Subgroups — C₁₃×#61165 #15747504

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3328	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3324	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3313	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3311	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3304	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3302	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3093	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3056	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2896	C₂	1	2	yes	maximal, complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
21	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
22	C₁₃×#556	—	2	1	no	—
23	C₁₃×#556	—	2	2	no	—
24	C₁₃×#556	—	2	1	no	—
25	C₁₃×#556	C₂²	1	2	yes	—
26	C₁₃×#556	C₂²	1	2	yes	complemented
27	C₁₃×#556	C₂²	1	4	yes	complemented
28	C₁₃×#550	C₂²	1	1	yes	characteristic
29	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#548	C₂²	1	2	yes	—
31	C₁₃×#547	—	2	1	no	—
32	C₁₃×#547	C₂²	1	1	yes	characteristic
33	C₁₃×#546	—	2	2	no	—
34	C₁₃×#546	C₂²	1	2	yes	—
35	D₄²×C₁₃	—	2	1	no	—
36	D₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#532	—	2	1	no	—
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#126	—	2	2	no	—
41	C₂×C₁₃×#124	—	2	1	no	—
42	C₁₃×#525	—	2	2	no	—
43	C₁₃×#525	C₂²	1	2	yes	—
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₁₃	—	2	1	no	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#117	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×#485	C₂²	1	4	yes	complemented
55	C₁₃×#485	C₂²	1	4	yes	complemented
56	C₁₃×#482	C₂²	1	4	yes	complemented
57	C₁₃×#482	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×#470	C₂²	1	4	yes	complemented
63	C₁₃×#468	C₂²	1	4	yes	complemented
64	C₁₃×#467	C₂²	1	4	yes	complemented
65	C₁₃×#465	C₂²	1	4	yes	complemented
66	C₁₃×#464	C₂²	1	4	yes	complemented
67	C₁₃×#462	C₂²	1	2	yes	complemented
68	C₁₃×#460	C₂²	1	2	yes	complemented
69	C₁₃×#452	C₂²	1	4	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#451	C₂²	1	4	yes	complemented
72	C₁₃×#450	C₂²	1	4	yes	complemented
73	C₁₃×#441	C₂²	1	2	yes	complemented
74	C₁₃×#440	C₂²	1	2	yes	complemented
75	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
76	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
77	C₁₃×#436	C₂²	1	2	yes	—
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×#419	C₂²	1	1	yes	characteristic, complemented
84	C₁₃×#419	C₂²	1	4	yes	complemented
85	C₁₃×#418	C₂²	1	4	yes	complemented
86	C₁₃×#417	C₂²	1	2	yes	—
87	C₁₃×#417	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	2	yes	complemented
89	C₁₃×#417	C₂²	1	2	yes	complemented
90	C₁₃×#417	C₂²	1	2	yes	complemented
91	C₁₃×#416	C₂²	1	4	yes	complemented
92	C₁₃×#416	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	2	no	—
97	C₂×C₁₃×#41	—	2	8	no	—
98	C₂×C₁₃×#41	—	4	4	no	—
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂×C₁₃×#41	C₂³	1	2	yes	—
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₁₃	—	2	1	no	—
104	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₁₃	—	2	2	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	—	2	2	no	—
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₁₃×#137	—	2	4	no	—
113	C₁₃×#137	—	4	4	no	—
114	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
115	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×M₁₆	—	4	4	no	—
119	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
122	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
123	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
124	C₁₃×C₄⋊Q₈	—	2	1	no	—
125	C₁₃×C₄⋊Q₈	—	2	1	no	—
