Subgroups — C₁₃×#61323 #15747662

Order 3328.

1814 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3377	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3140	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3078	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3040	C₂	1	2	yes	maximal
14	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#557	C₂²	1	2	yes	complemented
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#556	—	2	2	no	—
25	C₁₃×#556	—	2	1	no	—
26	C₁₃×#556	C₂²	1	2	yes	—
27	C₁₃×#556	C₂²	1	2	yes	—
28	C₁₃×#556	C₂²	1	4	yes	—
29	C₁₃×#554	—	2	1	no	—
30	C₁₃×#554	—	2	2	no	—
31	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#554	C₂²	1	2	yes	complemented
33	D₄×Q₈×C₁₃	—	2	1	no	—
34	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#533	—	2	1	no	—
36	C₁₃×#533	—	2	2	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	2	yes	—
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#126	—	2	2	no	—
41	C₂×C₁₃×#124	C₂²	1	2	yes	—
42	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×#41	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
46	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#117	—	2	1	no	—
50	C₁₃×#491	C₂²	1	4	yes	complemented
51	C₁₃×#489	C₂²	1	4	yes	—
52	C₁₃×#489	C₂²	1	4	yes	—
53	C₁₃×#488	C₂²	1	4	yes	—
54	C₁₃×#488	C₂²	1	4	yes	—
55	C₁₃×#487	C₂²	1	2	yes	complemented
56	C₁₃×#487	C₂²	1	2	yes	complemented
57	C₁₃×#479	C₂²	1	4	yes	complemented
58	C₁₃×#479	C₂²	1	4	yes	complemented
59	C₁₃×#478	C₂²	1	4	yes	—
60	C₁₃×#477	C₂²	1	4	yes	complemented
61	C₁₃×#476	C₂²	1	2	yes	—
62	C₁₃×#475	C₂²	1	4	yes	complemented
63	C₁₃×#474	C₂²	1	2	yes	—
64	C₁₃×#464	C₂²	1	4	yes	—
65	C₁₃×#464	C₂²	1	4	yes	—
66	C₁₃×#463	C₂²	1	4	yes	—
67	C₁₃×#463	C₂²	1	4	yes	—
68	C₁₃×#462	C₂²	1	2	yes	complemented
69	C₁₃×#462	C₂²	1	2	yes	complemented
70	C₁₃×#461	C₂²	1	2	yes	complemented
71	C₁₃×#461	C₂²	1	2	yes	complemented
72	C₁₃×#446	C₂²	1	2	yes	complemented
73	C₁₃×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
75	C₁₃×#442	C₂²	1	2	yes	—
76	C₁₃×#441	C₂²	1	4	yes	complemented
77	C₁₃×#440	C₂²	1	2	yes	—
78	C₁₃×#440	C₂²	1	4	yes	complemented
79	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
80	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
81	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
82	C₄×C₁₃×D₈	C₂²	1	2	yes	—
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₁₃×#428	C₂²	1	1	yes	characteristic
85	C₁₃×#423	C₂²	1	1	yes	characteristic
86	C₁₃×#423	C₂²	1	2	yes	—
87	C₁₃×#419	C₂²	1	2	yes	—
88	C₁₃×#419	C₂²	1	2	yes	—
89	C₁₃×#419	C₂²	1	2	yes	—
90	C₁₃×#418	C₂²	1	2	yes	—
91	C₁₃×#418	C₂²	1	1	yes	characteristic
92	C₁₃×#417	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	—	2	1	no	—
97	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	—	2	1	no	—
101	C₁₃×#137	—	2	8	no	—
102	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×D₈	C₂³	1	2	yes	—
107	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	2	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	—	2	1	no	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₁₃×#126	—	2	4	no	—
123	C₁₃×#126	—	2	4	no	—
124	C₁₃×#126	—	2	4	no	—
125	C₁₃×#126	—	2	4	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	—	2	2	no	—
129	C₁₃×#125	C₂³	1	2	yes	—
130	C₁₃×#125	C₂³	1	2	yes	—
131	C₁₃×#125	C₂³	1	2	yes	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	C₂³	1	4	yes	—
135	C₁₃×#124	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	4	no	—
