Subgroups — C₁₃×#62135 #15748474

Order 3328.

1756 conjugacy classes of subgroups.

The subgroup lattice has 872 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×#3483	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3348	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3340	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3317	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3304	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3246	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3235	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×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3076	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	C₂²	1	2	yes	—
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	C₂²	1	2	yes	—
23	C₁₃×#555	—	2	1	no	—
24	C₁₃×#555	—	2	2	no	—
25	C₁₃×#555	C₂²	1	1	yes	characteristic
26	C₁₃×#555	C₂²	1	2	yes	—
27	C₁₃×#552	—	2	2	no	—
28	C₁₃×#552	C₂²	1	4	yes	—
29	C₁₃×#550	—	2	1	no	—
30	C₁₃×#550	C₂²	1	1	yes	characteristic
31	C₁₃×#550	C₂²	1	2	yes	—
32	C₁₃×#550	C₂²	1	1	yes	characteristic
33	C₁₃×#541	—	2	2	no	—
34	C₁₃×#536	—	2	1	no	—
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₁₃×#533	C₂²	1	2	yes	—
37	C₁₃×#533	C₂²	1	2	yes	—
38	C₁₃×#532	—	2	2	no	—
39	C₁₃×#532	—	2	1	no	—
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₁₃×#532	C₂²	1	2	yes	—
42	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₁₃×#519	—	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	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	4	yes	—
49	C₁₃×#498	C₂²	1	2	yes	—
50	C₁₃×#490	C₂²	1	4	yes	—
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	4	yes	—
53	C₁₃×#485	C₂²	1	2	yes	—
54	C₁₃×#482	C₂²	1	4	yes	—
55	C₁₃×#482	C₂²	1	4	yes	—
56	C₁₃×#481	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#478	C₂²	1	4	yes	—
59	C₁₃×#477	C₂²	1	2	yes	—
60	C₁₃×#477	C₂²	1	2	yes	—
61	C₁₃×#476	C₂²	1	2	yes	—
62	C₁₃×#476	C₂²	1	2	yes	—
63	C₁₃×#476	C₂²	1	2	yes	—
64	C₁₃×#475	C₂²	1	2	yes	—
65	C₁₃×#475	C₂²	1	1	yes	characteristic
66	C₁₃×#475	C₂²	1	4	yes	—
67	C₁₃×#474	C₂²	1	2	yes	—
68	C₁₃×#474	C₂²	1	2	yes	—
69	C₁₃×#474	C₂²	1	1	yes	characteristic
70	C₁₃×#468	C₂²	1	4	yes	—
71	C₁₃×#465	C₂²	1	4	yes	—
72	C₁₃×#465	C₂²	1	4	yes	—
73	C₁₃×#462	C₂²	1	1	yes	characteristic
74	C₁₃×#461	C₂²	1	1	yes	characteristic
75	C₁₃×#461	C₂²	1	2	yes	—
76	C₁₃×#460	C₂²	1	2	yes	—
77	C₁₃×#460	C₂²	1	4	yes	—
78	C₁₃×#452	C₂²	1	4	yes	—
79	C₁₃×#452	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×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	C₁₃×#427	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	C₁₃×#416	C₂²	1	4	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₁₃	—	2	1	no	—
102	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
106	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	—	2	1	no	—
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×#127	—	2	1	no	—
119	C₁₃×#127	—	2	2	no	—
120	C₁₃×#127	C₂³	1	1	yes	characteristic
121	C₁₃×#127	C₂³	1	2	yes	—
122	C₁₃×#126	—	2	4	no	—
123	C₁₃×#126	—	2	4	no	—
124	C₁₃×#125	—	2	4	no	—
125	C₁₃×#125	—	2	4	no	—
126	C₁₃×#125	—	2	1	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	C₂³	1	4	yes	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	—	2	1	no	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	1	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₁₃×#121	—	2	1	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	—	2	2	no	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	C₂³	1	2	yes	—
152	C₁₃×#121	C₂³	1	2	yes	—
153	C₁₃×#121	C₂³	1	2	yes	—
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	2	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
162	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	D₄	1	2	yes	—
