Subgroups — C₁₃×#61256 #15747595

Order 3328.

1892 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3357	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3354	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3348	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3347	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3341	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3340	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3094	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3093	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3055	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	C₁₃×#2911	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
20	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#555	—	2	1	no	—
22	C₁₃×#555	—	2	2	no	—
23	C₁₃×#555	—	2	1	no	—
24	C₁₃×#555	C₂²	1	2	yes	—
25	C₁₃×#555	C₂²	1	4	yes	—
26	C₁₃×#555	C₂²	1	2	yes	—
27	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#553	C₂²	1	2	yes	complemented
30	C₁₃×#552	—	2	1	no	—
31	C₁₃×#552	C₂²	1	2	yes	complemented
32	C₁₃×#551	—	2	2	no	—
33	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#546	—	2	1	no	—
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₁₃×#529	—	2	2	no	—
38	C₁₃×#529	—	2	1	no	—
39	C₂×C₁₃×#124	—	2	2	no	—
40	C₁₃×#525	C₂²	1	2	yes	—
41	C₂×C₁₃×#121	—	2	1	no	—
42	C₂×C₁₃×#121	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	—	2	1	no	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#117	—	2	1	no	—
48	C₂×C₁₃×#117	C₂²	1	2	yes	—
49	C₂×C₁₃×#117	C₂²	1	2	yes	—
50	C₁₃×#501	C₂²	1	4	yes	complemented
51	C₁₃×#500	C₂²	1	2	yes	complemented
52	C₁₃×#498	C₂²	1	2	yes	complemented
53	C₁₃×#485	C₂²	1	4	yes	complemented
54	C₁₃×#485	C₂²	1	4	yes	complemented
55	C₁₃×#482	C₂²	1	4	yes	complemented
56	C₁₃×#482	C₂²	1	4	yes	complemented
57	C₁₃×#482	C₂²	1	4	yes	complemented
58	C₁₃×#482	C₂²	1	4	yes	complemented
59	C₁₃×#481	C₂²	1	4	yes	complemented
60	C₁₃×#480	C₂²	1	4	yes	complemented
61	C₁₃×#478	C₂²	1	4	yes	complemented
62	C₁₃×#477	C₂²	1	2	yes	complemented
63	C₁₃×#476	C₂²	1	2	yes	complemented
64	C₁₃×#476	C₂²	1	2	yes	complemented
65	C₁₃×#475	C₂²	1	2	yes	complemented
66	C₁₃×#474	C₂²	1	2	yes	complemented
67	C₁₃×#474	C₂²	1	2	yes	complemented
68	C₁₃×#469	C₂²	1	4	yes	complemented
69	C₁₃×#468	C₂²	1	4	yes	complemented
70	C₁₃×#466	C₂²	1	4	yes	complemented
71	C₁₃×#465	C₂²	1	4	yes	complemented
72	C₁₃×#442	C₂²	1	2	yes	complemented
73	C₁₃×#440	C₂²	1	2	yes	complemented
74	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
75	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
76	C₁₃×#436	C₂²	1	2	yes	complemented
77	C₁₃×#435	C₂²	1	4	yes	complemented
78	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
79	C₁₃×#428	C₂²	1	2	yes	—
80	C₁₃×#428	C₂²	1	2	yes	—
81	C₁₃×#428	C₂²	1	2	yes	—
82	C₁₃×#428	C₂²	1	2	yes	—
83	C₁₃×#428	C₂²	1	1	yes	characteristic
84	C₁₃×#428	C₂²	1	4	yes	complemented
85	C₁₃×#428	C₂²	1	4	yes	complemented
86	C₁₃×#427	C₂²	1	4	yes	complemented
87	C₁₃×#427	C₂²	1	4	yes	complemented
88	C₁₃×#423	C₂²	1	1	yes	characteristic
89	C₁₃×#418	C₂²	1	2	yes	—
90	C₁₃×#418	C₂²	1	1	yes	characteristic
91	C₁₃×#417	C₂²	1	2	yes	—
92	C₁₃×#417	C₂²	1	1	yes	characteristic
93	C₁₃×#407	C₂²	1	2	yes	—
94	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	—	2	1	no	—
98	C₂²×D₄×C₁₃	—	2	2	no	—
99	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	—	2	1	no	—
102	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