126	C₁₃×C₄⋊Q₈	—	2	1	no	—
127	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₁₃×#127	—	2	1	no	—
131	C₁₃×#127	C₂³	1	1	yes	characteristic
132	C₁₃×#126	—	2	4	no	—
133	C₁₃×#126	—	2	4	no	—
134	C₁₃×#126	—	2	4	no	—
135	C₁₃×#126	—	2	4	no	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	—	2	2	no	—
138	C₁₃×#124	—	2	4	no	—
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	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#121	C₂³	1	2	yes	—
161	C₁₃×#120	—	2	2	no	—
162	C₁₃×#120	—	2	2	no	—
163	C₁₃×#120	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	—	2	2	no	—
166	C₄×Q₈×C₁₃	—	2	4	no	—
167	C₄×Q₈×C₁₃	—	2	1	no	—
168	C₄×Q₈×C₁₃	—	2	1	no	—
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
183	C₄×D₄×C₁₃	D₄	1	2	yes	—
184	C₄×D₄×C₁₃	D₄	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	1	yes	characteristic
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	—	2	1	no	—
193	C₁₃×#117	C₂³	1	4	yes	—
194	C₁₃×#117	C₂³	1	4	yes	—
195	C₁₃×#117	C₂³	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
207	C₂×C₄²×C₁₃	—	2	2	no	—
208	C₂×C₄²×C₁₃	—	2	1	no	—
209	C₂×C₄²×C₁₃	—	2	1	no	—
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₁₃×#107	C₂³	1	2	yes	—
212	C₁₃×#107	C₂³	1	4	yes	—
213	C₁₃×#106	C₂³	1	2	yes	—
214	C₁₃×#106	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	4	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	2	yes	—
223	C₁₃×#103	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	2	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	4	yes	—
229	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×#97	C₂³	1	2	yes	—
232	C₄×C₈×C₁₃	C₂³	1	2	yes	—
233	#61165	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂⁴×C₁₃	—	2	2	no	—
235	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
236	C₁₃×#41	—	2	2	no	—
237	C₁₃×#41	—	2	4	no	—
238	C₁₃×#41	—	2	4	no	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	4	8	no	—
242	C₁₃×#41	—	4	2	no	—
243	C₁₃×#41	—	4	2	no	—
244	C₁₃×#41	—	4	8	no	—
245	C₁₃×#41	#41	1	4	yes	—
246	C₂×Q₈×C₁₃	—	2	1	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	—	2	2	no	—
250	C₂×Q₈×C₁₃	—	2	4	no	—
251	C₂×Q₈×C₁₃	—	2	2	no	—
252	C₂×Q₈×C₁₃	—	2	2	no	—
253	C₂×Q₈×C₁₃	—	4	2	no	—
254	C₂×Q₈×C₁₃	—	4	4	no	—
255	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
256	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
257	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	—	2	4	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	2	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	1	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	1	no	—
268	C₂×D₄×C₁₃	—	4	2	no	—
269	C₂×D₄×C₁₃	—	4	2	no	—
270	C₂×D₄×C₁₃	—	4	8	no	—
271	C₂×D₄×C₁₃	—	4	4	no	—
272	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
275	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
276	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	—	2	1	no	—
278	C₂²×C₄×C₁₃	—	2	4	no	—
279	C₂²×C₄×C₁₃	—	2	4	no	—
280	C₂²×C₄×C₁₃	—	2	1	no	—
281	C₂²×C₄×C₁₃	—	2	1	no	—
282	C₂²×C₄×C₁₃	—	2	2	no	—
283	C₂²×C₄×C₁₃	—	2	2	no	—
284	C₂²×C₄×C₁₃	—	2	1	no	—
285	C₂²×C₄×C₁₃	—	2	2	no	—
286	C₂²×C₄×C₁₃	—	2	2	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	1	no	—
289	C₂²×C₄×C₁₃	—	4	8	no	—
290	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₁₃×Q₁₆	—	2	4	no	—
299	C₁₃×Q₁₆	—	4	4	no	—
300	C₁₃×SD₁₆	—	2	4	no	—
301	C₁₃×SD₁₆	—	4	4	no	—
302	C₁₃×M₁₆	—	2	2	no	—
303	C₁₃×M₁₆	—	2	2	no	—
304	C₁₃×M₁₆	—	2	4	no	—
305	C₁₃×M₁₆	—	4	4	no	—
306	C₂×C₈×C₁₃	—	4	4	no	—
307	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
308	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
