Subgroups — C₁₃×#61161 #15747500

Order 3328.

2378 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3332	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3330	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3308	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3306	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3298	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3092	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#417	C₂	1	2	yes	maximal, complemented
18	C₂²×C₁₃×#41	—	2	1	no	—
19	C₂²×C₁₃×#41	C₂²	1	2	yes	—
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
23	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
24	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#548	C₂²	1	2	yes	complemented
26	C₁₃×#547	—	2	1	no	—
27	C₁₃×#547	—	2	2	no	—
28	C₁₃×#547	—	2	1	no	—
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#547	C₂²	1	2	yes	—
31	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#547	C₂²	1	4	yes	complemented
33	C₁₃×#547	C₂²	1	2	yes	complemented
34	C₁₃×#546	—	2	2	no	—
35	C₁₃×#546	C₂²	1	2	yes	complemented
36	D₄²×C₁₃	—	2	1	no	—
37	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#532	—	2	1	no	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#525	—	2	2	no	—
42	C₁₃×#525	C₂²	1	2	yes	—
43	C₂×C₁₃×#123	—	2	2	no	—
44	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₃	—	2	1	no	—
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
51	C₁₃×#489	C₂²	1	4	yes	complemented
52	C₁₃×#487	C₂²	1	2	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	complemented
54	C₁₃×#484	C₂²	1	4	yes	complemented
55	C₁₃×#483	C₂²	1	4	yes	complemented
56	C₁₃×#481	C₂²	1	4	yes	complemented
57	C₁₃×#480	C₂²	1	4	yes	complemented
58	C₁₃×#477	C₂²	1	2	yes	complemented
59	C₁₃×#476	C₂²	1	2	yes	complemented
60	C₁₃×#475	C₂²	1	2	yes	complemented
61	C₁₃×#474	C₂²	1	2	yes	complemented
62	C₁₃×#469	C₂²	1	4	yes	complemented
63	C₁₃×#468	C₂²	1	4	yes	complemented
64	C₁₃×#466	C₂²	1	4	yes	complemented
65	C₁₃×#465	C₂²	1	4	yes	complemented
66	C₁₃×#463	C₂²	1	4	yes	complemented
67	C₁₃×#461	C₂²	1	2	yes	complemented
68	C₁₃×#459	C₂²	1	2	yes	complemented
69	C₁₃×#449	C₂²	1	4	yes	complemented
70	C₁₃×#449	C₂²	1	4	yes	complemented
71	C₁₃×#448	C₂²	1	4	yes	complemented
72	C₁₃×#447	C₂²	1	4	yes	complemented
73	C₁₃×#442	C₂²	1	2	yes	complemented
74	C₁₃×#440	C₂²	1	2	yes	complemented
75	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
76	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
77	C₁₃×#436	C₂²	1	2	yes	complemented
78	C₁₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
80	C₁₃×#428	C₂²	1	2	yes	complemented
81	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
84	C₁₃×#417	C₂²	1	2	yes	—
85	C₁₃×#417	C₂²	1	1	yes	characteristic
86	C₁₃×#417	C₂²	1	2	yes	complemented
87	C₁₃×#417	C₂²	1	2	yes	complemented
88	C₁₃×#417	C₂²	1	4	yes	complemented
89	C₁₃×#417	C₂²	1	4	yes	complemented
90	C₁₃×#417	C₂²	1	2	yes	complemented
91	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
93	C₁₃×#407	C₂²	1	2	yes	complemented
94	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	—	2	4	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	—	2	2	no	—
100	C₂×C₁₃×#41	—	2	8	no	—
101	C₂×C₁₃×#41	—	4	4	no	—
102	C₂×C₁₃×#41	—	4	8	no	—
103	C₂×C₁₃×#41	C₂³	1	2	yes	—
104	C₂×C₁₃×#41	C₂³	1	2	yes	—
105	C₂×C₁₃×#41	C₂³	1	2	yes	—
106	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃	—	2	1	no	—
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	—	2	2	no	—
110	C₂²×D₄×C₁₃	—	2	2	no	—
111	C₂²×D₄×C₁₃	—	2	1	no	—
112	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	—	2	2	no	—
116	C₂³×C₄×C₁₃	—	2	2	no	—
117	C₂³×C₄×C₁₃	—	2	1	no	—
118	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
119	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
120	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
121	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
122	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
123	C₂×C₁₃×D₈	C₂³	1	2	yes	—
124	C₂×C₁₃×D₈	C₂³	1	4	yes	—
