Subgroups — C₂×#13129111 #16770210

Order 3328.

7418 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129111	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719299	C₂	1	2	yes	maximal, complemented
3	C₂×#11719300	C₂	1	2	yes	maximal, complemented
4	C₂×#11719369	C₂	1	2	yes	maximal, complemented
5	C₂×#11719247	C₂	1	2	yes	maximal, complemented
6	C₂×#11719268	C₂	1	2	yes	maximal, complemented
7	C₂×#11719364	C₂	1	2	yes	maximal, complemented
8	C₂×#11719257	C₂	1	2	yes	maximal, complemented
9	C₂×#11719255	C₂	1	2	yes	maximal, complemented
10	C₂×#11719239	C₂	1	2	yes	maximal, complemented
11	C₂×#11719345	C₂	1	4	yes	maximal, complemented
12	C₂×#11719318	C₂	1	4	yes	maximal, complemented
13	C₂×#11719530	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11719535	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#11719496	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#6127	C₂²	1	2	yes	—
20	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
21	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#525	C₂²	1	16	yes	complemented
23	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
32	C₂×#88207	C₂²	1	4	yes	complemented
33	#11719535	C₂²	1	16	yes	complemented
34	#11719530	C₂²	1	16	yes	complemented
35	C₂×#88201	C₂²	1	2	yes	complemented
36	C₂×#88198	C₂²	1	2	yes	complemented
37	C₂×#88194	C₂²	1	2	yes	—
38	C₂×#88193	C₂²	1	4	yes	complemented
39	C₂×#88192	C₂²	1	4	yes	complemented
40	C₂×#88191	C₂²	1	4	yes	—
41	C₂×#88191	C₂²	1	2	yes	—
42	C₂×#88191	C₂²	1	2	yes	complemented
43	C₂×#88190	C₂²	1	2	yes	—
44	C₂×#88190	C₂²	1	4	yes	—
45	C₂×#88189	C₂²	1	2	yes	complemented
46	C₂×#88189	C₂²	1	2	yes	complemented
47	#11719496	C₂²	1	32	yes	complemented
48	C₂×#88184	C₂²	1	2	yes	—
49	C₂×#88184	C₂²	1	2	yes	—
50	C₂×#88184	C₂²	1	2	yes	complemented
51	C₂×#88183	C₂²	1	4	yes	complemented
52	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
53	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
54	C₂×#88180	C₂²	1	2	yes	complemented
55	C₂×#88180	C₂²	1	1	yes	characteristic, complemented
56	C₂×#88180	C₂²	1	1	yes	characteristic, complemented
57	C₂×#88178	C₂²	1	2	yes	complemented
58	C₂×#88178	C₂²	1	2	yes	complemented
59	C₂×#88178	C₂²	1	2	yes	complemented
60	#11719369	C₂²	1	32	yes	complemented
61	#11719364	C₂²	1	32	yes	complemented
62	#11719345	C₂²	1	64	yes	complemented
63	#11719318	C₂²	1	64	yes	complemented
64	#11719300	C₂²	1	32	yes	complemented
65	#11719299	C₂²	1	32	yes	complemented
66	#11719268	C₂²	1	32	yes	complemented
67	#11719257	C₂²	1	32	yes	complemented
68	#11719255	C₂²	1	32	yes	complemented
69	#11719247	C₂²	1	32	yes	complemented
70	#11719239	C₂²	1	32	yes	complemented
71	C₂×#88152	C₂²	1	4	yes	complemented
72	C₂×#88150	C₂²	1	4	yes	complemented
73	C₂×#88150	C₂²	1	4	yes	complemented
74	C₂×#88148	C₂²	1	4	yes	complemented
75	C₂×#88146	C₂²	1	4	yes	complemented
76	C₂×#88141	C₂²	1	4	yes	complemented
77	C₂×#88139	C₂²	1	4	yes	complemented
78	C₂×#88139	C₂²	1	4	yes	complemented
79	C₂×#88139	C₂²	1	4	yes	complemented
80	C₂×#88139	C₂²	1	4	yes	complemented
81	C₂×#88138	C₂²	1	4	yes	—
82	C₂×#88137	C₂²	1	4	yes	complemented
83	C₂×#88135	C₂²	1	4	yes	complemented
84	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
85	C₂×#88133	C₂²	1	4	yes	complemented
86	C₂×#88133	C₂²	1	4	yes	complemented
87	C₂×#88129	C₂²	1	2	yes	complemented
