Subgroups — C₁₃×#62112 #15748451

Order 3328.

1740 conjugacy classes of subgroups.

The subgroup lattice has 858 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×#3480	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3356	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3346	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3333	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3316	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3238	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3116	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3079	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	—	2	1	no	—
19	C₁₃×#559	C₂²	1	1	yes	characteristic
20	Q₈²×C₁₃	C₂²	1	2	yes	—
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#557	C₂²	1	1	yes	characteristic
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#556	C₂²	1	1	yes	characteristic
25	C₁₃×#554	C₂²	1	4	yes	—
26	C₁₃×#554	C₂²	1	2	yes	—
27	C₁₃×#553	—	2	2	no	—
28	C₁₃×#553	C₂²	1	2	yes	—
29	C₁₃×#550	C₂²	1	1	yes	characteristic
30	D₄×Q₈×C₁₃	—	2	2	no	—
31	D₄×Q₈×C₁₃	—	2	1	no	—
32	C₁₃×#548	C₂²	1	2	yes	—
33	C₁₃×#544	—	2	1	no	—
34	C₁₃×#544	—	2	2	no	—
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₁₃×#533	C₂²	1	2	yes	—
37	C₁₃×#532	—	2	1	no	—
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
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	2	yes	—
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	4	yes	—
49	C₁₃×#498	C₂²	1	2	yes	—
50	C₁₃×#489	C₂²	1	4	yes	—
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	4	yes	—
53	C₁₃×#484	C₂²	1	2	yes	—
54	C₁₃×#483	C₂²	1	4	yes	—
55	C₁₃×#481	C₂²	1	4	yes	—
56	C₁₃×#480	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#477	C₂²	1	2	yes	—
59	C₁₃×#477	C₂²	1	2	yes	—
60	C₁₃×#477	C₂²	1	2	yes	—
61	C₁₃×#477	C₂²	1	2	yes	—
62	C₁₃×#477	C₂²	1	1	yes	characteristic
63	C₁₃×#477	C₂²	1	1	yes	characteristic
64	C₁₃×#476	C₂²	1	2	yes	—
65	C₁₃×#476	C₂²	1	2	yes	—
66	C₁₃×#476	C₂²	1	2	yes	—
67	C₁₃×#475	C₂²	1	4	yes	—
68	C₁₃×#475	C₂²	1	2	yes	—
69	C₁₃×#474	C₂²	1	4	yes	—
70	C₁₃×#470	C₂²	1	4	yes	—
71	C₁₃×#468	C₂²	1	4	yes	—
72	C₁₃×#465	C₂²	1	4	yes	—
73	C₁₃×#464	C₂²	1	4	yes	—
74	C₁₃×#462	C₂²	1	1	yes	characteristic
75	C₁₃×#462	C₂²	1	1	yes	characteristic
76	C₁₃×#461	C₂²	1	2	yes	—
77	C₁₃×#460	C₂²	1	2	yes	—
78	C₁₃×#452	C₂²	1	4	yes	—
79	C₁₃×#451	C₂²	1	2	yes	—
80	C₁₃×#446	C₂²	1	2	yes	—
81	C₁₃×#441	C₂²	1	4	yes	—
82	C₁₃×#440	C₂²	1	4	yes	—
83	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
84	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
85	C₁₃×#436	C₂²	1	2	yes	—
86	C₁₃×#435	C₂²	1	4	yes	—
87	C₁₃×#432	C₂²	1	2	yes	—
88	C₁₃×#431	C₂²	1	1	yes	characteristic
89	C₁₃×#428	C₂²	1	4	yes	—
90	C₂×C₁₃×#107	C₂²	1	2	yes	—
91	C₁₃×#423	C₂²	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	C₁₃×#417	C₂²	1	4	yes	—
94	C₂×C₁₃×#103	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	—	2	1	no	—
99	C₂²×Q₈×C₁₃	—	2	2	no	—
100	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
105	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
106	C₁₃×C₄⋊Q₈	—	2	1	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	4	no	—
109	C₁₃×C₄⋊Q₈	—	2	2	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	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
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	2	yes	—
119	C₁₃×#127	—	2	1	no	—
120	C₁₃×#127	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	1	no	—
134	C₁₃×#124	C₂³	1	2	yes	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	1	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	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	C₂³	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	—	2	1	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	C₂³	1	2	yes	—
