
80	C₁₃×#446	C₂²	1	2	yes	—
81	C₁₃×#441	C₂²	1	4	yes	—
82	C₁₃×#441	C₂²	1	4	yes	—
83	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
85	C₁₃×#435	C₂²	1	4	yes	—
86	C₈×D₄×C₁₃	C₂²	1	2	yes	—
87	C₁₃×#432	C₂²	1	2	yes	—
88	C₁₃×#431	C₂²	1	1	yes	characteristic
89	C₁₃×#428	C₂²	1	2	yes	—
90	C₂×C₁₃×#106	C₂²	1	4	yes	—
91	C₁₃×#423	C₂²	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
93	C₁₃×#417	C₂²	1	2	yes	—
94	C₂×C₁₃×#103	C₂²	1	4	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	—	2	2	no	—
99	C₂²×Q₈×C₁₃	—	2	1	no	—
100	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
101	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
105	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
106	C₁₃×C₄⋊Q₈	—	2	1	no	—
107	C₁₃×C₄⋊Q₈	—	2	1	no	—
108	C₁₃×C₄⋊Q₈	—	2	2	no	—
109	C₁₃×C₄⋊Q₈	—	2	4	no	—
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	2	no	—
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	—	2	4	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	—	2	1	no	—
129	C₁₃×#125	—	2	2	no	—
130	C₁₃×#125	—	2	1	no	—
131	C₁₃×#125	C₂³	1	2	yes	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	C₂³	1	2	yes	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	1	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	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	4	no	—
146	C₁₃×C₂²⋊Q₈	—	2	4	no	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₃×#121	—	2	2	no	—
152	C₁₃×#121	C₂³	1	2	yes	—
153	C₄×Q₈×C₁₃	—	2	2	no	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	2	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	—	2	1	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	—	2	4	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
177	C₄×D₄×C₁₃	D₄	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	1	yes	characteristic
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₁₃×#117	—	2	2	no	—
183	C₁₃×#117	—	2	1	no	—
184	C₁₃×#117	—	2	1	no	—
185	C₁₃×#117	—	2	1	no	—
186	C₁₃×#117	—	2	2	no	—
187	C₁₃×#117	—	2	1	no	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	D₄	1	2	yes	—
190	C₁₃×#117	D₄	1	1	yes	characteristic
191	C₁₃×#117	C₂³	1	1	yes	characteristic
192	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₃	—	2	2	no	—
199	C₂×C₄²×C₁₃	—	2	1	no	—
200	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₁₃×#107	C₂³	1	4	yes	—
203	C₁₃×#107	C₂³	1	2	yes	—
204	C₁₃×#106	C₂³	1	2	yes	—
205	C₁₃×#106	C₂³	1	4	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×#106	C₂³	1	4	yes	—
208	C₁₃×#106	C₂³	1	4	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#62131	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₁₃×#41	—	2	4	no	—
230	C₁₃×#41	—	2	2	no	—
231	C₁₃×#41	—	4	1	no	—
232	C₁₃×#41	—	4	4	no	—
233	C₂×Q₈×C₁₃	—	2	2	no	—
234	C₂×Q₈×C₁₃	—	2	1	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	4	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	4	no	—
240	C₂×Q₈×C₁₃	—	4	2	no	—
241	C₂×Q₈×C₁₃	—	8	4	no	—
242	C₂×Q₈×C₁₃	—	8	2	no	—
243	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	—	2	2	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	4	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₁₃×Q₁₆	—	2	4	no	—
266	C₁₃×Q₁₆	—	4	4	no	—
267	C₁₃×SD₁₆	—	4	2	no	—
268	C₁₃×M₁₆	—	4	2	no	—
269	C₂×C₈×C₁₃	—	4	4	no	—
270	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
271	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
272	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	4	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
299	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
