Subgroups — C₁₃×#62593 #15748932

Order 3328.

1734 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3514	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3328	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3327	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3324	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3323	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3172	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3140	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	C₂²	1	1	yes	characteristic
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	C₂²	1	2	yes	complemented
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	C₂²	1	1	yes	characteristic
23	C₁₃×#556	C₂²	1	2	yes	—
24	C₁₃×#555	—	2	1	no	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#552	C₂²	1	4	yes	complemented
27	C₁₃×#551	—	2	2	no	—
28	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#548	C₂²	1	2	yes	—
30	C₁₃×#546	—	2	1	no	—
31	C₁₃×#546	C₂²	1	2	yes	—
32	D₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#542	—	2	1	no	—
34	C₁₃×#541	—	2	2	no	—
35	C₁₃×#538	—	2	2	no	—
36	C₁₃×#536	—	2	1	no	—
37	C₁₃×#533	C₂²	1	2	yes	complemented
38	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#533	C₂²	1	2	yes	complemented
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#529	C₂²	1	1	yes	characteristic
43	C₁₃×#529	C₂²	1	2	yes	—
44	C₂×C₁₃×#124	C₂²	1	2	yes	—
45	C₁₃×#519	—	2	1	no	—
46	C₁₃×#518	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	2	yes	complemented
49	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#497	C₂²	1	1	yes	characteristic
51	C₁₃×#497	C₂²	1	2	yes	complemented
52	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#489	C₂²	1	1	yes	characteristic
54	C₁₃×#489	C₂²	1	2	yes	—
55	C₁₃×#489	C₂²	1	2	yes	complemented
56	C₁₃×#489	C₂²	1	2	yes	complemented
57	C₁₃×#489	C₂²	1	2	yes	complemented
58	C₁₃×#488	C₂²	1	4	yes	—
59	C₁₃×#488	C₂²	1	4	yes	complemented
60	C₁₃×#487	C₂²	1	2	yes	complemented
61	C₁₃×#486	C₂²	1	2	yes	—
62	C₁₃×#485	C₂²	1	4	yes	complemented
63	C₁₃×#484	C₂²	1	2	yes	complemented
64	C₁₃×#482	C₂²	1	4	yes	—
65	C₁₃×#481	C₂²	1	2	yes	—
66	C₁₃×#479	C₂²	1	4	yes	complemented
67	C₁₃×#478	C₂²	1	4	yes	complemented
68	C₁₃×#475	C₂²	1	2	yes	complemented
69	C₁₃×#474	C₂²	1	2	yes	—
70	C₁₃×#470	C₂²	1	4	yes	complemented
71	C₁₃×#470	C₂²	1	2	yes	complemented
72	C₁₃×#468	C₂²	1	2	yes	—
73	C₁₃×#468	C₂²	1	4	yes	—
74	C₁₃×#464	C₂²	1	4	yes	—
75	C₁₃×#464	C₂²	1	4	yes	complemented
76	C₁₃×#462	C₂²	1	2	yes	complemented
77	C₁₃×#460	C₂²	1	2	yes	—
78	C₁₃×#452	C₂²	1	4	yes	complemented
79	C₁₃×#451	C₂²	1	4	yes	complemented
80	C₁₃×#450	C₂²	1	4	yes	—
81	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
82	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
83	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
85	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
86	C₁₃×#436	C₂²	1	2	yes	—
87	C₁₃×#436	C₂²	1	4	yes	complemented
88	C₁₃×#432	C₂²	1	2	yes	complemented
89	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#419	C₂²	1	4	yes	complemented
91	C₁₃×#418	C₂²	1	4	yes	—
92	C₁₃×#417	C₂²	1	4	yes	complemented
93	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
94	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
