Subgroups — C₁₃×#60918 #15747257

Order 3328.

1888 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3255	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3254	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3252	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3249	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3248	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3246	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3079	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3078	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3056	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3039	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#137	C₂²	1	4	yes	—
16	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
17	C₁₃×#533	—	2	1	no	—
18	C₁₃×#533	—	2	1	no	—
19	C₁₃×#533	—	2	1	no	—
20	C₁₃×#533	—	2	1	no	—
21	C₁₃×#533	C₂²	1	2	yes	—
22	C₁₃×#533	C₂²	1	2	yes	—
23	C₁₃×#533	C₂²	1	2	yes	—
24	C₁₃×#533	C₂²	1	2	yes	—
25	C₁₃×#533	C₂²	1	1	yes	characteristic
26	C₁₃×#533	C₂²	1	1	yes	characteristic
27	C₁₃×#533	C₂²	1	1	yes	characteristic
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₁₃×#532	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₃×#529	—	2	1	no	—
34	C₁₃×#529	—	2	1	no	—
35	C₁₃×#529	—	2	1	no	—
36	C₁₃×#529	—	2	1	no	—
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₁₃×#529	C₂²	1	2	yes	—
39	C₂×C₁₃×#125	—	2	1	no	—
40	C₁₃×#525	—	2	1	no	—
41	C₁₃×#525	—	2	1	no	—
42	C₁₃×#525	C₂²	1	2	yes	—
43	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₄×C₁₃×#41	—	2	1	no	—
46	C₄×C₁₃×#41	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	2	yes	—
48	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
49	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
50	C₂×C₁₃×#117	—	2	1	no	—
51	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
52	C₁₃×#479	C₂²	1	8	yes	complemented
53	C₁₃×#477	C₂²	1	4	yes	complemented
54	C₁₃×#477	C₂²	1	4	yes	complemented
55	C₁₃×#476	C₂²	1	4	yes	complemented
56	C₁₃×#475	C₂²	1	4	yes	complemented
57	C₁₃×#475	C₂²	1	4	yes	complemented
58	C₁₃×#474	C₂²	1	4	yes	complemented
59	C₁₃×#470	C₂²	1	8	yes	—
60	C₁₃×#468	C₂²	1	8	yes	—
61	C₁₃×#467	C₂²	1	8	yes	—
62	C₁₃×#465	C₂²	1	8	yes	—
63	C₁₃×#464	C₂²	1	8	yes	complemented
64	C₁₃×#462	C₂²	1	4	yes	complemented
65	C₁₃×#462	C₂²	1	4	yes	complemented
66	C₁₃×#462	C₂²	1	4	yes	complemented
67	C₁₃×#461	C₂²	1	4	yes	complemented
68	C₁₃×#461	C₂²	1	4	yes	complemented
69	C₁₃×#460	C₂²	1	4	yes	complemented
70	C₁₃×#428	C₂²	1	4	yes	—
71	C₁₃×#423	C₂²	1	2	yes	—
72	C₁₃×#423	C₂²	1	2	yes	—
73	C₁₃×#423	C₂²	1	2	yes	—
74	C₁₃×#423	C₂²	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
77	C₁₃×#419	C₂²	1	4	yes	—
78	C₁₃×#417	C₂²	1	4	yes	—
79	C₂×C₁₃×#41	—	2	1	no	—
80	C₂×C₁₃×#41	—	2	1	no	—
81	C₂×C₁₃×#41	C₂³	1	2	yes	—
82	C₂²×Q₈×C₁₃	—	2	1	no	—
83	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#137	—	4	8	no	—
88	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
90	C₂×C₁₃×M₁₆	—	4	4	no	—
91	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
92	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
93	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
94	C₁₃×C₄⋊Q₈	—	2	1	no	—
95	C₁₃×C₄⋊Q₈	—	2	1	no	—
96	C₁₃×C₄⋊Q₈	—	2	1	no	—
97	C₁₃×C₄⋊Q₈	—	2	1	no	—
98	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
104	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₁₃×#127	C₂³	1	1	yes	characteristic
