Subgroups — C₁₃×#34736 #15721075

Order 3328.

5758 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2409	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2408	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2407	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2406	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2405	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2404	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2403	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2388	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×#120	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2297	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	—	2	16	no	—
16	C₂²×C₁₃×#41	—	2	8	no	—
17	C₂²×C₁₃×#41	C₂²	1	2	yes	—
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
21	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
22	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
27	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#525	—	2	16	no	—
29	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
31	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#120	C₂²	1	4	yes	—
33	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
34	C₂×C₄×D₄×C₁₃	—	2	8	no	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
38	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
39	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
41	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#395	C₂²	1	4	yes	complemented
46	C₁₃×#394	C₂²	1	8	yes	complemented
47	C₁₃×#394	C₂²	1	4	yes	complemented
48	C₁₃×#393	C₂²	1	4	yes	complemented
49	C₁₃×#392	C₂²	1	8	yes	complemented
50	C₁₃×#392	C₂²	1	4	yes	complemented
51	C₁₃×#391	C₂²	1	4	yes	complemented
52	C₁₃×#390	C₂²	1	4	yes	complemented
53	C₁₃×#386	C₂²	1	4	yes	—
54	C₁₃×#386	C₂²	1	4	yes	complemented
55	C₁₃×#386	C₂²	1	4	yes	complemented
56	C₁₃×#386	C₂²	1	8	yes	complemented
57	C₁₃×#385	C₂²	1	4	yes	complemented
58	C₁₃×#385	C₂²	1	8	yes	complemented
59	C₁₃×#381	C₂²	1	2	yes	complemented
60	C₁₃×#380	C₂²	1	2	yes	complemented
61	C₁₃×#380	C₂²	1	2	yes	complemented
62	C₁₃×#379	C₂²	1	2	yes	—
63	C₁₃×#379	C₂²	1	4	yes	complemented
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
67	C₂⁵×C₁₃	C₂³	1	2	yes	—
68	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
69	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×#41	—	2	128	no	—
71	C₂×C₁₃×#41	—	2	8	no	—
72	C₂×C₁₃×#41	—	2	16	no	—
73	C₂×C₁₃×#41	—	2	8	no	—
74	C₂×C₁₃×#41	—	2	8	no	—
75	C₂×C₁₃×#41	—	2	8	no	—
76	C₂×C₁₃×#41	—	2	8	no	—
77	C₂×C₁₃×#41	—	2	8	no	—
78	C₂×C₁₃×#41	—	2	8	no	—
79	C₂×C₁₃×#41	—	2	16	no	—
80	C₂×C₁₃×#41	D₄	1	16	yes	complemented
81	C₂²×Q₈×C₁₃	—	2	8	no	—
82	C₂²×Q₈×C₁₃	—	2	4	no	—
83	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
84	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃	—	2	4	no	—
86	C₂²×D₄×C₁₃	—	2	8	no	—
87	C₂²×D₄×C₁₃	—	2	16	no	—
88	C₂²×D₄×C₁₃	—	2	8	no	—
89	C₂²×D₄×C₁₃	—	2	8	no	—
90	C₂²×D₄×C₁₃	—	2	4	no	—
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃	—	2	8	no	—
99	C₂³×C₄×C₁₃	—	2	8	no	—
100	C₂³×C₄×C₁₃	—	2	16	no	—
101	C₂³×C₄×C₁₃	—	2	4	no	—
102	C₂³×C₄×C₁₃	—	2	8	no	—
103	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
104	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#123	—	2	16	no	—
119	C₁₃×C₂²⋊Q₈	—	2	16	no	—
120	C₁₃×#121	—	2	16	no	—
121	C₁₃×#120	—	2	16	no	—
122	C₁₃×#120	—	2	16	no	—
123	C₄×D₄×C₁₃	—	2	8	no	—
124	C₄×D₄×C₁₃	—	2	8	no	—
125	C₄×D₄×C₁₃	—	2	8	no	—
126	C₄×D₄×C₁₃	—	2	8	no	—
127	C₄×D₄×C₁₃	—	2	32	no	—
128	C₁₃×#117	—	2	8	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