302	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	1	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
318	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
319	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
320	C₄²×C₁₃	—	2	1	no	—
321	C₄²×C₁₃	—	2	1	no	—
322	C₄²×C₁₃	—	2	2	no	—
323	C₄²×C₁₃	—	2	2	no	—
324	C₄²×C₁₃	—	2	1	no	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	4	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₃	C₂×D₄	1	2	yes	—
331	C₄²×C₁₃	C₂×D₄	1	2	yes	—
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3482	C₂×C₁₃	1	1	yes	characteristic
337	#3387	C₂×C₁₃	1	2	yes	complemented
338	#3369	C₂×C₁₃	1	2	yes	complemented
339	#3344	C₂×C₁₃	1	4	yes	complemented
340	#3335	C₂×C₁₃	1	2	yes	complemented
341	#3316	C₂×C₁₃	1	4	yes	complemented
342	#3299	C₂×C₁₃	1	2	yes	complemented
343	#3255	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3248	C₂×C₁₃	1	2	yes	complemented
345	#3239	C₂×C₁₃	1	2	yes	complemented
346	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3113	C₂×C₁₃	1	2	yes	complemented
348	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₂×#475	C₂×C₁₃	1	2	yes	complemented
351	#2990	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
354	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
355	Q₈×C₁₃	—	2	2	no	—
356	Q₈×C₁₃	—	2	1	no	—
357	Q₈×C₁₃	—	2	2	no	—
358	Q₈×C₁₃	—	2	2	no	—
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	4	4	no	—
362	Q₈×C₁₃	—	4	2	no	—
363	Q₈×C₁₃	—	4	2	no	—
364	Q₈×C₁₃	—	4	4	no	—
365	Q₈×C₁₃	—	8	4	no	—
366	Q₈×C₁₃	—	8	2	no	—
367	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
368	D₄×C₁₃	—	2	4	no	—
369	D₄×C₁₃	—	2	1	no	—
370	D₄×C₁₃	—	2	1	no	—
371	D₄×C₁₃	—	4	2	no	—
372	D₄×C₁₃	—	4	4	no	—
373	D₄×C₁₃	#137	1	4	yes	—
374	C₂×C₄×C₁₃	—	2	4	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	4	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	4	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	4	2	no	—
391	C₂×C₄×C₁₃	—	4	4	no	—
392	C₂×C₄×C₁₃	—	4	4	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	4	2	no	—
395	C₂×C₄×C₁₃	—	8	4	no	—
396	C₂×C₄×C₁₃	—	8	2	no	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
406	C₈×C₁₃	—	2	2	no	—
407	C₈×C₁₃	—	2	2	no	—
408	C₈×C₁₃	—	2	4	no	—
409	Q₈²	C₂²×C₁₃	1	2	yes	—
410	#557	—	2	1	no	—
411	#557	C₂²×C₁₃	1	1	yes	characteristic
412	#556	—	2	1	no	—
413	#556	C₂²×C₁₃	1	1	yes	characteristic
414	#554	C₂²×C₁₃	1	2	yes	—
415	#554	C₂²×C₁₃	1	4	yes	—
416	#552	—	2	2	no	—
417	#552	C₂²×C₁₃	1	2	yes	—
418	D₄×Q₈	—	2	1	no	—
419	D₄×Q₈	—	2	2	no	—
420	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
421	#548	C₂²×C₁₃	1	2	yes	—
422	#547	—	2	1	no	—
423	#547	C₂²×C₁₃	1	1	yes	characteristic
424	#544	—	2	2	no	—
425	#544	—	2	1	no	—
426	#533	—	2	1	no	—
427	#533	C₂²×C₁₃	1	1	yes	characteristic
428	#533	C₂²×C₁₃	1	2	yes	—
429	#533	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
431	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
432	#529	—	2	2	no	—
433	#529	C₂²×C₁₃	1	2	yes	—
434	#520	—	2	1	no	—
435	C₄×#41	—	2	1	no	—
436	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
437	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
439	#501	C₂²×C₁₃	1	4	yes	—
440	#498	C₂²×C₁₃	1	2	yes	—
441	#489	C₂²×C₁₃	1	4	yes	—
442	#487	C₂²×C₁₃	1	2	yes	—
443	#485	C₂²×C₁₃	1	2	yes	—
444	#484	C₂²×C₁₃	1	4	yes	—
445	#483	C₂²×C₁₃	1	4	yes	—
446	#483	C₂²×C₁₃	1	4	yes	—
447	#481	C₂²×C₁₃	1	4	yes	—
448	#479	C₂²×C₁₃	1	4	yes	—
449	#477	C₂²×C₁₃	1	2	yes	—
450	#476	C₂²×C₁₃	1	2	yes	—
451	#475	C₂²×C₁₃	1	1	yes	characteristic
452	#475	C₂²×C₁₃	1	2	yes	—
453	#475	C₂²×C₁₃	1	4	yes	—