106	C₁₃×#126	—	2	2	no	—
107	C₁₃×#126	—	2	2	no	—
108	C₁₃×#125	—	2	2	no	—
109	C₁₃×#125	—	2	2	no	—
110	C₁₃×#125	—	2	2	no	—
111	C₁₃×#125	—	2	2	no	—
112	C₁₃×#125	—	2	1	no	—
113	C₁₃×#125	—	2	1	no	—
114	C₁₃×#125	C₂³	1	2	yes	—
115	C₁₃×#124	—	2	1	no	—
116	C₁₃×#124	—	2	1	no	—
117	C₁₃×#124	C₂³	1	2	yes	—
118	C₁₃×#123	—	2	2	no	—
119	C₁₃×#123	—	2	2	no	—
120	C₁₃×#123	—	2	2	no	—
121	C₁₃×C₂²⋊Q₈	—	2	2	no	—
122	C₁₃×C₂²⋊Q₈	—	2	2	no	—
123	C₁₃×C₂²⋊Q₈	—	2	2	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	2	no	—
126	C₁₃×C₂²⋊Q₈	—	2	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	1	no	—
128	C₁₃×C₂²⋊Q₈	—	2	1	no	—
129	C₁₃×C₂²⋊Q₈	—	2	1	no	—
130	C₁₃×C₂²⋊Q₈	—	2	1	no	—
131	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×#121	—	2	1	no	—
136	C₁₃×#121	—	2	1	no	—
137	C₁₃×#121	—	2	1	no	—
138	C₁₃×#121	—	2	1	no	—
139	C₁₃×#121	C₂³	1	2	yes	—
140	C₁₃×#121	C₂³	1	2	yes	—
141	C₁₃×#120	—	2	2	no	—
142	C₄×Q₈×C₁₃	—	2	2	no	—
143	C₄×Q₈×C₁₃	—	2	2	no	—
144	C₄×Q₈×C₁₃	—	2	2	no	—
145	C₄×Q₈×C₁₃	—	2	2	no	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	2	no	—
148	C₄×Q₈×C₁₃	—	2	1	no	—
149	C₄×Q₈×C₁₃	—	2	1	no	—
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
153	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	2	no	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	1	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	C₂³	1	2	yes	—
167	C₄×D₄×C₁₃	C₂³	1	2	yes	—
168	C₁₃×#117	—	2	2	no	—
169	C₁₃×#117	—	2	2	no	—
170	C₁₃×#117	—	2	2	no	—
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	—	2	1	no	—
173	C₁₃×#117	—	2	1	no	—
174	C₁₃×#117	—	2	2	no	—
175	C₁₃×#117	—	2	2	no	—
176	C₁₃×#117	—	2	2	no	—
177	C₁₃×#117	C₂³	1	2	yes	—
178	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₂×C₄²×C₁₃	—	2	2	no	—
186	C₂×C₄²×C₁₃	—	2	2	no	—
187	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₁₃×#107	C₂³	1	8	yes	—
200	C₁₃×#106	C₂³	1	8	yes	—
201	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
202	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
204	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
205	C₁₃×#103	C₂³	1	8	yes	—
206	C₁₃×#103	C₂³	1	8	yes	—
207	C₁₃×#103	C₂³	1	8	yes	—
208	C₁₃×#102	C₂³	1	8	yes	—
209	#60918	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₁₃×#41	—	2	4	no	—
212	C₁₃×#41	—	2	4	no	—
213	C₁₃×#41	—	4	4	no	—
214	C₁₃×#41	—	4	4	no	—
215	C₂×Q₈×C₁₃	—	2	1	no	—
216	C₂×Q₈×C₁₃	—	2	1	no	—
217	C₂×Q₈×C₁₃	—	2	2	no	—
218	C₂×Q₈×C₁₃	—	2	2	no	—
219	C₂×Q₈×C₁₃	—	2	2	no	—
220	C₂×Q₈×C₁₃	—	2	4	no	—
221	C₂×Q₈×C₁₃	—	2	4	no	—
222	C₂×Q₈×C₁₃	—	4	4	no	—
223	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
224	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
225	C₂×D₄×C₁₃	—	2	2	no	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	2	2	no	—
234	C₂²×C₄×C₁₃	—	2	2	no	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	2	2	no	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	2	2	no	—
239	C₂²×C₄×C₁₃	—	4	2	no	—
240	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₁₃×Q₁₆	—	4	8	no	—
259	C₁₃×SD₁₆	—	4	8	no	—
260	C₁₃×M₁₆	—	2	8	no	—
261	C₁₃×M₁₆	—	4	4	no	—
262	C₂×C₈×C₁₃	—	4	4	no	—
263	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
264	C₁₃×C₄⋊C₄	—	2	2	no	—
265	C₁₃×C₄⋊C₄	—	2	2	no	—
266	C₁₃×C₄⋊C₄	—	2	2	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	2	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	—	2	2	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₁₃×C₂²⋊C₄	—	2	2	no	—
