Subgroups — C₁₃×#61949 #15748288

Order 3328.

1942 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3305	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3296	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3284	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3280	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3212	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3106	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3035	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
20	C₁₃×#559	—	2	1	no	—
21	C₁₃×#559	C₂²	1	2	yes	complemented
22	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#553	—	2	1	no	—
26	C₁₃×#552	—	2	1	no	—
27	C₁₃×#552	C₂²	1	2	yes	—
28	C₁₃×#551	—	2	2	no	—
29	C₁₃×#550	—	2	1	no	—
30	C₁₃×#550	C₂²	1	2	yes	complemented
31	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#546	—	2	2	no	—
33	C₁₃×#546	C₂²	1	2	yes	—
34	C₁₃×#546	C₂²	1	4	yes	—
35	C₁₃×#540	—	2	2	no	—
36	C₁₃×#535	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	2	yes	complemented
40	C₁₃×#532	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
42	C₁₃×#529	—	2	2	no	—
43	C₁₃×#529	C₂²	1	2	yes	complemented
44	C₁₃×#525	—	2	1	no	—
45	C₁₃×#518	—	2	1	no	—
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#117	—	2	1	no	—
50	C₁₃×#495	C₂²	1	4	yes	complemented
51	C₁₃×#492	C₂²	1	2	yes	complemented
52	C₁₃×#488	C₂²	1	4	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	complemented
54	C₁₃×#483	C₂²	1	2	yes	—
55	C₁₃×#482	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	complemented
57	C₁₃×#477	C₂²	1	2	yes	complemented
58	C₁₃×#477	C₂²	1	2	yes	complemented
59	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#467	C₂²	1	4	yes	—
62	C₁₃×#466	C₂²	1	4	yes	complemented
63	C₁₃×#465	C₂²	1	4	yes	complemented
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	complemented
66	C₁₃×#463	C₂²	1	4	yes	complemented
67	C₁₃×#462	C₂²	1	2	yes	complemented
68	C₁₃×#462	C₂²	1	2	yes	complemented
69	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#460	C₂²	1	2	yes	complemented
72	C₁₃×#460	C₂²	1	2	yes	complemented
73	C₁₃×#459	C₂²	1	2	yes	—
74	C₁₃×#459	C₂²	1	2	yes	—
75	C₁₃×#459	C₂²	1	2	yes	—
76	C₁₃×#459	C₂²	1	2	yes	—
77	C₁₃×#452	C₂²	1	4	yes	complemented
78	C₁₃×#450	C₂²	1	2	yes	—
79	C₁₃×#450	C₂²	1	4	yes	—
80	C₁₃×#449	C₂²	1	4	yes	complemented
81	C₁₃×#449	C₂²	1	4	yes	complemented
82	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
84	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
86	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
87	C₈×D₄×C₁₃	C₂²	1	4	yes	—
88	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
89	C₁₃×#431	C₂²	1	1	yes	characteristic
90	C₁₃×#431	C₂²	1	2	yes	complemented
91	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₁₃×#416	C₂²	1	4	yes	complemented
94	C₂×C₁₃×#102	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂×C₁₃×#41	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	—	2	1	no	—
104	C₁₃×#135	—	4	8	no	—
105	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×D₈	—	4	4	no	—
111	C₂×C₁₃×D₈	C₂³	1	4	yes	—
112	C₂×C₁₃×D₈	C₂³	1	4	yes	—
113	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
114	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×#127	—	2	2	no	—
120	C₁₃×#127	—	2	1	no	—
121	C₁₃×#127	—	2	1	no	—
122	C₁₃×#127	C₂³	1	2	yes	—
123	C₁₃×#127	C₂³	1	2	yes	—
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	—	2	1	no	—
129	C₁₃×#125	—	2	1	no	—
130	C₁₃×#125	C₂³	1	2	yes	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	C₂³	1	2	yes	—