139	C₁₃×C₂²⋊Q₈	—	2	1	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	—	2	2	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	2	no	—
155	C₄×Q₈×C₁₃	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	2	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
160	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	D₄	1	2	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
171	C₄×D₄×C₁₃	—	2	1	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
183	C₁₃×#117	—	2	2	no	—
184	C₁₃×#117	—	2	4	no	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	1	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	C₂³	1	2	yes	—
189	C₁₃×#117	C₂³	1	1	yes	characteristic
190	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²×C₁₃	—	2	2	no	—
202	C₂×C₄²×C₁₃	—	2	1	no	—
203	C₂×C₄²×C₁₃	—	2	2	no	—
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
206	C₁₃×#107	C₂³	1	2	yes	—
207	C₁₃×#107	C₂³	1	4	yes	—
208	C₁₃×#106	C₂³	1	2	yes	—
209	C₁₃×#106	C₂³	1	4	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	2	yes	—
227	C₁₃×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	C₄×C₈×C₁₃	C₂³	1	4	yes	—
230	#61323	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂⁴×C₁₃	—	2	1	no	—
232	C₁₃×#41	—	2	2	no	—
233	C₁₃×#41	#41	1	4	yes	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	4	no	—
240	C₂×Q₈×C₁₃	—	2	4	no	—
241	C₂×Q₈×C₁₃	—	4	2	no	—
242	C₂×Q₈×C₁₃	—	4	4	no	—
243	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	—	2	1	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	4	4	no	—
264	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₁₃×Q₁₆	—	2	8	no	—
270	C₁₃×SD₁₆	—	2	4	no	—
271	C₁₃×SD₁₆	—	2	8	no	—
272	C₁₃×D₈	—	2	4	no	—
273	C₁₃×M₁₆	—	2	2	no	—
274	C₁₃×M₁₆	—	2	4	no	—
275	C₁₃×M₁₆	—	2	2	no	—
276	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
277	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
278	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
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	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	4	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
308	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	1	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	1	no	—
323	C₁₃×C₂²⋊C₄	—	2	1	no	—
324	C₄²×C₁₃	—	2	4	no	—
325	C₄²×C₁₃	—	2	4	no	—
326	C₄²×C₁₃	—	2	1	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	1	no	—
332	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₁₃	C₂×D₄	1	2	yes	—
334	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₁₃	C₂×D₄	1	2	yes	—
336	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
337	C₄²×C₁₃	C₂⁴	1	2	yes	—
338	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₁₃	C₂⁴	1	2	yes	—
340	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3377	C₂×C₁₃	1	4	yes	complemented
343	#3376	C₂×C₁₃	1	4	yes	complemented
344	#3369	C₂×C₁₃	1	2	yes	complemented
345	#3367	C₂×C₁₃	1	2	yes	complemented
346	#3364	C₂×C₁₃	1	2	yes	complemented
347	#3360	C₂×C₁₃	1	2	yes	complemented
348	#3140	C₂×C₁₃	1	2	yes	complemented
349	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3078	C₂×C₁₃	1	2	yes	complemented
351	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3040	C₂×C₁₃	1	2	yes	—
353	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
354	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₄×#137	C₂×C₁₃	1	2	yes	complemented
