Subgroups — C₂×#13128523 #16770828

Order 3328.

9502 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128523	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719292	C₂	1	4	yes	maximal, complemented
3	C₂×#11719200	C₂	1	4	yes	maximal, complemented
4	C₂×#11719511	C₂	1	4	yes	maximal, complemented
5	C₂×#11719296	C₂	1	4	yes	maximal, complemented
6	C₂×#11719188	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11719298	C₂	1	4	yes	maximal, complemented
8	C₂×#11719509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11719291	C₂	1	4	yes	maximal, complemented
10	C₂²×#88207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11719503	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11719191	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×C₂²⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
18	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
19	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
20	C₂⁴×Dic₁₃	C₂²	1	2	yes	complemented
21	C₂²×#6129	C₂²	1	4	yes	complemented
22	C₂×C₁₃×#120	C₂²	1	4	yes	—
23	C₂×C₁₃×#120	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#120	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#120	C₂²	1	16	yes	complemented
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
28	C₂×#88207	C₂²	1	4	yes	—
29	C₂×#88207	C₂²	1	2	yes	complemented
30	C₂×#88207	C₂²	1	2	yes	complemented
31	C₂×#88207	C₂²	1	16	yes	complemented
32	C₂×#88207	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
37	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
38	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
40	C₂²×C₂²⋊Dic₁₃	C₂²	1	16	yes	complemented
41	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
42	#11719511	C₂²	1	64	yes	complemented
43	#11719509	C₂²	1	16	yes	complemented
44	C₂×#88193	C₂²	1	4	yes	complemented
45	C₂×#88193	C₂²	1	4	yes	complemented
46	C₂×#88193	C₂²	1	4	yes	complemented
47	C₂×#88192	C₂²	1	4	yes	complemented
48	C₂×#88191	C₂²	1	2	yes	complemented
49	#11719503	C₂²	1	16	yes	complemented
50	C₂×#88190	C₂²	1	4	yes	complemented
51	C₂×#88189	C₂²	1	4	yes	complemented
52	C₂×#88189	C₂²	1	4	yes	complemented
53	C₂×#88189	C₂²	1	2	yes	complemented
54	C₂×D₄×Dic₁₃	C₂²	1	4	yes	complemented
55	C₂×D₄×Dic₁₃	C₂²	1	4	yes	complemented
56	C₂×D₄×Dic₁₃	C₂²	1	4	yes	complemented
57	C₂×#88183	C₂²	1	2	yes	complemented
58	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
59	C₂×#88180	C₂²	1	2	yes	complemented
60	C₂×#88178	C₂²	1	4	yes	complemented
61	#11719298	C₂²	1	64	yes	complemented
62	#11719296	C₂²	1	64	yes	complemented
63	#11719292	C₂²	1	64	yes	complemented
64	#11719291	C₂²	1	64	yes	complemented
65	#11719200	C₂²	1	64	yes	complemented
66	C₂×#88140	C₂²	1	4	yes	complemented
67	C₂×#88139	C₂²	1	4	yes	complemented
68	C₂×#88137	C₂²	1	4	yes	complemented
69	#11719191	C₂²	1	16	yes	complemented
70	C₂×#88135	C₂²	1	4	yes	complemented
71	C₂×#88135	C₂²	1	4	yes	complemented
72	C₂×C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
73	#11719188	C₂²	1	16	yes	complemented
74	C₂×#88133	C₂²	1	4	yes	complemented
75	C₂×#88133	C₂²	1	4	yes	complemented
76	C₂×#88132	C₂²	1	4	yes	complemented
77	C₂×#88132	C₂²	1	4	yes	complemented
78	C₂×#88132	C₂²	1	4	yes	complemented
79	C₂×#88131	C₂²	1	2	yes	complemented
80	C₂×#88131	C₂²	1	4	yes	complemented
81	C₂⁵×C₁₃	—	2	8	no	—
82	C₂⁵×C₁₃	—	4	8	no	—
83	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
84	C₂⁵×C₁₃	C₂³	1	2	yes	—
85	C₂⁵×C₁₃	C₂³	1	2	yes	—
86	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
87	C₂⁵×C₁₃	C₂³	1	8	yes	—
88	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
89	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
90	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	—	2	8	no	—
92	C₂²×D₄×C₁₃	—	4	8	no	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
101	C₂²×C₂²⋊D₁₃	—	2	8	no	—
102	C₂²×C₂²⋊D₁₃	—	4	8	no	—
103	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
104	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
105	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
106	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
107	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