309	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	4	no	—
313	C₁₃×C₄⋊C₄	—	2	4	no	—
314	C₁₃×C₄⋊C₄	—	2	2	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	1	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	1	no	—
321	C₁₃×C₄⋊C₄	—	2	1	no	—
322	C₁₃×C₄⋊C₄	—	2	1	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
325	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
326	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
330	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
331	C₁₃×C₂²⋊C₄	—	2	4	no	—
332	C₁₃×C₂²⋊C₄	—	2	4	no	—
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	4	no	—
335	C₁₃×C₂²⋊C₄	—	2	4	no	—
336	C₁₃×C₂²⋊C₄	—	2	1	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	—	2	2	no	—
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	—	2	1	no	—
341	C₁₃×C₂²⋊C₄	—	2	1	no	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	2	no	—
344	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
345	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
346	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
347	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
348	C₄²×C₁₃	—	2	1	no	—
349	C₄²×C₁₃	—	2	4	no	—
350	C₄²×C₁₃	—	2	4	no	—
351	C₄²×C₁₃	—	2	1	no	—
352	C₄²×C₁₃	—	2	1	no	—
353	C₄²×C₁₃	—	2	2	no	—
354	C₄²×C₁₃	—	2	2	no	—
355	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
356	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
357	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
358	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
360	D₄×#41	C₂×C₁₃	1	1	yes	characteristic
361	#3328	C₂×C₁₃	1	2	yes	complemented
362	#3324	C₂×C₁₃	1	2	yes	complemented
363	#3313	C₂×C₁₃	1	4	yes	complemented
364	#3311	C₂×C₁₃	1	4	yes	complemented
365	#3304	C₂×C₁₃	1	2	yes	complemented
366	#3302	C₂×C₁₃	1	2	yes	complemented
367	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
368	#3093	C₂×C₁₃	1	2	yes	complemented
369	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
370	#3056	C₂×C₁₃	1	2	yes	complemented
371	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
372	#3007	C₂×C₁₃	1	2	yes	complemented
373	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
374	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
375	#2896	C₂×C₁₃	1	2	yes	complemented
376	C₂³×C₁₃	—	2	1	no	—
377	C₂³×C₁₃	—	2	4	no	—
378	C₂³×C₁₃	—	2	2	no	—
379	C₂³×C₁₃	—	4	2	no	—
380	C₂³×C₁₃	—	4	2	no	—
381	C₂³×C₁₃	—	4	4	no	—
382	C₂³×C₁₃	—	4	4	no	—
383	C₂³×C₁₃	—	8	2	no	—
384	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
385	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
386	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
387	Q₈×C₁₃	—	2	1	no	—
388	Q₈×C₁₃	—	2	2	no	—
389	Q₈×C₁₃	—	2	2	no	—
390	Q₈×C₁₃	—	2	2	no	—
391	Q₈×C₁₃	—	2	2	no	—
392	Q₈×C₁₃	—	4	4	no	—
393	Q₈×C₁₃	—	4	4	no	—
394	Q₈×C₁₃	—	4	2	no	—
395	Q₈×C₁₃	—	4	4	no	—
396	Q₈×C₁₃	C₂×#41	1	2	yes	—
397	D₄×C₁₃	—	2	4	no	—
398	D₄×C₁₃	—	2	2	no	—
399	D₄×C₁₃	—	2	2	no	—
400	D₄×C₁₃	—	2	2	no	—
401	D₄×C₁₃	—	2	1	no	—
402	D₄×C₁₃	—	2	2	no	—
403	D₄×C₁₃	—	4	2	no	—
404	D₄×C₁₃	—	4	4	no	—
405	D₄×C₁₃	—	4	4	no	—
406	D₄×C₁₃	—	4	4	no	—
407	D₄×C₁₃	—	4	4	no	—
408	D₄×C₁₃	—	4	4	no	—
409	D₄×C₁₃	—	4	2	no	—
410	D₄×C₁₃	—	8	1	no	—
411	D₄×C₁₃	—	8	2	no	—
412	D₄×C₁₃	C₂×#41	1	2	yes	—
413	C₂×C₄×C₁₃	—	2	4	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	4	no	—
416	C₂×C₄×C₁₃	—	2	4	no	—
417	C₂×C₄×C₁₃	—	2	4	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	4	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	4	1	no	—
430	C₂×C₄×C₁₃	—	4	4	no	—
431	C₂×C₄×C₁₃	—	4	4	no	—
432	C₂×C₄×C₁₃	—	4	4	no	—
433	C₂×C₄×C₁₃	—	4	2	no	—
434	C₂×C₄×C₁₃	—	4	4	no	—
435	C₂×C₄×C₁₃	—	4	2	no	—