356	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
357	C₂³×C₁₃	—	2	1	no	—
358	C₂³×C₁₃	—	2	2	no	—
359	C₂³×C₁₃	—	4	2	no	—
360	C₂³×C₁₃	—	4	2	no	—
361	C₂³×C₁₃	—	4	2	no	—
362	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	2	no	—
365	Q₈×C₁₃	—	2	1	no	—
366	Q₈×C₁₃	—	2	4	no	—
367	Q₈×C₁₃	—	2	4	no	—
368	Q₈×C₁₃	—	4	2	no	—
369	Q₈×C₁₃	—	4	4	no	—
370	Q₈×C₁₃	—	4	4	no	—
371	Q₈×C₁₃	—	4	2	no	—
372	Q₈×C₁₃	—	8	2	no	—
373	Q₈×C₁₃	—	8	1	no	—
374	Q₈×C₁₃	C₂×#41	1	2	yes	—
375	D₄×C₁₃	—	2	4	no	—
376	D₄×C₁₃	—	2	2	no	—
377	D₄×C₁₃	—	2	1	no	—
378	D₄×C₁₃	—	2	2	no	—
379	D₄×C₁₃	—	4	2	no	—
380	D₄×C₁₃	C₂×#41	1	2	yes	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	4	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	4	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	4	2	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	4	4	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	—	4	4	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	4	2	no	—
399	C₂×C₄×C₁₃	—	8	2	no	—
400	C₂×C₄×C₁₃	—	8	1	no	—
401	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
411	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
412	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
413	C₈×C₁₃	—	2	2	no	—
414	C₈×C₁₃	—	2	4	no	—
415	C₈×C₁₃	—	2	2	no	—
416	C₂×#137	C₂²×C₁₃	1	2	yes	—
417	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
418	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	#557	C₂²×C₁₃	1	2	yes	complemented
421	#556	—	2	1	no	—
422	#556	—	2	2	no	—
423	#556	—	2	1	no	—
424	#556	C₂²×C₁₃	1	2	yes	—
425	#556	C₂²×C₁₃	1	2	yes	—
426	#556	C₂²×C₁₃	1	4	yes	—
427	#554	—	2	1	no	—
428	#554	—	2	2	no	—
429	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	#554	C₂²×C₁₃	1	2	yes	complemented
431	D₄×Q₈	—	2	1	no	—
432	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	#533	—	2	1	no	—
434	#533	—	2	2	no	—
435	#533	C₂²×C₁₃	1	1	yes	characteristic
436	#533	C₂²×C₁₃	1	2	yes	—
437	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#126	—	2	2	no	—
439	C₂×#124	C₂²×C₁₃	1	2	yes	—
440	C₂×C₂²⋊Q₈	—	2	1	no	—
441	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
442	C₄×#41	C₂²×C₁₃	1	2	yes	—
443	C₂×C₄×Q₈	—	2	1	no	—
444	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
445	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×#117	—	2	1	no	—
448	#491	C₂²×C₁₃	1	4	yes	complemented
449	#489	C₂²×C₁₃	1	4	yes	—
450	#489	C₂²×C₁₃	1	4	yes	—
451	#488	C₂²×C₁₃	1	4	yes	—
452	#488	C₂²×C₁₃	1	4	yes	—
453	#487	C₂²×C₁₃	1	2	yes	complemented
454	#487	C₂²×C₁₃	1	2	yes	complemented
455	#479	C₂²×C₁₃	1	4	yes	complemented
456	#479	C₂²×C₁₃	1	4	yes	complemented
457	#478	C₂²×C₁₃	1	4	yes	—
458	#477	C₂²×C₁₃	1	4	yes	complemented
459	#476	C₂²×C₁₃	1	2	yes	—
460	#475	C₂²×C₁₃	1	4	yes	complemented
461	#474	C₂²×C₁₃	1	2	yes	—
462	#464	C₂²×C₁₃	1	4	yes	—
463	#464	C₂²×C₁₃	1	4	yes	—
464	#463	C₂²×C₁₃	1	4	yes	—
465	#463	C₂²×C₁₃	1	4	yes	—
466	#462	C₂²×C₁₃	1	2	yes	complemented
467	#462	C₂²×C₁₃	1	2	yes	complemented
468	#461	C₂²×C₁₃	1	2	yes	complemented
469	#461	C₂²×C₁₃	1	2	yes	complemented
470	#446	C₂²×C₁₃	1	2	yes	complemented
471	#446	C₂²×C₁₃	1	4	yes	complemented
472	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
473	#442	C₂²×C₁₃	1	2	yes	—
474	#441	C₂²×C₁₃	1	4	yes	complemented
475	#440	C₂²×C₁₃	1	2	yes	—
476	#440	C₂²×C₁₃	1	4	yes	complemented
477	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
478	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