177	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₁₃×#117	—	2	1	no	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	1	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	—	2	4	no	—
189	C₁₃×#117	—	2	2	no	—
190	C₁₃×#117	—	2	1	no	—
191	C₁₃×#117	D₄	1	1	yes	characteristic
192	C₁₃×#117	D₄	1	2	yes	—
193	C₁₃×#117	C₂³	1	4	yes	—
194	C₁₃×#117	C₂³	1	2	yes	—
195	C₁₃×#117	C₂³	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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	4	yes	—
204	C₁₃×#107	C₂³	1	2	yes	—
205	C₁₃×#106	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	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	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	2	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	#62135	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	2	no	—
232	C₁₃×#41	—	4	2	no	—
233	C₁₃×#41	—	4	1	no	—
234	C₁₃×#41	—	4	4	no	—
235	C₁₃×#41	—	8	2	no	—
236	C₁₃×#41	—	8	4	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	1	no	—
242	C₂×Q₈×C₁₃	—	4	4	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	1	yes	characteristic
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	1	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	1	no	—
255	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₁₃×Q₁₆	—	2	4	no	—
273	C₁₃×SD₁₆	—	4	2	no	—
274	C₁₃×SD₁₆	—	4	4	no	—
275	C₁₃×M₁₆	—	4	2	no	—
276	C₂×C₈×C₁₃	—	4	4	no	—
277	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
278	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
279	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
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	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
291	C₁₃×C₄⋊C₄	—	2	4	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	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	1	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	1	no	—
318	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
319	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
320	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
321	C₄²×C₁₃	—	2	1	no	—
322	C₄²×C₁₃	—	2	2	no	—
323	C₄²×C₁₃	—	2	1	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	4	no	—
327	C₄²×C₁₃	—	2	4	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂×D₄	1	2	yes	—
332	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₄²×C₁₃	C₂⁴	1	2	yes	—
335	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
336	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3483	C₂×C₁₃	1	1	yes	characteristic
338	#3387	C₂×C₁₃	1	2	yes	complemented
339	#3368	C₂×C₁₃	1	2	yes	complemented
340	#3348	C₂×C₁₃	1	4	yes	complemented
341	#3340	C₂×C₁₃	1	2	yes	complemented
342	#3317	C₂×C₁₃	1	4	yes	complemented
343	#3304	C₂×C₁₃	1	2	yes	complemented
344	#3254	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3246	C₂×C₁₃	1	2	yes	complemented
346	#3235	C₂×C₁₃	1	2	yes	complemented
347	#3227	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3116	C₂×C₁₃	1	2	yes	complemented
349	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3076	C₂×C₁₃	1	2	yes	complemented
352	#2990	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	1	no	—
355	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
356	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₁₃	—	2	2	no	—
358	Q₈×C₁₃	—	2	1	no	—
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	4	4	no	—
362	Q₈×C₁₃	—	4	4	no	—
363	Q₈×C₁₃	—	4	2	no	—
364	Q₈×C₁₃	—	8	2	no	—
365	Q₈×C₁₃	—	8	1	no	—
366	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
367	D₄×C₁₃	—	2	2	no	—
368	D₄×C₁₃	—	2	2	no	—
369	D₄×C₁₃	—	2	1	no	—
370	D₄×C₁₃	—	2	1	no	—
371	D₄×C₁₃	—	2	2	no	—
372	D₄×C₁₃	—	4	2	no	—
373	D₄×C₁₃	—	4	4	no	—
374	D₄×C₁₃	—	4	2	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	4	2	no	—
377	D₄×C₁₃	—	8	2	no	—