135	C₁₃×#124	C₂³	1	4	yes	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	4	no	—
140	C₁₃×#123	—	2	4	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	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	C₂³	1	2	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₁₃×#121	—	2	1	no	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	4	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#121	C₂³	1	4	yes	—
160	C₁₃×#120	—	2	2	no	—
161	C₁₃×#120	—	2	4	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	—	2	1	no	—
164	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	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	2	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	D₄	1	2	yes	—
180	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₄×D₄×C₁₃	C₂³	1	4	yes	—
183	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	—	2	1	no	—
191	C₁₃×#117	—	2	1	no	—
192	C₁₃×#117	—	2	1	no	—
193	C₁₃×#117	—	2	2	no	—
194	C₁₃×#117	—	2	2	no	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	D₄	1	1	yes	characteristic
197	C₁₃×#117	D₄	1	2	yes	—
198	C₁₃×#117	C₂³	1	2	yes	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
203	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₂×C₄²×C₁₃	—	2	2	no	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₁₃×#107	C₂³	1	4	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×#106	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	C₄×C₈×C₁₃	C₂³	1	4	yes	—
230	#61949	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂⁴×C₁₃	—	2	1	no	—
232	C₂⁴×C₁₃	—	2	2	no	—
233	C₁₃×#41	—	2	4	no	—
234	C₁₃×#41	—	2	4	no	—
235	C₁₃×#41	—	4	2	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₁₃×#41	—	8	4	no	—
239	C₂×Q₈×C₁₃	—	2	1	no	—
240	C₂×Q₈×C₁₃	—	2	1	no	—
241	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	2	4	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	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	4	1	no	—
256	C₂×D₄×C₁₃	—	4	2	no	—
257	C₂×D₄×C₁₃	—	4	2	no	—
258	C₂×D₄×C₁₃	—	4	4	no	—
259	C₂×D₄×C₁₃	—	8	2	no	—
260	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
263	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	4	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	4	4	no	—
275	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₁₃×Q₁₆	—	4	4	no	—
282	C₁₃×SD₁₆	—	2	4	no	—
283	C₁₃×SD₁₆	—	4	2	no	—
284	C₁₃×SD₁₆	—	4	4	no	—
285	C₁₃×SD₁₆	—	4	4	no	—
286	C₁₃×D₈	—	2	8	no	—
287	C₁₃×D₈	—	4	4	no	—
288	C₂×C₈×C₁₃	—	4	2	no	—
289	C₂×C₈×C₁₃	—	4	4	no	—
290	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
291	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
292	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
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	2	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	1	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
309	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
313	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
314	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	1	no	—
326	C₁₃×C₂²⋊C₄	—	2	1	no	—
327	C₁₃×C₂²⋊C₄	—	2	1	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	4	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	4	no	—
332	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
333	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
334	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
335	C₄²×C₁₃	—	2	2	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	—	2	2	no	—
338	C₄²×C₁₃	—	2	2	no	—
339	C₄²×C₁₃	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	C₂×D₄	1	2	yes	—