95	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃	—	2	1	no	—
98	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×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×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	4	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	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×#127	C₂³	1	1	yes	characteristic
117	C₁₃×#126	—	2	2	no	—
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#126	—	2	2	no	—
121	C₁₃×#126	—	2	1	no	—
122	C₁₃×#125	—	2	4	no	—
123	C₁₃×#125	—	2	4	no	—
124	C₁₃×#125	—	2	1	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	C₂³	1	4	yes	—
127	C₁₃×#125	C₂³	1	1	yes	characteristic
128	C₁₃×#124	—	2	1	no	—
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	C₂³	1	2	yes	—
134	C₁₃×#124	C₂³	1	2	yes	—
135	C₁₃×#124	C₂³	1	1	yes	characteristic
136	C₁₃×#124	C₂³	1	2	yes	—
137	C₁₃×#123	—	2	4	no	—
138	C₁₃×#123	—	2	1	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	C₂³	1	1	yes	characteristic
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#120	—	2	2	no	—
161	C₁₃×#120	—	2	2	no	—
162	C₄×Q₈×C₁₃	—	2	2	no	—
163	C₄×Q₈×C₁₃	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	—	2	2	no	—
166	C₄×Q₈×C₁₃	—	2	2	no	—
167	C₄×Q₈×C₁₃	—	2	1	no	—
168	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	1	no	—
181	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
182	C₄×D₄×C₁₃	D₄	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	2	yes	—
187	C₁₃×#117	—	2	1	no	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	—	2	4	no	—
191	C₁₃×#117	—	2	1	no	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	D₄	1	1	yes	characteristic
194	C₁₃×#117	D₄	1	2	yes	—
195	C₁₃×#117	C₂³	1	4	yes	—
196	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×#103	C₂³	1	4	yes	—
210	C₁₃×#103	C₂³	1	4	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	2	yes	—
216	C₁₃×#102	C₂³	1	4	yes	—
217	C₁₃×#102	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	2	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
222	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₁₃×#97	C₂³	1	1	yes	characteristic
224	C₁₃×#97	C₂³	1	2	yes	—
225	C₁₃×#97	C₂³	1	1	yes	characteristic
226	C₄×C₈×C₁₃	C₂³	1	2	yes	—
227	C₄×C₈×C₁₃	C₂³	1	4	yes	—
228	#62593	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	2	no	—
230	C₁₃×#41	—	4	2	no	—
231	C₁₃×#41	—	4	4	no	—
232	C₂×Q₈×C₁₃	—	2	1	no	—
233	C₂×Q₈×C₁₃	—	2	2	no	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	4	4	no	—
237	C₂×Q₈×C₁₃	—	4	4	no	—
238	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	4	4	no	—
249	C₂×D₄×C₁₃	—	4	4	no	—
250	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₁₃×Q₁₆	—	4	2	no	—
266	C₁₃×Q₁₆	—	4	4	no	—
267	C₁₃×SD₁₆	—	4	2	no	—
268	C₁₃×SD₁₆	—	4	4	no	—
269	C₁₃×M₁₆	—	4	4	no	—
270	C₁₃×M₁₆	—	4	2	no	—
271	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
272	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
273	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	1	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	4	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	4	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	4	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