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	1	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	—	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	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₁₃	—	2	4	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	D₄	1	2	yes	—
180	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	1	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	D₄	1	1	yes	characteristic
190	C₁₃×#117	D₄	1	2	yes	—
191	C₁₃×#117	C₂³	1	2	yes	—
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	2	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×C₄²×C₁₃	—	2	1	no	—
199	C₂×C₄²×C₁₃	—	2	2	no	—
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
202	C₁₃×#107	C₂³	1	4	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	2	yes	—
205	C₁₃×#107	C₂³	1	2	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	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	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	#62112	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₁₃×#41	—	2	4	no	—
230	C₁₃×#41	—	2	4	no	—
231	C₁₃×#41	—	4	2	no	—
232	C₁₃×#41	—	4	4	no	—
233	C₂×Q₈×C₁₃	—	2	1	no	—
234	C₂×Q₈×C₁₃	—	2	1	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	4	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	4	1	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	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	—	2	1	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	4	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₁₃×Q₁₆	—	2	4	no	—
269	C₁₃×Q₁₆	—	4	2	no	—
270	C₁₃×SD₁₆	—	4	4	no	—
271	C₁₃×M₁₆	—	4	4	no	—
272	C₂×C₈×C₁₃	—	4	2	no	—
273	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	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	4	no	—
295	C₁₃×C₄⋊C₄	—	2	2	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	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	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	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	1	no	—
326	C₄²×C₁₃	—	2	4	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	C₂×D₄	1	2	yes	—
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	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	#3480	C₂×C₁₃	1	1	yes	characteristic
337	#3387	C₂×C₁₃	1	2	yes	complemented
338	#3375	C₂×C₁₃	1	2	yes	complemented
339	#3356	C₂×C₁₃	1	2	yes	complemented
340	#3346	C₂×C₁₃	1	4	yes	complemented
341	#3333	C₂×C₁₃	1	2	yes	complemented
342	#3316	C₂×C₁₃	1	4	yes	complemented
343	#3252	C₂×C₁₃	1	2	yes	complemented
344	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3238	C₂×C₁₃	1	2	yes	complemented
346	#3227	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3116	C₂×C₁₃	1	2	yes	complemented
348	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3079	C₂×C₁₃	1	2	yes	complemented
350	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
354	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
355	Q₈×C₁₃	—	2	2	no	—
356	Q₈×C₁₃	—	2	1	no	—
357	Q₈×C₁₃	—	2	2	no	—
358	Q₈×C₁₃	—	2	1	no	—
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	2	1	no	—
361	Q₈×C₁₃	—	4	2	no	—
362	Q₈×C₁₃	—	4	4	no	—
363	Q₈×C₁₃	—	4	2	no	—
364	Q₈×C₁₃	—	4	2	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	2	no	—
370	D₄×C₁₃	—	2	2	no	—
371	D₄×C₁₃	—	2	2	no	—
372	D₄×C₁₃	—	4	4	no	—
373	D₄×C₁₃	—	4	4	no	—
374	D₄×C₁₃	—	4	2	no	—
375	D₄×C₁₃	—	8	1	no	—
376	D₄×C₁₃	—	8	2	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	4	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	2	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	1	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	1	no	—
392	C₂×C₄×C₁₃	—	4	4	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	8	2	no	—
396	C₂×C₄×C₁₃	—	8	1	no	—