88	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
89	C₂×#88123	C₂²	1	2	yes	complemented
90	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
91	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
92	C₂⁴×D₁₃	C₂³	1	2	yes	—
93	C₂×C₁₃×#41	—	4	4	no	—
94	C₂×C₁₃×#41	C₂³	1	8	yes	—
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃	—	4	4	no	—
102	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
109	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
110	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
111	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
112	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
113	C₂³×Dic₁₃	C₂³	1	2	yes	—
114	C₂×#6127	—	4	8	no	—
115	C₂×#6127	C₂³	1	16	yes	—
116	C₂²×D₅₂	—	4	4	no	—
117	C₂²×D₅₂	C₂³	1	2	yes	—
118	C₂²×D₅₂	C₂³	1	2	yes	—
119	C₂²×D₅₂	C₂³	1	8	yes	complemented
120	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
121	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
122	C₂²×Dic₂₆	—	4	4	no	—
123	C₂²×Dic₂₆	C₂³	1	2	yes	—
124	C₂²×Dic₂₆	C₂³	1	4	yes	—
125	C₂²×Dic₂₆	C₂³	1	2	yes	—
126	C₂²×Dic₂₆	C₂³	1	8	yes	complemented
127	C₁₃×#123	C₂³	1	8	yes	—
128	C₁₃×#123	C₂³	1	8	yes	complemented
129	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
130	C₁₃×#121	C₂³	1	16	yes	—
131	C₁₃×#120	C₂³	1	8	yes	—
132	C₁₃×#120	C₂³	1	8	yes	complemented
133	C₄×D₄×C₁₃	C₂³	1	16	yes	—
134	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
135	C₁₃×#117	C₂³	1	8	yes	complemented
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	#88207	C₂³	1	32	yes	complemented
147	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
149	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
150	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
151	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
152	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
153	#88201	C₂³	1	16	yes	complemented
154	#88198	C₂³	1	16	yes	complemented
155	#88194	C₂³	1	16	yes	—
156	#88193	C₂³	1	32	yes	complemented
157	#88192	C₂³	1	32	yes	complemented
158	#88191	C₂³	1	32	yes	—
159	#88191	C₂³	1	16	yes	—
160	#88191	C₂³	1	16	yes	complemented
161	#88190	C₂³	1	32	yes	—
162	#88190	C₂³	1	16	yes	—
163	#88189	C₂³	1	16	yes	complemented
164	#88189	C₂³	1	16	yes	complemented
165	#88184	C₂³	1	16	yes	—
166	#88184	C₂³	1	16	yes	—
167	#88184	C₂³	1	16	yes	complemented
168	#88183	C₂³	1	32	yes	complemented
169	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
170	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
171	C₂×#6103	C₂³	1	4	yes	—
172	C₂×#6103	C₂³	1	4	yes	—
173	C₂×#6103	C₂³	1	4	yes	—
174	C₂×#6103	C₂³	1	4	yes	—
175	C₂×#6103	C₂³	1	4	yes	—
176	C₂×#6103	C₂³	1	4	yes	—
177	#88180	C₂³	1	16	yes	complemented
178	#88180	C₂³	1	8	yes	complemented
179	#88180	C₂³	1	8	yes	complemented
180	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
181	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
182	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
183	#88178	C₂³	1	16	yes	complemented
184	#88178	C₂³	1	16	yes	complemented
185	#88178	C₂³	1	16	yes	complemented
186	C₂×#6101	C₂³	1	4	yes	—
187	C₂×#6101	C₂³	1	4	yes	—
188	C₂×#6101	C₂³	1	4	yes	—
189	C₂×#6101	C₂³	1	4	yes	—
190	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
191	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