341	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₁₃	C₂⁴	1	2	yes	—
344	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
346	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3475	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3394	C₂×C₁₃	1	2	yes	complemented
349	#3361	C₂×C₁₃	1	2	yes	complemented
350	#3305	C₂×C₁₃	1	2	yes	complemented
351	#3296	C₂×C₁₃	1	4	yes	complemented
352	#3284	C₂×C₁₃	1	2	yes	complemented
353	#3280	C₂×C₁₃	1	4	yes	complemented
354	#3249	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3247	C₂×C₁₃	1	2	yes	complemented
356	#3212	C₂×C₁₃	1	2	yes	complemented
357	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3106	C₂×C₁₃	1	2	yes	complemented
359	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3035	C₂×C₁₃	1	2	yes	complemented
361	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#2988	C₂×C₁₃	1	1	yes	characteristic, complemented
363	C₂³×C₁₃	—	2	1	no	—
364	C₂³×C₁₃	—	2	1	no	—
365	C₂³×C₁₃	—	2	4	no	—
366	C₂³×C₁₃	—	4	2	no	—
367	C₂³×C₁₃	—	4	2	no	—
368	C₂³×C₁₃	—	4	4	no	—
369	C₂³×C₁₃	—	8	1	no	—
370	C₂³×C₁₃	—	8	2	no	—
371	C₂³×C₁₃	—	8	2	no	—
372	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
373	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	Q₈×C₁₃	—	2	2	no	—
375	Q₈×C₁₃	—	2	2	no	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	2	2	no	—
378	Q₈×C₁₃	—	2	2	no	—
379	Q₈×C₁₃	—	4	2	no	—
380	Q₈×C₁₃	—	8	1	no	—
381	D₄×C₁₃	—	2	4	no	—
382	D₄×C₁₃	—	2	2	no	—
383	D₄×C₁₃	—	2	4	no	—
384	D₄×C₁₃	—	2	1	no	—
385	D₄×C₁₃	—	2	1	no	—
386	D₄×C₁₃	—	2	1	no	—
387	D₄×C₁₃	—	2	4	no	—
388	D₄×C₁₃	—	4	2	no	—
389	D₄×C₁₃	—	4	4	no	—
390	D₄×C₁₃	—	4	4	no	—
391	D₄×C₁₃	—	4	4	no	—
392	D₄×C₁₃	—	4	4	no	—
393	D₄×C₁₃	—	8	2	no	—
394	D₄×C₁₃	—	8	2	no	—
395	D₄×C₁₃	—	8	2	no	—
396	D₄×C₁₃	—	8	4	no	—
397	D₄×C₁₃	—	8	4	no	—
398	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
399	C₂×C₄×C₁₃	—	2	4	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	4	1	no	—
411	C₂×C₄×C₁₃	—	4	2	no	—
412	C₂×C₄×C₁₃	—	4	4	no	—
413	C₂×C₄×C₁₃	—	4	2	no	—
414	C₂×C₄×C₁₃	—	4	2	no	—
415	C₂×C₄×C₁₃	—	4	2	no	—
416	C₂×C₄×C₁₃	—	4	2	no	—
417	C₂×C₄×C₁₃	—	4	2	no	—
418	C₂×C₄×C₁₃	—	8	2	no	—
419	C₂×C₄×C₁₃	—	8	4	no	—
420	C₂×C₄×C₁₃	—	8	4	no	—
421	C₂×C₄×C₁₃	#135	1	4	yes	complemented
422	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
431	C₈×C₁₃	—	2	4	no	—
432	C₈×C₁₃	—	2	2	no	—
433	C₈×C₁₃	—	2	2	no	—
434	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
435	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
436	#559	—	2	1	no	—
437	#559	C₂²×C₁₃	1	2	yes	complemented
438	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
440	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#553	—	2	1	no	—
442	#552	—	2	1	no	—
443	#552	C₂²×C₁₃	1	2	yes	—
444	#551	—	2	2	no	—
445	#550	—	2	1	no	—
446	#550	C₂²×C₁₃	1	2	yes	complemented
447	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	#546	—	2	2	no	—
449	#546	C₂²×C₁₃	1	2	yes	—
450	#546	C₂²×C₁₃	1	4	yes	—
451	#540	—	2	2	no	—
452	#535	—	2	1	no	—
453	#533	C₂²×C₁₃	1	1	yes	characteristic
454	#533	C₂²×C₁₃	1	1	yes	characteristic
455	#532	C₂²×C₁₃	1	2	yes	complemented
456	#532	C₂²×C₁₃	1	2	yes	complemented
457	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
458	#529	—	2	2	no	—
459	#529	C₂²×C₁₃	1	2	yes	complemented
460	#525	—	2	1	no	—
461	#518	—	2	1	no	—
462	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
463	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
464	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
465	C₂×#117	—	2	1	no	—
466	#495	C₂²×C₁₃	1	4	yes	complemented
