Subgroups — C₁₃×#60924 #15747263

Order 3328.

1868 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3260	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3257	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3254	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3246	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3081	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3062	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3057	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3042	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₂×C₁₃×#131	C₂²	1	2	yes	—
21	C₁₃×#559	—	2	1	no	—
22	C₁₃×#559	—	2	1	no	—
23	C₁₃×#550	—	2	1	no	—
24	C₁₃×#550	—	2	1	no	—
25	C₁₃×#546	—	2	2	no	—
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#544	C₂²	1	1	yes	characteristic
28	C₁₃×#542	—	2	1	no	—
29	C₁₃×#542	C₂²	1	2	yes	complemented
30	C₁₃×#541	—	2	1	no	—
31	C₁₃×#541	C₂²	1	2	yes	complemented
32	C₁₃×#540	C₂²	1	4	yes	—
33	C₁₃×#539	—	2	2	no	—
34	C₁₃×#537	C₂²	1	1	yes	characteristic
35	C₁₃×#536	C₂²	1	1	yes	characteristic
36	C₁₃×#536	C₂²	1	1	yes	characteristic
37	C₁₃×#535	C₂²	1	2	yes	—
38	C₁₃×#533	—	2	1	no	—
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₁₃×#533	C₂²	1	2	yes	complemented
41	C₁₃×#532	C₂²	1	2	yes	—
42	C₁₃×#532	C₂²	1	2	yes	—
43	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	2	no	—
45	C₁₃×#529	—	2	1	no	—
46	C₁₃×#529	C₂²	1	2	yes	complemented
47	C₁₃×#518	C₂²	1	2	yes	—
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#479	C₂²	1	2	yes	complemented
52	C₁₃×#479	C₂²	1	4	yes	complemented
53	C₁₃×#478	C₂²	1	2	yes	complemented
54	C₁₃×#478	C₂²	1	4	yes	complemented
55	C₁₃×#478	C₂²	1	4	yes	complemented
56	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#477	C₂²	1	2	yes	complemented
58	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#476	C₂²	1	4	yes	complemented
60	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#475	C₂²	1	2	yes	complemented
62	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#474	C₂²	1	4	yes	complemented
64	C₁₃×#469	C₂²	1	4	yes	complemented
65	C₁₃×#468	C₂²	1	4	yes	complemented
66	C₁₃×#468	C₂²	1	4	yes	complemented
67	C₁₃×#468	C₂²	1	4	yes	complemented
68	C₁₃×#466	C₂²	1	4	yes	complemented
69	C₁₃×#465	C₂²	1	4	yes	complemented
70	C₁₃×#465	C₂²	1	4	yes	complemented
71	C₁₃×#465	C₂²	1	4	yes	complemented
72	C₁₃×#463	C₂²	1	4	yes	complemented
73	C₁₃×#463	C₂²	1	4	yes	complemented
74	C₁₃×#461	C₂²	1	4	yes	complemented
75	C₁₃×#461	C₂²	1	4	yes	complemented
76	C₁₃×#460	C₂²	1	2	yes	—
77	C₁₃×#460	C₂²	1	2	yes	—
78	C₁₃×#460	C₂²	1	4	yes	—
79	C₁₃×#460	C₂²	1	2	yes	—
80	C₁₃×#460	C₂²	1	2	yes	—
81	C₁₃×#459	C₂²	1	2	yes	—
82	C₁₃×#459	C₂²	1	2	yes	—
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₁₃×#427	C₂²	1	2	yes	—
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₁₃×#424	C₂²	1	4	yes	complemented
87	C₁₃×#423	C₂²	1	1	yes	characteristic
88	C₁₃×#423	C₂²	1	2	yes	complemented
89	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
91	C₁₃×#419	C₂²	1	2	yes	—
92	C₁₃×#418	C₂²	1	2	yes	—
93	C₁₃×#416	C₂²	1	2	yes	—
94	C₂×C₁₃×#102	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
104	C₂×C₁₃×SD₁₆	—	4	4	no	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×D₈	C₂³	1	4	yes	—
109	C₁₃×#131	—	4	4	no	—
110	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
111	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