192	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
193	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
194	#88152	C₂³	1	32	yes	complemented
195	#88150	C₂³	1	32	yes	complemented
196	#88150	C₂³	1	32	yes	complemented
197	#88148	C₂³	1	32	yes	complemented
198	#88146	C₂³	1	32	yes	complemented
199	#88141	C₂³	1	32	yes	complemented
200	#88139	C₂³	1	32	yes	complemented
201	#88139	C₂³	1	32	yes	complemented
202	#88139	C₂³	1	32	yes	complemented
203	#88139	C₂³	1	32	yes	complemented
204	#88138	C₂³	1	32	yes	—
205	#88137	C₂³	1	32	yes	complemented
206	#88135	C₂³	1	32	yes	complemented
207	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
208	#88133	C₂³	1	32	yes	complemented
209	#88133	C₂³	1	32	yes	complemented
210	#88129	C₂³	1	16	yes	complemented
211	C₄×D₅₂	C₂³	1	16	yes	complemented
212	#88123	C₂³	1	16	yes	complemented
213	C₄×Dic₂₆	C₂³	1	16	yes	complemented
214	C₂×#3540	—	13	1	no	maximal, Sylow
215	C₂⁴×C₁₃	—	4	2	no	—
216	C₂⁴×C₁₃	—	4	4	no	—
217	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
219	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
222	C₂³×D₁₃	—	4	4	no	—
223	C₂³×D₁₃	—	4	8	no	—
224	C₂³×D₁₃	C₂⁴	1	4	yes	—
225	C₂³×D₁₃	C₂⁴	1	8	yes	—
226	C₁₃×#41	—	4	16	no	—
227	C₂×Q₈×C₁₃	—	4	2	no	—
228	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
229	C₂×D₄×C₁₃	—	4	4	no	—
230	C₂×D₄×C₁₃	—	4	4	no	—
231	C₂×D₄×C₁₃	—	4	2	no	—
232	C₂×D₄×C₁₃	—	4	2	no	—
233	C₂×D₄×C₁₃	—	4	2	no	—
234	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
235	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
236	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
237	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
239	C₂²×C₄×C₁₃	—	2	4	no	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	2	8	no	—
242	C₂²×C₄×C₁₃	—	2	4	no	—
243	C₂²×C₄×C₁₃	—	4	16	no	—
244	C₂²×C₄×C₁₃	—	4	2	no	—
245	C₂²×C₄×C₁₃	—	4	4	no	—
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₂²⋊D₁₃	—	4	8	no	—
260	C₂×C₂²⋊D₁₃	—	4	8	no	—
261	C₂×C₂²⋊D₁₃	—	4	8	no	—
262	C₂×C₂²⋊D₁₃	—	4	8	no	—
263	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
264	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
265	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
266	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
267	C₂²×Dic₁₃	—	4	4	no	—
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	#6127	—	4	32	no	—
273	C₂×D₅₂	—	2	8	no	—
274	C₂×D₅₂	—	4	16	no	—
275	C₂×D₅₂	—	4	4	no	—
276	C₂×D₅₂	C₂⁴	1	8	yes	—
277	C₂×D₅₂	C₂⁴	1	8	yes	—
278	C₂×C₄×D₁₃	—	4	8	no	—
279	C₂×C₄×D₁₃	—	4	8	no	—
280	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
281	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
282	C₂×Dic₂₆	—	2	8	no	—
283	C₂×Dic₂₆	—	4	16	no	—
284	C₂×Dic₂₆	—	4	4	no	—
285	C₂×Dic₂₆	—	4	8	no	—
286	C₂×Dic₂₆	C₂⁴	1	8	yes	—
287	C₂×Dic₂₆	C₂⁴	1	16	yes	—
288	C₂×Dic₂₆	C₂⁴	1	8	yes	—
289	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
290	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
291	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
292	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
293	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
294	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
295	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
296	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
297	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