103	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
104	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×D₈	C₂³	1	2	yes	—
106	C₂×C₁₃×M₁₆	—	2	8	no	—
107	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×#126	—	2	2	no	—
119	C₁₃×#126	—	2	2	no	—
120	C₁₃×#126	—	2	2	no	—
121	C₁₃×#125	—	2	2	no	—
122	C₁₃×#125	—	2	1	no	—
123	C₁₃×#125	C₂³	1	2	yes	—
124	C₁₃×#124	—	2	1	no	—
125	C₁₃×#124	—	2	4	no	—
126	C₁₃×#124	—	2	4	no	—
127	C₁₃×#124	—	2	4	no	—
128	C₁₃×#124	—	2	4	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#123	—	2	2	no	—
131	C₁₃×#123	—	2	2	no	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×#121	—	2	2	no	—
141	C₁₃×#121	—	2	2	no	—
142	C₁₃×#121	—	2	4	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	—	2	2	no	—
146	C₁₃×#121	—	2	2	no	—
147	C₁₃×#121	C₂³	1	4	yes	—
148	C₁₃×#121	C₂³	1	2	yes	—
149	C₁₃×#121	C₂³	1	4	yes	—
150	C₁₃×#121	C₂³	1	2	yes	—
151	C₁₃×#120	—	2	2	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
157	C₄×D₄×C₁₃	—	2	1	no	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	1	no	—
160	C₄×D₄×C₁₃	—	2	1	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	2	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
166	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
167	C₄×D₄×C₁₃	D₄	1	2	yes	—
168	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₁₃	C₂³	1	2	yes	—
170	C₄×D₄×C₁₃	C₂³	1	2	yes	—
171	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₁₃	C₂³	1	2	yes	—
174	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
175	C₁₃×#117	—	2	2	no	—
176	C₁₃×#117	—	2	2	no	—
177	C₁₃×#117	—	2	2	no	—
178	C₁₃×#117	—	2	2	no	—
179	C₁₃×#117	—	2	2	no	—
180	C₁₃×#117	—	2	2	no	—
181	C₁₃×#117	—	2	4	no	—
182	C₁₃×#117	—	2	1	no	—
183	C₁₃×#117	—	2	2	no	—
184	C₁₃×#117	—	2	1	no	—
185	C₁₃×#117	C₂³	1	1	yes	characteristic
186	C₁₃×#117	C₂³	1	2	yes	—
187	C₁₃×#117	C₂³	1	2	yes	—
188	C₁₃×#117	C₂³	1	2	yes	—
189	C₁₃×#117	C₂³	1	4	yes	—
190	C₁₃×#117	C₂³	1	4	yes	—
191	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
202	C₂×C₄²×C₁₃	—	2	2	no	—
203	C₂×C₄²×C₁₃	—	2	2	no	—
204	C₂×C₄²×C₁₃	—	2	1	no	—
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₁₃×#107	C₂³	1	2	yes	—
207	C₁₃×#107	C₂³	1	4	yes	—
208	C₁₃×#107	C₂³	1	4	yes	—
209	C₁₃×#107	C₂³	1	4	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×#106	C₂³	1	2	yes	—
212	C₁₃×#106	C₂³	1	4	yes	—
213	C₁₃×#106	C₂³	1	4	yes	—
214	C₁₃×#106	C₂³	1	4	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×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	4	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×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₁₃×#97	C₂³	1	2	yes	—
229	C₄×C₈×C₁₃	C₂³	1	2	yes	—
230	#61256	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂⁴×C₁₃	—	2	1	no	—
232	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	4	4	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	8	2	no	—
241	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	4	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	4	2	no	—
251	C₂×D₄×C₁₃	—	8	4	no	—
252	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	—	2	4	no	—
258	C₂²×C₄×C₁₃	—	2	4	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	4	4	no	—
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₁₃×SD₁₆	—	2	4	no	—
278	C₁₃×D₈	—	2	4	no	—
279	C₁₃×M₁₆	—	2	4	no	—
280	C₁₃×M₁₆	—	2	2	no	—
281	C₁₃×M₁₆	—	2	8	no	—
282	C₁₃×M₁₆	#41	1	4	yes	complemented
283	C₂×C₈×C₁₃	—	2	8	no	—
