Subgroups — C₁₃×#60917 #15747256

Order 3328.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1022 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, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3256	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3250	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3248	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3080	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3056	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#532	C₂²	1	1	yes	characteristic
25	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#529	—	2	1	no	—
28	C₁₃×#529	—	2	1	no	—
29	C₁₃×#529	—	2	1	no	—
30	C₁₃×#529	—	2	1	no	—
31	C₁₃×#529	—	2	1	no	—
32	C₁₃×#529	—	2	1	no	—
33	C₁₃×#529	—	2	1	no	—
34	C₁₃×#529	—	2	1	no	—
35	C₁₃×#529	C₂²	1	2	yes	—
36	C₁₃×#529	C₂²	1	2	yes	—
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₁₃×#529	C₂²	1	2	yes	—
39	C₁₃×#529	C₂²	1	2	yes	complemented
40	C₁₃×#529	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#126	—	2	1	no	—
42	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
44	C₁₃×#525	—	2	1	no	—
45	C₁₃×#525	—	2	1	no	—
46	C₁₃×#525	C₂²	1	2	yes	—
47	C₂×C₁₃×#123	—	2	1	no	—
48	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×#41	—	2	1	no	—
51	C₄×C₁₃×#41	—	2	1	no	—
52	C₄×C₁₃×#41	C₂²	1	2	yes	—
53	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₁₃	—	2	1	no	—
55	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#117	—	2	1	no	—
57	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
58	C₁₃×#479	C₂²	1	4	yes	complemented
59	C₁₃×#479	C₂²	1	4	yes	complemented
60	C₁₃×#479	C₂²	1	4	yes	complemented
61	C₁₃×#478	C₂²	1	4	yes	complemented
62	C₁₃×#478	C₂²	1	4	yes	complemented
63	C₁₃×#478	C₂²	1	4	yes	complemented
64	C₁₃×#477	C₂²	1	2	yes	complemented
65	C₁₃×#476	C₂²	1	2	yes	complemented
66	C₁₃×#475	C₂²	1	2	yes	complemented
67	C₁₃×#474	C₂²	1	2	yes	complemented
68	C₁₃×#470	C₂²	1	4	yes	complemented
69	C₁₃×#469	C₂²	1	4	yes	—
70	C₁₃×#468	C₂²	1	4	yes	—
71	C₁₃×#468	C₂²	1	4	yes	complemented
72	C₁₃×#467	C₂²	1	4	yes	complemented
73	C₁₃×#466	C₂²	1	4	yes	—
74	C₁₃×#465	C₂²	1	4	yes	—
75	C₁₃×#465	C₂²	1	4	yes	complemented
76	C₁₃×#464	C₂²	1	4	yes	complemented
77	C₁₃×#464	C₂²	1	4	yes	complemented
78	C₁₃×#464	C₂²	1	4	yes	complemented
79	C₁₃×#463	C₂²	1	4	yes	complemented
80	C₁₃×#463	C₂²	1	4	yes	complemented
81	C₁₃×#463	C₂²	1	4	yes	complemented
82	C₁₃×#462	C₂²	1	2	yes	complemented
83	C₁₃×#461	C₂²	1	2	yes	complemented
84	C₁₃×#460	C₂²	1	2	yes	complemented
85	C₁₃×#459	C₂²	1	2	yes	complemented
86	C₁₃×#428	C₂²	1	2	yes	—
87	C₁₃×#428	C₂²	1	2	yes	—
88	C₁₃×#423	C₂²	1	1	yes	characteristic
89	C₁₃×#423	C₂²	1	1	yes	characteristic
90	C₁₃×#423	C₂²	1	2	yes	—
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₁₃×#423	C₂²	1	2	yes	complemented
93	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
94	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
95	C₁₃×#419	C₂²	1	2	yes	—
96	C₁₃×#418	C₂²	1	2	yes	—
97	C₁₃×#417	C₂²	1	2	yes	—
98	C₁₃×#417	C₂²	1	2	yes	—
99	C₂×C₁₃×#41	—	2	1	no	—
100	C₂×C₁₃×#41	—	2	1	no	—
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	—	2	1	no	—
104	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	—	2	1	no	—
106	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#137	—	4	4	no	—
110	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
111	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×D₈	C₂³	1	4	yes	—
115	C₂×C₁₃×M₁₆	—	4	4	no	—
116	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
118	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