108	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	complemented
109	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	complemented
110	C₂³×Dic₁₃	—	4	8	no	—
111	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
112	C₂³×Dic₁₃	C₂³	1	4	yes	—
113	C₂³×Dic₁₃	C₂³	1	2	yes	—
114	C₂³×Dic₁₃	C₂³	1	2	yes	—
115	C₂³×Dic₁₃	C₂³	1	4	yes	—
116	C₂³×Dic₁₃	C₂³	1	2	yes	—
117	C₂³×Dic₁₃	C₂³	1	16	yes	complemented
118	C₂³×Dic₁₃	C₂³	1	4	yes	complemented
119	C₂×#6129	—	4	16	no	—
120	C₂×#6129	C₂³	1	32	yes	complemented
121	C₂²×C₄×D₁₃	C₂³	1	4	yes	complemented
122	C₂²×Dic₂₆	C₂³	1	4	yes	complemented
123	C₁₃×#120	C₂³	1	32	yes	—
124	C₁₃×#120	C₂³	1	16	yes	complemented
125	C₁₃×#120	C₂³	1	16	yes	complemented
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
132	#88207	C₂³	1	32	yes	—
133	#88207	C₂³	1	16	yes	complemented
134	#88207	C₂³	1	16	yes	complemented
135	#88207	C₂³	1	16	yes	complemented
136	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
137	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
141	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
142	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
143	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
144	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
145	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
146	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	complemented
150	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	complemented
151	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	complemented
152	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	complemented
153	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	complemented
154	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	complemented
155	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	complemented
156	#88193	C₂³	1	32	yes	complemented
157	#88193	C₂³	1	32	yes	complemented
158	#88193	C₂³	1	32	yes	complemented
159	#88192	C₂³	1	32	yes	complemented
160	#88191	C₂³	1	16	yes	complemented
161	#88190	C₂³	1	32	yes	complemented
162	#88189	C₂³	1	32	yes	complemented
163	#88189	C₂³	1	16	yes	complemented
164	#88189	C₂³	1	32	yes	complemented
165	D₄×Dic₁₃	C₂³	1	32	yes	complemented
166	D₄×Dic₁₃	C₂³	1	32	yes	complemented
167	D₄×Dic₁₃	C₂³	1	32	yes	complemented
168	#88183	C₂³	1	16	yes	complemented
169	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
170	C₂×#6103	C₂³	1	4	yes	complemented
171	C₂×#6103	C₂³	1	4	yes	complemented
172	#88180	C₂³	1	16	yes	complemented
173	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	complemented
174	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	complemented
175	#88178	C₂³	1	32	yes	complemented
176	C₂×#6101	C₂³	1	4	yes	complemented
177	C₂×#6101	C₂³	1	4	yes	complemented
178	C₂×#6101	C₂³	1	4	yes	complemented
179	C₂×#6101	C₂³	1	4	yes	complemented
180	C₂×C₄×Dic₁₃	C₂³	1	4	yes	complemented
181	C₂×C₄×Dic₁₃	C₂³	1	4	yes	complemented
182	#88140	C₂³	1	32	yes	complemented
183	#88139	C₂³	1	32	yes	complemented
184	#88137	C₂³	1	32	yes	complemented
185	#88135	C₂³	1	32	yes	complemented
186	#88135	C₂³	1	32	yes	complemented
187	C₂²⋊C₄×D₁₃	C₂³	1	16	yes	complemented
188	#88133	C₂³	1	32	yes	complemented
189	#88133	C₂³	1	32	yes	complemented
190	#88132	C₂³	1	32	yes	complemented
191	#88132	C₂³	1	32	yes	complemented
192	#88132	C₂³	1	32	yes	complemented
193	#88131	C₂³	1	16	yes	complemented
194	#88131	C₂³	1	32	yes	complemented
195	C₂×#3490	—	13	1	no	maximal, Sylow
196	C₂⁴×C₁₃	—	2	4	no	—
197	C₂⁴×C₁₃	—	2	8	no	—
198	C₂⁴×C₁₃	—	2	8	no	—
199	C₂⁴×C₁₃	—	2	8	no	—
200	C₂⁴×C₁₃	—	2	4	no	—
201	C₂⁴×C₁₃	—	2	32	no	—
202	C₂⁴×C₁₃	—	2	8	no	—
203	C₂⁴×C₁₃	—	2	8	no	—
204	C₂⁴×C₁₃	—	2	4	no	—
205	C₂⁴×C₁₃	—	4	4	no	—
206	C₂⁴×C₁₃	—	4	4	no	—
207	C₂⁴×C₁₃	—	4	4	no	—
208	C₂⁴×C₁₃	—	4	32	no	—
209	C₂⁴×C₁₃	—	4	4	no	—
210	C₂⁴×C₁₃	—	4	4	no	—
211	C₂⁴×C₁₃	—	4	64	no	—
212	C₂⁴×C₁₃	#41	1	8	yes	complemented
213	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
214	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
215	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
216	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