296	C₁₃×C₂²⋊C₄	—	2	2	no	—
297	C₁₃×C₂²⋊C₄	—	2	2	no	—
298	C₁₃×C₂²⋊C₄	—	2	2	no	—
299	C₄²×C₁₃	—	2	2	no	—
300	C₄²×C₁₃	—	2	2	no	—
301	C₄²×C₁₃	—	2	4	no	—
302	C₄²×C₁₃	—	2	4	no	—
303	C₄²×C₁₃	—	2	2	no	—
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
318	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
319	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
320	#3444	C₂×C₁₃	1	1	yes	characteristic
321	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#3255	C₂×C₁₃	1	2	yes	complemented
323	#3254	C₂×C₁₃	1	2	yes	complemented
324	#3252	C₂×C₁₃	1	4	yes	complemented
325	#3249	C₂×C₁₃	1	2	yes	complemented
326	#3248	C₂×C₁₃	1	4	yes	complemented
327	#3246	C₂×C₁₃	1	2	yes	complemented
328	#3079	C₂×C₁₃	1	2	yes	complemented
329	#3078	C₂×C₁₃	1	2	yes	complemented
330	#3056	C₂×C₁₃	1	4	yes	complemented
331	#3039	C₂×C₁₃	1	2	yes	complemented
332	#3037	C₂×C₁₃	1	2	yes	complemented
333	C₂×#423	C₂×C₁₃	1	1	yes	characteristic, complemented
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	2	2	no	—
336	C₂³×C₁₃	—	2	2	no	—
337	C₂³×C₁₃	—	4	1	no	—
338	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
339	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
340	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₁₃	—	2	4	no	—
342	Q₈×C₁₃	—	2	2	no	—
343	Q₈×C₁₃	—	2	4	no	—
344	Q₈×C₁₃	—	2	2	no	—
345	Q₈×C₁₃	—	4	4	no	—
346	Q₈×C₁₃	—	4	2	no	—
347	Q₈×C₁₃	—	4	4	no	—
348	Q₈×C₁₃	—	4	2	no	—
349	Q₈×C₁₃	—	4	4	no	—
350	D₄×C₁₃	—	2	2	no	—
351	D₄×C₁₃	—	2	2	no	—
352	D₄×C₁₃	—	4	2	no	—
353	D₄×C₁₃	—	4	4	no	—
354	D₄×C₁₃	—	4	4	no	—
355	D₄×C₁₃	—	4	4	no	—
356	D₄×C₁₃	—	4	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	4	no	—
376	C₂×C₄×C₁₃	—	2	4	no	—
377	C₂×C₄×C₁₃	—	4	1	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	4	no	—
381	C₂×C₄×C₁₃	—	4	4	no	—
382	C₂×C₄×C₁₃	—	4	4	no	—
383	C₂×C₄×C₁₃	—	4	4	no	—
384	C₂×C₄×C₁₃	—	4	4	no	—
385	C₂×C₄×C₁₃	#137	1	4	yes	complemented
386	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
398	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
399	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
400	C₈×C₁₃	—	2	8	no	—
401	C₂×#137	C₂²×C₁₃	1	4	yes	—
402	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
403	#533	—	2	1	no	—
404	#533	—	2	1	no	—
405	#533	—	2	1	no	—
406	#533	—	2	1	no	—
407	#533	C₂²×C₁₃	1	2	yes	—
408	#533	C₂²×C₁₃	1	2	yes	—
409	#533	C₂²×C₁₃	1	2	yes	—
410	#533	C₂²×C₁₃	1	2	yes	—
411	#533	C₂²×C₁₃	1	1	yes	characteristic
412	#533	C₂²×C₁₃	1	1	yes	characteristic
413	#533	C₂²×C₁₃	1	1	yes	characteristic
414	#532	C₂²×C₁₃	1	1	yes	characteristic
415	#532	C₂²×C₁₃	1	1	yes	characteristic
416	#532	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
419	#529	—	2	1	no	—
420	#529	—	2	1	no	—
421	#529	—	2	1	no	—
422	#529	—	2	1	no	—
423	#529	C₂²×C₁₃	1	2	yes	—
424	#529	C₂²×C₁₃	1	2	yes	—
425	C₂×#125	—	2	1	no	—
426	#525	—	2	1	no	—
427	#525	—	2	1	no	—
428	#525	C₂²×C₁₃	1	2	yes	—
429	C₂×C₂²⋊Q₈	—	2	1	no	—
430	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
431	C₄×#41	—	2	1	no	—
432	C₄×#41	—	2	1	no	—
433	C₄×#41	C₂²×C₁₃	1	2	yes	—
434	C₂×C₄×Q₈	—	2	1	no	—
435	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
436	C₂×#117	—	2	1	no	—
437	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
438	#479	C₂²×C₁₃	1	8	yes	complemented
439	#477	C₂²×C₁₃	1	4	yes	complemented
440	#477	C₂²×C₁₃	1	4	yes	complemented