298	C₄²×C₁₃	C₂⁴	1	8	yes	—
299	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
300	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
301	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
302	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
303	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
304	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
305	#6103	C₂⁴	1	16	yes	—
306	#6103	C₂⁴	1	16	yes	—
307	#6103	C₂⁴	1	16	yes	—
308	#6103	C₂⁴	1	16	yes	—
309	#6103	C₂⁴	1	16	yes	—
310	#6103	C₂⁴	1	16	yes	—
311	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
312	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
313	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
314	#6101	C₂⁴	1	16	yes	—
315	#6101	C₂⁴	1	16	yes	—
316	#6101	C₂⁴	1	16	yes	—
317	#6101	C₂⁴	1	16	yes	—
318	C₄×Dic₁₃	C₂⁴	1	16	yes	—
319	C₄×Dic₁₃	C₂⁴	1	8	yes	—
320	C₄×Dic₁₃	C₂⁴	1	16	yes	—
321	C₄×Dic₁₃	C₂⁴	1	8	yes	—
322	#3540	—	13	32	no	—
323	C₂×H(3,𝔽₄)	—	13	2	no	—
324	C₂×#560	—	13	2	no	—
325	C₂×#559	—	13	2	no	—
326	C₂×#556	—	13	2	no	—
327	C₂×#555	—	13	2	no	—
328	C₂×#551	—	13	2	no	—
329	C₂×#548	—	13	2	no	—
330	C₂×#546	—	13	2	no	—
331	C₂×#542	—	13	4	no	—
332	C₂×#542	—	13	2	no	—
333	C₂×#538	—	13	4	no	—
334	C₂×#536	—	13	1	no	—
335	C₂×#535	—	13	1	no	—
336	C₂×#525	—	13	2	no	—
337	C₂×#525	D₁₃	1	1	yes	characteristic, complemented
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	2	4	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	4	no	—
343	C₂³×C₁₃	—	2	4	no	—
344	C₂³×C₁₃	—	2	4	no	—
345	C₂³×C₁₃	—	2	4	no	—
346	C₂³×C₁₃	—	2	4	no	—
347	C₂³×C₁₃	—	4	4	no	—
348	C₂³×C₁₃	—	4	8	no	—
349	C₂³×C₁₃	—	4	16	no	—
350	C₂³×C₁₃	C₂⁵	1	2	yes	—
351	C₂³×C₁₃	C₂⁵	1	4	yes	—
352	C₂³×C₁₃	C₂⁵	1	2	yes	—
353	C₂³×C₁₃	C₂⁵	1	2	yes	—
354	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
355	C₂²×D₁₃	—	2	8	no	—
356	C₂²×D₁₃	—	2	8	no	—
357	C₂²×D₁₃	—	2	8	no	—
358	C₂²×D₁₃	—	4	8	no	—
359	C₂²×D₁₃	—	4	16	no	—
360	C₂²×D₁₃	—	8	16	no	—
361	C₂²×D₁₃	C₂⁵	1	8	yes	—
362	Q₈×C₁₃	—	4	4	no	—
363	D₄×C₁₃	—	4	8	no	—
364	D₄×C₁₃	—	4	8	no	—
365	D₄×C₁₃	—	4	4	no	—
366	D₄×C₁₃	—	4	4	no	—
367	D₄×C₁₃	—	4	4	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	4	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	4	no	—
373	C₂×C₄×C₁₃	—	2	4	no	—
374	C₂×C₄×C₁₃	—	2	8	no	—
375	C₂×C₄×C₁₃	—	2	8	no	—
376	C₂×C₄×C₁₃	—	2	16	no	—
377	C₂×C₄×C₁₃	—	2	8	no	—
378	C₂×C₄×C₁₃	—	4	4	no	—
379	C₂×C₄×C₁₃	—	4	8	no	—
380	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
381	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
382	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
383	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
384	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
385	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
386	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
387	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
388	C₂²⋊D₁₃	—	4	16	no	—
389	C₂²⋊D₁₃	—	4	16	no	—
390	C₂²⋊D₁₃	—	4	16	no	—
391	C₂²⋊D₁₃	—	4	16	no	—
392	C₂×Dic₁₃	—	2	8	no	—
393	C₂×Dic₁₃	—	2	8	no	—
394	C₂×Dic₁₃	—	2	8	no	—
395	C₂×Dic₁₃	—	4	8	no	—
396	C₂×Dic₁₃	C₂⁵	1	8	yes	—
397	C₂×Dic₁₃	C₂⁵	1	8	yes	—
398	C₂×Dic₁₃	C₂⁵	1	8	yes	—
399	D₅₂	—	2	16	no	—
400	D₅₂	—	4	8	no	—
401	C₄×D₁₃	—	4	16	no	—
402	C₄×D₁₃	—	4	16	no	—
403	Dic₂₆	—	2	16	no	—
404	Dic₂₆	—	4	8	no	—