378	D₄×C₁₃	—	8	1	no	—
379	D₄×C₁₃	—	8	2	no	—
380	D₄×C₁₃	—	8	2	no	—
381	D₄×C₁₃	—	8	2	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	4	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	4	no	—
396	C₂×C₄×C₁₃	—	4	2	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	4	2	no	—
399	C₂×C₄×C₁₃	—	4	4	no	—
400	C₂×C₄×C₁₃	—	4	4	no	—
401	C₂×C₄×C₁₃	—	4	2	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
413	C₈×C₁₃	—	2	2	no	—
414	C₈×C₁₃	—	2	2	no	—
415	C₈×C₁₃	—	2	4	no	—
416	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
417	#557	—	2	1	no	—
418	#557	C₂²×C₁₃	1	2	yes	—
419	#556	—	2	1	no	—
420	#556	C₂²×C₁₃	1	2	yes	—
421	#555	—	2	1	no	—
422	#555	—	2	2	no	—
423	#555	C₂²×C₁₃	1	1	yes	characteristic
424	#555	C₂²×C₁₃	1	2	yes	—
425	#552	—	2	2	no	—
426	#552	C₂²×C₁₃	1	4	yes	—
427	#550	—	2	1	no	—
428	#550	C₂²×C₁₃	1	1	yes	characteristic
429	#550	C₂²×C₁₃	1	2	yes	—
430	#550	C₂²×C₁₃	1	1	yes	characteristic
431	#541	—	2	2	no	—
432	#536	—	2	1	no	—
433	#533	C₂²×C₁₃	1	1	yes	characteristic
434	#533	C₂²×C₁₃	1	2	yes	—
435	#533	C₂²×C₁₃	1	2	yes	—
436	#532	—	2	2	no	—
437	#532	—	2	1	no	—
438	#532	C₂²×C₁₃	1	1	yes	characteristic
439	#532	C₂²×C₁₃	1	2	yes	—
440	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
441	#519	—	2	1	no	—
442	C₄×#41	—	2	1	no	—
443	C₄×#41	C₂²×C₁₃	1	2	yes	—
444	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
445	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
446	#501	C₂²×C₁₃	1	4	yes	—
447	#498	C₂²×C₁₃	1	2	yes	—
448	#490	C₂²×C₁₃	1	4	yes	—
449	#486	C₂²×C₁₃	1	2	yes	—
450	#485	C₂²×C₁₃	1	4	yes	—
451	#485	C₂²×C₁₃	1	2	yes	—
452	#482	C₂²×C₁₃	1	4	yes	—
453	#482	C₂²×C₁₃	1	4	yes	—
454	#481	C₂²×C₁₃	1	4	yes	—
455	#479	C₂²×C₁₃	1	4	yes	—
456	#478	C₂²×C₁₃	1	4	yes	—
457	#477	C₂²×C₁₃	1	2	yes	—
458	#477	C₂²×C₁₃	1	2	yes	—
459	#476	C₂²×C₁₃	1	2	yes	—
460	#476	C₂²×C₁₃	1	2	yes	—
461	#476	C₂²×C₁₃	1	2	yes	—
462	#475	C₂²×C₁₃	1	1	yes	characteristic
463	#475	C₂²×C₁₃	1	2	yes	—
464	#475	C₂²×C₁₃	1	4	yes	—
465	#474	C₂²×C₁₃	1	2	yes	—
466	#474	C₂²×C₁₃	1	2	yes	—
467	#474	C₂²×C₁₃	1	1	yes	characteristic
468	#468	C₂²×C₁₃	1	4	yes	—
469	#465	C₂²×C₁₃	1	4	yes	—
470	#465	C₂²×C₁₃	1	4	yes	—
471	#462	C₂²×C₁₃	1	1	yes	characteristic
472	#461	C₂²×C₁₃	1	1	yes	characteristic
473	#461	C₂²×C₁₃	1	2	yes	—
474	#460	C₂²×C₁₃	1	4	yes	—
475	#460	C₂²×C₁₃	1	2	yes	—
476	#452	C₂²×C₁₃	1	2	yes	—
477	#452	C₂²×C₁₃	1	4	yes	—
478	#446	C₂²×C₁₃	1	2	yes	—
479	#441	C₂²×C₁₃	1	4	yes	—
480	#440	C₂²×C₁₃	1	4	yes	—
481	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
482	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
483	#435	C₂²×C₁₃	1	4	yes	—
484	C₈×D₄	C₂²×C₁₃	1	2	yes	—
485	#432	C₂²×C₁₃	1	2	yes	—
486	#431	C₂²×C₁₃	1	1	yes	characteristic
487	#428	C₂²×C₁₃	1	2	yes	—
488	#427	C₂²×C₁₃	1	4	yes	—
489	#423	C₂²×C₁₃	1	1	yes	characteristic
490	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
491	#417	C₂²×C₁₃	1	2	yes	—
492	#416	C₂²×C₁₃	1	4	yes	—
493	C₂²×C₁₃	—	2	2	no	—
494	C₂²×C₁₃	—	2	1	no	—
495	C₂²×C₁₃	—	2	1	no	—
496	C₂²×C₁₃	—	2	2	no	—
497	C₂²×C₁₃	—	2	2	no	—
498	C₂²×C₁₃	—	2	1	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	1	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	—	4	1	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	1	no	—
505	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
506	C₄×C₁₃	—	2	2	no	—
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	2	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	2	no	—
512	C₄×C₁₃	—	2	1	no	—
513	C₄×C₁₃	—	4	2	no	—
514	C₄×C₁₃	—	4	1	no	—
515	C₄×C₁₃	—	4	4	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	—	4	1	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	#575	1	2	yes	—
520	C₄×C₁₃	#577	1	2	yes	—
521	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
522	C₄×C₁₃	#585	1	1	yes	characteristic