125	C₂×C₁₃×M₁₆	—	4	4	no	—
126	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
130	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
131	C₁₃×C₄⋊Q₈	—	2	1	no	—
132	C₁₃×C₄⋊Q₈	—	2	1	no	—
133	C₁₃×C₄⋊Q₈	—	2	1	no	—
134	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×#127	—	2	1	no	—
138	C₁₃×#127	C₂³	1	1	yes	characteristic
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	4	no	—
146	C₁₃×#123	—	2	4	no	—
147	C₁₃×#123	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	4	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	—	2	2	no	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	—	2	1	no	—
160	C₁₃×#121	—	2	1	no	—
161	C₁₃×#121	—	2	1	no	—
162	C₁₃×#121	—	2	2	no	—
163	C₁₃×#121	—	2	2	no	—
164	C₁₃×#121	C₂³	1	4	yes	—
165	C₁₃×#121	C₂³	1	4	yes	—
166	C₁₃×#121	C₂³	1	2	yes	—
167	C₁₃×#121	C₂³	1	2	yes	—
168	C₁₃×#120	—	2	2	no	—
169	C₁₃×#120	—	2	2	no	—
170	C₁₃×#120	—	2	2	no	—
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	1	no	—
181	C₄×D₄×C₁₃	—	2	1	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	—	2	1	no	—
184	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₁₃	D₄	1	2	yes	—
186	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	2	yes	—
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₁₃	C₂³	1	2	yes	—
193	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	C₂³	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
206	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
209	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
210	C₂×C₄²×C₁₃	—	2	1	no	—
211	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
212	C₁₃×#107	C₂³	1	2	yes	—
213	C₁₃×#107	C₂³	1	4	yes	—
214	C₁₃×#106	C₂³	1	2	yes	—
215	C₁₃×#106	C₂³	1	4	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×#102	C₂³	1	4	yes	—
228	C₁₃×#102	C₂³	1	2	yes	—
229	C₁₃×#102	C₂³	1	2	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₁₃×#97	C₂³	1	2	yes	—
233	C₄×C₈×C₁₃	C₂³	1	2	yes	—
234	#61161	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	1	no	—
236	C₂⁴×C₁₃	—	2	2	no	—
237	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
238	C₁₃×#41	—	2	2	no	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	2	4	no	—
242	C₁₃×#41	—	2	4	no	—
243	C₁₃×#41	—	4	8	no	—
244	C₁₃×#41	—	4	2	no	—
245	C₁₃×#41	—	4	2	no	—
246	C₁₃×#41	—	4	8	no	—
247	C₁₃×#41	—	4	16	no	—
248	C₁₃×#41	—	4	8	no	—
249	C₁₃×#41	—	4	8	no	—
250	C₁₃×#41	#41	1	4	yes	complemented
251	C₂×Q₈×C₁₃	—	2	2	no	—
252	C₂×Q₈×C₁₃	—	2	2	no	—
253	C₂×Q₈×C₁₃	—	2	2	no	—
254	C₂×Q₈×C₁₃	—	2	4	no	—
255	C₂×Q₈×C₁₃	—	4	2	no	—
256	C₂×Q₈×C₁₃	—	4	4	no	—
257	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
258	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×D₄×C₁₃	—	2	1	no	—
260	C₂×D₄×C₁₃	—	2	4	no	—
261	C₂×D₄×C₁₃	—	2	4	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	2	2	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	4	no	—
267	C₂×D₄×C₁₃	—	2	4	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	1	no	—
270	C₂×D₄×C₁₃	—	2	1	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	1	no	—
273	C₂×D₄×C₁₃	—	2	2	no	—
274	C₂×D₄×C₁₃	—	2	2	no	—
275	C₂×D₄×C₁₃	—	4	2	no	—
276	C₂×D₄×C₁₃	—	4	8	no	—
277	C₂×D₄×C₁₃	—	4	8	no	—
278	C₂×D₄×C₁₃	—	4	4	no	—
279	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
280	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
283	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	—	2	1	no	—
286	C₂²×C₄×C₁₃	—	2	4	no	—
287	C₂²×C₄×C₁₃	—	2	4	no	—
288	C₂²×C₄×C₁₃	—	2	1	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	4	no	—
291	C₂²×C₄×C₁₃	—	2	4	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	1	no	—
294	C₂²×C₄×C₁₃	—	2	2	no	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	—	2	2	no	—
297	C₂²×C₄×C₁₃	—	2	2	no	—
298	C₂²×C₄×C₁₃	—	2	2	no	—
299	C₂²×C₄×C₁₃	—	2	1	no	—
300	C₂²×C₄×C₁₃	—	4	8	no	—
301	C₂²×C₄×C₁₃	—	4	4	no	—
302	C₂²×C₄×C₁₃	—	4	8	no	—
303	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
305	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
306	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