436	C₂×C₄×C₁₃	—	4	4	no	—
437	C₂×C₄×C₁₃	—	4	2	no	—
438	C₂×C₄×C₁₃	—	8	1	no	—
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
442	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
447	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
448	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
449	C₈×C₁₃	—	2	2	no	—
450	C₈×C₁₃	—	2	2	no	—
451	C₈×C₁₃	—	2	4	no	—
452	C₂²×#41	C₂²×C₁₃	1	2	yes	—
453	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
455	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
456	#556	—	2	1	no	—
457	#556	—	2	2	no	—
458	#556	—	2	1	no	—
459	#556	C₂²×C₁₃	1	2	yes	—
460	#556	C₂²×C₁₃	1	2	yes	complemented
461	#556	C₂²×C₁₃	1	4	yes	complemented
462	#550	C₂²×C₁₃	1	1	yes	characteristic
463	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
464	#548	C₂²×C₁₃	1	2	yes	—
465	#547	—	2	1	no	—
466	#547	C₂²×C₁₃	1	1	yes	characteristic
467	#546	—	2	2	no	—
468	#546	C₂²×C₁₃	1	2	yes	—
469	D₄²	—	2	1	no	—
470	D₄²	C₂²×C₁₃	1	1	yes	characteristic
471	#532	—	2	1	no	—
472	#532	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	C₂×#126	—	2	2	no	—
475	C₂×#124	—	2	1	no	—
476	#525	—	2	2	no	—
477	#525	C₂²×C₁₃	1	2	yes	—
478	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
479	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
480	C₂×C₄×Q₈	—	2	1	no	—
481	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	C₂×C₄×D₄	—	2	1	no	—
483	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
485	#489	C₂²×C₁₃	1	4	yes	complemented
486	#487	C₂²×C₁₃	1	2	yes	complemented
487	#486	C₂²×C₁₃	1	2	yes	complemented
488	#485	C₂²×C₁₃	1	4	yes	complemented
489	#485	C₂²×C₁₃	1	4	yes	complemented
490	#482	C₂²×C₁₃	1	4	yes	complemented
491	#482	C₂²×C₁₃	1	4	yes	complemented
492	#477	C₂²×C₁₃	1	2	yes	complemented
493	#476	C₂²×C₁₃	1	2	yes	complemented
494	#475	C₂²×C₁₃	1	2	yes	complemented
495	#474	C₂²×C₁₃	1	2	yes	complemented
496	#470	C₂²×C₁₃	1	4	yes	complemented
497	#468	C₂²×C₁₃	1	4	yes	complemented
498	#467	C₂²×C₁₃	1	4	yes	complemented
499	#465	C₂²×C₁₃	1	4	yes	complemented
500	#464	C₂²×C₁₃	1	4	yes	complemented
501	#462	C₂²×C₁₃	1	2	yes	complemented
502	#460	C₂²×C₁₃	1	2	yes	complemented
503	#452	C₂²×C₁₃	1	4	yes	complemented
504	#452	C₂²×C₁₃	1	4	yes	complemented
505	#451	C₂²×C₁₃	1	4	yes	complemented
506	#450	C₂²×C₁₃	1	4	yes	complemented
507	#441	C₂²×C₁₃	1	2	yes	complemented
508	#440	C₂²×C₁₃	1	2	yes	complemented
509	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
510	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
511	#436	C₂²×C₁₃	1	2	yes	—
512	#435	C₂²×C₁₃	1	4	yes	complemented
513	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
514	#428	C₂²×C₁₃	1	2	yes	complemented
515	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
516	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	#419	C₂²×C₁₃	1	4	yes	complemented
518	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
519	#418	C₂²×C₁₃	1	4	yes	complemented
520	#417	C₂²×C₁₃	1	2	yes	—
521	#417	C₂²×C₁₃	1	1	yes	characteristic
522	#417	C₂²×C₁₃	1	2	yes	complemented
523	#417	C₂²×C₁₃	1	2	yes	complemented
524	#417	C₂²×C₁₃	1	2	yes	complemented
525	#416	C₂²×C₁₃	1	4	yes	complemented
526	#416	C₂²×C₁₃	1	4	yes	complemented
527	#407	C₂²×C₁₃	1	2	yes	complemented
528	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
529	C₂²×C₁₃	—	2	1	no	—
530	C₂²×C₁₃	—	2	1	no	—
531	C₂²×C₁₃	—	2	2	no	—
532	C₂²×C₁₃	—	2	2	no	—
533	C₂²×C₁₃	—	2	2	no	—
534	C₂²×C₁₃	—	2	2	no	—
535	C₂²×C₁₃	—	2	2	no	—
536	C₂²×C₁₃	—	2	2	no	—
537	C₂²×C₁₃	—	2	2	no	—
538	C₂²×C₁₃	—	4	1	no	—
539	C₂²×C₁₃	—	4	1	no	—
540	C₂²×C₁₃	—	4	2	no	—
541	C₂²×C₁₃	—	4	2	no	—