295	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
296	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
297	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
298	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
302	C₁₃×C₂²⋊C₄	—	2	2	no	—
303	C₁₃×C₂²⋊C₄	—	2	2	no	—
304	C₁₃×C₂²⋊C₄	—	2	4	no	—
305	C₁₃×C₂²⋊C₄	—	2	4	no	—
306	C₁₃×C₂²⋊C₄	—	2	1	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	1	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	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	—	2	1	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
320	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
321	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
322	C₄²×C₁₃	—	2	2	no	—
323	C₄²×C₁₃	—	2	4	no	—
324	C₄²×C₁₃	—	2	4	no	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
334	#3514	C₂×C₁₃	1	1	yes	characteristic
335	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3365	C₂×C₁₃	1	2	yes	complemented
337	#3364	C₂×C₁₃	1	2	yes	complemented
338	#3328	C₂×C₁₃	1	2	yes	complemented
339	#3327	C₂×C₁₃	1	4	yes	complemented
340	#3324	C₂×C₁₃	1	2	yes	complemented
341	#3323	C₂×C₁₃	1	4	yes	complemented
342	#3240	C₂×C₁₃	1	2	yes	complemented
343	#3239	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3215	C₂×C₁₃	1	2	yes	complemented
346	#3172	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3172	C₂×C₁₃	1	2	yes	complemented
348	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3140	C₂×C₁₃	1	2	yes	complemented
350	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
351	C₂³×C₁₃	—	2	1	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	4	4	no	—
354	C₂³×C₁₃	—	8	2	no	—
355	C₂³×C₁₃	—	8	2	no	—
356	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
357	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₁₃	—	2	2	no	—
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	4	no	—
363	Q₈×C₁₃	—	4	2	no	—
364	Q₈×C₁₃	—	4	4	no	—
365	Q₈×C₁₃	—	4	4	no	—
366	Q₈×C₁₃	—	8	2	no	—
367	D₄×C₁₃	—	2	2	no	—
368	D₄×C₁₃	—	2	2	no	—
369	D₄×C₁₃	—	2	4	no	—
370	D₄×C₁₃	—	4	2	no	—
371	D₄×C₁₃	—	4	4	no	—
372	D₄×C₁₃	—	4	2	no	—
373	D₄×C₁₃	—	8	1	no	—
374	D₄×C₁₃	—	8	2	no	—
375	D₄×C₁₃	—	8	1	no	—
376	D₄×C₁₃	—	8	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	4	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	4	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	4	2	no	—
388	C₂×C₄×C₁₃	—	4	1	no	—
389	C₂×C₄×C₁₃	—	4	2	no	—
390	C₂×C₄×C₁₃	—	4	4	no	—
391	C₂×C₄×C₁₃	—	4	2	no	—
392	C₂×C₄×C₁₃	—	8	2	no	—
393	C₂×C₄×C₁₃	—	8	2	no	—
394	C₂×C₄×C₁₃	—	8	2	no	—
395	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
404	C₈×C₁₃	—	2	2	no	—
405	C₈×C₁₃	—	2	2	no	—
406	C₈×C₁₃	—	2	4	no	—
407	#559	C₂²×C₁₃	1	1	yes	characteristic
408	#557	—	2	1	no	—
409	#557	C₂²×C₁₃	1	2	yes	complemented
410	#556	—	2	1	no	—
411	#556	C₂²×C₁₃	1	1	yes	characteristic
412	#556	C₂²×C₁₃	1	2	yes	—
413	#555	—	2	1	no	—
414	#552	—	2	2	no	—
415	#552	C₂²×C₁₃	1	4	yes	complemented
416	#551	—	2	2	no	—
417	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
418	#548	C₂²×C₁₃	1	2	yes	—
419	#546	—	2	1	no	—
420	#546	C₂²×C₁₃	1	2	yes	—
421	D₄²	C₂²×C₁₃	1	1	yes	characteristic
422	#542	—	2	1	no	—
423	#541	—	2	2	no	—
424	#538	—	2	2	no	—
425	#536	—	2	1	no	—
426	#533	C₂²×C₁₃	1	2	yes	complemented