307	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₁₃×SD₁₆	—	2	4	no	—
312	C₁₃×SD₁₆	—	4	4	no	—
313	C₁₃×D₈	—	2	4	no	—
314	C₁₃×D₈	—	4	4	no	—
315	C₁₃×M₁₆	—	2	2	no	—
316	C₁₃×M₁₆	—	2	2	no	—
317	C₁₃×M₁₆	—	2	4	no	—
318	C₁₃×M₁₆	—	4	4	no	—
319	C₂×C₈×C₁₃	—	4	4	no	—
320	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
321	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
322	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
323	C₁₃×C₄⋊C₄	—	2	1	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	4	no	—
326	C₁₃×C₄⋊C₄	—	2	4	no	—
327	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
335	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
336	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
337	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
338	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
339	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
340	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
341	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	1	no	—
344	C₁₃×C₂²⋊C₄	—	2	2	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	4	no	—
350	C₁₃×C₂²⋊C₄	—	2	4	no	—
351	C₁₃×C₂²⋊C₄	—	2	1	no	—
352	C₁₃×C₂²⋊C₄	—	2	1	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
356	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
357	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
358	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
359	C₄²×C₁₃	—	2	1	no	—
360	C₄²×C₁₃	—	2	1	no	—
361	C₄²×C₁₃	—	2	1	no	—
362	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
364	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
366	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
367	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
368	#3332	C₂×C₁₃	1	2	yes	complemented
369	#3330	C₂×C₁₃	1	2	yes	complemented
370	#3308	C₂×C₁₃	1	4	yes	complemented
371	#3306	C₂×C₁₃	1	4	yes	complemented
372	#3298	C₂×C₁₃	1	2	yes	complemented
373	#3294	C₂×C₁₃	1	2	yes	complemented
374	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
375	#3092	C₂×C₁₃	1	2	yes	complemented
376	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
377	#3055	C₂×C₁₃	1	2	yes	complemented
378	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#3006	C₂×C₁₃	1	2	yes	complemented
380	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
381	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
382	C₂×#417	C₂×C₁₃	1	2	yes	complemented
383	C₂³×C₁₃	—	2	4	no	—
384	C₂³×C₁₃	—	2	4	no	—
385	C₂³×C₁₃	—	2	1	no	—
386	C₂³×C₁₃	—	2	2	no	—
387	C₂³×C₁₃	—	2	2	no	—
388	C₂³×C₁₃	—	4	2	no	—
389	C₂³×C₁₃	—	4	4	no	—
390	C₂³×C₁₃	—	4	2	no	—
391	C₂³×C₁₃	—	4	2	no	—
392	C₂³×C₁₃	—	4	2	no	—
393	C₂³×C₁₃	—	4	4	no	—
394	C₂³×C₁₃	—	8	2	no	—
395	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
396	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
397	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
398	Q₈×C₁₃	—	2	1	no	—
399	Q₈×C₁₃	—	2	2	no	—
400	Q₈×C₁₃	—	2	2	no	—
401	Q₈×C₁₃	—	4	4	no	—
402	Q₈×C₁₃	—	4	4	no	—
403	Q₈×C₁₃	—	4	4	no	—
404	Q₈×C₁₃	C₂×#41	1	2	yes	complemented
405	D₄×C₁₃	—	2	4	no	—
406	D₄×C₁₃	—	2	4	no	—
407	D₄×C₁₃	—	2	2	no	—
408	D₄×C₁₃	—	2	2	no	—
409	D₄×C₁₃	—	2	2	no	—
410	D₄×C₁₃	—	2	1	no	—
411	D₄×C₁₃	—	2	2	no	—
412	D₄×C₁₃	—	2	2	no	—
413	D₄×C₁₃	—	4	4	no	—
414	D₄×C₁₃	—	4	4	no	—
415	D₄×C₁₃	—	4	4	no	—
416	D₄×C₁₃	—	4	8	no	—
417	D₄×C₁₃	—	4	4	no	—
418	D₄×C₁₃	—	4	4	no	—
419	D₄×C₁₃	—	4	8	no	—
420	D₄×C₁₃	—	4	2	no	—
421	D₄×C₁₃	—	4	2	no	—
422	D₄×C₁₃	—	8	1	no	—
423	D₄×C₁₃	—	8	2	no	—
424	D₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
425	D₄×C₁₃	C₂×#41	1	2	yes	complemented
426	C₂×C₄×C₁₃	—	2	4	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	4	no	—
429	C₂×C₄×C₁₃	—	2	4	no	—
430	C₂×C₄×C₁₃	—	2	4	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	1	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	4	no	—
441	C₂×C₄×C₁₃	—	4	1	no	—
442	C₂×C₄×C₁₃	—	4	4	no	—
443	C₂×C₄×C₁₃	—	4	4	no	—
444	C₂×C₄×C₁₃	—	4	4	no	—
445	C₂×C₄×C₁₃	—	4	4	no	—
446	C₂×C₄×C₁₃	—	4	2	no	—