405	Dic₂₆	—	4	16	no	—
406	C₂²×#41	—	13	2	no	—
407	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
408	C₂³×Q₈	—	13	1	no	—
409	C₂³×D₄	—	13	1	no	—
410	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
411	H(3,𝔽₄)	—	13	32	no	—
412	#560	—	13	32	no	—
413	#559	—	13	32	no	—
414	#556	—	13	32	no	—
415	#555	—	13	32	no	—
416	#551	—	13	32	no	—
417	#548	—	13	32	no	—
418	#546	—	13	32	no	—
419	#542	—	13	64	no	—
420	#542	—	13	32	no	—
421	#538	—	13	64	no	—
422	#536	—	13	16	no	—
423	#535	—	13	16	no	—
424	C₂×C₄⋊Q₈	—	13	2	no	—
425	C₂×C₄⋊Q₈	—	13	2	no	—
426	C₂×#127	—	13	2	no	—
427	C₂×#126	—	13	4	no	—
428	C₂×#126	—	13	4	no	—
429	C₂×#126	—	13	4	no	—
430	C₂×#124	—	13	2	no	—
431	C₂×#124	—	13	2	no	—
432	C₂×#124	—	13	4	no	—
433	C₂×#124	—	13	4	no	—
434	C₂×#124	—	13	4	no	—
435	C₂×#124	—	13	4	no	—
436	C₂×#124	—	13	4	no	—
437	C₂×#124	—	13	2	no	—
438	#525	—	13	32	no	—
439	#525	C₂×D₁₃	1	16	yes	complemented
440	C₂×#123	—	13	2	no	—
441	C₂×#123	—	13	2	no	—
442	C₂×#123	—	13	4	no	—
443	C₂×#123	—	13	4	no	—
444	C₂×#123	—	13	4	no	—
445	C₂×#123	C₂×D₁₃	1	1	yes	characteristic
446	C₂×#123	C₂×D₁₃	1	1	yes	characteristic, complemented
447	C₂×C₂²⋊Q₈	—	13	2	no	—
448	C₂×C₂²⋊Q₈	—	13	2	no	—
449	C₂×C₂²⋊Q₈	—	13	2	no	—
450	C₂×C₂²⋊Q₈	—	13	4	no	—
451	C₂×C₂²⋊Q₈	—	13	4	no	—
452	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
453	C₂×#121	—	13	4	no	—
454	C₂×#121	—	13	4	no	—
455	C₂×#121	—	13	2	no	—
456	C₂×#121	—	13	2	no	—
457	C₂×#121	—	13	2	no	—
458	C₂×#121	—	13	4	no	—
459	C₂×#121	C₂×D₁₃	1	2	yes	—
460	C₂×#120	—	13	4	no	—
461	C₂×#120	—	13	2	no	—
462	C₂×#120	—	13	4	no	—
463	C₂×#120	—	13	2	no	—
464	C₂×#120	C₂×D₁₃	1	1	yes	characteristic
465	C₂×#120	C₂×D₁₃	1	1	yes	characteristic, complemented
466	C₂×C₄×Q₈	—	13	4	no	—
467	C₂×C₄×Q₈	—	13	2	no	—
468	C₂×C₄×D₄	—	13	4	no	—
469	C₂×C₄×D₄	—	13	4	no	—
470	C₂×C₄×D₄	—	13	4	no	—
471	C₂×C₄×D₄	—	13	2	no	—
472	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
473	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
474	C₂×#117	—	13	2	no	—
475	C₂×#117	—	13	1	no	—
476	C₂×#117	—	13	1	no	—
477	C₂×#117	—	13	4	no	—
478	C₂×#117	C₂×D₁₃	1	1	yes	characteristic, complemented
479	C₂²×C₂²⋊C₄	—	13	4	no	—
480	C₂²×C₁₃	—	2	2	no	—
481	C₂²×C₁₃	—	2	4	no	—
482	C₂²×C₁₃	—	2	2	no	—
483	C₂²×C₁₃	—	2	2	no	—
484	C₂²×C₁₃	—	2	4	no	—
485	C₂²×C₁₃	—	2	4	no	—
486	C₂²×C₁₃	—	2	4	no	—
487	C₂²×C₁₃	—	2	4	no	—
488	C₂²×C₁₃	—	2	4	no	—
489	C₂²×C₁₃	—	4	16	no	—
490	C₂²×C₁₃	—	4	4	no	—
491	C₂²×C₁₃	—	4	4	no	—
492	C₂²×C₁₃	—	4	8	no	—
493	C₂²×C₁₃	—	4	4	no	—
494	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
495	C₂²×C₁₃	#585	1	4	yes	—
496	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
497	C₂×D₁₃	—	2	8	no	—
498	C₂×D₁₃	—	2	8	no	—
499	C₂×D₁₃	—	2	8	no	—
500	C₂×D₁₃	—	4	16	no	—
501	C₂×D₁₃	—	8	16	no	—
502	C₄×C₁₃	—	2	2	no	—
503	C₄×C₁₃	—	2	4	no	—
504	C₄×C₁₃	—	2	2	no	—
505	C₄×C₁₃	—	2	2	no	—
506	C₄×C₁₃	—	2	4	no	—
507	C₄×C₁₃	—	2	4	no	—
508	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
509	Dic₁₃	—	2	8	no	—
510	Dic₁₃	—	2	8	no	—
511	Dic₁₃	—	2	8	no	—
512	C₂⁵	—	13	2	no	—
513	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
514	C₂×#41	—	4	4	no	—
515	C₂×#41	—	13	16	no	—
516	C₂×#41	—	52	8	no	—
517	C₂×#41	C₂²×D₁₃	1	8	yes	—
518	C₂²×Q₈	—	13	2	no	—
519	C₂²×Q₈	—	13	4	no	—
520	C₂²×Q₈	—	13	2	no	—
521	C₂²×Q₈	—	13	8	no	—
522	C₂²×Q₈	—	52	4	no	—