147	C₂×C₄²×C₁₃	—	2	4	no	—
148	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
151	C₁₃×#95	C₂³	1	4	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	8	yes	—
154	C₁₃×#95	C₂³	1	8	yes	—
155	#34736	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂⁴×C₁₃	—	2	2	no	—
157	C₂⁴×C₁₃	—	2	8	no	—
158	C₂⁴×C₁₃	—	2	4	no	—
159	C₂⁴×C₁₃	—	2	4	no	—
160	C₂⁴×C₁₃	—	2	4	no	—
161	C₂⁴×C₁₃	—	2	4	no	—
162	C₂⁴×C₁₃	—	2	4	no	—
163	C₂⁴×C₁₃	—	2	8	no	—
164	C₂⁴×C₁₃	—	4	2	no	—
165	C₂⁴×C₁₃	—	4	2	no	—
166	C₂⁴×C₁₃	—	4	4	no	—
167	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
168	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
169	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
171	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×#41	—	2	64	no	—
174	C₁₃×#41	—	2	64	no	—
175	C₁₃×#41	—	2	64	no	—
176	C₁₃×#41	—	2	64	no	—
177	C₂×Q₈×C₁₃	—	2	32	no	—
178	C₂×Q₈×C₁₃	—	2	8	no	—
179	C₂×Q₈×C₁₃	—	2	4	no	—
180	C₂×Q₈×C₁₃	—	2	4	no	—
181	C₂×Q₈×C₁₃	—	2	4	no	—
182	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
183	C₂×D₄×C₁₃	—	2	32	no	—
184	C₂×D₄×C₁₃	—	2	64	no	—
185	C₂×D₄×C₁₃	—	2	32	no	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	4	no	—
188	C₂×D₄×C₁₃	—	2	8	no	—
189	C₂×D₄×C₁₃	—	2	8	no	—
190	C₂×D₄×C₁₃	—	2	8	no	—
191	C₂×D₄×C₁₃	—	2	8	no	—
192	C₂×D₄×C₁₃	—	2	8	no	—
193	C₂×D₄×C₁₃	—	2	4	no	—
194	C₂×D₄×C₁₃	—	2	4	no	—
195	C₂×D₄×C₁₃	—	2	16	no	—
196	C₂×D₄×C₁₃	—	2	16	no	—
197	C₂×D₄×C₁₃	—	2	8	no	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	4	no	—
202	C₂×D₄×C₁₃	—	4	8	no	—
203	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
204	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	complemented
205	C₂×D₄×C₁₃	#41	1	8	yes	complemented
206	C₂²×C₄×C₁₃	—	2	64	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	4	no	—
209	C₂²×C₄×C₁₃	—	2	8	no	—
210	C₂²×C₄×C₁₃	—	2	4	no	—
211	C₂²×C₄×C₁₃	—	2	32	no	—
212	C₂²×C₄×C₁₃	—	2	4	no	—
213	C₂²×C₄×C₁₃	—	2	8	no	—
214	C₂²×C₄×C₁₃	—	2	4	no	—
215	C₂²×C₄×C₁₃	—	2	8	no	—
216	C₂²×C₄×C₁₃	—	2	8	no	—
217	C₂²×C₄×C₁₃	—	2	4	no	—
218	C₂²×C₄×C₁₃	—	2	4	no	—
219	C₂²×C₄×C₁₃	—	2	8	no	—
220	C₂²×C₄×C₁₃	—	2	8	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	4	no	—
226	C₂²×C₄×C₁₃	—	2	8	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	8	no	—
229	C₂²×C₄×C₁₃	—	4	2	no	—
230	C₂²×C₄×C₁₃	—	4	16	no	—
231	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
238	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	8	no	—
251	C₁₃×C₄⋊C₄	—	2	16	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	8	no	—
255	C₁₃×C₂²⋊C₄	—	2	16	no	—
256	C₁₃×C₂²⋊C₄	—	2	8	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	16	no	—
260	C₁₃×C₂²⋊C₄	—	2	16	no	—
261	C₁₃×C₂²⋊C₄	—	4	8	no	—
262	C₁₃×C₂²⋊C₄	—	4	4	no	—
263	C₄²×C₁₃	—	2	4	no	—
264	C₄²×C₁₃	—	2	4	no	—
265	C₄²×C₁₃	—	2	8	no	—
266	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
267	C₂×#525	C₂×C₁₃	1	2	yes	complemented
268	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#2409	C₂×C₁₃	1	2	yes	complemented
270	#2408	C₂×C₁₃	1	2	yes	complemented
271	#2407	C₂×C₁₃	1	4	yes	complemented
272	#2406	C₂×C₁₃	1	2	yes	complemented
273	#2405	C₂×C₁₃	1	2	yes	complemented
274	#2404	C₂×C₁₃	1	2	yes	complemented
275	#2403	C₂×C₁₃	1	2	yes	complemented
276	#2388	C₂×C₁₃	1	4	yes	complemented
277	C₄×#120	C₂×C₁₃	1	4	yes	complemented
278	#2297	C₂×C₁₃	1	2	yes	complemented
279	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	2	2	no	—
282	C₂³×C₁₃	—	2	2	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	16	no	—
285	C₂³×C₁₃	—	2	8	no	—
286	C₂³×C₁₃	—	2	8	no	—
287	C₂³×C₁₃	—	2	8	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	4	no	—