284	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
286	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	1	no	—
301	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
302	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	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	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	1	no	—
324	C₁₃×C₂²⋊C₄	—	2	1	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
327	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
328	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	—	2	1	no	—
331	C₄²×C₁₃	—	2	4	no	—
332	C₄²×C₁₃	—	2	4	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	1	no	—
335	C₄²×C₁₃	—	2	2	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	—	2	1	no	—
338	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
342	#3475	C₂×C₁₃	1	1	yes	characteristic, complemented
343	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3357	C₂×C₁₃	1	2	yes	complemented
345	#3354	C₂×C₁₃	1	2	yes	complemented
346	#3348	C₂×C₁₃	1	4	yes	complemented
347	#3347	C₂×C₁₃	1	4	yes	complemented
348	#3341	C₂×C₁₃	1	2	yes	complemented
349	#3340	C₂×C₁₃	1	2	yes	complemented
350	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3094	C₂×C₁₃	1	2	yes	complemented
352	#3093	C₂×C₁₃	1	2	yes	complemented
353	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3055	C₂×C₁₃	1	2	yes	complemented
356	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
357	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#2911	C₂×C₁₃	1	2	yes	complemented
359	C₂³×C₁₃	—	2	4	no	—
360	C₂³×C₁₃	—	2	1	no	—
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	4	2	no	—
363	C₂³×C₁₃	—	4	2	no	—
364	C₂³×C₁₃	—	4	2	no	—
365	C₂³×C₁₃	—	4	2	no	—
366	C₂³×C₁₃	—	4	2	no	—
367	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
368	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
369	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	Q₈×C₁₃	—	2	1	no	—
371	Q₈×C₁₃	—	2	1	no	—
372	Q₈×C₁₃	—	4	2	no	—
373	Q₈×C₁₃	—	8	1	no	—
374	Q₈×C₁₃	—	8	2	no	—
375	Q₈×C₁₃	—	8	2	no	—
376	D₄×C₁₃	—	2	2	no	—
377	D₄×C₁₃	—	2	2	no	—
378	D₄×C₁₃	—	2	1	no	—
379	D₄×C₁₃	—	2	2	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	2	1	no	—
382	D₄×C₁₃	—	4	2	no	—
383	D₄×C₁₃	—	4	4	no	—
384	D₄×C₁₃	—	4	2	no	—
385	D₄×C₁₃	—	4	2	no	—
386	D₄×C₁₃	—	8	2	no	—
387	D₄×C₁₃	—	8	4	no	—
388	D₄×C₁₃	—	8	4	no	—
389	C₂×C₄×C₁₃	—	2	4	no	—
390	C₂×C₄×C₁₃	—	2	4	no	—
391	C₂×C₄×C₁₃	—	2	4	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	4	no	—
404	C₂×C₄×C₁₃	—	4	1	no	—
405	C₂×C₄×C₁₃	—	4	4	no	—
406	C₂×C₄×C₁₃	—	4	2	no	—
407	C₂×C₄×C₁₃	—	4	4	no	—
408	C₂×C₄×C₁₃	—	4	4	no	—
409	C₂×C₄×C₁₃	—	4	2	no	—
410	C₂×C₄×C₁₃	—	4	4	no	—
411	C₂×C₄×C₁₃	—	4	2	no	—
412	C₂×C₄×C₁₃	—	8	1	no	—
413	C₂×C₄×C₁₃	—	8	2	no	—
414	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
422	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
423	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
424	C₈×C₁₃	—	2	4	no	—
425	C₈×C₁₃	—	2	2	no	—
426	C₈×C₁₃	C₂×#41	1	4	yes	—
427	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
429	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	#555	—	2	1	no	—
431	#555	—	2	2	no	—
432	#555	—	2	1	no	—
433	#555	C₂²×C₁₃	1	2	yes	—
434	#555	C₂²×C₁₃	1	4	yes	—
435	#555	C₂²×C₁₃	1	2	yes	—
436	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	#553	C₂²×C₁₃	1	2	yes	complemented
439	#552	—	2	1	no	—
440	#552	C₂²×C₁₃	1	2	yes	complemented
441	#551	—	2	2	no	—