112	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	—	2	1	no	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×#127	—	2	2	no	—
121	C₁₃×#127	—	2	1	no	—
122	C₁₃×#127	—	2	1	no	—
123	C₁₃×#127	C₂³	1	2	yes	—
124	C₁₃×#127	C₂³	1	2	yes	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#126	—	2	2	no	—
129	C₁₃×#125	—	2	2	no	—
130	C₁₃×#125	—	2	1	no	—
131	C₁₃×#125	—	2	2	no	—
132	C₁₃×#125	—	2	2	no	—
133	C₁₃×#125	C₂³	1	2	yes	—
134	C₁₃×#125	C₂³	1	2	yes	—
135	C₁₃×#124	—	2	2	no	—
136	C₁₃×#124	—	2	1	no	—
137	C₁₃×#124	—	2	2	no	—
138	C₁₃×#124	—	2	2	no	—
139	C₁₃×#124	—	2	2	no	—
140	C₁₃×#124	C₂³	1	2	yes	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×#123	—	2	4	no	—
144	C₁₃×#123	—	2	4	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	1	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	1	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	1	no	—
152	C₁₃×C₂²⋊Q₈	—	2	1	no	—
153	C₁₃×C₂²⋊Q₈	—	2	2	no	—
154	C₁₃×C₂²⋊Q₈	—	2	2	no	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
157	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	—	2	1	no	—
160	C₁₃×#121	—	2	2	no	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	—	2	4	no	—
163	C₁₃×#121	—	2	4	no	—
164	C₁₃×#121	C₂³	1	4	yes	—
165	C₁₃×#121	C₂³	1	4	yes	—
166	C₁₃×#121	C₂³	1	2	yes	—
167	C₁₃×#120	—	2	4	no	—
168	C₄×Q₈×C₁₃	—	2	1	no	—
169	C₄×Q₈×C₁₃	—	2	1	no	—
170	C₄×Q₈×C₁₃	—	2	2	no	—
171	C₄×Q₈×C₁₃	—	2	1	no	—
172	C₄×Q₈×C₁₃	—	2	1	no	—
173	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
175	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
178	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	1	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	—	2	2	no	—
185	C₄×D₄×C₁₃	—	2	2	no	—
186	C₄×D₄×C₁₃	D₄	1	2	yes	—
187	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₃	D₄	1	2	yes	—
189	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₁₃	C₂³	1	4	yes	—
193	C₄×D₄×C₁₃	C₂³	1	4	yes	—
194	C₁₃×#117	—	2	2	no	—
195	C₁₃×#117	—	2	1	no	—
196	C₁₃×#117	—	2	2	no	—
197	C₁₃×#117	C₂³	1	2	yes	—
198	C₁₃×#117	C₂³	1	1	yes	characteristic
199	C₁₃×#117	C₂³	1	1	yes	characteristic
200	C₁₃×#117	C₂³	1	2	yes	—
201	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₂×C₄²×C₁₃	—	2	1	no	—
205	C₂×C₄²×C₁₃	—	2	1	no	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₁₃×#107	C₂³	1	2	yes	—
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×#106	C₂³	1	2	yes	—
212	C₁₃×#106	C₂³	1	2	yes	—
213	C₁₃×#106	C₂³	1	4	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
219	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	2	yes	—
222	C₁₃×#103	C₂³	1	2	yes	—
223	C₁₃×#103	C₂³	1	4	yes	—
224	C₁₃×#103	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×#102	C₂³	1	2	yes	—
228	C₁₃×#102	C₂³	1	2	yes	—
229	C₁₃×#102	C₂³	1	4	yes	—
230	C₁₃×#102	C₂³	1	4	yes	—
231	#60924	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	2	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	—	2	2	no	—
237	C₁₃×#41	—	8	4	no	—
238	C₁₃×#41	—	8	4	no	—
239	C₂×Q₈×C₁₃	—	2	1	no	—
240	C₂×Q₈×C₁₃	—	2	1	no	—
241	C₂×Q₈×C₁₃	—	2	1	no	—
242	C₂×Q₈×C₁₃	—	2	2	no	—
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	4	no	—
251	C₂×D₄×C₁₃	—	2	4	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	4	no	—
258	C₂×D₄×C₁₃	—	2	4	no	—
259	C₂×D₄×C₁₃	—	8	2	no	—
260	C₂×D₄×C₁₃	—	8	2	no	—
261	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	4	no	—
271	C₂²×C₄×C₁₃	—	2	4	no	—
272	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₁₃×SD₁₆	—	4	4	no	—
279	C₁₃×SD₁₆	—	4	4	no	—