427	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#533	C₂²×C₁₃	1	2	yes	complemented
429	#532	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#529	C₂²×C₁₃	1	1	yes	characteristic
432	#529	C₂²×C₁₃	1	2	yes	—
433	C₂×#124	C₂²×C₁₃	1	2	yes	—
434	#519	—	2	1	no	—
435	#518	—	2	1	no	—
436	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
437	#501	C₂²×C₁₃	1	2	yes	complemented
438	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#497	C₂²×C₁₃	1	1	yes	characteristic
440	#497	C₂²×C₁₃	1	2	yes	complemented
441	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	#489	C₂²×C₁₃	1	1	yes	characteristic
443	#489	C₂²×C₁₃	1	2	yes	—
444	#489	C₂²×C₁₃	1	2	yes	complemented
445	#489	C₂²×C₁₃	1	2	yes	complemented
446	#489	C₂²×C₁₃	1	2	yes	complemented
447	#488	C₂²×C₁₃	1	4	yes	—
448	#488	C₂²×C₁₃	1	4	yes	complemented
449	#487	C₂²×C₁₃	1	2	yes	complemented
450	#486	C₂²×C₁₃	1	2	yes	—
451	#485	C₂²×C₁₃	1	4	yes	complemented
452	#484	C₂²×C₁₃	1	2	yes	complemented
453	#482	C₂²×C₁₃	1	4	yes	—
454	#481	C₂²×C₁₃	1	2	yes	—
455	#479	C₂²×C₁₃	1	4	yes	complemented
456	#478	C₂²×C₁₃	1	4	yes	complemented
457	#475	C₂²×C₁₃	1	2	yes	complemented
458	#474	C₂²×C₁₃	1	2	yes	—
459	#470	C₂²×C₁₃	1	4	yes	complemented
460	#470	C₂²×C₁₃	1	2	yes	complemented
461	#468	C₂²×C₁₃	1	2	yes	—
462	#468	C₂²×C₁₃	1	4	yes	—
463	#464	C₂²×C₁₃	1	4	yes	—
464	#464	C₂²×C₁₃	1	4	yes	complemented
465	#462	C₂²×C₁₃	1	2	yes	complemented
466	#460	C₂²×C₁₃	1	2	yes	—
467	#452	C₂²×C₁₃	1	4	yes	complemented
468	#451	C₂²×C₁₃	1	4	yes	complemented
469	#450	C₂²×C₁₃	1	4	yes	—
470	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
471	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
472	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
473	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
474	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
475	#436	C₂²×C₁₃	1	2	yes	—
476	#436	C₂²×C₁₃	1	4	yes	complemented
477	#432	C₂²×C₁₃	1	2	yes	complemented
478	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	#419	C₂²×C₁₃	1	4	yes	complemented
480	#418	C₂²×C₁₃	1	4	yes	—
481	#417	C₂²×C₁₃	1	4	yes	complemented
482	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
483	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	C₂²×C₁₃	—	2	1	no	—
485	C₂²×C₁₃	—	2	2	no	—
486	C₂²×C₁₃	—	2	2	no	—
487	C₂²×C₁₃	—	2	1	no	—
488	C₂²×C₁₃	—	2	1	no	—
489	C₂²×C₁₃	—	2	2	no	—
490	C₂²×C₁₃	—	4	2	no	—
491	C₂²×C₁₃	—	4	1	no	—
492	C₂²×C₁₃	—	4	2	no	—
493	C₂²×C₁₃	—	4	1	no	—
494	C₂²×C₁₃	—	4	1	no	—
495	C₂²×C₁₃	—	4	2	no	—
496	C₂²×C₁₃	—	16	4	no	—
497	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
498	C₄×C₁₃	—	2	1	no	—
499	C₄×C₁₃	—	2	2	no	—
500	C₄×C₁₃	—	2	1	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	—	4	1	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	2	no	—
508	C₄×C₁₃	—	4	1	no	—
509	C₄×C₁₃	—	4	2	no	—
510	C₄×C₁₃	—	4	1	no	—
511	C₄×C₁₃	—	4	4	no	—
512	C₄×C₁₃	#575	1	2	yes	—
513	C₄×C₁₃	#585	1	2	yes	—
514	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
515	C₂×#41	C₂³×C₁₃	1	2	yes	—
516	C₂²×Q₈	—	2	1	no	—
517	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	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×SD₁₆	C₂³×C₁₃	1	4	yes	—
524	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