442	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
443	#546	—	2	1	no	—
444	#533	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
446	#529	—	2	2	no	—
447	#529	—	2	1	no	—
448	C₂×#124	—	2	2	no	—
449	#525	C₂²×C₁₃	1	2	yes	—
450	C₂×#121	—	2	1	no	—
451	C₂×#121	C₂²×C₁₃	1	2	yes	—
452	C₄×#41	—	2	1	no	—
453	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×#117	—	2	1	no	—
457	C₂×#117	C₂²×C₁₃	1	2	yes	—
458	C₂×#117	C₂²×C₁₃	1	2	yes	—
459	#501	C₂²×C₁₃	1	4	yes	complemented
460	#500	C₂²×C₁₃	1	2	yes	complemented
461	#498	C₂²×C₁₃	1	2	yes	complemented
462	#485	C₂²×C₁₃	1	4	yes	complemented
463	#485	C₂²×C₁₃	1	4	yes	complemented
464	#482	C₂²×C₁₃	1	4	yes	complemented
465	#482	C₂²×C₁₃	1	4	yes	complemented
466	#482	C₂²×C₁₃	1	4	yes	complemented
467	#482	C₂²×C₁₃	1	4	yes	complemented
468	#481	C₂²×C₁₃	1	4	yes	complemented
469	#480	C₂²×C₁₃	1	4	yes	complemented
470	#478	C₂²×C₁₃	1	4	yes	complemented
471	#477	C₂²×C₁₃	1	2	yes	complemented
472	#476	C₂²×C₁₃	1	2	yes	complemented
473	#476	C₂²×C₁₃	1	2	yes	complemented
474	#475	C₂²×C₁₃	1	2	yes	complemented
475	#474	C₂²×C₁₃	1	2	yes	complemented
476	#474	C₂²×C₁₃	1	2	yes	complemented
477	#469	C₂²×C₁₃	1	4	yes	complemented
478	#468	C₂²×C₁₃	1	4	yes	complemented
479	#466	C₂²×C₁₃	1	4	yes	complemented
480	#465	C₂²×C₁₃	1	4	yes	complemented
481	#442	C₂²×C₁₃	1	2	yes	complemented
482	#440	C₂²×C₁₃	1	2	yes	complemented
483	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
484	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
485	#436	C₂²×C₁₃	1	2	yes	complemented
486	#435	C₂²×C₁₃	1	4	yes	complemented
487	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
488	#428	C₂²×C₁₃	1	2	yes	—
489	#428	C₂²×C₁₃	1	2	yes	—
490	#428	C₂²×C₁₃	1	2	yes	—
491	#428	C₂²×C₁₃	1	2	yes	—
492	#428	C₂²×C₁₃	1	1	yes	characteristic
493	#428	C₂²×C₁₃	1	4	yes	complemented
494	#428	C₂²×C₁₃	1	4	yes	complemented
495	#427	C₂²×C₁₃	1	4	yes	complemented
496	#427	C₂²×C₁₃	1	4	yes	complemented
497	#423	C₂²×C₁₃	1	1	yes	characteristic
498	#418	C₂²×C₁₃	1	2	yes	—
499	#418	C₂²×C₁₃	1	1	yes	characteristic
500	#417	C₂²×C₁₃	1	2	yes	—
501	#417	C₂²×C₁₃	1	1	yes	characteristic
502	#407	C₂²×C₁₃	1	2	yes	—
503	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	2	2	no	—
509	C₂²×C₁₃	—	2	2	no	—
510	C₂²×C₁₃	—	2	2	no	—
511	C₂²×C₁₃	—	2	2	no	—
512	C₂²×C₁₃	—	4	1	no	—
513	C₂²×C₁₃	—	4	2	no	—
514	C₂²×C₁₃	—	4	1	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	1	no	—
518	C₂²×C₁₃	—	8	4	no	—
519	C₂²×C₁₃	—	8	4	no	—
520	C₂²×C₁₃	#547	1	2	yes	—
521	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
522	C₄×C₁₃	—	2	1	no	—
523	C₄×C₁₃	—	2	1	no	—
524	C₄×C₁₃	—	2	2	no	—
525	C₄×C₁₃	—	2	2	no	—
526	C₄×C₁₃	—	2	1	no	—
527	C₄×C₁₃	—	4	4	no	—
528	C₄×C₁₃	—	4	1	no	—
529	C₄×C₁₃	—	4	2	no	—
530	C₄×C₁₃	—	4	1	no	—
531	C₄×C₁₃	—	4	2	no	—
532	C₄×C₁₃	—	4	1	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	#547	1	2	yes	—
535	C₄×C₁₃	#575	1	2	yes	—
536	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
537	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
538	C₂×#41	—	2	1	no	—
539	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
540	C₂²×Q₈	—	2	1	no	—
541	C₂²×D₄	—	2	2	no	—
542	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
544	C₂³×C₄	—	2	1	no	—
545	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
546	AGL(1,ℤ/8)	—	2	4	no	—
547	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
548	C₂×D₈	C₂³×C₁₃	1	2	yes	—
549	C₂×M₁₆	—	2	8	no	—