217	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
218	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
222	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
223	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
224	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
225	C₂³×D₁₃	—	2	4	no	—
226	C₂³×D₁₃	—	4	4	no	—
227	C₂³×D₁₃	C₂⁴	1	2	yes	—
228	C₂³×D₁₃	C₂⁴	1	4	yes	—
229	C₂×D₄×C₁₃	—	2	8	no	—
230	C₂×D₄×C₁₃	—	2	8	no	—
231	C₂×D₄×C₁₃	—	2	32	no	—
232	C₂×D₄×C₁₃	—	2	16	no	—
233	C₂×D₄×C₁₃	—	4	8	no	—
234	C₂×D₄×C₁₃	—	4	32	no	—
235	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
236	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
237	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
239	C₂²×C₄×C₁₃	—	2	4	no	—
240	C₂²×C₄×C₁₃	—	4	4	no	—
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
245	C₂×C₂²⋊D₁₃	—	2	8	no	—
246	C₂×C₂²⋊D₁₃	—	2	8	no	—
247	C₂×C₂²⋊D₁₃	—	2	32	no	—
248	C₂×C₂²⋊D₁₃	—	2	16	no	—
249	C₂×C₂²⋊D₁₃	—	4	8	no	—
250	C₂×C₂²⋊D₁₃	—	4	8	no	—
251	C₂×C₂²⋊D₁₃	—	4	32	no	—
252	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
253	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
254	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
255	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
256	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	complemented
257	C₂²×Dic₁₃	—	2	4	no	—
258	C₂²×Dic₁₃	—	2	16	no	—
259	C₂²×Dic₁₃	—	4	8	no	—
260	C₂²×Dic₁₃	—	4	4	no	—
261	C₂²×Dic₁₃	—	4	8	no	—
262	C₂²×Dic₁₃	—	4	4	no	—
263	C₂²×Dic₁₃	—	4	32	no	—
264	C₂²×Dic₁₃	—	4	4	no	—
265	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
266	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
267	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
268	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
269	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
270	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
271	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
272	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
273	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
274	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
275	C₂²×Dic₁₃	C₂⁴	1	16	yes	complemented
276	#6129	—	4	64	no	—
277	C₂×C₄×D₁₃	—	4	8	no	—
278	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
279	C₂×Dic₂₆	—	4	8	no	—
280	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
281	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
282	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
283	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
284	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
285	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
286	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
287	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
288	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
289	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
290	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
291	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
292	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
293	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
294	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
295	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	complemented
296	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	complemented
297	#6103	C₂⁴	1	16	yes	complemented
298	#6103	C₂⁴	1	16	yes	complemented
299	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
300	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
301	#6101	C₂⁴	1	16	yes	complemented
302	#6101	C₂⁴	1	16	yes	complemented
303	#6101	C₂⁴	1	16	yes	complemented
304	#6101	C₂⁴	1	16	yes	complemented
305	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
306	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
307	#3490	—	13	32	no	—
308	C₂×#551	—	13	4	no	—
309	C₂×#551	—	13	4	no	—
310	C₂×#546	—	13	4	no	—
311	C₂×#546	—	13	4	no	—
312	C₂×#543	—	13	1	no	—
313	C₂×#538	—	13	4	no	—
314	C₂×#534	—	13	1	no	—
315	C₂×#525	—	13	4	no	—
316	C₂²×#120	—	13	1	no	—
317	C₂²×#120	D₁₃	1	1	yes	characteristic, complemented
318	C₂×#518	—	13	1	no	—