397	C₂×C₄×C₁₃	—	8	2	no	—
398	C₂×C₄×C₁₃	—	8	4	no	—
399	C₂×C₄×C₁₃	#137	1	4	yes	—
400	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
409	C₈×C₁₃	—	2	2	no	—
410	C₈×C₁₃	—	2	4	no	—
411	C₈×C₁₃	—	2	2	no	—
412	#559	—	2	1	no	—
413	#559	C₂²×C₁₃	1	1	yes	characteristic
414	Q₈²	C₂²×C₁₃	1	2	yes	—
415	#557	—	2	1	no	—
416	#557	C₂²×C₁₃	1	1	yes	characteristic
417	#556	—	2	1	no	—
418	#556	C₂²×C₁₃	1	1	yes	characteristic
419	#554	C₂²×C₁₃	1	2	yes	—
420	#554	C₂²×C₁₃	1	4	yes	—
421	#553	—	2	2	no	—
422	#553	C₂²×C₁₃	1	2	yes	—
423	#550	C₂²×C₁₃	1	1	yes	characteristic
424	D₄×Q₈	—	2	2	no	—
425	D₄×Q₈	—	2	1	no	—
426	#548	C₂²×C₁₃	1	2	yes	—
427	#544	—	2	1	no	—
428	#544	—	2	2	no	—
429	#533	C₂²×C₁₃	1	1	yes	characteristic
430	#533	C₂²×C₁₃	1	2	yes	—
431	#532	—	2	1	no	—
432	#532	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
435	#529	—	2	2	no	—
436	#529	C₂²×C₁₃	1	2	yes	—
437	#520	—	2	1	no	—
438	C₄×#41	—	2	1	no	—
439	C₄×#41	C₂²×C₁₃	1	2	yes	—
440	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
442	#501	C₂²×C₁₃	1	4	yes	—
443	#498	C₂²×C₁₃	1	2	yes	—
444	#489	C₂²×C₁₃	1	4	yes	—
445	#486	C₂²×C₁₃	1	2	yes	—
446	#485	C₂²×C₁₃	1	4	yes	—
447	#484	C₂²×C₁₃	1	2	yes	—
448	#483	C₂²×C₁₃	1	4	yes	—
449	#481	C₂²×C₁₃	1	4	yes	—
450	#480	C₂²×C₁₃	1	4	yes	—
451	#479	C₂²×C₁₃	1	4	yes	—
452	#477	C₂²×C₁₃	1	2	yes	—
453	#477	C₂²×C₁₃	1	2	yes	—
454	#477	C₂²×C₁₃	1	2	yes	—
455	#477	C₂²×C₁₃	1	2	yes	—
456	#477	C₂²×C₁₃	1	1	yes	characteristic
457	#477	C₂²×C₁₃	1	1	yes	characteristic
458	#476	C₂²×C₁₃	1	2	yes	—
459	#476	C₂²×C₁₃	1	2	yes	—
460	#476	C₂²×C₁₃	1	2	yes	—
461	#475	C₂²×C₁₃	1	4	yes	—
462	#475	C₂²×C₁₃	1	2	yes	—
463	#474	C₂²×C₁₃	1	4	yes	—
464	#470	C₂²×C₁₃	1	4	yes	—
465	#468	C₂²×C₁₃	1	4	yes	—
466	#465	C₂²×C₁₃	1	4	yes	—
467	#464	C₂²×C₁₃	1	4	yes	—
468	#462	C₂²×C₁₃	1	1	yes	characteristic
469	#462	C₂²×C₁₃	1	1	yes	characteristic
470	#461	C₂²×C₁₃	1	2	yes	—
471	#460	C₂²×C₁₃	1	2	yes	—
472	#452	C₂²×C₁₃	1	4	yes	—
473	#451	C₂²×C₁₃	1	2	yes	—
474	#446	C₂²×C₁₃	1	2	yes	—
475	#441	C₂²×C₁₃	1	4	yes	—
476	#440	C₂²×C₁₃	1	4	yes	—
477	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
478	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
479	#436	C₂²×C₁₃	1	2	yes	—
480	#435	C₂²×C₁₃	1	4	yes	—
481	#432	C₂²×C₁₃	1	2	yes	—
482	#431	C₂²×C₁₃	1	1	yes	characteristic
483	#428	C₂²×C₁₃	1	4	yes	—
484	C₂×#107	C₂²×C₁₃	1	2	yes	—
485	#423	C₂²×C₁₃	1	2	yes	—
486	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
487	#417	C₂²×C₁₃	1	4	yes	—
488	C₂×#103	C₂²×C₁₃	1	2	yes	—
489	C₂²×C₁₃	—	2	1	no	—
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	2	2	no	—
492	C₂²×C₁₃	—	2	2	no	—
493	C₂²×C₁₃	—	2	2	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	4	2	no	—
496	C₂²×C₁₃	—	4	2	no	—
497	C₂²×C₁₃	C₂×#137	1	2	yes	—
498	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
499	C₄×C₁₃	—	2	1	no	—
500	C₄×C₁₃	—	2	2	no	—
501	C₄×C₁₃	—	2	1	no	—
502	C₄×C₁₃	—	2	2	no	—
503	C₄×C₁₃	—	2	1	no	—
504	C₄×C₁₃	—	2	2	no	—
505	C₄×C₁₃	—	2	2	no	—
506	C₄×C₁₃	—	4	1	no	—
507	C₄×C₁₃	—	4	4	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	—	4	1	no	—
510	C₄×C₁₃	—	4	1	no	—
511	C₄×C₁₃	—	4	2	no	—
512	C₄×C₁₃	—	4	2	no	—
513	C₄×C₁₃	C₂×#137	1	2	yes	—
514	C₄×C₁₃	C₂×#137	1	2	yes	—
515	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
516	C₄×C₁₃	#585	1	1	yes	characteristic
517	C₂×#41	—	2	1	no	—
518	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
519	C₂×#41	C₂³×C₁₃	1	2	yes	—
520	C₂²×Q₈	—	2	1	no	—
521	C₂²×Q₈	—	2	2	no	—
522	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
524	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
525	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
526	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
527	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	—	2	2	no	—