119	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₃×#127	C₂³	1	1	yes	characteristic
124	C₁₃×#126	—	2	2	no	—
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×#126	—	2	2	no	—
130	C₁₃×#125	—	2	1	no	—
131	C₁₃×#125	—	2	1	no	—
132	C₁₃×#125	—	2	1	no	—
133	C₁₃×#125	—	2	1	no	—
134	C₁₃×#125	C₂³	1	2	yes	—
135	C₁₃×#125	C₂³	1	2	yes	—
136	C₁₃×#125	C₂³	1	2	yes	—
137	C₁₃×#124	—	2	1	no	—
138	C₁₃×#124	—	2	1	no	—
139	C₁₃×#124	—	2	1	no	—
140	C₁₃×#124	—	2	1	no	—
141	C₁₃×#124	C₂³	1	2	yes	—
142	C₁₃×#124	C₂³	1	2	yes	—
143	C₁₃×#124	C₂³	1	2	yes	—
144	C₁₃×#123	—	2	2	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×#123	—	2	2	no	—
148	C₁₃×#123	—	2	2	no	—
149	C₁₃×#123	—	2	2	no	—
150	C₁₃×#123	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	1	no	—
152	C₁₃×C₂²⋊Q₈	—	2	1	no	—
153	C₁₃×C₂²⋊Q₈	—	2	1	no	—
154	C₁₃×C₂²⋊Q₈	—	2	1	no	—
155	C₁₃×C₂²⋊Q₈	—	2	1	no	—
156	C₁₃×C₂²⋊Q₈	—	2	1	no	—
157	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₁₃×#121	—	2	1	no	—
162	C₁₃×#121	—	2	1	no	—
163	C₁₃×#121	—	2	1	no	—
164	C₁₃×#121	—	2	1	no	—
165	C₁₃×#121	—	2	1	no	—
166	C₁₃×#121	—	2	1	no	—
167	C₁₃×#121	C₂³	1	2	yes	—
168	C₁₃×#121	C₂³	1	2	yes	—
169	C₁₃×#121	C₂³	1	2	yes	—
170	C₁₃×#121	C₂³	1	2	yes	—
171	C₁₃×#120	—	2	2	no	—
172	C₄×Q₈×C₁₃	—	2	1	no	—
173	C₄×Q₈×C₁₃	—	2	1	no	—
174	C₄×Q₈×C₁₃	—	2	1	no	—
175	C₄×Q₈×C₁₃	—	2	1	no	—
176	C₄×Q₈×C₁₃	—	2	1	no	—
177	C₄×Q₈×C₁₃	—	2	1	no	—
178	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
179	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
180	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
181	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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	—	2	2	no	—
187	C₄×D₄×C₁₃	—	2	2	no	—
188	C₄×D₄×C₁₃	—	2	2	no	—
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	2	no	—
192	C₄×D₄×C₁₃	—	2	1	no	—
193	C₄×D₄×C₁₃	—	2	1	no	—
194	C₄×D₄×C₁₃	—	2	1	no	—
195	C₄×D₄×C₁₃	—	2	1	no	—
196	C₄×D₄×C₁₃	—	2	1	no	—
197	C₄×D₄×C₁₃	—	2	1	no	—
198	C₄×D₄×C₁₃	C₂³	1	2	yes	—
199	C₄×D₄×C₁₃	C₂³	1	2	yes	—
200	C₄×D₄×C₁₃	C₂³	1	2	yes	—
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₁₃×#117	—	2	1	no	—
203	C₁₃×#117	—	2	1	no	—
204	C₁₃×#117	—	2	2	no	—
205	C₁₃×#117	—	2	2	no	—
206	C₁₃×#117	—	2	2	no	—
207	C₁₃×#117	—	2	2	no	—
208	C₁₃×#117	—	2	2	no	—
209	C₁₃×#117	—	2	2	no	—
210	C₁₃×#117	—	2	2	no	—
211	C₁₃×#117	C₂³	1	2	yes	—
212	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
219	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
220	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
223	C₂×C₄²×C₁₃	—	2	1	no	—
224	C₂×C₄²×C₁₃	—	2	2	no	—
225	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
226	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
228	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
229	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
230	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
231	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
237	C₁₃×#107	C₂³	1	4	yes	—
238	C₁₃×#107	C₂³	1	4	yes	—
239	C₁₃×#106	C₂³	1	4	yes	—
240	C₁₃×#106	C₂³	1	4	yes	—
241	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
242	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
243	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
244	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
245	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
246	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
247	C₁₃×#103	C₂³	1	4	yes	—
248	C₁₃×#103	C₂³	1	4	yes	—
249	C₁₃×#103	C₂³	1	4	yes	—
250	C₁₃×#103	C₂³	1	4	yes	—