290	C₂³×C₁₃	—	2	4	no	—
291	C₂³×C₁₃	—	2	4	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	8	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	2	8	no	—
298	C₂³×C₁₃	—	2	4	no	—
299	C₂³×C₁₃	—	4	4	no	—
300	C₂³×C₁₃	—	4	16	no	—
301	C₂³×C₁₃	—	4	32	no	—
302	C₂³×C₁₃	—	4	16	no	—
303	C₂³×C₁₃	—	4	4	no	—
304	C₂³×C₁₃	—	4	8	no	—
305	C₂³×C₁₃	—	4	4	no	—
306	C₂³×C₁₃	—	4	8	no	—
307	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
308	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
309	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
310	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
311	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
312	C₂³×C₁₃	C₂×#41	1	4	yes	—
313	C₂³×C₁₃	C₂×#41	1	4	yes	complemented
314	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
315	Q₈×C₁₃	—	2	16	no	—
316	Q₈×C₁₃	—	2	16	no	—
317	D₄×C₁₃	—	2	16	no	—
318	D₄×C₁₃	—	2	32	no	—
319	D₄×C₁₃	—	2	16	no	—
320	D₄×C₁₃	—	2	32	no	—
321	D₄×C₁₃	—	2	16	no	—
322	D₄×C₁₃	—	2	16	no	—
323	D₄×C₁₃	—	4	32	no	—
324	C₂×C₄×C₁₃	—	2	16	no	—
325	C₂×C₄×C₁₃	—	2	32	no	—
326	C₂×C₄×C₁₃	—	2	8	no	—
327	C₂×C₄×C₁₃	—	2	8	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	4	no	—
331	C₂×C₄×C₁₃	—	2	4	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	8	no	—
335	C₂×C₄×C₁₃	—	2	8	no	—
336	C₂×C₄×C₁₃	—	2	8	no	—
337	C₂×C₄×C₁₃	—	2	8	no	—
338	C₂×C₄×C₁₃	—	2	32	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	8	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	4	no	—
343	C₂×C₄×C₁₃	—	2	8	no	—
344	C₂×C₄×C₁₃	—	2	4	no	—
345	C₂×C₄×C₁₃	—	2	8	no	—
346	C₂×C₄×C₁₃	—	4	4	no	—
347	C₂×C₄×C₁₃	—	4	4	no	—
348	C₂×C₄×C₁₃	—	4	8	no	—
349	C₂×C₄×C₁₃	—	4	8	no	—
350	C₂×C₄×C₁₃	#120	1	16	yes	complemented
351	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
353	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
356	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
358	C₂×C₄×C₁₃	C₂×#41	1	4	yes	complemented
359	C₂²×#41	—	2	16	no	—
360	C₂²×#41	—	2	8	no	—
361	C₂²×#41	C₂²×C₁₃	1	2	yes	—
362	C₂²×#41	C₂²×C₁₃	1	2	yes	—
363	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
364	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
365	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
366	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
367	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
368	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
369	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
370	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
371	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
372	#525	—	2	16	no	—
373	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
374	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
375	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
376	C₂×#120	C₂²×C₁₃	1	4	yes	—
377	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
378	C₂×C₄×D₄	—	2	8	no	—
379	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
380	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
381	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
382	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
383	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
384	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
385	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
387	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	#395	C₂²×C₁₃	1	4	yes	complemented
390	#394	C₂²×C₁₃	1	8	yes	complemented
391	#394	C₂²×C₁₃	1	4	yes	complemented
392	#393	C₂²×C₁₃	1	4	yes	complemented
393	#392	C₂²×C₁₃	1	8	yes	complemented
394	#392	C₂²×C₁₃	1	4	yes	complemented