447	C₂×C₄×C₁₃	—	4	4	no	—
448	C₂×C₄×C₁₃	—	4	8	no	—
449	C₂×C₄×C₁₃	—	4	8	no	—
450	C₂×C₄×C₁₃	—	4	4	no	—
451	C₂×C₄×C₁₃	—	4	4	no	—
452	C₂×C₄×C₁₃	—	4	2	no	—
453	C₂×C₄×C₁₃	—	8	1	no	—
454	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
462	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
463	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
464	C₈×C₁₃	—	2	2	no	—
465	C₈×C₁₃	—	2	2	no	—
466	C₈×C₁₃	—	2	4	no	—
467	C₂²×#41	—	2	1	no	—
468	C₂²×#41	C₂²×C₁₃	1	2	yes	—
469	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
470	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
471	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
472	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
473	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	#548	C₂²×C₁₃	1	2	yes	complemented
475	#547	—	2	1	no	—
476	#547	—	2	2	no	—
477	#547	—	2	1	no	—
478	#547	—	2	1	no	—
479	#547	C₂²×C₁₃	1	2	yes	—
480	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	#547	C₂²×C₁₃	1	2	yes	complemented
482	#547	C₂²×C₁₃	1	4	yes	complemented
483	#546	—	2	2	no	—
484	#546	C₂²×C₁₃	1	2	yes	complemented
485	D₄²	—	2	1	no	—
486	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	#532	—	2	1	no	—
488	#532	C₂²×C₁₃	1	1	yes	characteristic
489	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#525	—	2	2	no	—
491	#525	C₂²×C₁₃	1	2	yes	—
492	C₂×#123	—	2	2	no	—
493	C₂×C₂²⋊Q₈	—	2	1	no	—
494	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
495	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
496	C₂×C₄×D₄	—	2	1	no	—
497	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
498	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
499	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
500	#489	C₂²×C₁₃	1	4	yes	complemented
501	#487	C₂²×C₁₃	1	2	yes	complemented
502	#486	C₂²×C₁₃	1	2	yes	complemented
503	#484	C₂²×C₁₃	1	4	yes	complemented
504	#483	C₂²×C₁₃	1	4	yes	complemented
505	#481	C₂²×C₁₃	1	4	yes	complemented
506	#480	C₂²×C₁₃	1	4	yes	complemented
507	#477	C₂²×C₁₃	1	2	yes	complemented
508	#476	C₂²×C₁₃	1	2	yes	complemented
509	#475	C₂²×C₁₃	1	2	yes	complemented
510	#474	C₂²×C₁₃	1	2	yes	complemented
511	#469	C₂²×C₁₃	1	4	yes	complemented
512	#468	C₂²×C₁₃	1	4	yes	complemented
513	#466	C₂²×C₁₃	1	4	yes	complemented
514	#465	C₂²×C₁₃	1	4	yes	complemented
515	#463	C₂²×C₁₃	1	4	yes	complemented
516	#461	C₂²×C₁₃	1	2	yes	complemented
517	#459	C₂²×C₁₃	1	2	yes	complemented
518	#449	C₂²×C₁₃	1	4	yes	complemented
519	#449	C₂²×C₁₃	1	4	yes	complemented
520	#448	C₂²×C₁₃	1	4	yes	complemented
521	#447	C₂²×C₁₃	1	4	yes	complemented
522	#442	C₂²×C₁₃	1	2	yes	complemented
523	#440	C₂²×C₁₃	1	2	yes	complemented
524	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
525	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
526	#436	C₂²×C₁₃	1	2	yes	complemented
527	#435	C₂²×C₁₃	1	4	yes	complemented
528	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
529	#428	C₂²×C₁₃	1	2	yes	complemented
530	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
531	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
532	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
533	#417	C₂²×C₁₃	1	2	yes	—
534	#417	C₂²×C₁₃	1	1	yes	characteristic
535	#417	C₂²×C₁₃	1	4	yes	complemented
536	#417	C₂²×C₁₃	1	4	yes	complemented
537	#417	C₂²×C₁₃	1	2	yes	complemented
538	#417	C₂²×C₁₃	1	2	yes	complemented
539	#417	C₂²×C₁₃	1	2	yes	complemented
540	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
541	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
542	#407	C₂²×C₁₃	1	2	yes	complemented
543	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
544	C₂²×C₁₃	—	2	1	no	—
545	C₂²×C₁₃	—	2	2	no	—
546	C₂²×C₁₃	—	2	2	no	—
547	C₂²×C₁₃	—	2	1	no	—
548	C₂²×C₁₃	—	2	2	no	—
549	C₂²×C₁₃	—	2	2	no	—
550	C₂²×C₁₃	—	2	2	no	—
551	C₂²×C₁₃	—	2	2	no	—
552	C₂²×C₁₃	—	4	8	no	—
553	C₂²×C₁₃	—	4	1	no	—
554	C₂²×C₁₃	—	4	1	no	—
555	C₂²×C₁₃	—	4	2	no	—
556	C₂²×C₁₃	—	4	2	no	—
557	C₂²×C₁₃	—	4	2	no	—
558	C₂²×C₁₃	—	4	2	no	—
559	C₂²×C₁₃	—	4	2	no	—