454	#475	C₂²×C₁₃	1	4	yes	—
455	#475	C₂²×C₁₃	1	2	yes	—
456	#475	C₂²×C₁₃	1	2	yes	—
457	#475	C₂²×C₁₃	1	2	yes	—
458	#475	C₂²×C₁₃	1	2	yes	—
459	#474	C₂²×C₁₃	1	2	yes	—
460	#474	C₂²×C₁₃	1	1	yes	characteristic
461	#470	C₂²×C₁₃	1	4	yes	—
462	#467	C₂²×C₁₃	1	4	yes	—
463	#465	C₂²×C₁₃	1	4	yes	—
464	#464	C₂²×C₁₃	1	4	yes	—
465	#462	C₂²×C₁₃	1	1	yes	characteristic
466	#462	C₂²×C₁₃	1	2	yes	—
467	#462	C₂²×C₁₃	1	2	yes	—
468	#461	C₂²×C₁₃	1	1	yes	characteristic
469	#452	C₂²×C₁₃	1	2	yes	—
470	#451	C₂²×C₁₃	1	4	yes	—
471	#446	C₂²×C₁₃	1	2	yes	—
472	#441	C₂²×C₁₃	1	4	yes	—
473	#441	C₂²×C₁₃	1	4	yes	—
474	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
475	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
476	#435	C₂²×C₁₃	1	4	yes	—
477	C₈×D₄	C₂²×C₁₃	1	2	yes	—
478	#432	C₂²×C₁₃	1	2	yes	—
479	#431	C₂²×C₁₃	1	1	yes	characteristic
480	#428	C₂²×C₁₃	1	2	yes	—
481	C₂×#106	C₂²×C₁₃	1	4	yes	—
482	#423	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
484	#417	C₂²×C₁₃	1	2	yes	—
485	C₂×#103	C₂²×C₁₃	1	4	yes	—
486	C₂²×C₁₃	—	2	2	no	—
487	C₂²×C₁₃	—	2	2	no	—
488	C₂²×C₁₃	—	2	1	no	—
489	C₂²×C₁₃	—	2	1	no	—
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	4	1	no	—
492	C₂²×C₁₃	—	4	1	no	—
493	C₂²×C₁₃	—	4	1	no	—
494	C₂²×C₁₃	C₂×#137	1	4	yes	—
495	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
496	C₄×C₁₃	—	2	1	no	—
497	C₄×C₁₃	—	2	2	no	—
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	2	1	no	—
500	C₄×C₁₃	—	2	2	no	—
501	C₄×C₁₃	—	2	2	no	—
502	C₄×C₁₃	—	2	1	no	—
503	C₄×C₁₃	—	4	2	no	—
504	C₄×C₁₃	—	4	2	no	—
505	C₄×C₁₃	—	4	1	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	1	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	—	4	4	no	—
510	C₄×C₁₃	C₂×#137	1	2	yes	—
511	C₄×C₁₃	#577	1	2	yes	—
512	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
513	C₄×C₁₃	#585	1	1	yes	characteristic
514	C₂×#41	—	2	1	no	—
515	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
516	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×Q₈	—	2	2	no	—
518	C₂²×Q₈	—	2	1	no	—
519	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
520	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
521	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
522	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
523	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
524	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	—	2	2	no	—
528	C₄⋊Q₈	—	2	4	no	—
529	C₄⋊Q₈	—	2	1	no	—
530	C₄⋊Q₈	—	2	2	no	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	2	no	—
533	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
536	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
537	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
538	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
539	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#126	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	—	2	2	no	—
545	#125	—	2	4	no	—
546	#125	—	2	2	no	—
547	#125	—	2	1	no	—
548	#125	—	2	2	no	—
549	#125	—	2	1	no	—
550	#125	C₂³×C₁₃	1	2	yes	—
551	#124	—	2	2	no	—
552	#124	C₂³×C₁₃	1	2	yes	—
553	#123	—	2	2	no	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	4	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
567	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
568	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
569	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
570	#121	—	2	2	no	—
571	#121	C₂³×C₁₃	1	2	yes	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	2	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