523	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
524	C₂²×D₄	—	13	4	no	—
525	C₂²×D₄	—	13	4	no	—
526	C₂²×D₄	—	13	4	no	—
527	C₂²×D₄	—	13	4	no	—
528	C₂²×D₄	—	13	2	no	—
529	C₂²×D₄	—	13	2	no	—
530	C₂²×D₄	—	13	8	no	—
531	C₂²×D₄	—	52	4	no	—
532	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
533	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
534	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
535	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
536	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
537	C₂³×C₄	—	4	4	no	—
538	C₂³×C₄	—	13	2	no	—
539	C₂³×C₄	—	13	4	no	—
540	C₂³×C₄	—	13	4	no	—
541	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
542	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
543	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
544	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
545	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
546	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
547	C₂³×C₄	C₂²×D₁₃	1	8	yes	complemented
548	C₄⋊Q₈	—	13	16	no	—
549	C₄⋊Q₈	—	13	16	no	—
550	#127	—	13	16	no	—
551	#126	—	13	32	no	—
552	#126	—	13	32	no	—
553	#126	—	13	32	no	—
554	#124	—	13	16	no	—
555	#124	—	13	16	no	—
556	#124	—	13	32	no	—
557	#124	—	13	32	no	—
558	#124	—	13	32	no	—
559	#124	—	13	32	no	—
560	#124	—	13	32	no	—
561	#124	—	13	16	no	—
562	#123	—	13	16	no	—
563	#123	—	13	16	no	—
564	#123	—	13	32	no	—
565	#123	—	13	32	no	—
566	#123	—	13	32	no	—
567	#123	C₂²×D₁₃	1	8	yes	—
568	#123	C₂²×D₁₃	1	8	yes	complemented
569	C₂²⋊Q₈	—	13	16	no	—
570	C₂²⋊Q₈	—	13	16	no	—
571	C₂²⋊Q₈	—	13	16	no	—
572	C₂²⋊Q₈	—	13	32	no	—
573	C₂²⋊Q₈	—	13	32	no	—
574	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
575	#121	—	13	32	no	—
576	#121	—	13	32	no	—
577	#121	—	13	16	no	—
578	#121	—	13	16	no	—
579	#121	—	13	16	no	—
580	#121	—	13	32	no	—
581	#121	C₂²×D₁₃	1	16	yes	—
582	#120	—	13	32	no	—
583	#120	—	13	16	no	—
584	#120	—	13	16	no	—
585	#120	—	13	32	no	—
586	#120	C₂²×D₁₃	1	8	yes	—
587	#120	C₂²×D₁₃	1	8	yes	complemented
588	C₄×Q₈	—	13	32	no	—
589	C₄×Q₈	—	13	16	no	—
590	C₄×D₄	—	13	32	no	—
591	C₄×D₄	—	13	32	no	—
592	C₄×D₄	—	13	32	no	—
593	C₄×D₄	—	13	16	no	—
594	C₄×D₄	C₂²×D₁₃	1	16	yes	—
595	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
596	#117	—	13	16	no	—
597	#117	—	13	8	no	—
598	#117	—	13	8	no	—
599	#117	—	13	32	no	—
600	#117	C₂²×D₁₃	1	8	yes	complemented
601	C₂×C₄⋊C₄	—	13	2	no	—
602	C₂×C₄⋊C₄	—	13	2	no	—
603	C₂×C₄⋊C₄	—	13	4	no	—
604	C₂×C₄⋊C₄	—	13	4	no	—
605	C₂×C₄⋊C₄	—	13	4	no	—
606	C₂×C₄⋊C₄	—	13	4	no	—
607	C₂×C₄⋊C₄	—	13	4	no	—
608	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
611	C₂×C₂²⋊C₄	—	13	4	no	—
612	C₂×C₂²⋊C₄	—	13	2	no	—
613	C₂×C₂²⋊C₄	—	13	4	no	—
614	C₂×C₂²⋊C₄	—	13	2	no	—
615	C₂×C₂²⋊C₄	—	13	4	no	—
616	C₂×C₂²⋊C₄	—	13	4	no	—
617	C₂×C₂²⋊C₄	—	13	4	no	—
618	C₂×C₂²⋊C₄	—	13	4	no	—
619	C₂×C₂²⋊C₄	—	13	4	no	—
620	C₂×C₂²⋊C₄	—	13	4	no	—
621	C₂×C₂²⋊C₄	—	13	4	no	—
622	C₂×C₂²⋊C₄	—	13	4	no	—
623	C₂×C₂²⋊C₄	—	13	32	no	—
624	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
630	C₂×C₄²	—	13	2	no	—
631	C₂×C₄²	—	13	4	no	—
632	C₂×C₄²	—	13	2	no	—
633	C₂×C₄²	—	13	4	no	—
634	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
635	C₂×C₁₃	—	4	2	no	—
636	C₂×C₁₃	—	4	2	no	—
637	C₂×C₁₃	—	4	4	no	—
638	C₂×C₁₃	—	4	2	no	—
639	C₂×C₁₃	#3540	1	4	yes	complemented