560	C₂²×C₁₃	—	4	2	no	—
561	C₂²×C₁₃	—	8	8	no	—
562	C₂²×C₁₃	—	8	4	no	—
563	C₂²×C₁₃	#546	1	2	yes	—
564	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
565	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₁₃	—	2	1	no	—
567	C₄×C₁₃	—	2	1	no	—
568	C₄×C₁₃	—	2	2	no	—
569	C₄×C₁₃	—	2	2	no	—
570	C₄×C₁₃	—	2	2	no	—
571	C₄×C₁₃	—	2	1	no	—
572	C₄×C₁₃	—	4	1	no	—
573	C₄×C₁₃	—	4	2	no	—
574	C₄×C₁₃	—	4	2	no	—
575	C₄×C₁₃	—	4	4	no	—
576	C₄×C₁₃	—	4	1	no	—
577	C₄×C₁₃	#546	1	2	yes	—
578	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
579	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
580	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂×#41	—	2	2	no	—
582	C₂×#41	—	2	4	no	—
583	C₂×#41	—	2	2	no	—
584	C₂×#41	—	2	2	no	—
585	C₂×#41	—	2	2	no	—
586	C₂×#41	—	2	8	no	—
587	C₂×#41	—	4	4	no	—
588	C₂×#41	—	4	8	no	—
589	C₂×#41	C₂³×C₁₃	1	2	yes	—
590	C₂×#41	C₂³×C₁₃	1	2	yes	—
591	C₂×#41	C₂³×C₁₃	1	2	yes	—
592	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
593	C₂²×Q₈	—	2	1	no	—
594	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
595	C₂²×D₄	—	2	2	no	—
596	C₂²×D₄	—	2	2	no	—
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
599	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
601	C₂³×C₄	—	2	2	no	—
602	C₂³×C₄	—	2	2	no	—
603	C₂³×C₄	—	2	1	no	—
604	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
605	AGL(1,ℤ/8)	—	2	4	no	—
606	AGL(1,ℤ/8)	—	4	4	no	—
607	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
608	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
609	C₂×D₈	C₂³×C₁₃	1	2	yes	—
610	C₂×D₈	C₂³×C₁₃	1	4	yes	—
611	C₂×M₁₆	—	4	4	no	—
612	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
614	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
616	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
617	C₄⋊Q₈	—	2	1	no	—
618	C₄⋊Q₈	—	2	1	no	—
619	C₄⋊Q₈	—	2	1	no	—
620	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
621	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
622	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
623	#127	—	2	1	no	—
624	#127	C₂³×C₁₃	1	1	yes	characteristic
625	#124	—	2	2	no	—
626	#124	C₂³×C₁₃	1	2	yes	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	4	no	—
630	#123	—	2	4	no	—
631	#123	—	2	4	no	—
632	#123	—	2	4	no	—
633	#123	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	4	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
640	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
641	#121	—	2	2	no	—
642	#121	—	2	1	no	—
643	#121	—	2	2	no	—
644	#121	—	2	2	no	—
645	#121	—	2	1	no	—
646	#121	—	2	1	no	—
647	#121	—	2	1	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	C₂³×C₁₃	1	4	yes	—
651	#121	C₂³×C₁₃	1	4	yes	—
652	#121	C₂³×C₁₃	1	2	yes	—
653	#121	C₂³×C₁₃	1	2	yes	—
654	#120	—	2	2	no	—
655	#120	—	2	2	no	—
656	#120	—	2	2	no	—
657	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
658	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	1	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	1	no	—
667	C₄×D₄	—	2	1	no	—
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	—	2	1	no	—
670	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
671	C₄×D₄	D₄×C₁₃	1	2	yes	—
672	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
673	C₄×D₄	C₂³×C₁₃	1	2	yes	—
674	C₄×D₄	C₂³×C₁₃	1	2	yes	—
675	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
676	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
677	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
678	C₄×D₄	C₂³×C₁₃	1	2	yes	—
679	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
680	#117	—	2	1	no	—
681	#117	C₂³×C₁₃	1	1	yes	characteristic
682	C₂×C₄⋊C₄	—	2	2	no	—
683	C₂×C₄⋊C₄	—	2	2	no	—
684	C₂×C₄⋊C₄	—	2	2	no	—
685	C₂×C₄⋊C₄	—	2	1	no	—
686	C₂×C₄⋊C₄	—	2	1	no	—
687	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
691	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
692	C₂×C₂²⋊C₄	—	2	1	no	—
693	C₂×C₂²⋊C₄	—	2	2	no	—
694	C₂×C₂²⋊C₄	—	2	2	no	—
695	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
696	C₂×C₄²	—	2	1	no	—