525	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	—	2	1	no	—
530	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
534	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
535	#127	C₂³×C₁₃	1	1	yes	characteristic
536	#126	—	2	2	no	—
537	#126	—	2	4	no	—
538	#126	—	2	4	no	—
539	#126	—	2	2	no	—
540	#126	—	2	1	no	—
541	#125	—	2	4	no	—
542	#125	—	2	4	no	—
543	#125	—	2	1	no	—
544	#125	—	2	2	no	—
545	#125	C₂³×C₁₃	1	1	yes	characteristic
546	#125	C₂³×C₁₃	1	4	yes	—
547	#124	—	2	1	no	—
548	#124	—	2	2	no	—
549	#124	—	2	2	no	—
550	#124	—	2	2	no	—
551	#124	—	2	2	no	—
552	#124	C₂³×C₁₃	1	1	yes	characteristic
553	#124	C₂³×C₁₃	1	2	yes	—
554	#124	C₂³×C₁₃	1	2	yes	—
555	#124	C₂³×C₁₃	1	2	yes	—
556	#123	—	2	4	no	—
557	#123	—	2	1	no	—
558	#123	—	2	2	no	—
559	#123	—	2	2	no	—
560	#123	—	2	2	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
569	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
570	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
571	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
572	#121	—	2	2	no	—
573	#121	—	2	1	no	—
574	#121	—	2	1	no	—
575	#121	—	2	1	no	—
576	#121	—	2	2	no	—
577	#121	C₂³×C₁₃	1	2	yes	—
578	#121	C₂³×C₁₃	1	1	yes	characteristic
579	#120	—	2	2	no	—
580	#120	—	2	2	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
588	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
591	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
601	C₄×D₄	D₄×C₁₃	1	2	yes	—
602	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₁₃	1	2	yes	—
604	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₄×D₄	C₂³×C₁₃	1	2	yes	—
606	#117	—	2	1	no	—
607	#117	—	2	2	no	—
608	#117	—	2	1	no	—
609	#117	—	2	4	no	—
610	#117	—	2	1	no	—
611	#117	—	2	2	no	—
612	#117	D₄×C₁₃	1	1	yes	characteristic
613	#117	D₄×C₁₃	1	2	yes	—
614	#117	C₂³×C₁₃	1	4	yes	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₂²⋊C₄	—	2	2	no	—
618	C₂×C₂²⋊C₄	—	2	2	no	—
619	C₂×C₂²⋊C₄	—	2	2	no	—
620	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
621	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
622	#107	C₂³×C₁₃	1	4	yes	—
623	#107	C₂³×C₁₃	1	2	yes	—
624	#106	C₂³×C₁₃	1	2	yes	—
625	#106	C₂³×C₁₃	1	4	yes	—
626	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
627	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
628	#103	C₂³×C₁₃	1	4	yes	—
629	#103	C₂³×C₁₃	1	4	yes	—
630	#103	C₂³×C₁₃	1	2	yes	—
631	#103	C₂³×C₁₃	1	4	yes	—
632	#103	C₂³×C₁₃	1	4	yes	—
633	#103	C₂³×C₁₃	1	2	yes	—
634	#103	C₂³×C₁₃	1	2	yes	—
635	#102	C₂³×C₁₃	1	4	yes	—
636	#102	C₂³×C₁₃	1	4	yes	—
637	#102	C₂³×C₁₃	1	2	yes	—
638	#102	C₂³×C₁₃	1	4	yes	—
639	#102	C₂³×C₁₃	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
641	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
642	#97	C₂³×C₁₃	1	1	yes	characteristic
643	#97	C₂³×C₁₃	1	2	yes	—
644	#97	C₂³×C₁₃	1	1	yes	characteristic
645	C₄×C₈	C₂³×C₁₃	1	2	yes	—
646	C₄×C₈	C₂³×C₁₃	1	4	yes	—
647	C₂×C₁₃	—	4	1	no	—
648	C₂×C₁₃	—	4	2	no	—
649	C₂×C₁₃	—	8	2	no	—
650	C₂×C₁₃	—	8	1	no	—
651	C₂×C₁₃	#3500	1	1	yes	characteristic
652	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
653	C₂×C₁₃	#3586	1	1	yes	characteristic
654	C₂⁴	—	2	2	no	—
655	#41	—	4	2	no	—