251	C₁₃×#102	C₂³	1	4	yes	—
252	C₁₃×#102	C₂³	1	4	yes	—
253	C₁₃×#102	C₂³	1	4	yes	—
254	C₁₃×#102	C₂³	1	4	yes	—
255	#60917	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂⁴×C₁₃	—	2	1	no	—
257	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₁₃×#41	—	2	4	no	—
259	C₁₃×#41	—	2	4	no	—
260	C₁₃×#41	—	4	4	no	—
261	C₁₃×#41	—	4	4	no	—
262	C₂×Q₈×C₁₃	—	2	1	no	—
263	C₂×Q₈×C₁₃	—	2	1	no	—
264	C₂×Q₈×C₁₃	—	2	1	no	—
265	C₂×Q₈×C₁₃	—	2	2	no	—
266	C₂×Q₈×C₁₃	—	2	2	no	—
267	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
268	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	2	no	—
274	C₂×D₄×C₁₃	—	2	1	no	—
275	C₂×D₄×C₁₃	—	2	1	no	—
276	C₂×D₄×C₁₃	—	2	1	no	—
277	C₂×D₄×C₁₃	—	2	2	no	—
278	C₂×D₄×C₁₃	—	2	2	no	—
279	C₂×D₄×C₁₃	—	4	4	no	—
280	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃	—	2	2	no	—
283	C₂²×C₄×C₁₃	—	2	2	no	—
284	C₂²×C₄×C₁₃	—	2	1	no	—
285	C₂²×C₄×C₁₃	—	2	1	no	—
286	C₂²×C₄×C₁₃	—	2	1	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	2	no	—
291	C₂²×C₄×C₁₃	—	2	2	no	—
292	C₂²×C₄×C₁₃	—	4	2	no	—
293	C₂²×C₄×C₁₃	—	4	2	no	—
294	C₂²×C₄×C₁₃	—	4	4	no	—
295	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₁₃×Q₁₆	—	4	4	no	—
314	C₁₃×SD₁₆	—	4	4	no	—
315	C₁₃×SD₁₆	—	4	4	no	—
316	C₁₃×D₈	—	4	4	no	—
317	C₁₃×M₁₆	—	2	4	no	—
318	C₁₃×M₁₆	—	2	4	no	—
319	C₁₃×M₁₆	—	4	4	no	—
320	C₂×C₈×C₁₃	—	4	4	no	—
321	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
322	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	1	no	—
332	C₁₃×C₄⋊C₄	—	2	1	no	—
333	C₁₃×C₄⋊C₄	—	2	1	no	—
334	C₁₃×C₄⋊C₄	—	2	1	no	—
335	C₁₃×C₄⋊C₄	—	2	1	no	—
336	C₁₃×C₄⋊C₄	—	2	1	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
344	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
345	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	2	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	—	2	2	no	—
364	C₁₃×C₂²⋊C₄	—	2	2	no	—
365	C₁₃×C₂²⋊C₄	—	2	2	no	—
366	C₄²×C₁₃	—	2	2	no	—
367	C₄²×C₁₃	—	2	2	no	—
368	C₄²×C₁₃	—	2	2	no	—
369	C₄²×C₁₃	—	2	2	no	—
370	C₄²×C₁₃	—	2	2	no	—
371	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
387	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
388	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
389	#3256	C₂×C₁₃	1	4	yes	complemented
390	#3252	C₂×C₁₃	1	2	yes	complemented
391	#3251	C₂×C₁₃	1	2	yes	complemented
392	#3250	C₂×C₁₃	1	4	yes	complemented
393	#3248	C₂×C₁₃	1	2	yes	complemented
394	#3247	C₂×C₁₃	1	2	yes	complemented
395	#3080	C₂×C₁₃	1	2	yes	complemented
396	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
397	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
398	#3056	C₂×C₁₃	1	2	yes	complemented
399	#3055	C₂×C₁₃	1	2	yes	complemented
400	#3040	C₂×C₁₃	1	2	yes	complemented
401	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
402	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
403	C₂×#423	C₂×C₁₃	1	1	yes	characteristic, complemented
404	C₂³×C₁₃	—	2	2	no	—
405	C₂³×C₁₃	—	2	2	no	—
406	C₂³×C₁₃	—	2	2	no	—
407	C₂³×C₁₃	—	2	2	no	—
408	C₂³×C₁₃	—	4	1	no	—
409	C₂³×C₁₃	—	4	2	no	—
410	C₂³×C₁₃	—	4	2	no	—
411	C₂³×C₁₃	—	4	2	no	—
412	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	Q₈×C₁₃	—	2	2	no	—
416	Q₈×C₁₃	—	2	2	no	—
417	Q₈×C₁₃	—	2	2	no	—
418	Q₈×C₁₃	—	2	2	no	—
419	Q₈×C₁₃	—	4	2	no	—
420	Q₈×C₁₃	—	4	2	no	—
421	Q₈×C₁₃	—	4	2	no	—
422	D₄×C₁₃	—	2	2	no	—
423	D₄×C₁₃	—	2	2	no	—
424	D₄×C₁₃	—	2	2	no	—
425	D₄×C₁₃	—	2	2	no	—
426	D₄×C₁₃	—	4	2	no	—
427	D₄×C₁₃	—	4	4	no	—
428	D₄×C₁₃	—	4	4	no	—
429	D₄×C₁₃	—	4	4	no	—
430	D₄×C₁₃	—	4	4	no	—
431	D₄×C₁₃	—	4	4	no	—
432	D₄×C₁₃	—	4	2	no	—