280	C₁₃×SD₁₆	—	4	4	no	—
281	C₁₃×D₈	—	4	4	no	—
282	C₁₃×M₁₆	—	2	4	no	—
283	C₁₃×M₁₆	—	4	4	no	—
284	C₂×C₈×C₁₃	—	2	4	no	—
285	C₂×C₈×C₁₃	—	4	4	no	—
286	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
288	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
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	1	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	1	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
307	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
308	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
313	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	1	no	—
323	C₁₃×C₂²⋊C₄	—	2	1	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	4	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
331	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	1	no	—
334	C₄²×C₁₃	—	2	1	no	—
335	C₄²×C₁₃	—	2	1	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	—	2	2	no	—
338	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₁₃	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₁₃	C₂×D₄	1	2	yes	—
342	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₄²×C₁₃	C₂⁴	1	2	yes	—
344	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
345	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3461	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3260	C₂×C₁₃	1	4	yes	complemented
348	#3257	C₂×C₁₃	1	4	yes	complemented
349	#3254	C₂×C₁₃	1	2	yes	complemented
350	#3251	C₂×C₁₃	1	2	yes	complemented
351	#3247	C₂×C₁₃	1	2	yes	complemented
352	#3246	C₂×C₁₃	1	2	yes	complemented
353	#3081	C₂×C₁₃	1	2	yes	complemented
354	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#3062	C₂×C₁₃	1	2	yes	complemented
357	#3057	C₂×C₁₃	1	2	yes	complemented
358	#3042	C₂×C₁₃	1	2	yes	complemented
359	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
360	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	—	2	4	no	—
364	C₂³×C₁₃	—	4	4	no	—
365	C₂³×C₁₃	—	8	2	no	—
366	C₂³×C₁₃	—	8	2	no	—
367	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
368	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	Q₈×C₁₃	—	2	2	no	—
370	Q₈×C₁₃	—	2	2	no	—
371	Q₈×C₁₃	—	2	1	no	—
372	Q₈×C₁₃	—	2	2	no	—
373	Q₈×C₁₃	—	2	1	no	—
374	Q₈×C₁₃	—	4	2	no	—
375	Q₈×C₁₃	—	4	2	no	—
376	Q₈×C₁₃	—	4	2	no	—
377	Q₈×C₁₃	—	8	2	no	—
378	D₄×C₁₃	—	2	4	no	—
379	D₄×C₁₃	—	2	2	no	—
380	D₄×C₁₃	—	2	1	no	—
381	D₄×C₁₃	—	2	4	no	—
382	D₄×C₁₃	—	2	4	no	—
383	D₄×C₁₃	—	2	1	no	—
384	D₄×C₁₃	—	4	4	no	—
385	D₄×C₁₃	—	4	2	no	—
386	D₄×C₁₃	—	4	4	no	—
387	D₄×C₁₃	—	4	4	no	—
388	D₄×C₁₃	—	8	2	no	—
389	D₄×C₁₃	—	8	2	no	—
390	D₄×C₁₃	—	8	2	no	—
391	D₄×C₁₃	—	8	4	no	—
392	D₄×C₁₃	—	8	4	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	4	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	4	1	no	—
405	C₂×C₄×C₁₃	—	4	2	no	—
406	C₂×C₄×C₁₃	—	4	2	no	—
407	C₂×C₄×C₁₃	—	4	2	no	—
408	C₂×C₄×C₁₃	—	4	2	no	—
409	C₂×C₄×C₁₃	—	8	1	no	—
410	C₂×C₄×C₁₃	—	8	4	no	—
411	C₂×C₄×C₁₃	—	8	4	no	—
412	C₂×C₄×C₁₃	—	8	1	no	—
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
422	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
423	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
424	C₈×C₁₃	—	2	2	no	—
425	C₈×C₁₃	—	2	2	no	—
426	C₈×C₁₃	—	2	4	no	—
427	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
428	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
429	C₂×#131	C₂²×C₁₃	1	2	yes	—
430	#559	—	2	1	no	—
431	#559	—	2	1	no	—
432	#550	—	2	1	no	—
433	#550	—	2	1	no	—
434	#546	—	2	2	no	—
435	#546	—	2	2	no	—