395	#391	C₂²×C₁₃	1	4	yes	complemented
396	#390	C₂²×C₁₃	1	4	yes	complemented
397	#386	C₂²×C₁₃	1	4	yes	—
398	#386	C₂²×C₁₃	1	4	yes	complemented
399	#386	C₂²×C₁₃	1	4	yes	complemented
400	#386	C₂²×C₁₃	1	8	yes	complemented
401	#385	C₂²×C₁₃	1	4	yes	complemented
402	#385	C₂²×C₁₃	1	8	yes	complemented
403	#381	C₂²×C₁₃	1	2	yes	complemented
404	#380	C₂²×C₁₃	1	2	yes	complemented
405	#380	C₂²×C₁₃	1	2	yes	complemented
406	#379	C₂²×C₁₃	1	2	yes	—
407	#379	C₂²×C₁₃	1	4	yes	complemented
408	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
409	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
410	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
411	C₂²×C₁₃	—	2	2	no	—
412	C₂²×C₁₃	—	2	2	no	—
413	C₂²×C₁₃	—	2	2	no	—
414	C₂²×C₁₃	—	2	2	no	—
415	C₂²×C₁₃	—	2	8	no	—
416	C₂²×C₁₃	—	2	8	no	—
417	C₂²×C₁₃	—	2	8	no	—
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	4	no	—
421	C₂²×C₁₃	—	2	2	no	—
422	C₂²×C₁₃	—	2	8	no	—
423	C₂²×C₁₃	—	2	16	no	—
424	C₂²×C₁₃	—	4	16	no	—
425	C₂²×C₁₃	—	4	32	no	—
426	C₂²×C₁₃	—	4	16	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	4	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	4	no	—
431	C₂²×C₁₃	—	4	4	no	—
432	C₂²×C₁₃	—	4	8	no	—
433	C₂²×C₁₃	—	4	4	no	—
434	C₂²×C₁₃	C₂×#120	1	4	yes	—
435	C₂²×C₁₃	#525	1	4	yes	complemented
436	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
437	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
438	C₂²×C₁₃	C₂²×#41	1	2	yes	—
439	C₂²×C₁₃	#585	1	2	yes	—
440	C₄×C₁₃	—	2	2	no	—
441	C₄×C₁₃	—	2	8	no	—
442	C₄×C₁₃	—	2	2	no	—
443	C₄×C₁₃	—	2	4	no	—
444	C₄×C₁₃	—	4	2	no	—
445	C₄×C₁₃	—	4	2	no	—
446	C₄×C₁₃	—	4	8	no	—
447	C₄×C₁₃	C₂×#120	1	4	yes	—
448	C₄×C₁₃	C₂×#120	1	4	yes	—
449	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
450	C₂⁵	C₂³×C₁₃	1	2	yes	—
451	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×#41	—	2	128	no	—
453	C₂×#41	—	2	8	no	—
454	C₂×#41	—	2	16	no	—
455	C₂×#41	—	2	8	no	—
456	C₂×#41	—	2	8	no	—
457	C₂×#41	—	2	8	no	—
458	C₂×#41	—	2	8	no	—
459	C₂×#41	—	2	8	no	—
460	C₂×#41	—	2	8	no	—
461	C₂×#41	—	2	16	no	—
462	C₂×#41	D₄×C₁₃	1	16	yes	complemented
463	C₂²×Q₈	—	2	8	no	—
464	C₂²×Q₈	—	2	4	no	—
465	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
466	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
467	C₂²×D₄	—	2	4	no	—
468	C₂²×D₄	—	2	8	no	—
469	C₂²×D₄	—	2	16	no	—
470	C₂²×D₄	—	2	8	no	—
471	C₂²×D₄	—	2	8	no	—
472	C₂²×D₄	—	2	4	no	—
473	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
474	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
475	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
476	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
477	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
478	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
479	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
480	C₂³×C₄	—	2	8	no	—
481	C₂³×C₄	—	2	8	no	—
482	C₂³×C₄	—	2	16	no	—
483	C₂³×C₄	—	2	4	no	—
484	C₂³×C₄	—	2	8	no	—
485	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
486	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
489	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
490	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
491	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
492	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
498	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
500	#123	—	2	16	no	—
501	C₂²⋊Q₈	—	2	16	no	—
502	#121	—	2	16	no	—
503	#120	—	2	16	no	—
504	#120	—	2	16	no	—
505	C₄×D₄	—	2	8	no	—
506	C₄×D₄	—	2	8	no	—
507	C₄×D₄	—	2	8	no	—
508	C₄×D₄	—	2	8	no	—
509	C₄×D₄	—	2	32	no	—
510	#117	—	2	8	no	—