433	D₄×C₁₃	—	4	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	1	no	—
443	C₂×C₄×C₁₃	—	2	1	no	—
444	C₂×C₄×C₁₃	—	2	1	no	—
445	C₂×C₄×C₁₃	—	2	1	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	2	no	—
451	C₂×C₄×C₁₃	—	2	2	no	—
452	C₂×C₄×C₁₃	—	4	1	no	—
453	C₂×C₄×C₁₃	—	4	1	no	—
454	C₂×C₄×C₁₃	—	4	1	no	—
455	C₂×C₄×C₁₃	—	4	1	no	—
456	C₂×C₄×C₁₃	—	4	1	no	—
457	C₂×C₄×C₁₃	—	4	1	no	—
458	C₂×C₄×C₁₃	—	4	1	no	—
459	C₂×C₄×C₁₃	—	4	4	no	—
460	C₂×C₄×C₁₃	—	4	4	no	—
461	C₂×C₄×C₁₃	—	4	4	no	—
462	C₂×C₄×C₁₃	—	4	2	no	—
463	C₂×C₄×C₁₃	—	4	2	no	—
464	C₂×C₄×C₁₃	—	4	2	no	—
465	C₂×C₄×C₁₃	—	4	4	no	—
466	C₂×C₄×C₁₃	—	4	4	no	—
467	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
479	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
480	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
481	C₈×C₁₃	—	2	4	no	—
482	C₈×C₁₃	—	2	4	no	—
483	C₂×#137	C₂²×C₁₃	1	2	yes	—
484	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
485	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
486	#533	C₂²×C₁₃	1	1	yes	characteristic
487	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
489	#532	C₂²×C₁₃	1	1	yes	characteristic
490	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	#529	—	2	1	no	—
493	#529	—	2	1	no	—
494	#529	—	2	1	no	—
495	#529	—	2	1	no	—
496	#529	—	2	1	no	—
497	#529	—	2	1	no	—
498	#529	—	2	1	no	—
499	#529	—	2	1	no	—
500	#529	C₂²×C₁₃	1	2	yes	—
501	#529	C₂²×C₁₃	1	2	yes	—
502	#529	C₂²×C₁₃	1	2	yes	—
503	#529	C₂²×C₁₃	1	2	yes	—
504	#529	C₂²×C₁₃	1	2	yes	complemented
505	#529	C₂²×C₁₃	1	2	yes	complemented
506	C₂×#126	—	2	1	no	—
507	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
508	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
509	#525	—	2	1	no	—
510	#525	—	2	1	no	—
511	#525	C₂²×C₁₃	1	2	yes	—
512	C₂×#123	—	2	1	no	—
513	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
514	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
515	C₄×#41	—	2	1	no	—
516	C₄×#41	—	2	1	no	—
517	C₄×#41	C₂²×C₁₃	1	2	yes	—
518	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
519	C₂×C₄×D₄	—	2	1	no	—
520	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
521	C₂×#117	—	2	1	no	—
522	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
523	#479	C₂²×C₁₃	1	4	yes	complemented
524	#479	C₂²×C₁₃	1	4	yes	complemented
525	#479	C₂²×C₁₃	1	4	yes	complemented
526	#478	C₂²×C₁₃	1	4	yes	complemented
527	#478	C₂²×C₁₃	1	4	yes	complemented
528	#478	C₂²×C₁₃	1	4	yes	complemented
529	#477	C₂²×C₁₃	1	2	yes	complemented
530	#476	C₂²×C₁₃	1	2	yes	complemented
531	#475	C₂²×C₁₃	1	2	yes	complemented
532	#474	C₂²×C₁₃	1	2	yes	complemented
533	#470	C₂²×C₁₃	1	4	yes	complemented
534	#469	C₂²×C₁₃	1	4	yes	—
535	#468	C₂²×C₁₃	1	4	yes	—
536	#468	C₂²×C₁₃	1	4	yes	complemented
537	#467	C₂²×C₁₃	1	4	yes	complemented
538	#466	C₂²×C₁₃	1	4	yes	—
539	#465	C₂²×C₁₃	1	4	yes	—
540	#465	C₂²×C₁₃	1	4	yes	complemented
541	#464	C₂²×C₁₃	1	4	yes	complemented
542	#464	C₂²×C₁₃	1	4	yes	complemented
543	#464	C₂²×C₁₃	1	4	yes	complemented
544	#463	C₂²×C₁₃	1	4	yes	complemented
545	#463	C₂²×C₁₃	1	4	yes	complemented
546	#463	C₂²×C₁₃	1	4	yes	complemented
547	#462	C₂²×C₁₃	1	2	yes	complemented
548	#461	C₂²×C₁₃	1	2	yes	complemented
549	#460	C₂²×C₁₃	1	2	yes	complemented
550	#459	C₂²×C₁₃	1	2	yes	complemented
551	#428	C₂²×C₁₃	1	2	yes	—
552	#428	C₂²×C₁₃	1	2	yes	—
553	#423	C₂²×C₁₃	1	1	yes	characteristic
554	#423	C₂²×C₁₃	1	1	yes	characteristic
555	#423	C₂²×C₁₃	1	2	yes	—
556	#423	C₂²×C₁₃	1	2	yes	complemented
557	#423	C₂²×C₁₃	1	2	yes	complemented
558	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