319	C₂×#518	—	13	1	no	—
320	C₂³×C₂²⋊C₄	—	13	1	no	—
321	C₂³×C₁₃	—	2	32	no	—
322	C₂³×C₁₃	—	2	8	no	—
323	C₂³×C₁₃	—	2	4	no	—
324	C₂³×C₁₃	—	2	16	no	—
325	C₂³×C₁₃	—	2	4	no	—
326	C₂³×C₁₃	—	2	4	no	—
327	C₂³×C₁₃	—	2	4	no	—
328	C₂³×C₁₃	—	2	4	no	—
329	C₂³×C₁₃	—	2	4	no	—
330	C₂³×C₁₃	—	2	16	no	—
331	C₂³×C₁₃	—	2	16	no	—
332	C₂³×C₁₃	—	2	8	no	—
333	C₂³×C₁₃	—	2	4	no	—
334	C₂³×C₁₃	—	2	8	no	—
335	C₂³×C₁₃	—	2	16	no	—
336	C₂³×C₁₃	—	2	4	no	—
337	C₂³×C₁₃	—	2	16	no	—
338	C₂³×C₁₃	—	2	4	no	—
339	C₂³×C₁₃	—	2	8	no	—
340	C₂³×C₁₃	—	4	16	no	—
341	C₂³×C₁₃	—	4	8	no	—
342	C₂³×C₁₃	—	4	8	no	—
343	C₂³×C₁₃	—	4	8	no	—
344	C₂³×C₁₃	—	4	8	no	—
345	C₂³×C₁₃	—	4	8	no	—
346	C₂³×C₁₃	—	4	32	no	—
347	C₂³×C₁₃	—	4	32	no	—
348	C₂³×C₁₃	—	4	128	no	—
349	C₂³×C₁₃	—	4	16	no	—
350	C₂³×C₁₃	—	8	8	no	—
351	C₂³×C₁₃	C₂×#41	1	4	yes	—
352	C₂³×C₁₃	C₂×#41	1	4	yes	—
353	C₂³×C₁₃	C₂×#41	1	4	yes	—
354	C₂³×C₁₃	C₂×#41	1	16	yes	complemented
355	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
356	C₂³×C₁₃	C₂⁵	1	4	yes	—
357	C₂³×C₁₃	C₂⁵	1	4	yes	—
358	C₂³×C₁₃	C₂⁵	1	2	yes	—
359	C₂³×C₁₃	C₂⁵	1	2	yes	—
360	C₂³×C₁₃	C₂⁵	1	2	yes	—
361	C₂³×C₁₃	C₂⁵	1	4	yes	—
362	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
363	C₂²×D₁₃	—	2	4	no	—
364	C₂²×D₁₃	—	2	8	no	—
365	C₂²×D₁₃	—	2	8	no	—
366	C₂²×D₁₃	—	4	8	no	—
367	C₂²×D₁₃	—	8	8	no	—
368	C₂²×D₁₃	C₂⁵	1	4	yes	—
369	D₄×C₁₃	—	2	16	no	—
370	D₄×C₁₃	—	2	16	no	—
371	D₄×C₁₃	—	2	32	no	—
372	D₄×C₁₃	—	4	16	no	—
373	C₂×C₄×C₁₃	—	2	8	no	—
374	C₂×C₄×C₁₃	—	2	4	no	—
375	C₂×C₄×C₁₃	—	2	8	no	—
376	C₂×C₄×C₁₃	—	4	8	no	—
377	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
378	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
379	C₂²⋊D₁₃	—	2	16	no	—
380	C₂²⋊D₁₃	—	2	16	no	—
381	C₂²⋊D₁₃	—	2	32	no	—
382	C₂²⋊D₁₃	—	4	16	no	—
383	C₂²⋊D₁₃	—	4	16	no	—
384	C₂×Dic₁₃	—	2	8	no	—
385	C₂×Dic₁₃	—	2	4	no	—
386	C₂×Dic₁₃	—	2	8	no	—
387	C₂×Dic₁₃	—	2	8	no	—
388	C₂×Dic₁₃	—	2	8	no	—
389	C₂×Dic₁₃	—	2	32	no	—
390	C₂×Dic₁₃	—	4	16	no	—
391	C₂×Dic₁₃	—	4	8	no	—
392	C₂×Dic₁₃	—	4	16	no	—
393	C₂×Dic₁₃	—	4	8	no	—
394	C₂×Dic₁₃	—	4	8	no	—
395	C₂×Dic₁₃	C₂⁵	1	4	yes	—
396	C₂×Dic₁₃	C₂⁵	1	8	yes	—
397	C₂×Dic₁₃	C₂⁵	1	8	yes	—
398	C₂×Dic₁₃	C₂⁵	1	8	yes	—
399	C₄×D₁₃	—	4	16	no	—
400	Dic₂₆	—	4	16	no	—
401	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
402	C₂²×#41	—	13	4	no	—
403	C₂³×D₄	—	13	1	no	—
404	C₂³×D₄	—	13	2	no	—
405	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
406	C₂³×D₄	C₂×D₁₃	1	2	yes	complemented
407	C₂⁴×C₄	—	13	2	no	—
408	#551	—	13	64	no	—
409	#551	—	13	64	no	—
410	#546	—	13	64	no	—
411	#546	—	13	64	no	—
412	#543	—	13	16	no	—
413	#538	—	13	64	no	—
414	#534	—	13	16	no	—
415	C₂×#126	—	13	4	no	—
416	C₂×#126	—	13	4	no	—
417	C₂×#124	—	13	4	no	—
418	C₂×#124	—	13	4	no	—
419	#525	—	13	64	no	—
420	C₂×#123	—	13	4	no	—
421	C₂×#123	—	13	2	no	—
422	C₂×#123	—	13	4	no	—
423	C₂×#123	—	13	2	no	—
424	C₂×#123	—	13	4	no	—
425	C₂×#123	—	13	4	no	—
426	C₂×C₂²⋊Q₈	—	13	4	no	—
427	C₂×C₂²⋊Q₈	—	13	4	no	—
428	C₂×C₂²⋊Q₈	—	13	4	no	—
429	C₂×C₂²⋊Q₈	—	13	4	no	—
430	C₂×#121	—	13	4	no	—
431	C₂×#121	—	13	4	no	—
432	C₂×#121	—	13	4	no	—
433	C₂×#121	—	13	4	no	—
434	C₂×#120	—	13	2	no	—
435	C₂×#120	—	13	4	no	—
436	C₂×#120	—	13	2	no	—
437	C₂×#120	—	13	16	no	—
438	C₂×#120	—	13	2	no	—
439	C₂×#120	—	13	2	no	—
440	C₂×#120	C₂×D₁₃	1	4	yes	—
441	C₂×#120	C₂×D₁₃	1	2	yes	complemented
442	C₂×#120	C₂×D₁₃	1	2	yes	complemented
443	C₂×#120	C₂×D₁₃	1	16	yes	complemented
444	#518	—	13	16	no	—
445	#518	—	13	16	no	—
446	C₂×C₄×D₄	—	13	4	no	—
447	C₂×C₄×D₄	—	13	4	no	—
448	C₂×C₄×D₄	—	13	4	no	—
449	C₂×C₄×D₄	—	13	4	no	—
450	C₂×C₄×D₄	—	13	4	no	—
451	C₂×C₄×D₄	—	13	4	no	—
452	C₂×#117	—	13	2	no	—
453	C₂×#117	—	13	2	no	—
454	C₂×#117	—	13	4	no	—
455	C₂²×C₂²⋊C₄	—	13	1	no	—
456	C₂²×C₂²⋊C₄	—	13	1	no	—
457	C₂²×C₂²⋊C₄	—	13	2	no	—
458	C₂²×C₂²⋊C₄	—	13	4	no	—
459	C₂²×C₂²⋊C₄	—	13	4	no	—
460	C₂²×C₂²⋊C₄	—	13	16	no	—
461	C₂²×C₂²⋊C₄	—	13	1	no	—
462	C₂²×C₂²⋊C₄	—	13	2	no	—
463	C₂²×C₂²⋊C₄	—	13	2	no	—
464	C₂²×C₂²⋊C₄	—	13	2	no	—
465	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
466	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
467	C₂²×C₁₃	—	2	32	no	—
468	C₂²×C₁₃	—	2	4	no	—
469	C₂²×C₁₃	—	2	4	no	—
470	C₂²×C₁₃	—	2	4	no	—