640	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
641	C₂×C₁₃	C₂×#585	1	2	yes	—
642	D₁₃	—	4	8	no	—
643	C₂⁴	—	4	2	no	—
644	C₂⁴	—	4	4	no	—
645	C₂⁴	—	13	4	no	—
646	C₂⁴	—	13	8	no	—
647	C₂⁴	—	52	4	no	—
648	C₂⁴	—	52	8	no	—
649	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
650	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
651	C₂⁴	C₂³×D₁₃	1	2	yes	—
652	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
653	C₂⁴	C₂³×D₁₃	1	4	yes	—
654	#41	—	4	16	no	—
655	#41	—	52	32	no	—
656	C₂×Q₈	—	4	2	no	—
657	C₂×Q₈	—	13	8	no	—
658	C₂×Q₈	—	13	16	no	—
659	C₂×Q₈	—	13	8	no	—
660	C₂×Q₈	—	26	8	no	—
661	C₂×Q₈	—	52	4	no	—
662	C₂×Q₈	—	52	8	no	—
663	C₂×Q₈	—	52	16	no	—
664	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	4	no	—
669	C₂×D₄	—	4	4	no	—
670	C₂×D₄	—	13	16	no	—
671	C₂×D₄	—	13	16	no	—
672	C₂×D₄	—	13	16	no	—
673	C₂×D₄	—	13	16	no	—
674	C₂×D₄	—	13	8	no	—
675	C₂×D₄	—	13	8	no	—
676	C₂×D₄	—	26	8	no	—
677	C₂×D₄	—	52	16	no	—
678	C₂×D₄	—	52	4	no	—
679	C₂×D₄	—	52	8	no	—
680	C₂×D₄	—	52	8	no	—
681	C₂×D₄	—	52	8	no	—
682	C₂×D₄	—	52	8	no	—
683	C₂×D₄	C₂³×D₁₃	1	8	yes	—
684	C₂×D₄	C₂³×D₁₃	1	8	yes	—
685	C₂×D₄	C₂³×D₁₃	1	4	yes	—
686	C₂×D₄	C₂³×D₁₃	1	4	yes	—
687	C₂×D₄	C₂³×D₁₃	1	4	yes	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	8	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	4	16	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	4	no	—
695	C₂²×C₄	—	13	4	no	—
696	C₂²×C₄	—	13	4	no	—
697	C₂²×C₄	—	13	4	no	—
698	C₂²×C₄	—	13	8	no	—
699	C₂²×C₄	—	13	16	no	—
700	C₂²×C₄	—	13	16	no	—
701	C₂²×C₄	—	52	8	no	—
702	C₂²×C₄	—	52	8	no	—
703	C₂²×C₄	—	52	4	no	—
704	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
705	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
706	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
707	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
708	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
709	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
710	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
711	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
713	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
714	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
715	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
716	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
717	C₄⋊C₄	—	13	8	no	—
718	C₄⋊C₄	—	13	8	no	—
719	C₄⋊C₄	—	13	16	no	—
720	C₄⋊C₄	—	13	16	no	—
721	C₄⋊C₄	—	13	16	no	—
722	C₄⋊C₄	—	13	16	no	—
723	C₄⋊C₄	—	13	16	no	—
724	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
725	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
726	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
727	C₂²⋊C₄	—	13	16	no	—
728	C₂²⋊C₄	—	13	8	no	—
729	C₂²⋊C₄	—	13	16	no	—
730	C₂²⋊C₄	—	13	8	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	—	13	16	no	—
736	C₂²⋊C₄	—	13	16	no	—
737	C₂²⋊C₄	—	13	16	no	—
738	C₂²⋊C₄	—	13	16	no	—
739	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
740	C₂²⋊C₄	C₂³×D₁₃	1	4	yes	—
741	C₂²⋊C₄	C₂³×D₁₃	1	4	yes	—
742	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
743	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
744	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
745	C₄²	—	13	8	no	—
746	C₄²	—	13	16	no	—
747	C₄²	—	13	8	no	—
748	C₄²	—	13	16	no	—
749	C₄²	C₂³×D₁₃	1	8	yes	—
750	C₁₃	C₂×#3540	1	1	yes	characteristic, complemented, Sylow