656	#41	—	4	4	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	4	4	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
664	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
665	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
666	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
677	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
686	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
687	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
690	Q₁₆	—	4	2	no	—
691	Q₁₆	—	4	4	no	—
692	SD₁₆	—	4	2	no	—
693	SD₁₆	—	4	4	no	—
694	M₁₆	—	4	4	no	—
695	M₁₆	—	4	2	no	—
696	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
697	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
698	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
721	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
722	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
724	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	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	1	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	2	no	—
748	C₄²	—	2	4	no	—
749	C₄²	—	2	4	no	—
750	C₄²	—	2	1	no	—
751	C₄²	—	2	2	no	—
752	C₄²	C₂×D₄×C₁₃	1	2	yes	—
753	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
754	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
755	C₄²	C₂×D₄×C₁₃	1	2	yes	—
756	C₄²	C₂⁴×C₁₃	1	2	yes	—
757	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
758	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₁₃	#62593	1	1	yes	characteristic, direct product factor, Sylow
760	C₂³	—	2	1	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	8	2	no	—
764	C₂³	—	8	2	no	—
765	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
766	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	4	no	—
772	Q₈	—	4	4	no	—
773	Q₈	—	4	2	no	—
774	Q₈	—	4	4	no	—
775	Q₈	—	8	2	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	4	2	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	2	no	—
782	D₄	—	8	2	no	—
783	D₄	—	8	1	no	—
784	D₄	—	8	1	no	—
785	D₄	—	8	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	—	8	2	no	—
803	C₂×C₄	—	8	2	no	—
804	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	C₂⁵×C₁₃	1	1	yes	characteristic
813	C₈	—	2	2	no	—
814	C₈	—	2	2	no	—
815	C₈	—	2	4	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	16	4	no	—
829	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
830	C₄	—	2	1	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	2	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	4	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	1	no	—
843	C₄	—	4	2	no	—
844	C₄	C₁₃×#575	1	2	yes	—
845	C₄	C₁₃×#585	1	2	yes	—
846	C₂	—	4	2	no	—
847	C₂	—	4	1	no	—
848	C₂	—	8	1	no	—
849	C₂	—	8	2	no	—
850	C₂	C₁₃×#3500	1	1	yes	characteristic
851	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
852	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	C₁₃×#3514	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
2. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3365	C₂	semidirect
4. C₁₃×#3364	C₂	semidirect
5. C₁₃×#3328	C₂	semidirect
6. C₁₃×#3327	C₂	semidirect
7. C₁₃×#3324	C₂	semidirect
8. C₁₃×#3323	C₂	semidirect
9. C₁₃×#3240	C₂	semidirect
10. C₁₃×#3239	C₂	semidirect
11. C₁₃×#3216	C₂	semidirect
12. C₁₃×#3215	C₂	semidirect
13. C₁₃×#3172	C₂	semidirect