471	C₂²×C₁₃	—	2	4	no	—
472	C₂²×C₁₃	—	2	4	no	—
473	C₂²×C₁₃	—	2	8	no	—
474	C₂²×C₁₃	—	2	8	no	—
475	C₂²×C₁₃	—	2	16	no	—
476	C₂²×C₁₃	—	2	8	no	—
477	C₂²×C₁₃	—	2	4	no	—
478	C₂²×C₁₃	—	2	4	no	—
479	C₂²×C₁₃	—	2	8	no	—
480	C₂²×C₁₃	—	2	4	no	—
481	C₂²×C₁₃	—	2	4	no	—
482	C₂²×C₁₃	—	4	16	no	—
483	C₂²×C₁₃	—	4	32	no	—
484	C₂²×C₁₃	—	4	32	no	—
485	C₂²×C₁₃	—	4	16	no	—
486	C₂²×C₁₃	—	4	8	no	—
487	C₂²×C₁₃	—	4	8	no	—
488	C₂²×C₁₃	—	8	8	no	—
489	C₂²×C₁₃	C₂²×#41	1	4	yes	—
490	C₂²×C₁₃	C₂²×#41	1	4	yes	—
491	C₂²×C₁₃	C₂²×#41	1	4	yes	—
492	C₂²×C₁₃	C₂²×#41	1	2	yes	—
493	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	—
494	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
495	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
496	C₂×D₁₃	—	2	4	no	—
497	C₂×D₁₃	—	2	8	no	—
498	C₂×D₁₃	—	4	8	no	—
499	C₂×D₁₃	—	8	8	no	—
500	C₄×C₁₃	—	2	4	no	—
501	C₄×C₁₃	—	2	8	no	—
502	Dic₁₃	—	2	4	no	—
503	Dic₁₃	—	2	8	no	—
504	Dic₁₃	—	2	8	no	—
505	Dic₁₃	—	2	8	no	—
506	C₂⁵	—	2	8	no	—
507	C₂⁵	—	4	8	no	—
508	C₂⁵	—	13	1	no	—
509	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
510	C₂⁵	C₂²×D₁₃	1	2	yes	—
511	C₂⁵	C₂²×D₁₃	1	2	yes	—
512	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
513	C₂⁵	C₂²×D₁₃	1	8	yes	—
514	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
515	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
516	C₂×#41	—	13	32	no	—
517	C₂×#41	—	52	16	no	—
518	C₂²×Q₈	—	13	4	no	—
519	C₂²×D₄	—	2	8	no	—
520	C₂²×D₄	—	4	8	no	—
521	C₂²×D₄	—	13	2	no	—
522	C₂²×D₄	—	13	2	no	—
523	C₂²×D₄	—	13	4	no	—
524	C₂²×D₄	—	13	8	no	—
525	C₂²×D₄	—	13	4	no	—
526	C₂²×D₄	—	13	4	no	—
527	C₂²×D₄	—	13	16	no	—
528	C₂²×D₄	—	26	8	no	—
529	C₂²×D₄	—	52	8	no	—
530	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
531	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
532	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
533	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
534	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
535	C₂²×D₄	C₂²×D₁₃	1	16	yes	complemented
536	C₂³×C₄	—	13	1	no	—
537	C₂³×C₄	—	13	4	no	—
538	C₂³×C₄	—	13	2	no	—
539	C₂³×C₄	—	13	4	no	—
540	C₂³×C₄	—	13	2	no	—
541	C₂³×C₄	—	13	2	no	—
542	C₂³×C₄	—	13	16	no	—
543	C₂³×C₄	—	13	4	no	—
544	C₂³×C₄	—	13	4	no	—
545	C₂³×C₄	—	52	8	no	—
546	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
547	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
548	#126	—	13	32	no	—
549	#126	—	13	32	no	—
550	#124	—	13	32	no	—
551	#124	—	13	32	no	—
552	#123	—	13	32	no	—
553	#123	—	13	16	no	—
554	#123	—	13	32	no	—
555	#123	—	13	16	no	—
556	#123	—	13	32	no	—
557	#123	—	13	32	no	—
558	C₂²⋊Q₈	—	13	32	no	—
559	C₂²⋊Q₈	—	13	32	no	—
560	C₂²⋊Q₈	—	13	32	no	—
561	C₂²⋊Q₈	—	13	32	no	—
562	#121	—	13	32	no	—
563	#121	—	13	32	no	—
564	#121	—	13	32	no	—
565	#121	—	13	32	no	—
566	#120	—	13	16	no	—
567	#120	—	13	16	no	—
568	#120	—	13	32	no	—
569	#120	—	13	16	no	—
570	#120	—	13	16	no	—
571	#120	C₂²×D₁₃	1	32	yes	—
572	#120	C₂²×D₁₃	1	16	yes	complemented
573	#120	C₂²×D₁₃	1	16	yes	complemented
574	C₄×D₄	—	13	32	no	—
575	C₄×D₄	—	13	32	no	—
576	C₄×D₄	—	13	32	no	—
577	C₄×D₄	—	13	32	no	—
578	C₄×D₄	—	13	32	no	—
579	C₄×D₄	—	13	32	no	—
580	#117	—	13	16	no	—
581	#117	—	13	16	no	—
582	#117	—	13	32	no	—
583	C₂×C₄⋊C₄	—	13	4	no	—
584	C₂×C₄⋊C₄	—	13	4	no	—
585	C₂×C₄⋊C₄	—	13	4	no	—
586	C₂×C₄⋊C₄	—	13	4	no	—
587	C₂×C₄⋊C₄	—	13	4	no	—
588	C₂×C₄⋊C₄	—	13	4	no	—
589	C₂×C₂²⋊C₄	—	13	2	no	—
590	C₂×C₂²⋊C₄	—	13	2	no	—
591	C₂×C₂²⋊C₄	—	13	8	no	—
592	C₂×C₂²⋊C₄	—	13	2	no	—
593	C₂×C₂²⋊C₄	—	13	2	no	—
594	C₂×C₂²⋊C₄	—	13	4	no	—
595	C₂×C₂²⋊C₄	—	13	4	no	—
596	C₂×C₂²⋊C₄	—	13	8	no	—
597	C₂×C₂²⋊C₄	—	13	16	no	—
598	C₂×C₂²⋊C₄	—	13	32	no	—
599	C₂×C₂²⋊C₄	—	13	32	no	—
600	C₂×C₂²⋊C₄	—	13	2	no	—
601	C₂×C₂²⋊C₄	—	13	4	no	—
602	C₂×C₂²⋊C₄	—	13	2	no	—
603	C₂×C₂²⋊C₄	—	13	4	no	—
604	C₂×C₂²⋊C₄	—	13	8	no	—
605	C₂×C₂²⋊C₄	—	13	16	no	—
606	C₂×C₂²⋊C₄	—	13	4	no	—
607	C₂×C₂²⋊C₄	—	13	16	no	—
608	C₂×C₂²⋊C₄	—	13	4	no	—
609	C₂×C₂²⋊C₄	—	13	4	no	—
610	C₂×C₂²⋊C₄	—	13	4	no	—
611	C₂×C₂²⋊C₄	—	13	16	no	—
612	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
615	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
616	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