523	C₂×#41	—	2	1	no	—
524	C₂×#41	—	2	1	no	—
525	C₂×#41	—	2	2	no	—
526	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
527	C₂×#41	C₂³×C₁₃	1	2	yes	—
528	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
529	C₂²×Q₈	—	2	1	no	—
530	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
531	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
533	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
534	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
535	C₄⋊Q₈	—	2	2	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	—	2	2	no	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
542	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
543	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
544	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
545	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
546	#127	—	2	1	no	—
547	#127	—	2	2	no	—
548	#127	C₂³×C₁₃	1	1	yes	characteristic
549	#127	C₂³×C₁₃	1	2	yes	—
550	#126	—	2	4	no	—
551	#126	—	2	4	no	—
552	#125	—	2	4	no	—
553	#125	—	2	4	no	—
554	#125	—	2	1	no	—
555	#125	—	2	2	no	—
556	#125	C₂³×C₁₃	1	4	yes	—
557	#124	—	2	2	no	—
558	#124	—	2	2	no	—
559	#124	—	2	2	no	—
560	#124	—	2	2	no	—
561	#124	—	2	2	no	—
562	#124	—	2	1	no	—
563	#123	—	2	4	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
569	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
570	#121	—	2	1	no	—
571	#121	—	2	2	no	—
572	#121	—	2	1	no	—
573	#121	—	2	2	no	—
574	#121	—	2	1	no	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#121	—	2	2	no	—
578	#121	—	2	2	no	—
579	#121	C₂³×C₁₃	1	2	yes	—
580	#121	C₂³×C₁₃	1	2	yes	—
581	#121	C₂³×C₁₃	1	2	yes	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
593	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
594	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	D₄×C₁₃	1	2	yes	—
605	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₁₃	1	2	yes	—
607	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₄×D₄	C₂³×C₁₃	1	2	yes	—
610	C₄×D₄	C₂³×C₁₃	1	2	yes	—
611	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
612	#117	—	2	1	no	—
613	#117	—	2	2	no	—
614	#117	—	2	1	no	—
615	#117	—	2	2	no	—
616	#117	—	2	4	no	—
617	#117	—	2	2	no	—
618	#117	—	2	1	no	—
619	#117	D₄×C₁₃	1	1	yes	characteristic
620	#117	D₄×C₁₃	1	2	yes	—
621	#117	C₂³×C₁₃	1	2	yes	—
622	#117	C₂³×C₁₃	1	1	yes	characteristic
623	#117	C₂³×C₁₃	1	4	yes	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₄²	—	2	2	no	—
627	C₂×C₄²	—	2	1	no	—
628	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
630	#107	C₂³×C₁₃	1	4	yes	—
631	#107	C₂³×C₁₃	1	4	yes	—
632	#107	C₂³×C₁₃	1	2	yes	—
633	#106	C₂³×C₁₃	1	2	yes	—
634	#106	C₂³×C₁₃	1	4	yes	—
635	#106	C₂³×C₁₃	1	4	yes	—
636	#106	C₂³×C₁₃	1	4	yes	—
637	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
638	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
639	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
640	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
641	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
642	#103	C₂³×C₁₃	1	2	yes	—
643	#103	C₂³×C₁₃	1	4	yes	—
644	#103	C₂³×C₁₃	1	2	yes	—
645	#103	C₂³×C₁₃	1	2	yes	—
646	#103	C₂³×C₁₃	1	4	yes	—
647	#102	C₂³×C₁₃	1	4	yes	—
648	#102	C₂³×C₁₃	1	4	yes	—
649	#102	C₂³×C₁₃	1	4	yes	—
650	#102	C₂³×C₁₃	1	2	yes	—
651	#102	C₂³×C₁₃	1	4	yes	—
652	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
654	#97	C₂³×C₁₃	1	4	yes	—
655	C₄×C₈	C₂³×C₁₃	1	2	yes	—
656	C₂×C₁₃	—	4	1	no	—
657	C₂×C₁₃	—	4	2	no	—
658	C₂×C₁₃	—	8	2	no	—
659	C₂×C₁₃	—	8	1	no	—
660	C₂×C₁₃	#3489	1	1	yes	characteristic
661	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
662	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
663	#41	—	2	4	no	—
664	#41	—	2	2	no	—
665	#41	—	4	2	no	—
666	#41	—	4	2	no	—
667	#41	—	4	1	no	—
668	#41	—	4	4	no	—