467	#492	C₂²×C₁₃	1	2	yes	complemented
468	#488	C₂²×C₁₃	1	4	yes	complemented
469	#486	C₂²×C₁₃	1	2	yes	complemented
470	#483	C₂²×C₁₃	1	2	yes	—
471	#482	C₂²×C₁₃	1	4	yes	complemented
472	#478	C₂²×C₁₃	1	4	yes	complemented
473	#477	C₂²×C₁₃	1	2	yes	complemented
474	#477	C₂²×C₁₃	1	2	yes	complemented
475	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
476	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	#467	C₂²×C₁₃	1	4	yes	—
478	#466	C₂²×C₁₃	1	4	yes	complemented
479	#465	C₂²×C₁₃	1	4	yes	complemented
480	#464	C₂²×C₁₃	1	4	yes	complemented
481	#463	C₂²×C₁₃	1	4	yes	complemented
482	#463	C₂²×C₁₃	1	4	yes	complemented
483	#462	C₂²×C₁₃	1	2	yes	complemented
484	#462	C₂²×C₁₃	1	2	yes	complemented
485	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	#460	C₂²×C₁₃	1	2	yes	complemented
488	#460	C₂²×C₁₃	1	2	yes	complemented
489	#459	C₂²×C₁₃	1	2	yes	—
490	#459	C₂²×C₁₃	1	2	yes	—
491	#459	C₂²×C₁₃	1	2	yes	—
492	#459	C₂²×C₁₃	1	2	yes	—
493	#452	C₂²×C₁₃	1	4	yes	complemented
494	#450	C₂²×C₁₃	1	2	yes	—
495	#450	C₂²×C₁₃	1	4	yes	—
496	#449	C₂²×C₁₃	1	4	yes	complemented
497	#449	C₂²×C₁₃	1	4	yes	complemented
498	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
499	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
500	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
501	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
502	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
503	C₈×D₄	C₂²×C₁₃	1	4	yes	—
504	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
505	#431	C₂²×C₁₃	1	1	yes	characteristic
506	#431	C₂²×C₁₃	1	2	yes	complemented
507	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
508	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
509	#416	C₂²×C₁₃	1	4	yes	complemented
510	C₂×#102	C₂²×C₁₃	1	2	yes	—
511	C₂²×C₁₃	—	2	1	no	—
512	C₂²×C₁₃	—	2	1	no	—
513	C₂²×C₁₃	—	2	2	no	—
514	C₂²×C₁₃	—	2	2	no	—
515	C₂²×C₁₃	—	2	2	no	—
516	C₂²×C₁₃	—	2	2	no	—
517	C₂²×C₁₃	—	4	1	no	—
518	C₂²×C₁₃	—	4	1	no	—
519	C₂²×C₁₃	—	4	4	no	—
520	C₂²×C₁₃	—	4	1	no	—
521	C₂²×C₁₃	—	4	4	no	—
522	C₂²×C₁₃	—	4	1	no	—
523	C₂²×C₁₃	—	4	1	no	—
524	C₂²×C₁₃	—	4	4	no	—
525	C₂²×C₁₃	—	8	4	no	—
526	C₂²×C₁₃	—	16	4	no	—
527	C₂²×C₁₃	C₂×#135	1	2	yes	—
528	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
529	C₄×C₁₃	—	2	1	no	—
530	C₄×C₁₃	—	2	2	no	—
531	C₄×C₁₃	—	2	1	no	—
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	1	no	—
534	C₄×C₁₃	—	2	2	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	2	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	—	4	2	no	—
539	C₄×C₁₃	—	4	1	no	—
540	C₄×C₁₃	—	4	1	no	—
541	C₄×C₁₃	C₂×#135	1	2	yes	—
542	C₄×C₁₃	C₂×#135	1	2	yes	—
543	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
544	C₄×C₁₃	#585	1	1	yes	characteristic
545	C₂×#41	—	2	2	no	—
546	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
547	C₂×#41	C₂³×C₁₃	1	2	yes	—
548	C₂×#41	C₂³×C₁₃	1	4	yes	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
553	C₂³×C₄	—	2	1	no	—
554	#135	—	4	8	no	—
555	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
556	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
558	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
559	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
560	C₂×D₈	—	4	4	no	—
561	C₂×D₈	C₂³×C₁₃	1	4	yes	—
562	C₂×D₈	C₂³×C₁₃	1	4	yes	—
563	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
564	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
565	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
568	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
569	#127	—	2	2	no	—
570	#127	—	2	1	no	—