580	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
581	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
582	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
583	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
584	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
586	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
587	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	4	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
596	C₄×D₄	D₄×C₁₃	1	2	yes	—
597	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
598	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
599	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₄×D₄	C₂³×C₁₃	1	2	yes	—
601	#117	—	2	2	no	—
602	#117	—	2	1	no	—
603	#117	—	2	1	no	—
604	#117	—	2	1	no	—
605	#117	—	2	2	no	—
606	#117	—	2	1	no	—
607	#117	—	2	2	no	—
608	#117	D₄×C₁₃	1	2	yes	—
609	#117	D₄×C₁₃	1	1	yes	characteristic
610	#117	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	—	2	2	no	—
612	C₂×C₄⋊C₄	—	2	2	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄²	—	2	2	no	—
618	C₂×C₄²	—	2	1	no	—
619	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
620	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
621	#107	C₂³×C₁₃	1	4	yes	—
622	#107	C₂³×C₁₃	1	2	yes	—
623	#106	C₂³×C₁₃	1	2	yes	—
624	#106	C₂³×C₁₃	1	4	yes	—
625	#106	C₂³×C₁₃	1	4	yes	—
626	#106	C₂³×C₁₃	1	4	yes	—
627	#106	C₂³×C₁₃	1	4	yes	—
628	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
629	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
630	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
631	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
632	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
633	#103	C₂³×C₁₃	1	2	yes	—
634	#103	C₂³×C₁₃	1	4	yes	—
635	#103	C₂³×C₁₃	1	4	yes	—
636	#103	C₂³×C₁₃	1	4	yes	—
637	#103	C₂³×C₁₃	1	2	yes	—
638	#103	C₂³×C₁₃	1	2	yes	—
639	#103	C₂³×C₁₃	1	4	yes	—
640	#103	C₂³×C₁₃	1	4	yes	—
641	#102	C₂³×C₁₃	1	4	yes	—
642	#102	C₂³×C₁₃	1	2	yes	—
643	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
644	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
645	#97	C₂³×C₁₃	1	4	yes	—
646	C₄×C₈	C₂³×C₁₃	1	2	yes	—
647	C₂×C₁₃	—	2	4	no	—
648	C₂×C₁₃	—	4	1	no	—
649	C₂×C₁₃	—	8	1	no	—
650	C₂×C₁₃	#3489	1	1	yes	characteristic
651	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
652	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
653	#41	—	2	4	no	—
654	#41	—	2	2	no	—
655	#41	—	4	1	no	—
656	#41	—	4	4	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	4	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	4	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×Q₈	—	8	4	no	—
666	C₂×Q₈	—	8	2	no	—
667	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
668	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
669	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
670	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
674	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
684	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
685	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
689	Q₁₆	—	2	4	no	—
690	Q₁₆	—	4	4	no	—
691	SD₁₆	—	4	2	no	—
692	M₁₆	—	4	2	no	—
693	C₂×C₈	—	4	4	no	—
694	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
695	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
696	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
724	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
727	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
742	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