436	#544	C₂²×C₁₃	1	1	yes	characteristic
437	#542	—	2	1	no	—
438	#542	C₂²×C₁₃	1	2	yes	complemented
439	#541	—	2	1	no	—
440	#541	C₂²×C₁₃	1	2	yes	complemented
441	#540	C₂²×C₁₃	1	4	yes	—
442	#539	—	2	2	no	—
443	#537	C₂²×C₁₃	1	1	yes	characteristic
444	#536	C₂²×C₁₃	1	1	yes	characteristic
445	#536	C₂²×C₁₃	1	1	yes	characteristic
446	#535	C₂²×C₁₃	1	2	yes	—
447	#533	—	2	1	no	—
448	#533	C₂²×C₁₃	1	1	yes	characteristic
449	#533	C₂²×C₁₃	1	2	yes	complemented
450	#532	C₂²×C₁₃	1	2	yes	—
451	#532	C₂²×C₁₃	1	2	yes	—
452	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
453	#529	—	2	2	no	—
454	#529	—	2	1	no	—
455	#529	C₂²×C₁₃	1	2	yes	complemented
456	#518	C₂²×C₁₃	1	2	yes	—
457	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
458	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
459	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
460	#479	C₂²×C₁₃	1	2	yes	complemented
461	#479	C₂²×C₁₃	1	4	yes	complemented
462	#478	C₂²×C₁₃	1	2	yes	complemented
463	#478	C₂²×C₁₃	1	4	yes	complemented
464	#478	C₂²×C₁₃	1	4	yes	complemented
465	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	#477	C₂²×C₁₃	1	2	yes	complemented
467	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	#476	C₂²×C₁₃	1	4	yes	complemented
469	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
470	#475	C₂²×C₁₃	1	2	yes	complemented
471	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
472	#474	C₂²×C₁₃	1	4	yes	complemented
473	#469	C₂²×C₁₃	1	4	yes	complemented
474	#468	C₂²×C₁₃	1	4	yes	complemented
475	#468	C₂²×C₁₃	1	4	yes	complemented
476	#468	C₂²×C₁₃	1	4	yes	complemented
477	#466	C₂²×C₁₃	1	4	yes	complemented
478	#465	C₂²×C₁₃	1	4	yes	complemented
479	#465	C₂²×C₁₃	1	4	yes	complemented
480	#465	C₂²×C₁₃	1	4	yes	complemented
481	#463	C₂²×C₁₃	1	4	yes	complemented
482	#463	C₂²×C₁₃	1	4	yes	complemented
483	#461	C₂²×C₁₃	1	4	yes	complemented
484	#461	C₂²×C₁₃	1	4	yes	complemented
485	#460	C₂²×C₁₃	1	2	yes	—
486	#460	C₂²×C₁₃	1	2	yes	—
487	#460	C₂²×C₁₃	1	2	yes	—
488	#460	C₂²×C₁₃	1	4	yes	—
489	#460	C₂²×C₁₃	1	2	yes	—
490	#459	C₂²×C₁₃	1	2	yes	—
491	#459	C₂²×C₁₃	1	2	yes	—
492	#428	C₂²×C₁₃	1	2	yes	—
493	#427	C₂²×C₁₃	1	2	yes	—
494	#424	C₂²×C₁₃	1	2	yes	—
495	#424	C₂²×C₁₃	1	4	yes	complemented
496	#423	C₂²×C₁₃	1	1	yes	characteristic
497	#423	C₂²×C₁₃	1	2	yes	complemented
498	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
499	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
500	#419	C₂²×C₁₃	1	2	yes	—
501	#418	C₂²×C₁₃	1	2	yes	—
502	#416	C₂²×C₁₃	1	2	yes	—
503	C₂×#102	C₂²×C₁₃	1	2	yes	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	2	2	no	—
509	C₂²×C₁₃	—	4	4	no	—
510	C₂²×C₁₃	—	4	1	no	—
511	C₂²×C₁₃	—	4	1	no	—
512	C₂²×C₁₃	—	4	4	no	—
513	C₂²×C₁₃	—	4	1	no	—
514	C₂²×C₁₃	—	4	4	no	—
515	C₂²×C₁₃	—	16	4	no	—
516	C₂²×C₁₃	#537	1	2	yes	—
517	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	2	no	—
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	2	2	no	—
523	C₄×C₁₃	—	2	1	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	—	4	1	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	1	no	—
530	C₄×C₁₃	—	4	2	no	—
531	C₄×C₁₃	#537	1	2	yes	—
532	C₄×C₁₃	#577	1	2	yes	—
533	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
534	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	C₂×#41	—	2	2	no	—
536	C₂×#41	—	2	2	no	—
537	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
539	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	2	1	no	—