669	#41	—	8	2	no	—
670	#41	—	8	4	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
679	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
690	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
691	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
692	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
703	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
706	Q₁₆	—	2	4	no	—
707	SD₁₆	—	4	2	no	—
708	SD₁₆	—	4	4	no	—
709	M₁₆	—	4	2	no	—
710	C₂×C₈	—	4	4	no	—
711	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
712	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
713	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
736	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	2	no	—
763	C₄²	C₂×D₄×C₁₃	1	2	yes	—
764	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₁₃	1	2	yes	—
766	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
768	C₄²	C₂⁴×C₁₃	1	2	yes	—
769	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₁₃	#62135	1	1	yes	characteristic, direct product factor, Sylow
771	C₂³	—	2	2	no	—
772	C₂³	—	2	1	no	—
773	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
774	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
775	Q₈	—	2	2	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	4	4	no	—
780	Q₈	—	4	4	no	—
781	Q₈	—	4	2	no	—
782	Q₈	—	8	2	no	—
783	Q₈	—	8	1	no	—
784	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	2	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	2	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	2	no	—
795	D₄	—	8	2	no	—
796	D₄	—	8	1	no	—
797	D₄	—	8	2	no	—
798	D₄	—	8	2	no	—
799	D₄	—	8	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
830	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	—	2	4	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	1	no	—
846	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
847	C₄	—	2	1	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	4	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	C₁₃×#575	1	2	yes	—
861	C₄	C₁₃×#577	1	2	yes	—
862	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
863	C₄	C₁₃×#585	1	1	yes	characteristic
864	C₂	—	4	1	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	—	8	1	no	—
868	C₂	C₁₃×#3489	1	1	yes	characteristic
869	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
870	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×#3483	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×#3509	C₂	semidirect
3. C₁₃×#3387	C₂	semidirect
4. C₁₃×#3368	C₂	semidirect
5. C₁₃×#3348	C₂	semidirect
6. C₁₃×#3340	C₂	semidirect
7. C₁₃×#3317	C₂	semidirect
8. C₁₃×#3304	C₂	semidirect
9. C₁₃×#3254	C₂	semidirect
10. C₁₃×#3246	C₂	semidirect
11. C₁₃×#3235	C₂	semidirect
12. C₁₃×#3227	C₂	semidirect
13. C₁₃×#3116	C₂	semidirect
14. C₁₃×#3107	C₂	semidirect
15. C₁₃×#3079	C₂	semidirect
16. C₁₃×#3076	C₂	semidirect
17. C₁₃×#2990	C₂	semidirect
228. #62135	C₁₃	direct (N × H)
336. #3509	C₂×C₁₃	semidirect
338. #3387	C₂×C₁₃	semidirect
339. #3368	C₂×C₁₃	semidirect
340. #3348	C₂×C₁₃	semidirect
341. #3340	C₂×C₁₃	semidirect
342. #3317	C₂×C₁₃	semidirect
343. #3304	C₂×C₁₃	semidirect
344. #3254	C₂×C₁₃	semidirect
345. #3246	C₂×C₁₃	semidirect
346. #3235	C₂×C₁₃	semidirect
347. #3227	C₂×C₁₃	semidirect
348. #3116	C₂×C₁₃	semidirect
349. #3107	C₂×C₁₃	semidirect
350. #3079	C₂×C₁₃	semidirect
351. #3076	C₂×C₁₃	semidirect
352. #2990	C₂×C₁₃	semidirect
770. C₁₃	#62135	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×#3483	2
C₁₃×#3387	2
C₁₃×#3368	2
C₁₃×#3348	2
C₁₃×#3340	2
C₁₃×#3317	2
C₁₃×#3304	2
C₁₃×#3254	2
C₁₃×#3246	2
C₁₃×#3235	2
C₁₃×#3227	2
C₁₃×#3116	2
C₁₃×#3107	2
C₁₃×#3079	2
C₁₃×#3076	2
C₁₃×#2990	2
#62135	13

Subgroups — C13×#62135 #15748474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62135 #15748474