550	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
551	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
552	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
553	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
554	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
555	C₄⋊Q₈	—	2	1	no	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
559	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
560	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
561	#126	—	2	2	no	—
562	#126	—	2	2	no	—
563	#126	—	2	2	no	—
564	#125	—	2	2	no	—
565	#125	—	2	1	no	—
566	#125	C₂³×C₁₃	1	2	yes	—
567	#124	—	2	1	no	—
568	#124	—	2	4	no	—
569	#124	—	2	4	no	—
570	#124	—	2	4	no	—
571	#124	—	2	4	no	—
572	#124	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
582	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	4	no	—
586	#121	—	2	2	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	C₂³×C₁₃	1	4	yes	—
591	#121	C₂³×C₁₃	1	4	yes	—
592	#121	C₂³×C₁₃	1	2	yes	—
593	#121	C₂³×C₁₃	1	2	yes	—
594	#120	—	2	2	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
609	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
610	C₄×D₄	D₄×C₁₃	1	2	yes	—
611	C₄×D₄	C₂³×C₁₃	1	2	yes	—
612	C₄×D₄	C₂³×C₁₃	1	2	yes	—
613	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₁₃	1	2	yes	—
617	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
618	#117	—	2	2	no	—
619	#117	—	2	2	no	—
620	#117	—	2	2	no	—
621	#117	—	2	2	no	—
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	—	2	4	no	—
625	#117	—	2	1	no	—
626	#117	—	2	2	no	—
627	#117	—	2	1	no	—
628	#117	C₂³×C₁₃	1	1	yes	characteristic
629	#117	C₂³×C₁₃	1	2	yes	—
630	#117	C₂³×C₁₃	1	2	yes	—
631	#117	C₂³×C₁₃	1	2	yes	—
632	#117	C₂³×C₁₃	1	4	yes	—
633	#117	C₂³×C₁₃	1	4	yes	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₂²⋊C₄	—	2	2	no	—
641	C₂×C₂²⋊C₄	—	2	2	no	—
642	C₂×C₂²⋊C₄	—	2	2	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
645	C₂×C₄²	—	2	2	no	—
646	C₂×C₄²	—	2	2	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
649	#107	C₂³×C₁₃	1	2	yes	—
650	#107	C₂³×C₁₃	1	4	yes	—
651	#107	C₂³×C₁₃	1	4	yes	—
652	#107	C₂³×C₁₃	1	4	yes	—
653	#107	C₂³×C₁₃	1	4	yes	—
654	#106	C₂³×C₁₃	1	2	yes	—
655	#106	C₂³×C₁₃	1	4	yes	—
656	#106	C₂³×C₁₃	1	4	yes	—
657	#106	C₂³×C₁₃	1	4	yes	—
658	#106	C₂³×C₁₃	1	4	yes	—
659	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
660	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
661	#103	C₂³×C₁₃	1	2	yes	—
662	#103	C₂³×C₁₃	1	4	yes	—
663	#102	C₂³×C₁₃	1	2	yes	—
664	#102	C₂³×C₁₃	1	4	yes	—
665	#102	C₂³×C₁₃	1	2	yes	—
666	#102	C₂³×C₁₃	1	2	yes	—
667	#102	C₂³×C₁₃	1	4	yes	—
668	#102	C₂³×C₁₃	1	4	yes	—
669	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
670	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
671	#97	C₂³×C₁₃	1	2	yes	—
672	C₄×C₈	C₂³×C₁₃	1	2	yes	—
673	C₂×C₁₃	—	2	2	no	—
674	C₂×C₁₃	—	4	2	no	—
675	C₂×C₁₃	—	4	2	no	—
676	C₂×C₁₃	—	8	1	no	—
677	C₂×C₁₃	—	8	2	no	—
678	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
679	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
680	C₂×C₁₃	#3585	1	1	yes	characteristic
681	C₂⁴	—	2	1	no	—
682	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
683	#41	—	2	2	no	—
684	#41	—	2	2	no	—
685	#41	—	4	4	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	8	2	no	—
691	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	8	4	no	—
702	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