479	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
480	C₄×D₈	C₂²×C₁₃	1	2	yes	—
481	#428	C₂²×C₁₃	1	2	yes	—
482	#428	C₂²×C₁₃	1	1	yes	characteristic
483	#423	C₂²×C₁₃	1	1	yes	characteristic
484	#423	C₂²×C₁₃	1	2	yes	—
485	#419	C₂²×C₁₃	1	2	yes	—
486	#419	C₂²×C₁₃	1	2	yes	—
487	#419	C₂²×C₁₃	1	2	yes	—
488	#418	C₂²×C₁₃	1	2	yes	—
489	#418	C₂²×C₁₃	1	1	yes	characteristic
490	#417	C₂²×C₁₃	1	1	yes	characteristic
491	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
492	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
493	C₂²×C₁₃	—	2	1	no	—
494	C₂²×C₁₃	—	2	1	no	—
495	C₂²×C₁₃	—	2	2	no	—
496	C₂²×C₁₃	—	4	1	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	8	4	no	—
502	C₂²×C₁₃	#548	1	2	yes	—
503	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₁₃	—	2	2	no	—
505	C₄×C₁₃	—	2	1	no	—
506	C₄×C₁₃	—	2	2	no	—
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	2	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	2	no	—
512	C₄×C₁₃	—	4	2	no	—
513	C₄×C₁₃	—	4	1	no	—
514	C₄×C₁₃	—	4	4	no	—
515	C₄×C₁₃	—	4	2	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	—	4	1	no	—
518	C₄×C₁₃	#548	1	2	yes	—
519	C₄×C₁₃	#575	1	2	yes	—
520	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
521	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
522	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
523	C₂²×Q₈	—	2	1	no	—
524	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
525	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
526	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₂³×C₄	—	2	1	no	—
528	#137	—	2	8	no	—
529	AGL(1,ℤ/8)	—	2	4	no	—
530	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
531	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
533	C₂×D₈	C₂³×C₁₃	1	2	yes	—
534	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
536	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
544	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
545	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
546	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
549	#126	—	2	4	no	—
550	#126	—	2	4	no	—
551	#126	—	2	4	no	—
552	#126	—	2	4	no	—
553	#125	—	2	2	no	—
554	#125	—	2	2	no	—
555	#125	—	2	2	no	—
556	#125	C₂³×C₁₃	1	2	yes	—
557	#125	C₂³×C₁₃	1	2	yes	—
558	#125	C₂³×C₁₃	1	2	yes	—
559	#124	—	2	2	no	—
560	#124	—	2	2	no	—
561	#124	C₂³×C₁₃	1	4	yes	—
562	#124	C₂³×C₁₃	1	4	yes	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
587	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
588	C₄×Q₈	D₄×C₁₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
590	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
591	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	C₂³×C₁₃	1	2	yes	—
605	C₄×D₄	C₂³×C₁₃	1	2	yes	—
606	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₄×D₄	C₂³×C₁₃	1	2	yes	—
608	C₄×D₄	C₂³×C₁₃	1	2	yes	—
609	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
610	#117	—	2	2	no	—
611	#117	—	2	4	no	—
612	#117	—	2	2	no	—
613	#117	—	2	1	no	—
614	#117	—	2	2	no	—
615	#117	C₂³×C₁₃	1	1	yes	characteristic
616	#117	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	2	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	2	no	—
622	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₄²	—	2	2	no	—
629	C₂×C₄²	—	2	1	no	—
630	C₂×C₄²	—	2	2	no	—
631	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
633	#107	C₂³×C₁₃	1	2	yes	—
634	#107	C₂³×C₁₃	1	4	yes	—