511	C₂×C₄⋊C₄	—	2	4	no	—
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
516	C₂×C₂²⋊C₄	—	2	4	no	—
517	C₂×C₂²⋊C₄	—	2	4	no	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
529	C₂×C₄²	—	2	4	no	—
530	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
531	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
533	#95	C₂³×C₁₃	1	4	yes	—
534	#95	C₂³×C₁₃	1	4	yes	—
535	#95	C₂³×C₁₃	1	8	yes	—
536	#95	C₂³×C₁₃	1	8	yes	—
537	C₂×C₁₃	—	2	4	no	—
538	C₂×C₁₃	—	2	4	no	—
539	C₂×C₁₃	—	4	2	no	—
540	C₂×C₁₃	—	4	8	no	—
541	C₂×C₁₃	—	4	4	no	—
542	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
543	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
544	C₂×C₁₃	#3449	1	1	yes	characteristic
545	C₂×C₁₃	D₄×#41	1	4	yes	—
546	C₂⁴	—	2	2	no	—
547	C₂⁴	—	2	8	no	—
548	C₂⁴	—	2	4	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	2	8	no	—
554	C₂⁴	—	4	2	no	—
555	C₂⁴	—	4	2	no	—
556	C₂⁴	—	4	4	no	—
557	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
558	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
559	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
560	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
561	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
562	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
563	#41	—	2	64	no	—
564	#41	—	2	64	no	—
565	#41	—	2	64	no	—
566	#41	—	2	64	no	—
567	C₂×Q₈	—	2	32	no	—
568	C₂×Q₈	—	2	8	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	complemented
573	C₂×D₄	—	2	64	no	—
574	C₂×D₄	—	2	32	no	—
575	C₂×D₄	—	2	32	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	8	no	—
579	C₂×D₄	—	2	8	no	—
580	C₂×D₄	—	2	8	no	—
581	C₂×D₄	—	2	8	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	16	no	—
586	C₂×D₄	—	2	16	no	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	4	8	no	—
593	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
594	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	complemented
595	C₂×D₄	C₁₃×#41	1	8	yes	complemented
596	C₂²×C₄	—	2	64	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	8	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	32	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	8	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	8	no	—
606	C₂²×C₄	—	2	8	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	8	no	—
610	C₂²×C₄	—	2	8	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	8	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	4	16	no	—
621	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
622	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
623	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
624	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
625	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
626	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
627	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
628	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
629	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
631	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	8	no	—
641	C₄⋊C₄	—	2	16	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	8	no	—
645	C₂²⋊C₄	—	2	16	no	—
646	C₂²⋊C₄	—	2	8	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	16	no	—
650	C₂²⋊C₄	—	2	16	no	—
651	C₂²⋊C₄	—	4	8	no	—
652	C₂²⋊C₄	—	4	4	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	8	no	—
656	C₁₃	#34736	1	1	yes	characteristic, direct product factor, Sylow
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	16	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	8	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	8	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	16	no	—