697	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
698	#107	C₂³×C₁₃	1	2	yes	—
699	#107	C₂³×C₁₃	1	4	yes	—
700	#106	C₂³×C₁₃	1	2	yes	—
701	#106	C₂³×C₁₃	1	4	yes	—
702	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
703	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
704	#103	C₂³×C₁₃	1	2	yes	—
705	#103	C₂³×C₁₃	1	4	yes	—
706	#103	C₂³×C₁₃	1	4	yes	—
707	#103	C₂³×C₁₃	1	4	yes	—
708	#103	C₂³×C₁₃	1	4	yes	—
709	#102	C₂³×C₁₃	1	2	yes	—
710	#102	C₂³×C₁₃	1	4	yes	—
711	#102	C₂³×C₁₃	1	4	yes	—
712	#102	C₂³×C₁₃	1	4	yes	—
713	#102	C₂³×C₁₃	1	4	yes	—
714	#102	C₂³×C₁₃	1	2	yes	—
715	#102	C₂³×C₁₃	1	2	yes	—
716	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
717	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
718	#97	C₂³×C₁₃	1	2	yes	—
719	C₄×C₈	C₂³×C₁₃	1	2	yes	—
720	C₂×C₁₃	—	2	2	no	—
721	C₂×C₁₃	—	2	4	no	—
722	C₂×C₁₃	—	4	2	no	—
723	C₂×C₁₃	—	4	2	no	—
724	C₂×C₁₃	—	8	2	no	—
725	C₂×C₁₃	—	8	2	no	—
726	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
727	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
728	C₂×C₁₃	#3586	1	1	yes	characteristic
729	C₂⁴	—	2	1	no	—
730	C₂⁴	—	2	2	no	—
731	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
732	#41	—	2	2	no	—
733	#41	—	2	4	no	—
734	#41	—	2	4	no	—
735	#41	—	2	4	no	—
736	#41	—	2	4	no	—
737	#41	—	4	8	no	—
738	#41	—	4	2	no	—
739	#41	—	4	2	no	—
740	#41	—	4	8	no	—
741	#41	—	4	16	no	—
742	#41	—	4	8	no	—
743	#41	—	4	8	no	—
744	#41	C₁₃×#41	1	4	yes	complemented
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	4	2	no	—
750	C₂×Q₈	—	4	4	no	—
751	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
752	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₂×D₄	—	2	1	no	—
754	C₂×D₄	—	2	4	no	—
755	C₂×D₄	—	2	4	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	1	no	—
764	C₂×D₄	—	2	1	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	—	4	8	no	—
771	C₂×D₄	—	4	8	no	—
772	C₂×D₄	—	4	4	no	—
773	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
774	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
775	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
776	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
777	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
778	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	2	1	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	4	no	—
785	C₂²×C₄	—	2	4	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	1	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	4	8	no	—
795	C₂²×C₄	—	4	4	no	—
796	C₂²×C₄	—	4	8	no	—
797	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
799	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
800	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
801	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
803	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
805	SD₁₆	—	2	4	no	—
806	SD₁₆	—	4	4	no	—
807	D₈	—	2	4	no	—
808	D₈	—	4	4	no	—
809	M₁₆	—	2	2	no	—
810	M₁₆	—	2	2	no	—
811	M₁₆	—	2	4	no	—
812	M₁₆	—	4	4	no	—
813	C₂×C₈	—	4	4	no	—
814	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
815	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
816	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	4	no	—
820	C₄⋊C₄	—	2	4	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
830	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
831	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
832	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
833	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
834	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
835	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	1	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	4	no	—
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	1	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
850	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
851	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
852	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
853	C₄²	—	2	1	no	—
854	C₄²	—	2	1	no	—