617	C₂×C₂²⋊C₄	C₂²×D₁₃	1	16	yes	complemented
618	C₂×C₄²	—	13	4	no	—
619	C₂×C₄²	—	13	4	no	—
620	C₂×C₁₃	—	2	4	no	—
621	C₂×C₁₃	—	2	4	no	—
622	C₂×C₁₃	—	2	8	no	—
623	C₂×C₁₃	—	2	4	no	—
624	C₂×C₁₃	—	4	4	no	—
625	C₂×C₁₃	—	4	4	no	—
626	C₂×C₁₃	#3490	1	4	yes	complemented
627	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
628	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
629	D₁₃	—	4	4	no	—
630	C₂⁴	—	2	4	no	—
631	C₂⁴	—	2	8	no	—
632	C₂⁴	—	2	8	no	—
633	C₂⁴	—	2	8	no	—
634	C₂⁴	—	2	4	no	—
635	C₂⁴	—	2	32	no	—
636	C₂⁴	—	2	8	no	—
637	C₂⁴	—	2	8	no	—
638	C₂⁴	—	2	4	no	—
639	C₂⁴	—	4	4	no	—
640	C₂⁴	—	4	4	no	—
641	C₂⁴	—	4	4	no	—
642	C₂⁴	—	4	32	no	—
643	C₂⁴	—	4	4	no	—
644	C₂⁴	—	4	4	no	—
645	C₂⁴	—	4	64	no	—
646	C₂⁴	—	13	2	no	—
647	C₂⁴	—	13	4	no	—
648	C₂⁴	—	26	4	no	—
649	C₂⁴	—	52	4	no	—
650	C₂⁴	#6129	1	8	yes	complemented
651	C₂⁴	C₂³×D₁₃	1	4	yes	—
652	C₂⁴	C₂³×D₁₃	1	2	yes	—
653	C₂⁴	C₂³×D₁₃	1	2	yes	—
654	C₂⁴	C₂³×D₁₃	1	8	yes	—
655	C₂⁴	C₂³×D₁₃	1	8	yes	—
656	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
657	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
658	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
659	C₂⁴	C₂³×D₁₃	1	2	yes	—
660	C₂⁴	C₂³×D₁₃	1	4	yes	—
661	C₂⁴	C₂³×D₁₃	1	4	yes	—
662	C₂⁴	C₂³×D₁₃	1	4	yes	—
663	#41	—	52	64	no	—
664	C₂×Q₈	—	13	16	no	—
665	C₂×Q₈	—	52	8	no	—
666	C₂×D₄	—	2	8	no	—
667	C₂×D₄	—	2	8	no	—
668	C₂×D₄	—	2	32	no	—
669	C₂×D₄	—	2	16	no	—
670	C₂×D₄	—	4	8	no	—
671	C₂×D₄	—	4	32	no	—
672	C₂×D₄	—	13	8	no	—
673	C₂×D₄	—	13	8	no	—
674	C₂×D₄	—	13	16	no	—
675	C₂×D₄	—	13	16	no	—
676	C₂×D₄	—	13	16	no	—
677	C₂×D₄	—	26	8	no	—
678	C₂×D₄	—	26	8	no	—
679	C₂×D₄	—	26	32	no	—
680	C₂×D₄	—	26	16	no	—
681	C₂×D₄	—	52	8	no	—
682	C₂×D₄	—	52	8	no	—
683	C₂×D₄	—	52	32	no	—
684	C₂×D₄	C₂³×D₁₃	1	8	yes	—
685	C₂×D₄	C₂³×D₁₃	1	8	yes	—
686	C₂×D₄	C₂³×D₁₃	1	16	yes	—
687	C₂×D₄	C₂³×D₁₃	1	16	yes	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	4	4	no	—
690	C₂²×C₄	—	13	4	no	—
691	C₂²×C₄	—	13	16	no	—
692	C₂²×C₄	—	13	2	no	—
693	C₂²×C₄	—	13	4	no	—
694	C₂²×C₄	—	13	4	no	—
695	C₂²×C₄	—	13	4	no	—
696	C₂²×C₄	—	13	8	no	—
697	C₂²×C₄	—	13	16	no	—
698	C₂²×C₄	—	13	8	no	—
699	C₂²×C₄	—	13	8	no	—
700	C₂²×C₄	—	13	16	no	—
701	C₂²×C₄	—	13	16	no	—
702	C₂²×C₄	—	26	4	no	—
703	C₂²×C₄	—	26	16	no	—
704	C₂²×C₄	—	52	8	no	—
705	C₂²×C₄	—	52	4	no	—
706	C₂²×C₄	—	52	8	no	—
707	C₂²×C₄	—	52	4	no	—
708	C₂²×C₄	—	52	32	no	—
709	C₂²×C₄	—	52	4	no	—
710	C₂²×C₄	—	52	8	no	—
711	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
712	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
713	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
714	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
715	C₄⋊C₄	—	13	16	no	—
716	C₄⋊C₄	—	13	16	no	—
717	C₄⋊C₄	—	13	16	no	—
718	C₄⋊C₄	—	13	16	no	—
719	C₄⋊C₄	—	13	16	no	—
720	C₄⋊C₄	—	13	16	no	—
721	C₂²⋊C₄	—	13	8	no	—
722	C₂²⋊C₄	—	13	8	no	—
723	C₂²⋊C₄	—	13	8	no	—
724	C₂²⋊C₄	—	13	8	no	—
725	C₂²⋊C₄	—	13	16	no	—
726	C₂²⋊C₄	—	13	16	no	—
727	C₂²⋊C₄	—	13	8	no	—
728	C₂²⋊C₄	—	13	16	no	—
729	C₂²⋊C₄	—	13	8	no	—
730	C₂²⋊C₄	—	13	16	no	—
731	C₂²⋊C₄	—	13	16	no	—
732	C₂²⋊C₄	—	13	16	no	—
733	C₂²⋊C₄	—	13	16	no	—
734	C₂²⋊C₄	—	13	16	no	—
735	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
736	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
737	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
738	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
739	C₄²	—	13	16	no	—
740	C₄²	—	13	16	no	—
741	C₁₃	C₂×#3490	1	1	yes	characteristic, complemented, Sylow
742	C₂³	—	2	32	no	—
743	C₂³	—	2	8	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	16	no	—
747	C₂³	—	2	4	no	—
748	C₂³	—	2	4	no	—
749	C₂³	—	2	4	no	—
750	C₂³	—	2	4	no	—
751	C₂³	—	2	16	no	—
752	C₂³	—	2	16	no	—
753	C₂³	—	2	8	no	—
754	C₂³	—	2	4	no	—
755	C₂³	—	2	8	no	—
756	C₂³	—	2	16	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	16	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	2	8	no	—
761	C₂³	—	4	16	no	—
762	C₂³	—	4	8	no	—
763	C₂³	—	4	8	no	—
764	C₂³	—	4	8	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	8	no	—
767	C₂³	—	4	32	no	—
768	C₂³	—	4	32	no	—
769	C₂³	—	4	128	no	—
770	C₂³	—	4	16	no	—
771	C₂³	—	8	8	no	—