530	C₄⋊Q₈	—	2	4	no	—
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	—	2	2	no	—
534	C₄⋊Q₈	—	2	1	no	—
535	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
536	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
537	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
539	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
540	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
541	#127	—	2	1	no	—
542	#127	C₂³×C₁₃	1	1	yes	characteristic
543	#126	—	2	2	no	—
544	#126	—	2	2	no	—
545	#126	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	—	2	4	no	—
549	#125	—	2	2	no	—
550	#125	—	2	1	no	—
551	#125	C₂³×C₁₃	1	2	yes	—
552	#124	—	2	1	no	—
553	#124	—	2	1	no	—
554	#124	—	2	2	no	—
555	#124	—	2	1	no	—
556	#124	C₂³×C₁₃	1	2	yes	—
557	#123	—	2	2	no	—
558	#123	—	2	2	no	—
559	#123	—	2	2	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	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#121	—	2	1	no	—
572	#121	—	2	2	no	—
573	#121	C₂³×C₁₃	1	2	yes	—
574	#121	C₂³×C₁₃	1	2	yes	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
583	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
584	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
588	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
590	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	D₄×C₁₃	1	2	yes	—
602	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₁₃	1	2	yes	—
604	C₄×D₄	C₂³×C₁₃	1	2	yes	—
605	C₄×D₄	C₂³×C₁₃	1	2	yes	—
606	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
607	#117	—	2	2	no	—
608	#117	—	2	1	no	—
609	#117	—	2	2	no	—
610	#117	—	2	2	no	—
611	#117	D₄×C₁₃	1	1	yes	characteristic
612	#117	D₄×C₁₃	1	2	yes	—
613	#117	C₂³×C₁₃	1	2	yes	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
620	C₂×C₄²	—	2	1	no	—
621	C₂×C₄²	—	2	2	no	—
622	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
624	#107	C₂³×C₁₃	1	4	yes	—
625	#107	C₂³×C₁₃	1	4	yes	—
626	#107	C₂³×C₁₃	1	2	yes	—
627	#107	C₂³×C₁₃	1	2	yes	—
628	#106	C₂³×C₁₃	1	4	yes	—
629	#106	C₂³×C₁₃	1	4	yes	—
630	#106	C₂³×C₁₃	1	4	yes	—
631	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
632	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
633	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
634	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
635	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
636	#103	C₂³×C₁₃	1	4	yes	—
637	#103	C₂³×C₁₃	1	4	yes	—
638	#103	C₂³×C₁₃	1	2	yes	—
639	#103	C₂³×C₁₃	1	2	yes	—
640	#103	C₂³×C₁₃	1	2	yes	—
641	#103	C₂³×C₁₃	1	2	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	4	yes	—
646	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
647	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
648	#97	C₂³×C₁₃	1	4	yes	—
649	C₄×C₈	C₂³×C₁₃	1	2	yes	—
650	C₂×C₁₃	—	2	2	no	—
651	C₂×C₁₃	—	4	2	no	—
652	C₂×C₁₃	—	8	2	no	—
653	C₂×C₁₃	#3489	1	1	yes	characteristic
654	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
655	C₂×C₁₃	#3585	1	1	yes	characteristic
656	#41	—	2	4	no	—
657	#41	—	2	4	no	—
658	#41	—	4	2	no	—
659	#41	—	4	4	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	4	1	no	—
668	C₂×Q₈	—	8	4	no	—
669	C₂×Q₈	—	8	2	no	—
670	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
680	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
681	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
690	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
692	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
695	Q₁₆	—	2	4	no	—
696	Q₁₆	—	4	2	no	—
697	SD₁₆	—	4	4	no	—
698	M₁₆	—	4	4	no	—
699	C₂×C₈	—	4	2	no	—
700	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
701	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
702	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