705	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
706	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	4	4	no	—
719	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
720	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
721	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	SD₁₆	—	2	4	no	—
728	D₈	—	2	4	no	—
729	M₁₆	—	2	4	no	—
730	M₁₆	—	2	2	no	—
731	M₁₆	—	2	8	no	—
732	M₁₆	C₁₃×#41	1	4	yes	complemented
733	C₂×C₈	—	2	8	no	—
734	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
735	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
736	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
756	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
759	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
777	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	1	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	1	no	—
788	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
789	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
790	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
791	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
792	C₁₃	#61256	1	1	yes	characteristic, direct product factor, Sylow
793	C₂³	—	2	4	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	2	no	—
800	C₂³	—	4	2	no	—
801	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
802	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
803	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
804	Q₈	—	2	1	no	—
805	Q₈	—	2	1	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	8	2	no	—
808	Q₈	—	8	2	no	—
809	Q₈	—	8	1	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	1	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	2	1	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	2	no	—
819	D₄	—	4	2	no	—
820	D₄	—	8	4	no	—
821	D₄	—	8	4	no	—
822	D₄	—	8	2	no	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	8	1	no	—
847	C₂×C₄	—	8	2	no	—
848	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
849	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
850	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
855	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
856	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
857	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
858	C₈	—	2	4	no	—
859	C₈	—	2	2	no	—
860	C₈	C₂×C₁₃×#41	1	4	yes	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	8	4	no	—
876	C₂²	—	8	4	no	—
877	C₂²	C₁₃×#547	1	2	yes	—
878	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	4	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	1	no	—
891	C₄	C₁₃×#547	1	2	yes	—
892	C₄	C₁₃×#575	1	2	yes	—
893	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
894	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
895	C₂	—	2	2	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	2	no	—
898	C₂	—	8	2	no	—
899	C₂	—	8	1	no	—
900	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
901	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
902	C₂	C₁₃×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3475	C₂	semidirect
2. C₂×C₁₃×#555	C₂	semidirect
3. C₁₃×#3357	C₂	semidirect
4. C₁₃×#3354	C₂	semidirect
5. C₁₃×#3348	C₂	semidirect
6. C₁₃×#3347	C₂	semidirect
7. C₁₃×#3341	C₂	semidirect
8. C₁₃×#3340	C₂	semidirect
9. C₁₃×#3165	C₂	semidirect
10. C₁₃×#3094	C₂	semidirect
11. C₁₃×#3093	C₂	semidirect
12. C₁₃×#3079	C₂	semidirect
13. C₁₃×#3077	C₂	semidirect
14. C₁₃×#3055	C₂	semidirect
15. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
16. D₄×C₁₃×M₁₆	C₂	semidirect
17. C₁₃×#2911	C₂	semidirect
20. C₁₃×#556	C₂²	semidirect
27. C₁₃×#555	C₂²	semidirect
28. C₁₃×#554	C₂²	semidirect
29. C₁₃×#553	C₂²	semidirect
31. C₁₃×#552	C₂²	semidirect
33. C₁₃×#547	C₂²	semidirect
50. C₁₃×#501	C₂²	semidirect
51. C₁₃×#500	C₂²	semidirect
52. C₁₃×#498	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
55. C₁₃×#482	C₂²	semidirect
56. C₁₃×#482	C₂²	semidirect
57. C₁₃×#482	C₂²	semidirect
58. C₁₃×#482	C₂²	semidirect
59. C₁₃×#481	C₂²	semidirect
60. C₁₃×#480	C₂²	semidirect
61. C₁₃×#478	C₂²	semidirect
62. C₁₃×#477	C₂²	semidirect
63. C₁₃×#476	C₂²	semidirect
64. C₁₃×#476	C₂²	semidirect
65. C₁₃×#475	C₂²	semidirect
66. C₁₃×#474	C₂²	semidirect
67. C₁₃×#474	C₂²	semidirect
68. C₁₃×#469	C₂²	semidirect
69. C₁₃×#468	C₂²	semidirect
70. C₁₃×#466	C₂²	semidirect
71. C₁₃×#465	C₂²	semidirect
72. C₁₃×#442	C₂²	semidirect
73. C₁₃×#440	C₂²	semidirect
74. C₄×C₁₃×SD₁₆	C₂²	semidirect
75. C₄×C₁₃×D₈	C₂²	semidirect
76. C₁₃×#436	C₂²	semidirect
77. C₁₃×#435	C₂²	semidirect
78. C₈×D₄×C₁₃	C₂²	semidirect
84. C₁₃×#428	C₂²	semidirect
85. C₁₃×#428	C₂²	semidirect
86. C₁₃×#427	C₂²	semidirect
87. C₁₃×#427	C₂²	semidirect
230. #61256	C₁₃	direct (N × H)
282. C₁₃×M₁₆	#41	semidirect
342. #3475	C₂×C₁₃	semidirect
343. C₂×#555	C₂×C₁₃	semidirect
344. #3357	C₂×C₁₃	semidirect
345. #3354	C₂×C₁₃	semidirect
346. #3348	C₂×C₁₃	semidirect
347. #3347	C₂×C₁₃	semidirect
348. #3341	C₂×C₁₃	semidirect
349. #3340	C₂×C₁₃	semidirect
350. #3165	C₂×C₁₃	semidirect
351. #3094	C₂×C₁₃	semidirect
352. #3093	C₂×C₁₃	semidirect
353. #3079	C₂×C₁₃	semidirect
354. #3077	C₂×C₁₃	semidirect
355. #3055	C₂×C₁₃	semidirect
356. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
357. D₄×M₁₆	C₂×C₁₃	semidirect
358. #2911	C₂×C₁₃	semidirect
429. #556	C₂²×C₁₃	semidirect
436. #555	C₂²×C₁₃	semidirect
437. #554	C₂²×C₁₃	semidirect
438. #553	C₂²×C₁₃	semidirect
440. #552	C₂²×C₁₃	semidirect
442. #547	C₂²×C₁₃	semidirect
459. #501	C₂²×C₁₃	semidirect
460. #500	C₂²×C₁₃	semidirect
461. #498	C₂²×C₁₃	semidirect
462. #485	C₂²×C₁₃	semidirect
463. #485	C₂²×C₁₃	semidirect
464. #482	C₂²×C₁₃	semidirect
465. #482	C₂²×C₁₃	semidirect
466. #482	C₂²×C₁₃	semidirect
467. #482	C₂²×C₁₃	semidirect
468. #481	C₂²×C₁₃	semidirect
469. #480	C₂²×C₁₃	semidirect
470. #478	C₂²×C₁₃	semidirect
471. #477	C₂²×C₁₃	semidirect
472. #476	C₂²×C₁₃	semidirect
473. #476	C₂²×C₁₃	semidirect
474. #475	C₂²×C₁₃	semidirect
475. #474	C₂²×C₁₃	semidirect
476. #474	C₂²×C₁₃	semidirect
477. #469	C₂²×C₁₃	semidirect
478. #468	C₂²×C₁₃	semidirect
479. #466	C₂²×C₁₃	semidirect
480. #465	C₂²×C₁₃	semidirect
481. #442	C₂²×C₁₃	semidirect
482. #440	C₂²×C₁₃	semidirect
483. C₄×SD₁₆	C₂²×C₁₃	semidirect
484. C₄×D₈	C₂²×C₁₃	semidirect
485. #436	C₂²×C₁₃	semidirect
486. #435	C₂²×C₁₃	semidirect
487. C₈×D₄	C₂²×C₁₃	semidirect
493. #428	C₂²×C₁₃	semidirect
494. #428	C₂²×C₁₃	semidirect
495. #427	C₂²×C₁₃	semidirect
496. #427	C₂²×C₁₃	semidirect
732. M₁₆	C₁₃×#41	semidirect
792. C₁₃	#61256	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×#3475	2
C₂×C₁₃×#555	2
C₁₃×#3357	2
C₁₃×#3354	2
C₁₃×#3348	2
C₁₃×#3347	2
C₁₃×#3341	2
C₁₃×#3340	2
C₁₃×#3165	2
C₁₃×#3094	2
C₁₃×#3093	2
C₁₃×#3079	2
C₁₃×#3077	2
C₁₃×#3055	2
C₄×C₁₃×AGL(1,ℤ/8)	2
D₄×C₁₃×M₁₆	2
C₁₃×#2911	2
#61256	13

Subgroups — C13×#61256 #15747595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61256 #15747595