635	#106	C₂³×C₁₃	1	2	yes	—
636	#106	C₂³×C₁₃	1	4	yes	—
637	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
638	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
639	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
640	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
641	#103	C₂³×C₁₃	1	2	yes	—
642	#103	C₂³×C₁₃	1	4	yes	—
643	#103	C₂³×C₁₃	1	4	yes	—
644	#103	C₂³×C₁₃	1	4	yes	—
645	#103	C₂³×C₁₃	1	4	yes	—
646	#103	C₂³×C₁₃	1	4	yes	—
647	#103	C₂³×C₁₃	1	4	yes	—
648	#102	C₂³×C₁₃	1	2	yes	—
649	#102	C₂³×C₁₃	1	2	yes	—
650	#102	C₂³×C₁₃	1	2	yes	—
651	#102	C₂³×C₁₃	1	4	yes	—
652	#102	C₂³×C₁₃	1	4	yes	—
653	#97	C₂³×C₁₃	1	2	yes	—
654	#97	C₂³×C₁₃	1	4	yes	—
655	C₄×C₈	C₂³×C₁₃	1	2	yes	—
656	C₄×C₈	C₂³×C₁₃	1	4	yes	—
657	C₂×C₁₃	—	2	2	no	—
658	C₂×C₁₃	—	4	2	no	—
659	C₂×C₁₃	—	8	2	no	—
660	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
661	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
662	C₂×C₁₃	#3586	1	1	yes	characteristic
663	C₂⁴	—	2	1	no	—
664	#41	—	2	2	no	—
665	#41	C₁₃×#41	1	4	yes	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	4	no	—
672	C₂×Q₈	—	2	4	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×Q₈	—	4	4	no	—
675	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
678	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
679	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
685	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
698	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
701	Q₁₆	—	2	8	no	—
702	SD₁₆	—	2	4	no	—
703	SD₁₆	—	2	8	no	—
704	D₈	—	2	4	no	—
705	M₁₆	—	2	2	no	—
706	M₁₆	—	2	4	no	—
707	M₁₆	—	2	2	no	—
708	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
709	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
710	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
734	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
738	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
743	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	1	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	1	no	—
764	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₁₃	1	2	yes	—
766	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₁₃	1	2	yes	—
768	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
769	C₄²	C₂⁴×C₁₃	1	2	yes	—
770	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₄²	C₂⁴×C₁₃	1	2	yes	—
772	C₁₃	#61323	1	1	yes	characteristic, direct product factor, Sylow
773	C₂³	—	2	1	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	4	2	no	—
776	C₂³	—	4	2	no	—
777	C₂³	—	4	2	no	—
778	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
779	Q₈	—	2	2	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	4	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	4	2	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	4	no	—
787	Q₈	—	4	2	no	—
788	Q₈	—	8	2	no	—
789	Q₈	—	8	1	no	—
790	Q₈	C₂×C₁₃×#41	1	2	yes	—
791	D₄	—	2	4	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	2	no	—
795	D₄	—	4	2	no	—
796	D₄	C₂×C₁₃×#41	1	2	yes	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	8	2	no	—
816	C₂×C₄	—	8	1	no	—
817	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
826	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
827	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
828	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
829	C₈	—	2	2	no	—
830	C₈	—	2	4	no	—
831	C₈	—	2	2	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	8	4	no	—