441	#476	C₂²×C₁₃	1	4	yes	complemented
442	#475	C₂²×C₁₃	1	4	yes	complemented
443	#475	C₂²×C₁₃	1	4	yes	complemented
444	#474	C₂²×C₁₃	1	4	yes	complemented
445	#470	C₂²×C₁₃	1	8	yes	—
446	#468	C₂²×C₁₃	1	8	yes	—
447	#467	C₂²×C₁₃	1	8	yes	—
448	#465	C₂²×C₁₃	1	8	yes	—
449	#464	C₂²×C₁₃	1	8	yes	complemented
450	#462	C₂²×C₁₃	1	4	yes	complemented
451	#462	C₂²×C₁₃	1	4	yes	complemented
452	#462	C₂²×C₁₃	1	4	yes	complemented
453	#461	C₂²×C₁₃	1	4	yes	complemented
454	#461	C₂²×C₁₃	1	4	yes	complemented
455	#460	C₂²×C₁₃	1	4	yes	complemented
456	#428	C₂²×C₁₃	1	4	yes	—
457	#423	C₂²×C₁₃	1	2	yes	—
458	#423	C₂²×C₁₃	1	2	yes	—
459	#423	C₂²×C₁₃	1	2	yes	—
460	#423	C₂²×C₁₃	1	2	yes	—
461	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
462	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
463	#419	C₂²×C₁₃	1	4	yes	—
464	#417	C₂²×C₁₃	1	4	yes	—
465	C₂²×C₁₃	—	2	1	no	—
466	C₂²×C₁₃	—	2	1	no	—
467	C₂²×C₁₃	—	2	1	no	—
468	C₂²×C₁₃	—	2	1	no	—
469	C₂²×C₁₃	—	2	1	no	—
470	C₂²×C₁₃	—	2	1	no	—
471	C₂²×C₁₃	—	2	1	no	—
472	C₂²×C₁₃	—	4	4	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	#537	1	2	yes	—
477	C₂²×C₁₃	C₂×#137	1	2	yes	—
478	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
479	C₄×C₁₃	—	2	1	no	—
480	C₄×C₁₃	—	2	1	no	—
481	C₄×C₁₃	—	2	1	no	—
482	C₄×C₁₃	—	2	1	no	—
483	C₄×C₁₃	—	2	1	no	—
484	C₄×C₁₃	—	2	1	no	—
485	C₄×C₁₃	—	2	1	no	—
486	C₄×C₁₃	—	4	2	no	—
487	C₄×C₁₃	—	4	4	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	4	no	—
491	C₄×C₁₃	#537	1	2	yes	—
492	C₄×C₁₃	C₂×#137	1	2	yes	—
493	C₄×C₁₃	C₂×#137	1	2	yes	—
494	C₄×C₁₃	#575	1	2	yes	—
495	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
496	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
497	C₂×#41	—	2	1	no	—
498	C₂×#41	—	2	1	no	—
499	C₂×#41	C₂³×C₁₃	1	2	yes	—
500	C₂²×Q₈	—	2	1	no	—
501	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
502	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
503	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
505	#137	—	4	8	no	—
506	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
507	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
508	C₂×M₁₆	—	4	4	no	—
509	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
510	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
511	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
512	C₄⋊Q₈	—	2	1	no	—
513	C₄⋊Q₈	—	2	1	no	—
514	C₄⋊Q₈	—	2	1	no	—
515	C₄⋊Q₈	—	2	1	no	—
516	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
517	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
518	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
520	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
521	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
522	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
523	#127	C₂³×C₁₃	1	1	yes	characteristic
524	#126	—	2	2	no	—
525	#126	—	2	2	no	—
526	#125	—	2	2	no	—
527	#125	—	2	2	no	—
528	#125	—	2	2	no	—
529	#125	—	2	2	no	—
530	#125	—	2	1	no	—
531	#125	—	2	1	no	—
532	#125	C₂³×C₁₃	1	2	yes	—
533	#124	—	2	1	no	—
534	#124	—	2	1	no	—
535	#124	C₂³×C₁₃	1	2	yes	—
536	#123	—	2	2	no	—
537	#123	—	2	2	no	—
538	#123	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
550	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
551	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
552	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
553	#121	—	2	1	no	—