855	C₄²	—	2	1	no	—
856	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
857	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
858	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
859	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
860	C₁₃	#61161	1	1	yes	characteristic, direct product factor, Sylow
861	C₂³	—	2	4	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	4	no	—
868	C₂³	—	4	2	no	—
869	C₂³	—	4	2	no	—
870	C₂³	—	4	2	no	—
871	C₂³	—	4	4	no	—
872	C₂³	—	8	2	no	—
873	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
874	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
875	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
876	Q₈	—	2	1	no	—
877	Q₈	—	2	2	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	4	4	no	—
880	Q₈	—	4	4	no	—
881	Q₈	—	4	4	no	—
882	Q₈	C₂×C₁₃×#41	1	2	yes	complemented
883	D₄	—	2	4	no	—
884	D₄	—	2	4	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	2	no	—
888	D₄	—	2	1	no	—
889	D₄	—	2	2	no	—
890	D₄	—	2	2	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	8	no	—
895	D₄	—	4	4	no	—
896	D₄	—	4	4	no	—
897	D₄	—	4	8	no	—
898	D₄	—	4	2	no	—
899	D₄	—	4	2	no	—
900	D₄	—	8	1	no	—
901	D₄	—	8	2	no	—
902	D₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
903	D₄	C₂×C₁₃×#41	1	2	yes	complemented
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	4	no	—
907	C₂×C₄	—	2	4	no	—
908	C₂×C₄	—	2	4	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	4	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	4	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	8	no	—
927	C₂×C₄	—	4	8	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	8	1	no	—
932	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
939	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
940	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
941	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
942	C₈	—	2	2	no	—
943	C₈	—	2	2	no	—
944	C₈	—	2	4	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	4	8	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	8	8	no	—
963	C₂²	—	8	4	no	—
964	C₂²	C₁₃×#546	1	2	yes	—
965	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
966	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	4	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	2	no	—
978	C₄	C₁₃×#546	1	2	yes	—
979	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
980	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
981	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
982	C₂	—	2	2	no	—
983	C₂	—	2	4	no	—
984	C₂	—	4	2	no	—
985	C₂	—	4	2	no	—
986	C₂	—	8	2	no	—
987	C₂	—	8	2	no	—
988	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
989	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
990	C₂	C₁₃×#3586	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. D₄×C₁₃×#41	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3332	C₂	semidirect
4. C₁₃×#3330	C₂	semidirect
5. C₁₃×#3308	C₂	semidirect
6. C₁₃×#3306	C₂	semidirect
7. C₁₃×#3298	C₂	semidirect
8. C₁₃×#3294	C₂	semidirect
9. C₁₃×#3141	C₂	semidirect
10. C₁₃×#3092	C₂	semidirect
11. C₁₃×#3079	C₂	semidirect
12. C₁₃×#3055	C₂	semidirect
13. C₁₃×#3036	C₂	semidirect
14. C₁₃×#3006	C₂	semidirect
15. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
16. D₄×C₁₃×M₁₆	C₂	semidirect
17. C₂×C₁₃×#417	C₂	semidirect
21. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂²×C₁₃×M₁₆	C₂²	semidirect
23. C₁₃×#550	C₂²	semidirect
24. D₄×Q₈×C₁₃	C₂²	semidirect
25. C₁₃×#548	C₂²	semidirect
31. C₁₃×#547	C₂²	semidirect
32. C₁₃×#547	C₂²	semidirect
33. C₁₃×#547	C₂²	semidirect
35. C₁₃×#546	C₂²	semidirect
37. D₄²×C₁₃	C₂²	semidirect
40. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
45. C₂×C₁₃×#121	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃	C₂²	semidirect
50. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
51. C₁₃×#489	C₂²	semidirect
52. C₁₃×#487	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#484	C₂²	semidirect
55. C₁₃×#483	C₂²	semidirect
56. C₁₃×#481	C₂²	semidirect