571	#127	—	2	1	no	—
572	#127	C₂³×C₁₃	1	2	yes	—
573	#127	C₂³×C₁₃	1	2	yes	—
574	#126	—	2	2	no	—
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#125	—	2	2	no	—
578	#125	—	2	1	no	—
579	#125	—	2	1	no	—
580	#125	C₂³×C₁₃	1	2	yes	—
581	#124	—	2	2	no	—
582	#124	—	2	2	no	—
583	#124	—	2	2	no	—
584	#124	C₂³×C₁₃	1	2	yes	—
585	#124	C₂³×C₁₃	1	4	yes	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	4	no	—
590	#123	—	2	4	no	—
591	#123	—	2	2	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
600	#121	—	2	1	no	—
601	#121	—	2	1	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	—	2	2	no	—
606	#121	—	2	4	no	—
607	#121	—	2	4	no	—
608	#121	C₂³×C₁₃	1	2	yes	—
609	#121	C₂³×C₁₃	1	4	yes	—
610	#120	—	2	2	no	—
611	#120	—	2	4	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	—	2	1	no	—
614	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
616	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
617	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
618	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	D₄×C₁₃	1	2	yes	—
630	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
633	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₁₃	1	2	yes	—
636	C₄×D₄	C₂³×C₁₃	1	4	yes	—
637	C₄×D₄	C₂³×C₁₃	1	2	yes	—
638	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
639	#117	—	2	1	no	—
640	#117	—	2	1	no	—
641	#117	—	2	1	no	—
642	#117	—	2	1	no	—
643	#117	—	2	2	no	—
644	#117	—	2	2	no	—
645	#117	—	2	2	no	—
646	#117	D₄×C₁₃	1	1	yes	characteristic
647	#117	D₄×C₁₃	1	2	yes	—
648	#117	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	2	no	—
654	C₂×C₂²⋊C₄	—	2	4	no	—
655	C₂×C₄²	—	2	2	no	—
656	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
658	#107	C₂³×C₁₃	1	4	yes	—
659	#106	C₂³×C₁₃	1	2	yes	—
660	#106	C₂³×C₁₃	1	2	yes	—
661	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
662	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
663	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
664	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
665	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
666	#103	C₂³×C₁₃	1	2	yes	—
667	#103	C₂³×C₁₃	1	4	yes	—
668	#103	C₂³×C₁₃	1	4	yes	—
669	#103	C₂³×C₁₃	1	2	yes	—
670	#102	C₂³×C₁₃	1	4	yes	—
671	#102	C₂³×C₁₃	1	4	yes	—
672	#102	C₂³×C₁₃	1	4	yes	—
673	#102	C₂³×C₁₃	1	2	yes	—
674	#102	C₂³×C₁₃	1	4	yes	—
675	#102	C₂³×C₁₃	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
678	C₄×C₈	C₂³×C₁₃	1	2	yes	—
679	C₄×C₈	C₂³×C₁₃	1	4	yes	—
680	C₂×C₁₃	—	2	2	no	—
681	C₂×C₁₃	—	4	2	no	—
682	C₂×C₁₃	—	4	2	no	—
683	C₂×C₁₃	—	8	1	no	—
684	C₂×C₁₃	—	8	4	no	—
685	C₂×C₁₃	#3488	1	1	yes	characteristic
686	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
687	C₂×C₁₃	#3585	1	1	yes	characteristic
688	C₂⁴	—	2	1	no	—
689	C₂⁴	—	2	2	no	—
690	#41	—	2	4	no	—
691	#41	—	2	4	no	—
692	#41	—	4	2	no	—
693	#41	—	4	4	no	—
694	#41	—	4	4	no	—
695	#41	—	8	4	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	—	2	1	no	—
698	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
700	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	4	1	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	—	8	2	no	—
717	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
719	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
720	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
721	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	4	4	no	—
732	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
733	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
738	Q₁₆	—	4	4	no	—
739	SD₁₆	—	2	4	no	—
740	SD₁₆	—	4	4	no	—