542	C₂²×C₁₃	—	4	2	no	—
543	C₂²×C₁₃	—	8	4	no	—
544	C₂²×C₁₃	—	8	8	no	—
545	C₂²×C₁₃	#546	1	2	yes	—
546	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
547	C₄×C₁₃	—	2	1	no	—
548	C₄×C₁₃	—	2	1	no	—
549	C₄×C₁₃	—	2	2	no	—
550	C₄×C₁₃	—	2	2	no	—
551	C₄×C₁₃	—	2	2	no	—
552	C₄×C₁₃	—	2	1	no	—
553	C₄×C₁₃	—	4	2	no	—
554	C₄×C₁₃	—	4	1	no	—
555	C₄×C₁₃	—	4	2	no	—
556	C₄×C₁₃	—	4	2	no	—
557	C₄×C₁₃	—	4	1	no	—
558	C₄×C₁₃	—	4	4	no	—
559	C₄×C₁₃	#546	1	2	yes	—
560	C₄×C₁₃	#575	1	2	yes	—
561	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
562	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂×#41	—	2	2	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	2	8	no	—
566	C₂×#41	—	4	4	no	—
567	C₂×#41	C₂³×C₁₃	1	2	yes	—
568	C₂×#41	C₂³×C₁₃	1	2	yes	—
569	C₂×#41	C₂³×C₁₃	1	2	yes	—
570	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
571	C₂²×Q₈	—	2	1	no	—
572	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
573	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
574	C₂²×D₄	—	2	2	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
577	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
578	C₂³×C₄	—	2	2	no	—
579	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
580	#137	—	2	4	no	—
581	#137	—	4	4	no	—
582	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
583	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
584	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
585	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
586	C₂×M₁₆	—	4	4	no	—
587	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
589	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
590	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
591	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
592	C₄⋊Q₈	—	2	1	no	—
593	C₄⋊Q₈	—	2	1	no	—
594	C₄⋊Q₈	—	2	1	no	—
595	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
597	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	#127	—	2	1	no	—
599	#127	C₂³×C₁₃	1	1	yes	characteristic
600	#126	—	2	4	no	—
601	#126	—	2	4	no	—
602	#126	—	2	4	no	—
603	#126	—	2	4	no	—
604	#124	—	2	2	no	—
605	#124	—	2	2	no	—
606	#124	—	2	4	no	—
607	#124	—	2	2	no	—
608	#124	C₂³×C₁₃	1	2	yes	—
609	#123	—	2	2	no	—
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	C₂²⋊Q₈	—	2	2	no	—
614	C₂²⋊Q₈	—	2	2	no	—
615	C₂²⋊Q₈	—	2	2	no	—
616	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
617	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
618	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
619	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
620	#121	—	2	2	no	—
621	#121	—	2	1	no	—
622	#121	—	2	1	no	—
623	#121	—	2	1	no	—
624	#121	—	2	1	no	—
625	#121	—	2	2	no	—
626	#121	—	2	2	no	—
627	#121	C₂³×C₁₃	1	2	yes	—
628	#121	C₂³×C₁₃	1	2	yes	—
629	#120	—	2	2	no	—
630	#120	—	2	2	no	—
631	#120	—	2	2	no	—
632	C₄×Q₈	—	2	2	no	—
633	C₄×Q₈	—	2	2	no	—
634	C₄×Q₈	—	2	4	no	—
635	C₄×Q₈	—	2	1	no	—
636	C₄×Q₈	—	2	1	no	—
637	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
638	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
639	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
640	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
641	C₄×D₄	—	2	1	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
651	C₄×D₄	D₄×C₁₃	1	2	yes	—
652	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
653	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
656	C₄×D₄	C₂³×C₁₃	1	2	yes	—
657	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
658	#117	—	2	2	no	—
659	#117	—	2	2	no	—
660	#117	—	2	1	no	—
661	#117	C₂³×C₁₃	1	4	yes	—
662	#117	C₂³×C₁₃	1	4	yes	—