554	#121	—	2	1	no	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	C₂³×C₁₃	1	2	yes	—
558	#121	C₂³×C₁₃	1	2	yes	—
559	#120	—	2	2	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
571	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
572	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
573	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	C₂³×C₁₃	1	2	yes	—
585	C₄×D₄	C₂³×C₁₃	1	2	yes	—
586	#117	—	2	2	no	—
587	#117	—	2	2	no	—
588	#117	—	2	2	no	—
589	#117	—	2	2	no	—
590	#117	—	2	1	no	—
591	#117	—	2	1	no	—
592	#117	—	2	2	no	—
593	#117	—	2	2	no	—
594	#117	—	2	2	no	—
595	#117	C₂³×C₁₃	1	2	yes	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	2	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₂²⋊C₄	—	2	2	no	—
603	C₂×C₄²	—	2	2	no	—
604	C₂×C₄²	—	2	2	no	—
605	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
606	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
607	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
608	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
609	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
610	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
617	#107	C₂³×C₁₃	1	8	yes	—
618	#106	C₂³×C₁₃	1	8	yes	—
619	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
620	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
621	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
622	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
623	#103	C₂³×C₁₃	1	8	yes	—
624	#103	C₂³×C₁₃	1	8	yes	—
625	#103	C₂³×C₁₃	1	8	yes	—
626	#102	C₂³×C₁₃	1	8	yes	—
627	C₂×C₁₃	—	2	2	no	—
628	C₂×C₁₃	—	2	2	no	—
629	C₂×C₁₃	—	4	1	no	—
630	C₂×C₁₃	—	8	2	no	—
631	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
632	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
633	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
634	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
635	#41	—	2	4	no	—
636	#41	—	2	4	no	—
637	#41	—	4	4	no	—
638	#41	—	4	4	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	4	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	4	4	no	—
647	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
648	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
682	Q₁₆	—	4	8	no	—
683	SD₁₆	—	4	8	no	—
684	M₁₆	—	2	8	no	—
685	M₁₆	—	4	4	no	—
686	C₂×C₈	—	4	4	no	—
687	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
710	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	4	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	2	no	—
728	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
729	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
730	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
732	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
735	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
736	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
737	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
738	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
739	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
741	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
742	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
743	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
744	C₁₃	#60918	1	1	yes	characteristic, direct product factor, Sylow
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	4	1	no	—
749	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