542	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
543	AGL(1,ℤ/8)	—	4	4	no	—
544	C₂×SD₁₆	—	4	4	no	—
545	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
546	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
547	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
548	C₂×D₈	C₂³×C₁₃	1	4	yes	—
549	#131	—	4	4	no	—
550	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
551	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
552	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
553	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
554	C₄⋊Q₈	—	2	1	no	—
555	C₄⋊Q₈	—	2	1	no	—
556	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
559	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
560	#127	—	2	2	no	—
561	#127	—	2	1	no	—
562	#127	—	2	1	no	—
563	#127	C₂³×C₁₃	1	2	yes	—
564	#127	C₂³×C₁₃	1	2	yes	—
565	#126	—	2	2	no	—
566	#126	—	2	2	no	—
567	#126	—	2	2	no	—
568	#126	—	2	2	no	—
569	#125	—	2	2	no	—
570	#125	—	2	1	no	—
571	#125	—	2	2	no	—
572	#125	—	2	2	no	—
573	#125	C₂³×C₁₃	1	2	yes	—
574	#125	C₂³×C₁₃	1	2	yes	—
575	#124	—	2	2	no	—
576	#124	—	2	1	no	—
577	#124	—	2	2	no	—
578	#124	—	2	2	no	—
579	#124	—	2	2	no	—
580	#124	C₂³×C₁₃	1	2	yes	—
581	#123	—	2	2	no	—
582	#123	—	2	2	no	—
583	#123	—	2	4	no	—
584	#123	—	2	4	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
596	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
597	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	#121	—	2	2	no	—
599	#121	—	2	1	no	—
600	#121	—	2	2	no	—
601	#121	—	2	2	no	—
602	#121	—	2	4	no	—
603	#121	—	2	4	no	—
604	#121	C₂³×C₁₃	1	2	yes	—
605	#121	C₂³×C₁₃	1	4	yes	—
606	#121	C₂³×C₁₃	1	4	yes	—
607	#120	—	2	4	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	—	2	1	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
614	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
616	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
617	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	D₄×C₁₃	1	2	yes	—
627	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
628	C₄×D₄	D₄×C₁₃	1	2	yes	—
629	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₁₃	1	4	yes	—
633	C₄×D₄	C₂³×C₁₃	1	4	yes	—
634	#117	—	2	2	no	—
635	#117	—	2	1	no	—
636	#117	—	2	2	no	—
637	#117	C₂³×C₁₃	1	1	yes	characteristic
638	#117	C₂³×C₁₃	1	2	yes	—
639	#117	C₂³×C₁₃	1	1	yes	characteristic
640	#117	C₂³×C₁₃	1	2	yes	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	—	2	4	no	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
648	#107	C₂³×C₁₃	1	2	yes	—
649	#107	C₂³×C₁₃	1	2	yes	—
650	#107	C₂³×C₁₃	1	4	yes	—
651	#106	C₂³×C₁₃	1	2	yes	—
652	#106	C₂³×C₁₃	1	2	yes	—
653	#106	C₂³×C₁₃	1	4	yes	—
654	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
655	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
656	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
657	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
658	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
659	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
660	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
661	#103	C₂³×C₁₃	1	2	yes	—
662	#103	C₂³×C₁₃	1	2	yes	—
663	#103	C₂³×C₁₃	1	4	yes	—
664	#103	C₂³×C₁₃	1	4	yes	—
665	#102	C₂³×C₁₃	1	4	yes	—
666	#102	C₂³×C₁₃	1	4	yes	—
667	#102	C₂³×C₁₃	1	2	yes	—
668	#102	C₂³×C₁₃	1	2	yes	—
669	#102	C₂³×C₁₃	1	4	yes	—
670	#102	C₂³×C₁₃	1	4	yes	—
671	C₂×C₁₃	—	2	2	no	—
672	C₂×C₁₃	—	4	2	no	—
673	C₂×C₁₃	—	8	1	no	—
674	C₂×C₁₃	—	8	4	no	—