559	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
560	#419	C₂²×C₁₃	1	2	yes	—
561	#418	C₂²×C₁₃	1	2	yes	—
562	#417	C₂²×C₁₃	1	2	yes	—
563	#417	C₂²×C₁₃	1	2	yes	—
564	C₂²×C₁₃	—	2	1	no	—
565	C₂²×C₁₃	—	2	1	no	—
566	C₂²×C₁₃	—	2	1	no	—
567	C₂²×C₁₃	—	2	1	no	—
568	C₂²×C₁₃	—	2	1	no	—
569	C₂²×C₁₃	—	2	1	no	—
570	C₂²×C₁₃	—	2	1	no	—
571	C₂²×C₁₃	—	4	4	no	—
572	C₂²×C₁₃	—	4	2	no	—
573	C₂²×C₁₃	—	4	2	no	—
574	C₂²×C₁₃	—	4	2	no	—
575	C₂²×C₁₃	—	4	2	no	—
576	C₂²×C₁₃	—	4	2	no	—
577	C₂²×C₁₃	—	4	2	no	—
578	C₂²×C₁₃	—	8	4	no	—
579	C₂²×C₁₃	#537	1	2	yes	—
580	C₂²×C₁₃	#575	1	2	yes	—
581	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
582	C₄×C₁₃	—	2	1	no	—
583	C₄×C₁₃	—	2	1	no	—
584	C₄×C₁₃	—	2	1	no	—
585	C₄×C₁₃	—	2	1	no	—
586	C₄×C₁₃	—	2	1	no	—
587	C₄×C₁₃	—	2	1	no	—
588	C₄×C₁₃	—	2	1	no	—
589	C₄×C₁₃	—	2	1	no	—
590	C₄×C₁₃	—	2	1	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	2	no	—
593	C₄×C₁₃	—	4	2	no	—
594	C₄×C₁₃	—	4	2	no	—
595	C₄×C₁₃	—	4	2	no	—
596	C₄×C₁₃	—	4	2	no	—
597	C₄×C₁₃	#537	1	2	yes	—
598	C₄×C₁₃	#575	1	2	yes	—
599	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
600	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
601	C₂×#41	—	2	1	no	—
602	C₂×#41	—	2	1	no	—
603	C₂×#41	C₂³×C₁₃	1	2	yes	—
604	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
605	C₂²×D₄	—	2	1	no	—
606	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂³×C₄	—	2	1	no	—
608	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
609	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
611	#137	—	4	4	no	—
612	AGL(1,ℤ/8)	—	4	4	no	—
613	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
614	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
615	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
616	C₂×D₈	C₂³×C₁₃	1	4	yes	—
617	C₂×M₁₆	—	4	4	no	—
618	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
619	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
620	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
621	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
622	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
625	#127	C₂³×C₁₃	1	1	yes	characteristic
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#125	—	2	1	no	—
633	#125	—	2	1	no	—
634	#125	—	2	1	no	—
635	#125	—	2	1	no	—
636	#125	C₂³×C₁₃	1	2	yes	—
637	#125	C₂³×C₁₃	1	2	yes	—
638	#125	C₂³×C₁₃	1	2	yes	—
639	#124	—	2	1	no	—
640	#124	—	2	1	no	—
641	#124	—	2	1	no	—
642	#124	—	2	1	no	—
643	#124	C₂³×C₁₃	1	2	yes	—
644	#124	C₂³×C₁₃	1	2	yes	—
645	#124	C₂³×C₁₃	1	2	yes	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	C₂²⋊Q₈	—	2	1	no	—
654	C₂²⋊Q₈	—	2	1	no	—
655	C₂²⋊Q₈	—	2	1	no	—
656	C₂²⋊Q₈	—	2	1	no	—
657	C₂²⋊Q₈	—	2	1	no	—
658	C₂²⋊Q₈	—	2	1	no	—
659	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
660	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
661	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
662	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
663	#121	—	2	1	no	—
664	#121	—	2	1	no	—
665	#121	—	2	1	no	—
666	#121	—	2	1	no	—
667	#121	—	2	1	no	—
668	#121	—	2	1	no	—
669	#121	C₂³×C₁₃	1	2	yes	—
670	#121	C₂³×C₁₃	1	2	yes	—
671	#121	C₂³×C₁₃	1	2	yes	—
672	#121	C₂³×C₁₃	1	2	yes	—
673	#120	—	2	2	no	—
674	C₄×Q₈	—	2	1	no	—
675	C₄×Q₈	—	2	1	no	—
676	C₄×Q₈	—	2	1	no	—
677	C₄×Q₈	—	2	1	no	—
678	C₄×Q₈	—	2	1	no	—
679	C₄×Q₈	—	2	1	no	—
680	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
681	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
682	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
683	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	1	no	—