663	#117	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	—	2	2	no	—
665	C₂×C₄⋊C₄	—	2	1	no	—
666	C₂×C₄⋊C₄	—	2	1	no	—
667	C₂×C₄⋊C₄	—	2	1	no	—
668	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
671	C₂×C₂²⋊C₄	—	2	2	no	—
672	C₂×C₂²⋊C₄	—	2	2	no	—
673	C₂×C₂²⋊C₄	—	2	2	no	—
674	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
675	C₂×C₄²	—	2	2	no	—
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
679	#107	C₂³×C₁₃	1	2	yes	—
680	#107	C₂³×C₁₃	1	4	yes	—
681	#106	C₂³×C₁₃	1	2	yes	—
682	#106	C₂³×C₁₃	1	4	yes	—
683	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
684	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
685	#103	C₂³×C₁₃	1	2	yes	—
686	#103	C₂³×C₁₃	1	4	yes	—
687	#103	C₂³×C₁₃	1	4	yes	—
688	#103	C₂³×C₁₃	1	4	yes	—
689	#103	C₂³×C₁₃	1	4	yes	—
690	#103	C₂³×C₁₃	1	2	yes	—
691	#103	C₂³×C₁₃	1	2	yes	—
692	#102	C₂³×C₁₃	1	2	yes	—
693	#102	C₂³×C₁₃	1	4	yes	—
694	#102	C₂³×C₁₃	1	4	yes	—
695	#102	C₂³×C₁₃	1	4	yes	—
696	#102	C₂³×C₁₃	1	4	yes	—
697	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
698	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
699	#97	C₂³×C₁₃	1	2	yes	—
700	C₄×C₈	C₂³×C₁₃	1	2	yes	—
701	C₂×C₁₃	—	2	2	no	—
702	C₂×C₁₃	—	4	2	no	—
703	C₂×C₁₃	—	4	2	no	—
704	C₂×C₁₃	—	4	2	no	—
705	C₂×C₁₃	—	8	2	no	—
706	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
707	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
708	C₂×C₁₃	#3586	1	1	yes	characteristic
709	C₂⁴	—	2	2	no	—
710	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
711	#41	—	2	2	no	—
712	#41	—	2	4	no	—
713	#41	—	2	4	no	—
714	#41	—	2	4	no	—
715	#41	—	2	4	no	—
716	#41	—	4	8	no	—
717	#41	—	4	2	no	—
718	#41	—	4	2	no	—
719	#41	—	4	8	no	—
720	#41	C₁₃×#41	1	4	yes	—
721	C₂×Q₈	—	2	1	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	—	2	4	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	4	2	no	—
729	C₂×Q₈	—	4	4	no	—
730	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
731	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
732	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
733	C₂×D₄	—	2	1	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	1	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	8	no	—
746	C₂×D₄	—	4	4	no	—
747	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
750	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
751	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	1	no	—
764	C₂²×C₄	—	4	8	no	—
765	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
767	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
769	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
773	Q₁₆	—	2	4	no	—
774	Q₁₆	—	4	4	no	—
775	SD₁₆	—	2	4	no	—
776	SD₁₆	—	4	4	no	—
777	M₁₆	—	2	2	no	—
778	M₁₆	—	2	2	no	—
779	M₁₆	—	2	4	no	—
780	M₁₆	—	4	4	no	—
781	C₂×C₈	—	4	4	no	—
782	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
783	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
784	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
800	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
801	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
802	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
803	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
804	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
805	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	1	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	1	no	—
816	C₂²⋊C₄	—	2	1	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
820	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
821	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
822	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