675	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
676	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
677	C₂×C₁₃	#3585	1	1	yes	characteristic
678	C₂⁴	—	2	2	no	—
679	#41	—	2	2	no	—
680	#41	—	2	2	no	—
681	#41	—	2	2	no	—
682	#41	—	2	2	no	—
683	#41	—	8	4	no	—
684	#41	—	8	4	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
693	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	8	2	no	—
706	C₂×D₄	—	8	2	no	—
707	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
708	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
709	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
710	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
720	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
724	SD₁₆	—	4	4	no	—
725	SD₁₆	—	4	4	no	—
726	SD₁₆	—	4	4	no	—
727	D₈	—	4	4	no	—
728	M₁₆	—	2	4	no	—
729	M₁₆	—	4	4	no	—
730	C₂×C₈	—	2	4	no	—
731	C₂×C₈	—	4	4	no	—
732	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
733	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
734	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
756	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
776	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
777	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	1	no	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	1	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
785	C₄²	C₂×D₄×C₁₃	1	2	yes	—
786	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
787	C₄²	C₂×D₄×C₁₃	1	2	yes	—
788	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
789	C₄²	C₂⁴×C₁₃	1	2	yes	—
790	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
791	C₁₃	#60924	1	1	yes	characteristic, direct product factor, Sylow
792	C₂³	—	2	1	no	—
793	C₂³	—	2	4	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	8	2	no	—
796	C₂³	—	8	2	no	—
797	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
798	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	1	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	2	1	no	—
804	Q₈	—	4	2	no	—
805	Q₈	—	4	2	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	8	2	no	—
808	D₄	—	2	4	no	—
809	D₄	—	2	2	no	—
810	D₄	—	2	1	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	4	no	—
813	D₄	—	2	1	no	—
814	D₄	—	4	4	no	—
815	D₄	—	4	2	no	—
816	D₄	—	4	4	no	—
817	D₄	—	4	4	no	—
818	D₄	—	8	2	no	—
819	D₄	—	8	2	no	—
820	D₄	—	8	2	no	—
821	D₄	—	8	4	no	—
822	D₄	—	8	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	4	no	—
841	C₂×C₄	—	8	4	no	—
842	C₂×C₄	—	8	1	no	—
843	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
849	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
851	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
852	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
853	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
854	C₈	—	2	2	no	—
855	C₈	—	2	2	no	—
856	C₈	—	2	4	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	4	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	4	no	—
868	C₂²	—	16	4	no	—
869	C₂²	C₁₃×#537	1	2	yes	—
870	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	2	no	—
884	C₄	C₁₃×#537	1	2	yes	—
885	C₄	C₁₃×#577	1	2	yes	—
886	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
887	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
888	C₂	—	2	2	no	—
889	C₂	—	4	2	no	—
890	C₂	—	8	4	no	—
891	C₂	—	8	1	no	—
892	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
893	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