695	C₄×D₄	—	2	1	no	—
696	C₄×D₄	—	2	1	no	—
697	C₄×D₄	—	2	1	no	—
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	—	2	1	no	—
700	C₄×D₄	C₂³×C₁₃	1	2	yes	—
701	C₄×D₄	C₂³×C₁₃	1	2	yes	—
702	C₄×D₄	C₂³×C₁₃	1	2	yes	—
703	C₄×D₄	C₂³×C₁₃	1	2	yes	—
704	#117	—	2	1	no	—
705	#117	—	2	1	no	—
706	#117	—	2	2	no	—
707	#117	—	2	2	no	—
708	#117	—	2	2	no	—
709	#117	—	2	2	no	—
710	#117	—	2	2	no	—
711	#117	—	2	2	no	—
712	#117	—	2	2	no	—
713	#117	C₂³×C₁₃	1	2	yes	—
714	C₂×C₄⋊C₄	—	2	1	no	—
715	C₂×C₄⋊C₄	—	2	1	no	—
716	C₂×C₄⋊C₄	—	2	1	no	—
717	C₂×C₄⋊C₄	—	2	1	no	—
718	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
720	C₂×C₂²⋊C₄	—	2	1	no	—
721	C₂×C₂²⋊C₄	—	2	1	no	—
722	C₂×C₂²⋊C₄	—	2	1	no	—
723	C₂×C₂²⋊C₄	—	2	1	no	—
724	C₂×C₂²⋊C₄	—	2	1	no	—
725	C₂×C₄²	—	2	1	no	—
726	C₂×C₄²	—	2	2	no	—
727	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
728	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
729	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
730	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
731	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
732	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
739	#107	C₂³×C₁₃	1	4	yes	—
740	#107	C₂³×C₁₃	1	4	yes	—
741	#106	C₂³×C₁₃	1	4	yes	—
742	#106	C₂³×C₁₃	1	4	yes	—
743	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
744	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
745	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
746	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
747	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
748	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
749	#103	C₂³×C₁₃	1	4	yes	—
750	#103	C₂³×C₁₃	1	4	yes	—
751	#103	C₂³×C₁₃	1	4	yes	—
752	#103	C₂³×C₁₃	1	4	yes	—
753	#102	C₂³×C₁₃	1	4	yes	—
754	#102	C₂³×C₁₃	1	4	yes	—
755	#102	C₂³×C₁₃	1	4	yes	—
756	#102	C₂³×C₁₃	1	4	yes	—
757	C₂×C₁₃	—	2	2	no	—
758	C₂×C₁₃	—	2	2	no	—
759	C₂×C₁₃	—	4	1	no	—
760	C₂×C₁₃	—	8	2	no	—
761	C₂×C₁₃	—	8	2	no	—
762	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
763	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
764	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
765	C₂⁴	—	2	1	no	—
766	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
767	#41	—	2	4	no	—
768	#41	—	2	4	no	—
769	#41	—	4	4	no	—
770	#41	—	4	4	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	2	2	no	—
776	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
777	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	4	4	no	—
789	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
790	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	—	4	4	no	—
804	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
805	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
806	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
807	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
810	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
811	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
812	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
813	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
814	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
815	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
816	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
817	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
818	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
822	Q₁₆	—	4	4	no	—
823	SD₁₆	—	4	4	no	—
824	SD₁₆	—	4	4	no	—
825	D₈	—	4	4	no	—
826	M₁₆	—	2	4	no	—
827	M₁₆	—	2	4	no	—
828	M₁₆	—	4	4	no	—
829	C₂×C₈	—	4	4	no	—