823	C₄²	—	2	1	no	—
824	C₄²	—	2	4	no	—
825	C₄²	—	2	4	no	—
826	C₄²	—	2	1	no	—
827	C₄²	—	2	1	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
831	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
832	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
833	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
834	C₁₃	#61165	1	1	yes	characteristic, direct product factor, Sylow
835	C₂³	—	2	1	no	—
836	C₂³	—	2	4	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	4	2	no	—
839	C₂³	—	4	2	no	—
840	C₂³	—	4	4	no	—
841	C₂³	—	4	4	no	—
842	C₂³	—	8	2	no	—
843	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
844	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
845	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
846	Q₈	—	2	1	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	2	2	no	—
849	Q₈	—	2	2	no	—
850	Q₈	—	2	2	no	—
851	Q₈	—	4	4	no	—
852	Q₈	—	4	4	no	—
853	Q₈	—	4	2	no	—
854	Q₈	—	4	4	no	—
855	Q₈	C₂×C₁₃×#41	1	2	yes	—
856	D₄	—	2	4	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	2	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	1	no	—
861	D₄	—	2	2	no	—
862	D₄	—	4	2	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	4	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	4	no	—
867	D₄	—	4	4	no	—
868	D₄	—	4	2	no	—
869	D₄	—	8	1	no	—
870	D₄	—	8	2	no	—
871	D₄	C₂×C₁₃×#41	1	2	yes	—
872	C₂×C₄	—	2	4	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	4	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	4	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	2	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	8	1	no	—
898	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
900	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
901	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
903	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
905	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
906	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
907	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
908	C₈	—	2	2	no	—
909	C₈	—	2	2	no	—
910	C₈	—	2	4	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	8	4	no	—
926	C₂²	—	8	8	no	—
927	C₂²	C₁₃×#546	1	2	yes	—
928	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
929	C₄	—	2	1	no	—
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	4	1	no	—
936	C₄	—	4	4	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	C₁₃×#546	1	2	yes	—
942	C₄	C₁₃×#575	1	2	yes	—
943	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
944	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
945	C₂	—	2	2	no	—
946	C₂	—	4	2	no	—
947	C₂	—	4	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	8	2	no	—
950	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
951	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
952	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	D₄×C₁₃×#41	C₂
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. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3328	C₂	semidirect
4. C₁₃×#3324	C₂	semidirect
5. C₁₃×#3313	C₂	semidirect
6. C₁₃×#3311	C₂	semidirect
7. C₁₃×#3304	C₂	semidirect
8. C₁₃×#3302	C₂	semidirect
9. C₁₃×#3141	C₂	semidirect
10. C₁₃×#3093	C₂	semidirect
11. C₁₃×#3079	C₂	semidirect
12. C₁₃×#3056	C₂	semidirect
13. C₁₃×#3037	C₂	semidirect
14. C₁₃×#3007	C₂	semidirect
15. C₄×C₁₃×#137	C₂	semidirect
16. D₄×C₁₃×M₁₆	C₂	semidirect
17. C₁₃×#2896	C₂	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
21. C₂²×C₁₃×M₁₆	C₂²	semidirect
26. C₁₃×#556	C₂²	semidirect
27. C₁₃×#556	C₂²	semidirect
39. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
44. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
47. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
50. C₂×C₁₃×#117	C₂²	semidirect
51. C₁₃×#489	C₂²	semidirect
52. C₁₃×#487	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
55. C₁₃×#485	C₂²	semidirect
56. C₁₃×#482	C₂²	semidirect
57. C₁₃×#482	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#474	C₂²	semidirect
62. C₁₃×#470	C₂²	semidirect
63. C₁₃×#468	C₂²	semidirect
64. C₁₃×#467	C₂²	semidirect
65. C₁₃×#465	C₂²	semidirect
66. C₁₃×#464	C₂²	semidirect
67. C₁₃×#462	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#452	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
71. C₁₃×#451	C₂²	semidirect
72. C₁₃×#450	C₂²	semidirect
73. C₁₃×#441	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₄×C₁₃×Q₁₆	C₂²	semidirect
76. C₄×C₁₃×SD₁₆	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×#419	C₂²	semidirect
84. C₁₃×#419	C₂²	semidirect
85. C₁₃×#418	C₂²	semidirect
88. C₁₃×#417	C₂²	semidirect
89. C₁₃×#417	C₂²	semidirect
90. C₁₃×#417	C₂²	semidirect
91. C₁₃×#416	C₂²	semidirect
92. C₁₃×#416	C₂²	semidirect
93. C₁₃×#407	C₂²	semidirect
94. C₄×C₁₃×M₁₆	C₂²	semidirect
233. #61165	C₁₃	direct (N × H)
359. C₂×#556	C₂×C₁₃	semidirect
361. #3328	C₂×C₁₃	semidirect
362. #3324	C₂×C₁₃	semidirect
363. #3313	C₂×C₁₃	semidirect
364. #3311	C₂×C₁₃	semidirect
365. #3304	C₂×C₁₃	semidirect
366. #3302	C₂×C₁₃	semidirect
367. #3141	C₂×C₁₃	semidirect
368. #3093	C₂×C₁₃	semidirect
369. #3079	C₂×C₁₃	semidirect
370. #3056	C₂×C₁₃	semidirect
371. #3037	C₂×C₁₃	semidirect
372. #3007	C₂×C₁₃	semidirect
373. C₄×#137	C₂×C₁₃	semidirect
374. D₄×M₁₆	C₂×C₁₃	semidirect
375. #2896	C₂×C₁₃	semidirect
454. C₂×#137	C₂²×C₁₃	semidirect
455. C₂²×M₁₆	C₂²×C₁₃	semidirect
460. #556	C₂²×C₁₃	semidirect
461. #556	C₂²×C₁₃	semidirect
473. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
478. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
481. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
484. C₂×#117	C₂²×C₁₃	semidirect
485. #489	C₂²×C₁₃	semidirect
486. #487	C₂²×C₁₃	semidirect
487. #486	C₂²×C₁₃	semidirect
488. #485	C₂²×C₁₃	semidirect
489. #485	C₂²×C₁₃	semidirect
490. #482	C₂²×C₁₃	semidirect
491. #482	C₂²×C₁₃	semidirect
492. #477	C₂²×C₁₃	semidirect
493. #476	C₂²×C₁₃	semidirect
494. #475	C₂²×C₁₃	semidirect
495. #474	C₂²×C₁₃	semidirect
496. #470	C₂²×C₁₃	semidirect
497. #468	C₂²×C₁₃	semidirect
498. #467	C₂²×C₁₃	semidirect
499. #465	C₂²×C₁₃	semidirect
500. #464	C₂²×C₁₃	semidirect
501. #462	C₂²×C₁₃	semidirect
502. #460	C₂²×C₁₃	semidirect
503. #452	C₂²×C₁₃	semidirect
504. #452	C₂²×C₁₃	semidirect
505. #451	C₂²×C₁₃	semidirect
506. #450	C₂²×C₁₃	semidirect
507. #441	C₂²×C₁₃	semidirect
508. #440	C₂²×C₁₃	semidirect
509. C₄×Q₁₆	C₂²×C₁₃	semidirect
510. C₄×SD₁₆	C₂²×C₁₃	semidirect
512. #435	C₂²×C₁₃	semidirect
513. C₈×D₄	C₂²×C₁₃	semidirect
514. #428	C₂²×C₁₃	semidirect
515. #428	C₂²×C₁₃	semidirect
516. #423	C₂²×C₁₃	semidirect
517. #419	C₂²×C₁₃	semidirect
518. #419	C₂²×C₁₃	semidirect
519. #418	C₂²×C₁₃	semidirect
522. #417	C₂²×C₁₃	semidirect
523. #417	C₂²×C₁₃	semidirect
524. #417	C₂²×C₁₃	semidirect
525. #416	C₂²×C₁₃	semidirect
526. #416	C₂²×C₁₃	semidirect
527. #407	C₂²×C₁₃	semidirect
528. C₄×M₁₆	C₂²×C₁₃	semidirect
834. C₁₃	#61165	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#556	2
D₄×C₁₃×#41	2
C₁₃×#3328	2
C₁₃×#3324	2
C₁₃×#3313	2
C₁₃×#3311	2
C₁₃×#3304	2
C₁₃×#3302	2
C₁₃×#3141	2
C₁₃×#3093	2
C₁₃×#3079	2
C₁₃×#3056	2
C₁₃×#3037	2
C₁₃×#3007	2
C₄×C₁₃×#137	2
D₄×C₁₃×M₁₆	2
C₁₃×#2896	2
#61165	13

Subgroups — C13×#61165 #15747504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61165 #15747504