678	C₂³	—	4	32	no	—
679	C₂³	—	4	16	no	—
680	C₂³	—	4	4	no	—
681	C₂³	—	4	8	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	4	8	no	—
684	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
685	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
686	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
687	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
688	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
689	C₂³	C₂×C₁₃×#41	1	4	yes	—
690	C₂³	C₂×C₁₃×#41	1	4	yes	complemented
691	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
692	Q₈	—	2	16	no	—
693	Q₈	—	2	16	no	—
694	D₄	—	2	16	no	—
695	D₄	—	2	32	no	—
696	D₄	—	2	16	no	—
697	D₄	—	2	32	no	—
698	D₄	—	2	16	no	—
699	D₄	—	2	16	no	—
700	D₄	—	4	32	no	—
701	C₂×C₄	—	2	16	no	—
702	C₂×C₄	—	2	32	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	8	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	8	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	8	no	—
714	C₂×C₄	—	2	8	no	—
715	C₂×C₄	—	2	32	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	8	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	8	no	—
723	C₂×C₄	—	4	4	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	8	no	—
726	C₂×C₄	—	4	8	no	—
727	C₂×C₄	C₁₃×#120	1	16	yes	complemented
728	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
730	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
733	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
735	C₂×C₄	C₂×C₁₃×#41	1	4	yes	complemented
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	8	no	—
741	C₂²	—	2	8	no	—
742	C₂²	—	2	8	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	8	no	—
748	C₂²	—	2	16	no	—
749	C₂²	—	4	16	no	—
750	C₂²	—	4	32	no	—
751	C₂²	—	4	16	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	8	no	—
758	C₂²	—	4	4	no	—
759	C₂²	C₂×C₁₃×#120	1	4	yes	—
760	C₂²	C₁₃×#525	1	4	yes	complemented
761	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
762	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
763	C₂²	C₂²×C₁₃×#41	1	2	yes	—
764	C₂²	C₁₃×#585	1	2	yes	—
765	C₄	—	2	2	no	—
766	C₄	—	2	8	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	4	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	8	no	—
772	C₄	C₂×C₁₃×#120	1	4	yes	—
773	C₄	C₂×C₁₃×#120	1	4	yes	—
774	C₂	—	2	4	no	—
775	C₂	—	2	4	no	—
776	C₂	—	4	2	no	—
777	C₂	—	4	8	no	—
778	C₂	—	4	4	no	—
779	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
780	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
781	C₂	C₁₃×#3449	1	1	yes	characteristic
782	C₂	D₄×C₁₃×#41	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₃×#41	C₂	semidirect
2. C₂×C₁₃×#525	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃	C₂	semidirect
4. C₁₃×#2409	C₂	semidirect
5. C₁₃×#2408	C₂	semidirect
6. C₁₃×#2407	C₂	semidirect
7. C₁₃×#2406	C₂	semidirect
8. C₁₃×#2405	C₂	semidirect
9. C₁₃×#2404	C₂	semidirect
10. C₁₃×#2403	C₂	semidirect
11. C₁₃×#2388	C₂	semidirect
12. C₄×C₁₃×#120	C₂	semidirect
13. C₁₃×#2297	C₂	semidirect
14. C₁₃×#2280	C₂	semidirect
19. C₂²×C₁₃×#41	C₂²	semidirect
20. C₂²×C₁₃×#41	C₂²	semidirect
21. C₂³×Q₈×C₁₃	C₂²	semidirect
24. C₂³×D₄×C₁₃	C₂²	semidirect
26. C₂⁴×C₄×C₁₃	C₂²	semidirect
27. C₂⁴×C₄×C₁₃	C₂²	semidirect
29. C₂×C₁₃×#123	C₂²	semidirect
30. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₁₃×#121	C₂²	semidirect
33. C₂×C₁₃×#120	C₂²	semidirect
37. C₂×C₄×D₄×C₁₃	C₂²	semidirect
38. C₂×C₄×D₄×C₁₃	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃	C₂²	semidirect
40. C₂×C₁₃×#117	C₂²	semidirect
41. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
43. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
44. C₂²×C₄²×C₁₃	C₂²	semidirect
45. C₁₃×#395	C₂²	semidirect
46. C₁₃×#394	C₂²	semidirect
47. C₁₃×#394	C₂²	semidirect
48. C₁₃×#393	C₂²	semidirect
49. C₁₃×#392	C₂²	semidirect
50. C₁₃×#392	C₂²	semidirect
51. C₁₃×#391	C₂²	semidirect
52. C₁₃×#390	C₂²	semidirect
54. C₁₃×#386	C₂²	semidirect
55. C₁₃×#386	C₂²	semidirect
56. C₁₃×#386	C₂²	semidirect
57. C₁₃×#385	C₂²	semidirect
58. C₁₃×#385	C₂²	semidirect
59. C₁₃×#381	C₂²	semidirect
60. C₁₃×#380	C₂²	semidirect
61. C₁₃×#380	C₂²	semidirect
63. C₁₃×#379	C₂²	semidirect
64. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
65. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
66. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
80. C₂×C₁₃×#41	D₄	semidirect
103. C₂³×C₄×C₁₃	D₄	semidirect
155. #34736	C₁₃	direct (N × H)
182. C₂×Q₈×C₁₃	C₂×D₄	semidirect
204. C₂×D₄×C₁₃	C₂×D₄	semidirect
205. C₂×D₄×C₁₃	#41	semidirect
238. C₂²×C₄×C₁₃	C₂×D₄	semidirect
266. C₂³×#41	C₂×C₁₃	semidirect
267. C₂×#525	C₂×C₁₃	semidirect
268. C₂²×C₄×D₄	C₂×C₁₃	semidirect
269. #2409	C₂×C₁₃	semidirect
270. #2408	C₂×C₁₃	semidirect
271. #2407	C₂×C₁₃	semidirect
272. #2406	C₂×C₁₃	semidirect
273. #2405	C₂×C₁₃	semidirect
274. #2404	C₂×C₁₃	semidirect
275. #2403	C₂×C₁₃	semidirect
276. #2388	C₂×C₁₃	semidirect
277. C₄×#120	C₂×C₁₃	semidirect
278. #2297	C₂×C₁₃	semidirect
279. #2280	C₂×C₁₃	semidirect
313. C₂³×C₁₃	C₂×#41	semidirect
350. C₂×C₄×C₁₃	#120	semidirect
358. C₂×C₄×C₁₃	C₂×#41	semidirect
363. C₂²×#41	C₂²×C₁₃	semidirect
364. C₂²×#41	C₂²×C₁₃	semidirect
365. C₂³×Q₈	C₂²×C₁₃	semidirect
368. C₂³×D₄	C₂²×C₁₃	semidirect
370. C₂⁴×C₄	C₂²×C₁₃	semidirect
371. C₂⁴×C₄	C₂²×C₁₃	semidirect
373. C₂×#123	C₂²×C₁₃	semidirect
374. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
375. C₂×#121	C₂²×C₁₃	semidirect
377. C₂×#120	C₂²×C₁₃	semidirect
381. C₂×C₄×D₄	C₂²×C₁₃	semidirect
382. C₂×C₄×D₄	C₂²×C₁₃	semidirect
383. C₂×C₄×D₄	C₂²×C₁₃	semidirect
384. C₂×#117	C₂²×C₁₃	semidirect
385. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
387. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
388. C₂²×C₄²	C₂²×C₁₃	semidirect
389. #395	C₂²×C₁₃	semidirect
390. #394	C₂²×C₁₃	semidirect
391. #394	C₂²×C₁₃	semidirect
392. #393	C₂²×C₁₃	semidirect
393. #392	C₂²×C₁₃	semidirect
394. #392	C₂²×C₁₃	semidirect
395. #391	C₂²×C₁₃	semidirect
396. #390	C₂²×C₁₃	semidirect
398. #386	C₂²×C₁₃	semidirect
399. #386	C₂²×C₁₃	semidirect
400. #386	C₂²×C₁₃	semidirect
401. #385	C₂²×C₁₃	semidirect
402. #385	C₂²×C₁₃	semidirect
403. #381	C₂²×C₁₃	semidirect
404. #380	C₂²×C₁₃	semidirect
405. #380	C₂²×C₁₃	semidirect
407. #379	C₂²×C₁₃	semidirect
408. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
409. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
410. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
435. C₂²×C₁₃	#525	semidirect
462. C₂×#41	D₄×C₁₃	semidirect
485. C₂³×C₄	D₄×C₁₃	semidirect
572. C₂×Q₈	C₂×D₄×C₁₃	semidirect
594. C₂×D₄	C₂×D₄×C₁₃	semidirect
595. C₂×D₄	C₁₃×#41	semidirect
628. C₂²×C₄	C₂×D₄×C₁₃	semidirect
656. C₁₃	#34736	direct (N × H)
690. C₂³	C₂×C₁₃×#41	semidirect
727. C₂×C₄	C₁₃×#120	semidirect
735. C₂×C₄	C₂×C₁₃×#41	semidirect
760. C₂²	C₁₃×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×#41	2
C₂×C₁₃×#525	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2409	2
C₁₃×#2408	2
C₁₃×#2407	2
C₁₃×#2406	2
C₁₃×#2405	2
C₁₃×#2404	2
C₁₃×#2403	2
C₁₃×#2388	2
C₄×C₁₃×#120	2
C₁₃×#2297	2
C₁₃×#2280	2
#34736	13

Subgroups — C13×#34736 #15721075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34736 #15721075