772	C₂³	—	13	4	no	—
773	C₂³	—	26	4	no	—
774	C₂³	—	26	8	no	—
775	C₂³	—	26	8	no	—
776	C₂³	—	52	8	no	—
777	C₂³	—	104	8	no	—
778	C₂³	C₂×#6129	1	4	yes	—
779	C₂³	C₂×#6129	1	4	yes	—
780	C₂³	C₂×#6129	1	4	yes	—
781	C₂³	C₂×#6129	1	16	yes	complemented
782	C₂³	#88251	1	8	yes	—
783	C₂³	C₂⁴×D₁₃	1	4	yes	—
784	C₂³	C₂⁴×D₁₃	1	4	yes	—
785	C₂³	C₂⁴×D₁₃	1	2	yes	—
786	C₂³	C₂⁴×D₁₃	1	2	yes	—
787	C₂³	C₂⁴×D₁₃	1	2	yes	—
788	C₂³	C₂⁴×D₁₃	1	4	yes	—
789	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
790	Q₈	—	52	16	no	—
791	D₄	—	2	16	no	—
792	D₄	—	2	16	no	—
793	D₄	—	2	32	no	—
794	D₄	—	4	16	no	—
795	D₄	—	26	16	no	—
796	D₄	—	26	16	no	—
797	D₄	—	26	32	no	—
798	D₄	—	52	16	no	—
799	D₄	—	52	16	no	—
800	C₂×C₄	—	2	8	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	8	no	—
803	C₂×C₄	—	4	8	no	—
804	C₂×C₄	—	13	4	no	—
805	C₂×C₄	—	13	8	no	—
806	C₂×C₄	—	13	8	no	—
807	C₂×C₄	—	13	8	no	—
808	C₂×C₄	—	26	8	no	—
809	C₂×C₄	—	26	4	no	—
810	C₂×C₄	—	26	8	no	—
811	C₂×C₄	—	26	8	no	—
812	C₂×C₄	—	26	32	no	—
813	C₂×C₄	—	26	8	no	—
814	C₂×C₄	—	52	16	no	—
815	C₂×C₄	—	52	8	no	—
816	C₂×C₄	—	52	16	no	—
817	C₂×C₄	—	52	8	no	—
818	C₂×C₄	—	52	8	no	—
819	C₂×C₄	—	52	16	no	—
820	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
821	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
822	C₂²	—	2	32	no	—
823	C₂²	—	2	8	no	—
824	C₂²	—	2	16	no	—
825	C₂²	—	2	8	no	—
826	C₂²	—	2	8	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	8	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	4	16	no	—
838	C₂²	—	4	32	no	—
839	C₂²	—	4	32	no	—
840	C₂²	—	4	16	no	—
841	C₂²	—	4	8	no	—
842	C₂²	—	4	8	no	—
843	C₂²	—	8	8	no	—
844	C₂²	—	26	4	no	—
845	C₂²	—	26	8	no	—
846	C₂²	—	52	8	no	—
847	C₂²	—	104	8	no	—
848	C₂²	C₂²×#6129	1	4	yes	—
849	C₂²	C₂²×#6129	1	4	yes	—
850	C₂²	C₂²×#6129	1	4	yes	—
851	C₂²	C₂²×#6129	1	2	yes	—
852	C₂²	C₂×#88251	1	8	yes	—
853	C₂²	C₂×#88251	1	4	yes	—
854	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	26	4	no	—
858	C₄	—	26	8	no	—
859	C₄	—	26	8	no	—
860	C₄	—	26	8	no	—
861	C₂	—	2	4	no	—
862	C₂	—	2	8	no	—
863	C₂	—	2	4	no	—
864	C₂	—	2	4	no	—
865	C₂	—	4	4	no	—
866	C₂	—	4	4	no	—
867	C₂	—	52	4	no	—
868	C₂	#13128523	1	4	yes	direct product factor
869	C₂	C₂³×#6129	1	1	yes	characteristic
870	C₂	C₂²×#88251	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#120	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂²×#120	D₁₃
hypocenter	C₁₃	C₂×#3490
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. #13128523	C₂	direct (N × H)
2. C₂×#11719292	C₂	semidirect
3. C₂×#11719200	C₂	semidirect
4. C₂×#11719511	C₂	semidirect
5. C₂×#11719296	C₂	semidirect
6. C₂×#11719188	C₂	semidirect
7. C₂×#11719298	C₂	semidirect
8. C₂×#11719509	C₂	semidirect
9. C₂×#11719291	C₂	semidirect
10. C₂²×#88207	C₂	semidirect
11. C₂×#11719503	C₂	semidirect
12. C₂×#11719191	C₂	semidirect
13. C₂³×C₂²⋊Dic₁₃	C₂	semidirect
14. C₂²×C₁₃×#120	C₂	semidirect
17. C₂³×D₄×C₁₃	C₂²	semidirect
19. C₂³×C₂²⋊D₁₃	C₂²	semidirect
20. C₂⁴×Dic₁₃	C₂²	semidirect
21. C₂²×#6129	C₂²	semidirect
23. C₂×C₁₃×#120	C₂²	semidirect
24. C₂×C₁₃×#120	C₂²	semidirect
25. C₂×C₁₃×#120	C₂²	semidirect
27. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
29. C₂×#88207	C₂²	semidirect
30. C₂×#88207	C₂²	semidirect
31. C₂×#88207	C₂²	semidirect
32. C₂×#88207	C₂²	semidirect
36. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
37. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
38. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
39. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
40. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
41. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
42. #11719511	C₂²	semidirect
43. #11719509	C₂²	semidirect
44. C₂×#88193	C₂²	semidirect
45. C₂×#88193	C₂²	semidirect
46. C₂×#88193	C₂²	semidirect
47. C₂×#88192	C₂²	semidirect
48. C₂×#88191	C₂²	semidirect
49. #11719503	C₂²	semidirect
50. C₂×#88190	C₂²	semidirect
51. C₂×#88189	C₂²	semidirect
52. C₂×#88189	C₂²	semidirect
53. C₂×#88189	C₂²	semidirect
54. C₂×D₄×Dic₁₃	C₂²	semidirect
55. C₂×D₄×Dic₁₃	C₂²	semidirect
56. C₂×D₄×Dic₁₃	C₂²	semidirect
57. C₂×#88183	C₂²	semidirect
58. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