743	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
744	C₄²	—	2	1	no	—
745	C₄²	—	2	1	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	1	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	2	no	—
752	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
754	C₄²	C₂×D₄×C₁₃	1	2	yes	—
755	C₄²	C₂×D₄×C₁₃	1	2	yes	—
756	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
757	C₄²	C₂⁴×C₁₃	1	2	yes	—
758	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₁₃	#62131	1	1	yes	characteristic, direct product factor, Sylow
760	C₂³	—	2	1	no	—
761	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
762	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	1	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	2	no	—
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	4	4	no	—
770	Q₈	—	4	2	no	—
771	Q₈	—	4	2	no	—
772	Q₈	—	4	4	no	—
773	Q₈	—	8	4	no	—
774	Q₈	—	8	2	no	—
775	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
776	D₄	—	2	4	no	—
777	D₄	—	2	1	no	—
778	D₄	—	2	1	no	—
779	D₄	—	4	2	no	—
780	D₄	—	4	4	no	—
781	D₄	C₁₃×#137	1	4	yes	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	8	4	no	—
804	C₂×C₄	—	8	2	no	—
805	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
807	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
810	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
813	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
814	C₈	—	2	2	no	—
815	C₈	—	2	2	no	—
816	C₈	—	2	4	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	C₂×C₁₃×#137	1	4	yes	—
826	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
827	C₄	—	2	1	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	2	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	4	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	C₂×C₁₃×#137	1	2	yes	—
842	C₄	C₁₃×#577	1	2	yes	—
843	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
844	C₄	C₁₃×#585	1	1	yes	characteristic
845	C₂	—	2	4	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	1	no	—
848	C₂	C₁₃×#3489	1	1	yes	characteristic
849	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
850	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3482	C₂
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×#3503	C₂	semidirect
3. C₁₃×#3387	C₂	semidirect
4. C₁₃×#3369	C₂	semidirect
5. C₁₃×#3344	C₂	semidirect
6. C₁₃×#3335	C₂	semidirect
7. C₁₃×#3316	C₂	semidirect
8. C₁₃×#3299	C₂	semidirect
9. C₁₃×#3255	C₂	semidirect
10. C₁₃×#3248	C₂	semidirect
11. C₁₃×#3239	C₂	semidirect
12. C₁₃×#3229	C₂	semidirect
13. C₁₃×#3113	C₂	semidirect
14. C₁₃×#3107	C₂	semidirect
15. C₁₃×#3079	C₂	semidirect
16. C₂×C₁₃×#475	C₂	semidirect
17. C₁₃×#2990	C₂	semidirect
228. #62131	C₁₃	direct (N × H)
335. #3503	C₂×C₁₃	semidirect
337. #3387	C₂×C₁₃	semidirect
338. #3369	C₂×C₁₃	semidirect
339. #3344	C₂×C₁₃	semidirect
340. #3335	C₂×C₁₃	semidirect
341. #3316	C₂×C₁₃	semidirect
342. #3299	C₂×C₁₃	semidirect
343. #3255	C₂×C₁₃	semidirect
344. #3248	C₂×C₁₃	semidirect
345. #3239	C₂×C₁₃	semidirect
346. #3229	C₂×C₁₃	semidirect
347. #3113	C₂×C₁₃	semidirect
348. #3107	C₂×C₁₃	semidirect
349. #3079	C₂×C₁₃	semidirect
350. C₂×#475	C₂×C₁₃	semidirect
351. #2990	C₂×C₁₃	semidirect
759. C₁₃	#62131	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×#3503	2
C₁₃×#3482	2
C₁₃×#3387	2
C₁₃×#3369	2
C₁₃×#3344	2
C₁₃×#3335	2
C₁₃×#3316	2
C₁₃×#3299	2
C₁₃×#3255	2
C₁₃×#3248	2
C₁₃×#3239	2
C₁₃×#3229	2
C₁₃×#3113	2
C₁₃×#3107	2
C₁₃×#3079	2
C₂×C₁₃×#475	2
C₁₃×#2990	2
#62131	13

Subgroups — C13×#62131 #15748470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62131 #15748470