750	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
751	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
752	Q₈	—	2	4	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	4	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	4	4	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	4	4	no	—
759	Q₈	—	4	2	no	—
760	Q₈	—	4	4	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	4	no	—
767	D₄	—	4	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	C₁₃×#137	1	4	yes	complemented
797	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
808	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
809	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
810	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
811	C₈	—	2	8	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	C₁₃×#537	1	2	yes	—
824	C₂²	C₂×C₁₃×#137	1	2	yes	—
825	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	4	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	4	no	—
838	C₄	C₁₃×#537	1	2	yes	—
839	C₄	C₂×C₁₃×#137	1	2	yes	—
840	C₄	C₂×C₁₃×#137	1	2	yes	—
841	C₄	C₁₃×#575	1	2	yes	—
842	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
843	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	2	2	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
849	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
850	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3255	C₂	semidirect
4. C₁₃×#3254	C₂	semidirect
5. C₁₃×#3252	C₂	semidirect
6. C₁₃×#3249	C₂	semidirect
7. C₁₃×#3248	C₂	semidirect
8. C₁₃×#3246	C₂	semidirect
9. C₁₃×#3079	C₂	semidirect
10. C₁₃×#3078	C₂	semidirect
11. C₁₃×#3056	C₂	semidirect
12. C₁₃×#3039	C₂	semidirect
13. C₁₃×#3037	C₂	semidirect
14. C₂×C₁₃×#423	C₂	semidirect
52. C₁₃×#479	C₂²	semidirect
53. C₁₃×#477	C₂²	semidirect
54. C₁₃×#477	C₂²	semidirect
55. C₁₃×#476	C₂²	semidirect
56. C₁₃×#475	C₂²	semidirect
57. C₁₃×#475	C₂²	semidirect
58. C₁₃×#474	C₂²	semidirect
63. C₁₃×#464	C₂²	semidirect
64. C₁₃×#462	C₂²	semidirect
65. C₁₃×#462	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#461	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
209. #60918	C₁₃	direct (N × H)
321. C₂×#533	C₂×C₁₃	semidirect
322. #3255	C₂×C₁₃	semidirect
323. #3254	C₂×C₁₃	semidirect
324. #3252	C₂×C₁₃	semidirect
325. #3249	C₂×C₁₃	semidirect
326. #3248	C₂×C₁₃	semidirect
327. #3246	C₂×C₁₃	semidirect
328. #3079	C₂×C₁₃	semidirect
329. #3078	C₂×C₁₃	semidirect
330. #3056	C₂×C₁₃	semidirect
331. #3039	C₂×C₁₃	semidirect
332. #3037	C₂×C₁₃	semidirect
333. C₂×#423	C₂×C₁₃	semidirect
385. C₂×C₄×C₁₃	#137	semidirect
438. #479	C₂²×C₁₃	semidirect
439. #477	C₂²×C₁₃	semidirect
440. #477	C₂²×C₁₃	semidirect
441. #476	C₂²×C₁₃	semidirect
442. #475	C₂²×C₁₃	semidirect
443. #475	C₂²×C₁₃	semidirect
444. #474	C₂²×C₁₃	semidirect
449. #464	C₂²×C₁₃	semidirect
450. #462	C₂²×C₁₃	semidirect
451. #462	C₂²×C₁₃	semidirect
452. #462	C₂²×C₁₃	semidirect
453. #461	C₂²×C₁₃	semidirect
454. #461	C₂²×C₁₃	semidirect
455. #460	C₂²×C₁₃	semidirect
744. C₁₃	#60918	direct (N × H)
796. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3444	2
C₂×C₁₃×#533	2
C₁₃×#3255	2
C₁₃×#3254	2
C₁₃×#3252	2
C₁₃×#3249	2
C₁₃×#3248	2
C₁₃×#3246	2
C₁₃×#3079	2
C₁₃×#3078	2
C₁₃×#3056	2
C₁₃×#3039	2
C₁₃×#3037	2
C₂×C₁₃×#423	2
#60918	13

Subgroups — C13×#60918 #15747257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60918 #15747257