59. C₂×#88180	C₂²	semidirect
60. C₂×#88178	C₂²	semidirect
61. #11719298	C₂²	semidirect
62. #11719296	C₂²	semidirect
63. #11719292	C₂²	semidirect
64. #11719291	C₂²	semidirect
65. #11719200	C₂²	semidirect
66. C₂×#88140	C₂²	semidirect
67. C₂×#88139	C₂²	semidirect
68. C₂×#88137	C₂²	semidirect
69. #11719191	C₂²	semidirect
70. C₂×#88135	C₂²	semidirect
71. C₂×#88135	C₂²	semidirect
72. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
73. #11719188	C₂²	semidirect
74. C₂×#88133	C₂²	semidirect
75. C₂×#88133	C₂²	semidirect
76. C₂×#88132	C₂²	semidirect
77. C₂×#88132	C₂²	semidirect
78. C₂×#88132	C₂²	semidirect
79. C₂×#88131	C₂²	semidirect
80. C₂×#88131	C₂²	semidirect
98. C₂²×D₄×C₁₃	C₂³	semidirect
108. C₂²×C₂²⋊D₁₃	C₂³	semidirect
109. C₂²×C₂²⋊D₁₃	C₂³	semidirect
117. C₂³×Dic₁₃	C₂³	semidirect
118. C₂³×Dic₁₃	C₂³	semidirect
120. C₂×#6129	C₂³	semidirect
121. C₂²×C₄×D₁₃	C₂³	semidirect
122. C₂²×Dic₂₆	C₂³	semidirect
124. C₁₃×#120	C₂³	semidirect
125. C₁₃×#120	C₂³	semidirect
131. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
133. #88207	C₂³	semidirect
134. #88207	C₂³	semidirect
135. #88207	C₂³	semidirect
149. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
150. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
151. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
152. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
153. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
154. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
155. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
156. #88193	C₂³	semidirect
157. #88193	C₂³	semidirect
158. #88193	C₂³	semidirect
159. #88192	C₂³	semidirect
160. #88191	C₂³	semidirect
161. #88190	C₂³	semidirect
162. #88189	C₂³	semidirect
163. #88189	C₂³	semidirect
164. #88189	C₂³	semidirect
165. D₄×Dic₁₃	C₂³	semidirect
166. D₄×Dic₁₃	C₂³	semidirect
167. D₄×Dic₁₃	C₂³	semidirect
168. #88183	C₂³	semidirect
169. C₄×C₂²⋊D₁₃	C₂³	semidirect
170. C₂×#6103	C₂³	semidirect
171. C₂×#6103	C₂³	semidirect
172. #88180	C₂³	semidirect
173. C₂×C₄⋊Dic₁₃	C₂³	semidirect
174. C₂×C₄⋊Dic₁₃	C₂³	semidirect
175. #88178	C₂³	semidirect
176. C₂×#6101	C₂³	semidirect
177. C₂×#6101	C₂³	semidirect
178. C₂×#6101	C₂³	semidirect
179. C₂×#6101	C₂³	semidirect
180. C₂×C₄×Dic₁₃	C₂³	semidirect
181. C₂×C₄×Dic₁₃	C₂³	semidirect
182. #88140	C₂³	semidirect
183. #88139	C₂³	semidirect
184. #88137	C₂³	semidirect
185. #88135	C₂³	semidirect
186. #88135	C₂³	semidirect
187. C₂²⋊C₄×D₁₃	C₂³	semidirect
188. #88133	C₂³	semidirect
189. #88133	C₂³	semidirect
190. #88132	C₂³	semidirect
191. #88132	C₂³	semidirect
192. #88132	C₂³	semidirect
193. #88131	C₂³	semidirect
194. #88131	C₂³	semidirect
212. C₂⁴×C₁₃	#41	semidirect
256. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
275. C₂²×Dic₁₃	C₂⁴	semidirect
278. C₂×C₄×D₁₃	C₂⁴	semidirect
280. C₂×Dic₂₆	C₂⁴	semidirect
295. C₂²⋊Dic₁₃	C₂⁴	semidirect
296. C₂²⋊Dic₁₃	C₂⁴	semidirect
297. #6103	C₂⁴	semidirect
298. #6103	C₂⁴	semidirect
299. C₄⋊Dic₁₃	C₂⁴	semidirect
300. C₄⋊Dic₁₃	C₂⁴	semidirect
301. #6101	C₂⁴	semidirect
302. #6101	C₂⁴	semidirect
303. #6101	C₂⁴	semidirect
304. #6101	C₂⁴	semidirect
305. C₄×Dic₁₃	C₂⁴	semidirect
306. C₄×Dic₁₃	C₂⁴	semidirect
317. C₂²×#120	D₁₃	semidirect
354. C₂³×C₁₃	C₂×#41	semidirect
406. C₂³×D₄	C₂×D₁₃	semidirect
441. C₂×#120	C₂×D₁₃	semidirect
442. C₂×#120	C₂×D₁₃	semidirect
443. C₂×#120	C₂×D₁₃	semidirect
466. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
535. C₂²×D₄	C₂²×D₁₃	semidirect
572. #120	C₂²×D₁₃	semidirect
573. #120	C₂²×D₁₃	semidirect
617. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
626. C₂×C₁₃	#3490	semidirect
650. C₂⁴	#6129	semidirect
741. C₁₃	C₂×#3490	semidirect
781. C₂³	C₂×#6129	semidirect
868. C₂	#13128523	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128523	2
C₂×#11719292	2
C₂×#11719200	2
C₂×#11719511	2
C₂×#11719296	2
C₂×#11719188	2
C₂×#11719298	2
C₂×#11719509	2
C₂×#11719291	2
C₂²×#88207	2
C₂×#11719503	2
C₂×#11719191	2
C₂³×C₂²⋊Dic₁₃	2
C₂²×C₁₃×#120	2
C₂×#3490	13

Subgroups — C2×#13128523 #16770828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128523 #16770828