741	SD₁₆	—	4	2	no	—
742	SD₁₆	—	4	4	no	—
743	D₈	—	2	8	no	—
744	D₈	—	4	4	no	—
745	C₂×C₈	—	4	2	no	—
746	C₂×C₈	—	4	4	no	—
747	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
748	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
749	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
768	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
772	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
790	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
791	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	C₂×D₄×C₁₃	1	2	yes	—
797	C₄²	C₂×D₄×C₁₃	1	2	yes	—
798	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
799	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
800	C₄²	C₂⁴×C₁₃	1	2	yes	—
801	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
802	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
803	C₁₃	#61949	1	1	yes	characteristic, direct product factor, Sylow
804	C₂³	—	2	1	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	4	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	4	no	—
810	C₂³	—	8	1	no	—
811	C₂³	—	8	2	no	—
812	C₂³	—	8	2	no	—
813	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
814	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
815	Q₈	—	2	2	no	—
816	Q₈	—	2	2	no	—
817	Q₈	—	2	2	no	—
818	Q₈	—	2	2	no	—
819	Q₈	—	2	2	no	—
820	Q₈	—	4	2	no	—
821	Q₈	—	8	1	no	—
822	D₄	—	2	4	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	4	no	—
825	D₄	—	2	1	no	—
826	D₄	—	2	1	no	—
827	D₄	—	2	1	no	—
828	D₄	—	2	4	no	—
829	D₄	—	4	2	no	—
830	D₄	—	4	4	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	4	no	—
833	D₄	—	4	4	no	—
834	D₄	—	8	2	no	—
835	D₄	—	8	2	no	—
836	D₄	—	8	2	no	—
837	D₄	—	8	4	no	—
838	D₄	—	8	4	no	—
839	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	—	8	4	no	—
861	C₂×C₄	—	8	4	no	—
862	C₂×C₄	C₁₃×#135	1	4	yes	complemented
863	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
865	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
866	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
868	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
870	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
871	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
872	C₈	—	2	4	no	—
873	C₈	—	2	2	no	—
874	C₈	—	2	2	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	2	1	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	4	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	4	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	8	4	no	—
890	C₂²	—	16	4	no	—
891	C₂²	C₂×C₁₃×#135	1	2	yes	—
892	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
893	C₄	—	2	2	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	C₂×C₁₃×#135	1	2	yes	—
906	C₄	C₂×C₁₃×#135	1	2	yes	—
907	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
908	C₄	C₁₃×#585	1	1	yes	characteristic
909	C₂	—	2	2	no	—
910	C₂	—	4	2	no	—
911	C₂	—	4	2	no	—
912	C₂	—	8	1	no	—
913	C₂	—	8	4	no	—
914	C₂	C₁₃×#3488	1	1	yes	characteristic
915	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
916	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3475	C₂	semidirect
3. C₁₃×#3394	C₂	semidirect
4. C₁₃×#3361	C₂	semidirect
5. C₁₃×#3305	C₂	semidirect
6. C₁₃×#3296	C₂	semidirect
7. C₁₃×#3284	C₂	semidirect
8. C₁₃×#3280	C₂	semidirect
9. C₁₃×#3249	C₂	semidirect
10. C₁₃×#3247	C₂	semidirect
11. C₁₃×#3212	C₂	semidirect
12. C₁₃×#3208	C₂	semidirect
13. C₁₃×#3106	C₂	semidirect
14. C₁₃×#3101	C₂	semidirect
15. C₁₃×#3035	C₂	semidirect
16. C₂×C₁₃×#459	C₂	semidirect
17. C₁₃×#2988	C₂	semidirect
18. C₂×C₁₃×#135	C₂²	semidirect