57. C₁₃×#480	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#474	C₂²	semidirect
62. C₁₃×#469	C₂²	semidirect
63. C₁₃×#468	C₂²	semidirect
64. C₁₃×#466	C₂²	semidirect
65. C₁₃×#465	C₂²	semidirect
66. C₁₃×#463	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#459	C₂²	semidirect
69. C₁₃×#449	C₂²	semidirect
70. C₁₃×#449	C₂²	semidirect
71. C₁₃×#448	C₂²	semidirect
72. C₁₃×#447	C₂²	semidirect
73. C₁₃×#442	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₄×C₁₃×SD₁₆	C₂²	semidirect
76. C₄×C₁₃×D₈	C₂²	semidirect
77. C₁₃×#436	C₂²	semidirect
78. C₁₃×#435	C₂²	semidirect
79. C₈×D₄×C₁₃	C₂²	semidirect
80. C₁₃×#428	C₂²	semidirect
81. C₁₃×#428	C₂²	semidirect
82. C₁₃×#423	C₂²	semidirect
83. C₁₃×#418	C₂²	semidirect
86. C₁₃×#417	C₂²	semidirect
87. C₁₃×#417	C₂²	semidirect
88. C₁₃×#417	C₂²	semidirect
89. C₁₃×#417	C₂²	semidirect
90. C₁₃×#417	C₂²	semidirect
91. C₂×C₁₃×#103	C₂²	semidirect
92. C₂×C₁₃×#102	C₂²	semidirect
93. C₁₃×#407	C₂²	semidirect
94. C₄×C₁₃×M₁₆	C₂²	semidirect
234. #61161	C₁₃	direct (N × H)
250. C₁₃×#41	#41	semidirect
366. D₄×#41	C₂×C₁₃	semidirect
367. C₂×#547	C₂×C₁₃	semidirect
368. #3332	C₂×C₁₃	semidirect
369. #3330	C₂×C₁₃	semidirect
370. #3308	C₂×C₁₃	semidirect
371. #3306	C₂×C₁₃	semidirect
372. #3298	C₂×C₁₃	semidirect
373. #3294	C₂×C₁₃	semidirect
374. #3141	C₂×C₁₃	semidirect
375. #3092	C₂×C₁₃	semidirect
376. #3079	C₂×C₁₃	semidirect
377. #3055	C₂×C₁₃	semidirect
378. #3036	C₂×C₁₃	semidirect
379. #3006	C₂×C₁₃	semidirect
380. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
381. D₄×M₁₆	C₂×C₁₃	semidirect
382. C₂×#417	C₂×C₁₃	semidirect
404. Q₈×C₁₃	C₂×#41	semidirect
424. D₄×C₁₃	AGL(1,ℤ/8)	semidirect
425. D₄×C₁₃	C₂×#41	semidirect
470. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
471. C₂²×M₁₆	C₂²×C₁₃	semidirect
472. #550	C₂²×C₁₃	semidirect
473. D₄×Q₈	C₂²×C₁₃	semidirect
474. #548	C₂²×C₁₃	semidirect
480. #547	C₂²×C₁₃	semidirect
481. #547	C₂²×C₁₃	semidirect
482. #547	C₂²×C₁₃	semidirect
484. #546	C₂²×C₁₃	semidirect
486. D₄²	C₂²×C₁₃	semidirect
489. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
494. C₂×#121	C₂²×C₁₃	semidirect
498. C₂×C₄×D₄	C₂²×C₁₃	semidirect
499. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
500. #489	C₂²×C₁₃	semidirect
501. #487	C₂²×C₁₃	semidirect
502. #486	C₂²×C₁₃	semidirect
503. #484	C₂²×C₁₃	semidirect
504. #483	C₂²×C₁₃	semidirect
505. #481	C₂²×C₁₃	semidirect
506. #480	C₂²×C₁₃	semidirect
507. #477	C₂²×C₁₃	semidirect
508. #476	C₂²×C₁₃	semidirect
509. #475	C₂²×C₁₃	semidirect
510. #474	C₂²×C₁₃	semidirect
511. #469	C₂²×C₁₃	semidirect
512. #468	C₂²×C₁₃	semidirect
513. #466	C₂²×C₁₃	semidirect
514. #465	C₂²×C₁₃	semidirect
515. #463	C₂²×C₁₃	semidirect
516. #461	C₂²×C₁₃	semidirect
517. #459	C₂²×C₁₃	semidirect
518. #449	C₂²×C₁₃	semidirect
519. #449	C₂²×C₁₃	semidirect
520. #448	C₂²×C₁₃	semidirect
521. #447	C₂²×C₁₃	semidirect
522. #442	C₂²×C₁₃	semidirect
523. #440	C₂²×C₁₃	semidirect
524. C₄×SD₁₆	C₂²×C₁₃	semidirect
525. C₄×D₈	C₂²×C₁₃	semidirect
526. #436	C₂²×C₁₃	semidirect
527. #435	C₂²×C₁₃	semidirect
528. C₈×D₄	C₂²×C₁₃	semidirect
529. #428	C₂²×C₁₃	semidirect
530. #428	C₂²×C₁₃	semidirect
531. #423	C₂²×C₁₃	semidirect
532. #418	C₂²×C₁₃	semidirect
535. #417	C₂²×C₁₃	semidirect
536. #417	C₂²×C₁₃	semidirect
537. #417	C₂²×C₁₃	semidirect
538. #417	C₂²×C₁₃	semidirect
539. #417	C₂²×C₁₃	semidirect
540. C₂×#103	C₂²×C₁₃	semidirect
541. C₂×#102	C₂²×C₁₃	semidirect
542. #407	C₂²×C₁₃	semidirect
543. C₄×M₁₆	C₂²×C₁₃	semidirect
744. #41	C₁₃×#41	semidirect
860. C₁₃	#61161	direct (N × H)
882. Q₈	C₂×C₁₃×#41	semidirect
902. D₄	C₁₃×AGL(1,ℤ/8)	semidirect
903. D₄	C₂×C₁₃×#41	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₁₃×#41	2
C₂×C₁₃×#547	2
C₁₃×#3332	2
C₁₃×#3330	2
C₁₃×#3308	2
C₁₃×#3306	2
C₁₃×#3298	2
C₁₃×#3294	2
C₁₃×#3141	2
C₁₃×#3092	2
C₁₃×#3079	2
C₁₃×#3055	2
C₁₃×#3036	2
C₁₃×#3006	2
C₄×C₁₃×AGL(1,ℤ/8)	2
D₄×C₁₃×M₁₆	2
C₂×C₁₃×#417	2
#61161	13

Subgroups — C13×#61161 #15747500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61161 #15747500