841	C₂²	C₁₃×#548	1	2	yes	—
842	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
843	C₄	—	2	1	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	4	no	—
857	C₄	C₁₃×#548	1	2	yes	—
858	C₄	C₁₃×#575	1	2	yes	—
859	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
860	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
861	C₂	—	2	2	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	2	no	—
864	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
865	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
866	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×C₁₃×#41	C₂	semidirect
2. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3377	C₂	semidirect
4. C₁₃×#3376	C₂	semidirect
5. C₁₃×#3369	C₂	semidirect
6. C₁₃×#3367	C₂	semidirect
7. C₁₃×#3364	C₂	semidirect
8. C₁₃×#3360	C₂	semidirect
9. C₁₃×#3140	C₂	semidirect
10. C₁₃×#3139	C₂	semidirect
11. C₁₃×#3078	C₂	semidirect
12. C₁₃×#3077	C₂	semidirect
14. C₁₃×#3039	C₂	semidirect
15. Q₈×C₁₃×M₁₆	C₂	semidirect
16. C₄×C₁₃×#137	C₂	semidirect
20. Q₈²×C₁₃	C₂²	semidirect
21. C₁₃×#557	C₂²	semidirect
22. C₁₃×#557	C₂²	semidirect
31. C₁₃×#554	C₂²	semidirect
32. C₁₃×#554	C₂²	semidirect
34. D₄×Q₈×C₁₃	C₂²	semidirect
50. C₁₃×#491	C₂²	semidirect
55. C₁₃×#487	C₂²	semidirect
56. C₁₃×#487	C₂²	semidirect
57. C₁₃×#479	C₂²	semidirect
58. C₁₃×#479	C₂²	semidirect
60. C₁₃×#477	C₂²	semidirect
62. C₁₃×#475	C₂²	semidirect
68. C₁₃×#462	C₂²	semidirect
69. C₁₃×#462	C₂²	semidirect
70. C₁₃×#461	C₂²	semidirect
71. C₁₃×#461	C₂²	semidirect
72. C₁₃×#446	C₂²	semidirect
73. C₁₃×#446	C₂²	semidirect
74. C₈×Q₈×C₁₃	C₂²	semidirect
76. C₁₃×#441	C₂²	semidirect
78. C₁₃×#440	C₂²	semidirect
79. C₄×C₁₃×Q₁₆	C₂²	semidirect
81. C₄×C₁₃×SD₁₆	C₂²	semidirect
230. #61323	C₁₃	direct (N × H)
340. Q₈×#41	C₂×C₁₃	semidirect
341. C₂×#556	C₂×C₁₃	semidirect
342. #3377	C₂×C₁₃	semidirect
343. #3376	C₂×C₁₃	semidirect
344. #3369	C₂×C₁₃	semidirect
345. #3367	C₂×C₁₃	semidirect
346. #3364	C₂×C₁₃	semidirect
347. #3360	C₂×C₁₃	semidirect
348. #3140	C₂×C₁₃	semidirect
349. #3139	C₂×C₁₃	semidirect
350. #3078	C₂×C₁₃	semidirect
351. #3077	C₂×C₁₃	semidirect
353. #3039	C₂×C₁₃	semidirect
354. Q₈×M₁₆	C₂×C₁₃	semidirect
355. C₄×#137	C₂×C₁₃	semidirect
418. Q₈²	C₂²×C₁₃	semidirect
419. #557	C₂²×C₁₃	semidirect
420. #557	C₂²×C₁₃	semidirect
429. #554	C₂²×C₁₃	semidirect
430. #554	C₂²×C₁₃	semidirect
432. D₄×Q₈	C₂²×C₁₃	semidirect
448. #491	C₂²×C₁₃	semidirect
453. #487	C₂²×C₁₃	semidirect
454. #487	C₂²×C₁₃	semidirect
455. #479	C₂²×C₁₃	semidirect
456. #479	C₂²×C₁₃	semidirect
458. #477	C₂²×C₁₃	semidirect
460. #475	C₂²×C₁₃	semidirect
466. #462	C₂²×C₁₃	semidirect
467. #462	C₂²×C₁₃	semidirect
468. #461	C₂²×C₁₃	semidirect
469. #461	C₂²×C₁₃	semidirect
470. #446	C₂²×C₁₃	semidirect
471. #446	C₂²×C₁₃	semidirect
472. C₈×Q₈	C₂²×C₁₃	semidirect
474. #441	C₂²×C₁₃	semidirect
476. #440	C₂²×C₁₃	semidirect
477. C₄×Q₁₆	C₂²×C₁₃	semidirect
479. C₄×SD₁₆	C₂²×C₁₃	semidirect
772. C₁₃	#61323	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₁₃×#41	2
C₂×C₁₃×#556	2
C₁₃×#3377	2
C₁₃×#3376	2
C₁₃×#3369	2
C₁₃×#3367	2
C₁₃×#3364	2
C₁₃×#3360	2
C₁₃×#3140	2
C₁₃×#3139	2
C₁₃×#3078	2
C₁₃×#3077	2
C₁₃×#3040	2
C₁₃×#3039	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×#137	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61323	13

Subgroups — C13×#61323 #15747662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61323 #15747662