21. C₁₃×#559	C₂²	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#555	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
30. C₁₃×#550	C₂²	semidirect
31. C₁₃×#547	C₂²	semidirect
39. C₁₃×#532	C₂²	semidirect
40. C₁₃×#532	C₂²	semidirect
43. C₁₃×#529	C₂²	semidirect
47. C₄×C₁₃×#41	C₂²	semidirect
50. C₁₃×#495	C₂²	semidirect
51. C₁₃×#492	C₂²	semidirect
52. C₁₃×#488	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
55. C₁₃×#482	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#476	C₂²	semidirect
62. C₁₃×#466	C₂²	semidirect
63. C₁₃×#465	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#463	C₂²	semidirect
67. C₁₃×#462	C₂²	semidirect
68. C₁₃×#462	C₂²	semidirect
69. C₁₃×#461	C₂²	semidirect
70. C₁₃×#461	C₂²	semidirect
71. C₁₃×#460	C₂²	semidirect
72. C₁₃×#460	C₂²	semidirect
77. C₁₃×#452	C₂²	semidirect
80. C₁₃×#449	C₂²	semidirect
81. C₁₃×#449	C₂²	semidirect
82. C₈×Q₈×C₁₃	C₂²	semidirect
83. C₄×C₁₃×SD₁₆	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
85. C₄×C₁₃×SD₁₆	C₂²	semidirect
86. C₄×C₁₃×D₈	C₂²	semidirect
88. C₈×D₄×C₁₃	C₂²	semidirect
90. C₁₃×#431	C₂²	semidirect
92. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
93. C₁₃×#416	C₂²	semidirect
230. #61949	C₁₃	direct (N × H)
346. #3508	C₂×C₁₃	semidirect
347. #3475	C₂×C₁₃	semidirect
348. #3394	C₂×C₁₃	semidirect
349. #3361	C₂×C₁₃	semidirect
350. #3305	C₂×C₁₃	semidirect
351. #3296	C₂×C₁₃	semidirect
352. #3284	C₂×C₁₃	semidirect
353. #3280	C₂×C₁₃	semidirect
354. #3249	C₂×C₁₃	semidirect
355. #3247	C₂×C₁₃	semidirect
356. #3212	C₂×C₁₃	semidirect
357. #3208	C₂×C₁₃	semidirect
358. #3106	C₂×C₁₃	semidirect
359. #3101	C₂×C₁₃	semidirect
360. #3035	C₂×C₁₃	semidirect
361. C₂×#459	C₂×C₁₃	semidirect
362. #2988	C₂×C₁₃	semidirect
421. C₂×C₄×C₁₃	#135	semidirect
434. C₂×#135	C₂²×C₁₃	semidirect
437. #559	C₂²×C₁₃	semidirect
438. #556	C₂²×C₁₃	semidirect
439. #555	C₂²×C₁₃	semidirect
440. #554	C₂²×C₁₃	semidirect
446. #550	C₂²×C₁₃	semidirect
447. #547	C₂²×C₁₃	semidirect
455. #532	C₂²×C₁₃	semidirect
456. #532	C₂²×C₁₃	semidirect
459. #529	C₂²×C₁₃	semidirect
463. C₄×#41	C₂²×C₁₃	semidirect
466. #495	C₂²×C₁₃	semidirect
467. #492	C₂²×C₁₃	semidirect
468. #488	C₂²×C₁₃	semidirect
469. #486	C₂²×C₁₃	semidirect
471. #482	C₂²×C₁₃	semidirect
472. #478	C₂²×C₁₃	semidirect
473. #477	C₂²×C₁₃	semidirect
474. #477	C₂²×C₁₃	semidirect
475. #476	C₂²×C₁₃	semidirect
476. #476	C₂²×C₁₃	semidirect
478. #466	C₂²×C₁₃	semidirect
479. #465	C₂²×C₁₃	semidirect
480. #464	C₂²×C₁₃	semidirect
481. #463	C₂²×C₁₃	semidirect
482. #463	C₂²×C₁₃	semidirect
483. #462	C₂²×C₁₃	semidirect
484. #462	C₂²×C₁₃	semidirect
485. #461	C₂²×C₁₃	semidirect
486. #461	C₂²×C₁₃	semidirect
487. #460	C₂²×C₁₃	semidirect
488. #460	C₂²×C₁₃	semidirect
493. #452	C₂²×C₁₃	semidirect
496. #449	C₂²×C₁₃	semidirect
497. #449	C₂²×C₁₃	semidirect
498. C₈×Q₈	C₂²×C₁₃	semidirect
499. C₄×SD₁₆	C₂²×C₁₃	semidirect
500. C₄×SD₁₆	C₂²×C₁₃	semidirect
501. C₄×SD₁₆	C₂²×C₁₃	semidirect
502. C₄×D₈	C₂²×C₁₃	semidirect
504. C₈×D₄	C₂²×C₁₃	semidirect
506. #431	C₂²×C₁₃	semidirect
508. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
509. #416	C₂²×C₁₃	semidirect
803. C₁₃	#61949	direct (N × H)
862. C₂×C₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3508	2
C₁₃×#3475	2
C₁₃×#3394	2
C₁₃×#3361	2
C₁₃×#3305	2
C₁₃×#3296	2
C₁₃×#3284	2
C₁₃×#3280	2
C₁₃×#3249	2
C₁₃×#3247	2
C₁₃×#3212	2
C₁₃×#3208	2
C₁₃×#3106	2
C₁₃×#3101	2
C₁₃×#3035	2
C₂×C₁₃×#459	2
C₁₃×#2988	2
#61949	13

Subgroups — C13×#61949 #15748288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61949 #15748288