830	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
831	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
854	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
855	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
881	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
882	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
883	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
884	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
885	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
886	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
887	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
888	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
889	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
890	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
891	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
892	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
893	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
894	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
895	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
896	C₁₃	#60917	1	1	yes	characteristic, direct product factor, Sylow
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	4	1	no	—
902	C₂³	—	4	2	no	—
903	C₂³	—	4	2	no	—
904	C₂³	—	4	2	no	—
905	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
906	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
907	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
908	Q₈	—	2	2	no	—
909	Q₈	—	2	2	no	—
910	Q₈	—	2	2	no	—
911	Q₈	—	2	2	no	—
912	Q₈	—	4	2	no	—
913	Q₈	—	4	2	no	—
914	Q₈	—	4	2	no	—
915	D₄	—	2	2	no	—
916	D₄	—	2	2	no	—
917	D₄	—	2	2	no	—
918	D₄	—	2	2	no	—
919	D₄	—	4	2	no	—
920	D₄	—	4	4	no	—
921	D₄	—	4	4	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	4	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	2	no	—
926	D₄	—	4	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	1	no	—
948	C₂×C₄	—	4	1	no	—
949	C₂×C₄	—	4	1	no	—
950	C₂×C₄	—	4	1	no	—
951	C₂×C₄	—	4	1	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	4	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	4	4	no	—
959	C₂×C₄	—	4	4	no	—
960	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
962	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
963	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
966	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
968	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
969	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
970	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
971	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
972	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
973	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
974	C₈	—	2	4	no	—
975	C₈	—	2	4	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	4	4	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	8	4	no	—
991	C₂²	C₁₃×#537	1	2	yes	—
992	C₂²	C₁₃×#575	1	2	yes	—
993	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
994	C₄	—	2	1	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	2	no	—
1009	C₄	C₁₃×#537	1	2	yes	—
1010	C₄	C₁₃×#575	1	2	yes	—
1011	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1012	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1013	C₂	—	2	2	no	—
1014	C₂	—	2	2	no	—
1015	C₂	—	4	1	no	—
1016	C₂	—	8	2	no	—
1017	C₂	—	8	2	no	—
1018	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
1019	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1020	C₂	C₂×C₁₃×#575	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₂×C₁₃×#529	C₂	semidirect