894	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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×#3508	C₂	semidirect
2. C₁₃×#3461	C₂	semidirect
3. C₁₃×#3260	C₂	semidirect
4. C₁₃×#3257	C₂	semidirect
5. C₁₃×#3254	C₂	semidirect
6. C₁₃×#3251	C₂	semidirect
7. C₁₃×#3247	C₂	semidirect
8. C₁₃×#3246	C₂	semidirect
9. C₁₃×#3081	C₂	semidirect
10. C₁₃×#3078	C₂	semidirect
11. C₁₃×#3076	C₂	semidirect
12. C₁₃×#3062	C₂	semidirect
13. C₁₃×#3057	C₂	semidirect
14. C₁₃×#3042	C₂	semidirect
15. C₁₃×#3038	C₂	semidirect
16. C₂×C₁₃×#460	C₂	semidirect
17. C₁₃×#2906	C₂	semidirect
29. C₁₃×#542	C₂²	semidirect
31. C₁₃×#541	C₂²	semidirect
40. C₁₃×#533	C₂²	semidirect
46. C₁₃×#529	C₂²	semidirect
51. C₁₃×#479	C₂²	semidirect
52. C₁₃×#479	C₂²	semidirect
53. C₁₃×#478	C₂²	semidirect
54. C₁₃×#478	C₂²	semidirect
55. C₁₃×#478	C₂²	semidirect
56. C₁₃×#477	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#476	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#475	C₂²	semidirect
62. C₁₃×#474	C₂²	semidirect
63. C₁₃×#474	C₂²	semidirect
64. C₁₃×#469	C₂²	semidirect
65. C₁₃×#468	C₂²	semidirect
66. C₁₃×#468	C₂²	semidirect
67. C₁₃×#468	C₂²	semidirect
68. C₁₃×#466	C₂²	semidirect
69. C₁₃×#465	C₂²	semidirect
70. C₁₃×#465	C₂²	semidirect
71. C₁₃×#465	C₂²	semidirect
72. C₁₃×#463	C₂²	semidirect
73. C₁₃×#463	C₂²	semidirect
74. C₁₃×#461	C₂²	semidirect
75. C₁₃×#461	C₂²	semidirect
86. C₁₃×#424	C₂²	semidirect
88. C₁₃×#423	C₂²	semidirect
90. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
231. #60924	C₁₃	direct (N × H)
345. #3508	C₂×C₁₃	semidirect
346. #3461	C₂×C₁₃	semidirect
347. #3260	C₂×C₁₃	semidirect
348. #3257	C₂×C₁₃	semidirect
349. #3254	C₂×C₁₃	semidirect
350. #3251	C₂×C₁₃	semidirect
351. #3247	C₂×C₁₃	semidirect
352. #3246	C₂×C₁₃	semidirect
353. #3081	C₂×C₁₃	semidirect
354. #3078	C₂×C₁₃	semidirect
355. #3076	C₂×C₁₃	semidirect
356. #3062	C₂×C₁₃	semidirect
357. #3057	C₂×C₁₃	semidirect
358. #3042	C₂×C₁₃	semidirect
359. #3038	C₂×C₁₃	semidirect
360. C₂×#460	C₂×C₁₃	semidirect
361. #2906	C₂×C₁₃	semidirect
438. #542	C₂²×C₁₃	semidirect
440. #541	C₂²×C₁₃	semidirect
449. #533	C₂²×C₁₃	semidirect
455. #529	C₂²×C₁₃	semidirect
460. #479	C₂²×C₁₃	semidirect
461. #479	C₂²×C₁₃	semidirect
462. #478	C₂²×C₁₃	semidirect
463. #478	C₂²×C₁₃	semidirect
464. #478	C₂²×C₁₃	semidirect
465. #477	C₂²×C₁₃	semidirect
466. #477	C₂²×C₁₃	semidirect
467. #476	C₂²×C₁₃	semidirect
468. #476	C₂²×C₁₃	semidirect
469. #475	C₂²×C₁₃	semidirect
470. #475	C₂²×C₁₃	semidirect
471. #474	C₂²×C₁₃	semidirect
472. #474	C₂²×C₁₃	semidirect
473. #469	C₂²×C₁₃	semidirect
474. #468	C₂²×C₁₃	semidirect
475. #468	C₂²×C₁₃	semidirect
476. #468	C₂²×C₁₃	semidirect
477. #466	C₂²×C₁₃	semidirect
478. #465	C₂²×C₁₃	semidirect
479. #465	C₂²×C₁₃	semidirect
480. #465	C₂²×C₁₃	semidirect
481. #463	C₂²×C₁₃	semidirect
482. #463	C₂²×C₁₃	semidirect
483. #461	C₂²×C₁₃	semidirect
484. #461	C₂²×C₁₃	semidirect
495. #424	C₂²×C₁₃	semidirect
497. #423	C₂²×C₁₃	semidirect
499. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
791. C₁₃	#60924	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×#3508	2
C₁₃×#3461	2
C₁₃×#3260	2
C₁₃×#3257	2
C₁₃×#3254	2
C₁₃×#3251	2
C₁₃×#3247	2
C₁₃×#3246	2
C₁₃×#3081	2
C₁₃×#3078	2
C₁₃×#3076	2
C₁₃×#3062	2
C₁₃×#3057	2
C₁₃×#3042	2
C₁₃×#3038	2
C₂×C₁₃×#460	2
C₁₃×#2906	2
#60924	13

Subgroups — C13×#60924 #15747263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60924 #15747263