728	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
731	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
745	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
747	C₄²	—	2	1	no	—
748	C₄²	—	2	1	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	1	no	—
752	C₄²	—	2	1	no	—
753	C₄²	—	2	4	no	—
754	C₄²	—	2	2	no	—
755	C₄²	C₂×D₄×C₁₃	1	2	yes	—
756	C₄²	C₂×D₄×C₁₃	1	2	yes	—
757	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
758	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
759	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
760	C₄²	C₂⁴×C₁₃	1	2	yes	—
761	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₁₃	#62112	1	1	yes	characteristic, direct product factor, Sylow
763	C₂³	—	2	2	no	—
764	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
765	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
766	Q₈	—	2	2	no	—
767	Q₈	—	2	1	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	1	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	1	no	—
772	Q₈	—	4	2	no	—
773	Q₈	—	4	4	no	—
774	Q₈	—	4	2	no	—
775	Q₈	—	4	2	no	—
776	Q₈	—	8	4	no	—
777	Q₈	—	8	2	no	—
778	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
779	D₄	—	2	4	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	4	4	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	2	no	—
786	D₄	—	8	1	no	—
787	D₄	—	8	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	1	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	4	no	—
810	C₂×C₄	C₁₃×#137	1	4	yes	—
811	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
812	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
813	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
820	C₈	—	2	2	no	—
821	C₈	—	2	4	no	—
822	C₈	—	2	2	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	C₂×C₁₃×#137	1	2	yes	—
832	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
833	C₄	—	2	2	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	1	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	4	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	2	no	—
847	C₄	C₂×C₁₃×#137	1	2	yes	—
848	C₄	C₂×C₁₃×#137	1	2	yes	—
849	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
850	C₄	C₁₃×#585	1	1	yes	characteristic
851	C₂	—	2	2	no	—
852	C₂	—	4	2	no	—
853	C₂	—	8	2	no	—
854	C₂	C₁₃×#3489	1	1	yes	characteristic
855	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
856	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3480	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×#3375	C₂	semidirect
5. C₁₃×#3356	C₂	semidirect
6. C₁₃×#3346	C₂	semidirect
7. C₁₃×#3333	C₂	semidirect
8. C₁₃×#3316	C₂	semidirect
9. C₁₃×#3252	C₂	semidirect
10. C₁₃×#3246	C₂	semidirect
11. C₁₃×#3238	C₂	semidirect
12. C₁₃×#3227	C₂	semidirect
13. C₁₃×#3116	C₂	semidirect
14. C₁₃×#3104	C₂	semidirect
15. C₁₃×#3079	C₂	semidirect
16. C₂×C₁₃×#477	C₂	semidirect
17. C₁₃×#2989	C₂	semidirect
228. #62112	C₁₃	direct (N × H)
335. #3503	C₂×C₁₃	semidirect
337. #3387	C₂×C₁₃	semidirect
338. #3375	C₂×C₁₃	semidirect
339. #3356	C₂×C₁₃	semidirect
340. #3346	C₂×C₁₃	semidirect
341. #3333	C₂×C₁₃	semidirect
342. #3316	C₂×C₁₃	semidirect
343. #3252	C₂×C₁₃	semidirect
344. #3246	C₂×C₁₃	semidirect
345. #3238	C₂×C₁₃	semidirect
346. #3227	C₂×C₁₃	semidirect
347. #3116	C₂×C₁₃	semidirect
348. #3104	C₂×C₁₃	semidirect
349. #3079	C₂×C₁₃	semidirect
350. C₂×#477	C₂×C₁₃	semidirect
351. #2989	C₂×C₁₃	semidirect
762. C₁₃	#62112	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×#3480	2
C₁₃×#3387	2
C₁₃×#3375	2
C₁₃×#3356	2
C₁₃×#3346	2
C₁₃×#3333	2
C₁₃×#3316	2
C₁₃×#3252	2
C₁₃×#3246	2
C₁₃×#3238	2
C₁₃×#3227	2
C₁₃×#3116	2
C₁₃×#3104	2
C₁₃×#3079	2
C₂×C₁₃×#477	2
C₁₃×#2989	2
#62112	13

Subgroups — C13×#62112 #15748451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62112 #15748451