3. C₁₃×#3256	C₂	semidirect
4. C₁₃×#3252	C₂	semidirect
5. C₁₃×#3251	C₂	semidirect
6. C₁₃×#3250	C₂	semidirect
7. C₁₃×#3248	C₂	semidirect
8. C₁₃×#3247	C₂	semidirect
9. C₁₃×#3080	C₂	semidirect
10. C₁₃×#3078	C₂	semidirect
11. C₁₃×#3077	C₂	semidirect
12. C₁₃×#3056	C₂	semidirect
13. C₁₃×#3055	C₂	semidirect
14. C₁₃×#3040	C₂	semidirect
15. C₁₃×#3037	C₂	semidirect
16. C₁₃×#3036	C₂	semidirect
17. C₂×C₁₃×#423	C₂	semidirect
22. C₁₃×#533	C₂²	semidirect
23. C₁₃×#533	C₂²	semidirect
25. C₁₃×#532	C₂²	semidirect
26. C₁₃×#532	C₂²	semidirect
39. C₁₃×#529	C₂²	semidirect
40. C₁₃×#529	C₂²	semidirect
58. C₁₃×#479	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
60. C₁₃×#479	C₂²	semidirect
61. C₁₃×#478	C₂²	semidirect
62. C₁₃×#478	C₂²	semidirect
63. C₁₃×#478	C₂²	semidirect
64. C₁₃×#477	C₂²	semidirect
65. C₁₃×#476	C₂²	semidirect
66. C₁₃×#475	C₂²	semidirect
67. C₁₃×#474	C₂²	semidirect
68. C₁₃×#470	C₂²	semidirect
71. C₁₃×#468	C₂²	semidirect
72. C₁₃×#467	C₂²	semidirect
75. C₁₃×#465	C₂²	semidirect
76. C₁₃×#464	C₂²	semidirect
77. C₁₃×#464	C₂²	semidirect
78. C₁₃×#464	C₂²	semidirect
79. C₁₃×#463	C₂²	semidirect
80. C₁₃×#463	C₂²	semidirect
81. C₁₃×#463	C₂²	semidirect
82. C₁₃×#462	C₂²	semidirect
83. C₁₃×#461	C₂²	semidirect
84. C₁₃×#460	C₂²	semidirect
85. C₁₃×#459	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
92. C₁₃×#423	C₂²	semidirect
93. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
94. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
255. #60917	C₁₃	direct (N × H)
387. #3444	C₂×C₁₃	semidirect
388. C₂×#529	C₂×C₁₃	semidirect
389. #3256	C₂×C₁₃	semidirect
390. #3252	C₂×C₁₃	semidirect
391. #3251	C₂×C₁₃	semidirect
392. #3250	C₂×C₁₃	semidirect
393. #3248	C₂×C₁₃	semidirect
394. #3247	C₂×C₁₃	semidirect
395. #3080	C₂×C₁₃	semidirect
396. #3078	C₂×C₁₃	semidirect
397. #3077	C₂×C₁₃	semidirect
398. #3056	C₂×C₁₃	semidirect
399. #3055	C₂×C₁₃	semidirect
400. #3040	C₂×C₁₃	semidirect
401. #3037	C₂×C₁₃	semidirect
402. #3036	C₂×C₁₃	semidirect
403. C₂×#423	C₂×C₁₃	semidirect
487. #533	C₂²×C₁₃	semidirect
488. #533	C₂²×C₁₃	semidirect
490. #532	C₂²×C₁₃	semidirect
491. #532	C₂²×C₁₃	semidirect
504. #529	C₂²×C₁₃	semidirect
505. #529	C₂²×C₁₃	semidirect
523. #479	C₂²×C₁₃	semidirect
524. #479	C₂²×C₁₃	semidirect
525. #479	C₂²×C₁₃	semidirect
526. #478	C₂²×C₁₃	semidirect
527. #478	C₂²×C₁₃	semidirect
528. #478	C₂²×C₁₃	semidirect
529. #477	C₂²×C₁₃	semidirect
530. #476	C₂²×C₁₃	semidirect
531. #475	C₂²×C₁₃	semidirect
532. #474	C₂²×C₁₃	semidirect
533. #470	C₂²×C₁₃	semidirect
536. #468	C₂²×C₁₃	semidirect
537. #467	C₂²×C₁₃	semidirect
540. #465	C₂²×C₁₃	semidirect
541. #464	C₂²×C₁₃	semidirect
542. #464	C₂²×C₁₃	semidirect
543. #464	C₂²×C₁₃	semidirect
544. #463	C₂²×C₁₃	semidirect
545. #463	C₂²×C₁₃	semidirect
546. #463	C₂²×C₁₃	semidirect
547. #462	C₂²×C₁₃	semidirect
548. #461	C₂²×C₁₃	semidirect
549. #460	C₂²×C₁₃	semidirect
550. #459	C₂²×C₁₃	semidirect
556. #423	C₂²×C₁₃	semidirect
557. #423	C₂²×C₁₃	semidirect
558. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
559. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
896. C₁₃	#60917	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×#3444	2
C₂×C₁₃×#529	2
C₁₃×#3256	2
C₁₃×#3252	2
C₁₃×#3251	2
C₁₃×#3250	2
C₁₃×#3248	2
C₁₃×#3247	2
C₁₃×#3080	2
C₁₃×#3078	2
C₁₃×#3077	2
C₁₃×#3056	2
C₁₃×#3055	2
C₁₃×#3040	2
C₁₃×#3037	2
C₁₃×#3036	2
C₂×C₁₃×#423	2
#60917	13

Subgroups — C13×#60917 #15747256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60917 #15747256