14. C₁₃×#3172	C₂	semidirect
15. C₁₃×#3141	C₂	semidirect
16. C₁₃×#3140	C₂	semidirect
17. C₁₃×#2971	C₂	semidirect
20. C₁₃×#557	C₂²	semidirect
26. C₁₃×#552	C₂²	semidirect
37. C₁₃×#533	C₂²	semidirect
38. C₁₃×#533	C₂²	semidirect
39. C₁₃×#533	C₂²	semidirect
41. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#501	C₂²	semidirect
51. C₁₃×#497	C₂²	semidirect
52. C₁₃×#491	C₂²	semidirect
55. C₁₃×#489	C₂²	semidirect
56. C₁₃×#489	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
59. C₁₃×#488	C₂²	semidirect
60. C₁₃×#487	C₂²	semidirect
62. C₁₃×#485	C₂²	semidirect
63. C₁₃×#484	C₂²	semidirect
66. C₁₃×#479	C₂²	semidirect
67. C₁₃×#478	C₂²	semidirect
68. C₁₃×#475	C₂²	semidirect
70. C₁₃×#470	C₂²	semidirect
71. C₁₃×#470	C₂²	semidirect
75. C₁₃×#464	C₂²	semidirect
76. C₁₃×#462	C₂²	semidirect
78. C₁₃×#452	C₂²	semidirect
79. C₁₃×#451	C₂²	semidirect
81. C₈×Q₈×C₁₃	C₂²	semidirect
82. C₄×C₁₃×Q₁₆	C₂²	semidirect
83. C₄×C₁₃×Q₁₆	C₂²	semidirect
85. C₄×C₁₃×SD₁₆	C₂²	semidirect
87. C₁₃×#436	C₂²	semidirect
88. C₁₃×#432	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
90. C₁₃×#419	C₂²	semidirect
92. C₁₃×#417	C₂²	semidirect
93. C₄×C₁₃×M₁₆	C₂²	semidirect
94. C₄×C₁₃×M₁₆	C₂²	semidirect
228. #62593	C₁₃	direct (N × H)
335. #3509	C₂×C₁₃	semidirect
336. #3365	C₂×C₁₃	semidirect
337. #3364	C₂×C₁₃	semidirect
338. #3328	C₂×C₁₃	semidirect
339. #3327	C₂×C₁₃	semidirect
340. #3324	C₂×C₁₃	semidirect
341. #3323	C₂×C₁₃	semidirect
342. #3240	C₂×C₁₃	semidirect
343. #3239	C₂×C₁₃	semidirect
344. #3216	C₂×C₁₃	semidirect
345. #3215	C₂×C₁₃	semidirect
346. #3172	C₂×C₁₃	semidirect
347. #3172	C₂×C₁₃	semidirect
348. #3141	C₂×C₁₃	semidirect
349. #3140	C₂×C₁₃	semidirect
350. #2971	C₂×C₁₃	semidirect
409. #557	C₂²×C₁₃	semidirect
415. #552	C₂²×C₁₃	semidirect
426. #533	C₂²×C₁₃	semidirect
427. #533	C₂²×C₁₃	semidirect
428. #533	C₂²×C₁₃	semidirect
430. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
437. #501	C₂²×C₁₃	semidirect
438. #501	C₂²×C₁₃	semidirect
440. #497	C₂²×C₁₃	semidirect
441. #491	C₂²×C₁₃	semidirect
444. #489	C₂²×C₁₃	semidirect
445. #489	C₂²×C₁₃	semidirect
446. #489	C₂²×C₁₃	semidirect
448. #488	C₂²×C₁₃	semidirect
449. #487	C₂²×C₁₃	semidirect
451. #485	C₂²×C₁₃	semidirect
452. #484	C₂²×C₁₃	semidirect
455. #479	C₂²×C₁₃	semidirect
456. #478	C₂²×C₁₃	semidirect
457. #475	C₂²×C₁₃	semidirect
459. #470	C₂²×C₁₃	semidirect
460. #470	C₂²×C₁₃	semidirect
464. #464	C₂²×C₁₃	semidirect
465. #462	C₂²×C₁₃	semidirect
467. #452	C₂²×C₁₃	semidirect
468. #451	C₂²×C₁₃	semidirect
470. C₈×Q₈	C₂²×C₁₃	semidirect
471. C₄×Q₁₆	C₂²×C₁₃	semidirect
472. C₄×Q₁₆	C₂²×C₁₃	semidirect
474. C₄×SD₁₆	C₂²×C₁₃	semidirect
476. #436	C₂²×C₁₃	semidirect
477. #432	C₂²×C₁₃	semidirect
478. #432	C₂²×C₁₃	semidirect
479. #419	C₂²×C₁₃	semidirect
481. #417	C₂²×C₁₃	semidirect
482. C₄×M₁₆	C₂²×C₁₃	semidirect
483. C₄×M₁₆	C₂²×C₁₃	semidirect
759. C₁₃	#62593	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×#3514	2
C₁₃×#3509	2
C₁₃×#3365	2
C₁₃×#3364	2
C₁₃×#3328	2
C₁₃×#3327	2
C₁₃×#3324	2
C₁₃×#3323	2
C₁₃×#3240	2
C₁₃×#3239	2
C₁₃×#3216	2
C₁₃×#3215	2
C₁₃×#3172	2
C₁₃×#3141	2
C₁₃×#3140	2
C₁₃×#2971	2
#62593	13

Subgroups — C13×#62593 #15748932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62593 #15748932