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	4	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	4	4	no	—
761	C₂³	—	4	8	no	—
762	C₂³	—	4	16	no	—
763	C₂³	—	13	8	no	—
764	C₂³	—	26	8	no	—
765	C₂³	—	26	8	no	—
766	C₂³	—	26	8	no	—
767	C₂³	—	52	8	no	—
768	C₂³	—	52	16	no	—
769	C₂³	—	104	16	no	—
770	C₂³	C₂⁴×D₁₃	1	2	yes	—
771	C₂³	C₂⁴×D₁₃	1	2	yes	—
772	C₂³	C₂⁴×D₁₃	1	4	yes	—
773	C₂³	C₂⁴×D₁₃	1	2	yes	—
774	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
775	Q₈	—	4	4	no	—
776	Q₈	—	26	16	no	—
777	Q₈	—	52	16	no	—
778	Q₈	—	52	8	no	—
779	D₄	—	4	8	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	4	no	—
784	D₄	—	26	16	no	—
785	D₄	—	52	8	no	—
786	D₄	—	52	16	no	—
787	D₄	—	52	16	no	—
788	D₄	—	52	16	no	—
789	D₄	—	52	16	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	16	no	—
798	C₂×C₄	—	2	8	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	8	no	—
802	C₂×C₄	—	13	8	no	—
803	C₂×C₄	—	13	8	no	—
804	C₂×C₄	—	13	8	no	—
805	C₂×C₄	—	26	8	no	—
806	C₂×C₄	—	26	8	no	—
807	C₂×C₄	—	26	8	no	—
808	C₂×C₄	—	52	16	no	—
809	C₂×C₄	—	52	16	no	—
810	C₂×C₄	—	52	8	no	—
811	C₂×C₄	#88251	1	4	yes	—
812	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
813	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
814	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
815	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
816	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
817	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
818	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	4	16	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	8	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	26	8	no	—
834	C₂²	—	26	8	no	—
835	C₂²	—	26	8	no	—
836	C₂²	—	52	16	no	—
837	C₂²	—	104	16	no	—
838	C₂²	C₂×#88251	1	2	yes	—
839	C₂²	#11719648	1	4	yes	—
840	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
841	C₄	—	2	4	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	4	no	—
846	C₄	—	2	4	no	—
847	C₄	—	26	8	no	—
848	C₄	—	26	8	no	—
849	C₄	—	26	8	no	—
850	C₄	C₂×#88251	1	4	yes	—
851	C₂	—	4	2	no	—
852	C₂	—	4	4	no	—
853	C₂	—	4	2	no	—
854	C₂	—	4	2	no	—
855	C₂	—	52	8	no	—
856	C₂	#13129111	1	4	yes	direct product factor
857	C₂	C₂²×#88251	1	1	yes	characteristic
858	C₂	C₂×#11719648	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#525	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#525	D₁₃
hypocenter	C₁₃	C₂×#3540
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. #13129111	C₂	direct (N × H)
2. C₂×#11719299	C₂	semidirect
3. C₂×#11719300	C₂	semidirect
4. C₂×#11719369	C₂	semidirect
5. C₂×#11719247	C₂	semidirect
6. C₂×#11719268	C₂	semidirect
7. C₂×#11719364	C₂	semidirect
8. C₂×#11719257	C₂	semidirect
9. C₂×#11719255	C₂	semidirect
10. C₂×#11719239	C₂	semidirect
11. C₂×#11719345	C₂	semidirect
12. C₂×#11719318	C₂	semidirect
13. C₂×#11719530	C₂	semidirect
14. C₂×#11719535	C₂	semidirect
15. C₂×#11719496	C₂	semidirect
16. C₂×C₁₃×#525	C₂	semidirect
18. C₂⁴×C₄×C₁₃	C₂²	semidirect
20. C₂³×D₅₂	C₂²	semidirect
21. C₂³×Dic₂₆	C₂²	semidirect
22. C₁₃×#525	C₂²	semidirect
24. C₂×C₁₃×#123	C₂²	semidirect
25. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₁₃×#120	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂×C₁₃×#117	C₂²	semidirect
32. C₂×#88207	C₂²	semidirect
33. #11719535	C₂²	semidirect
34. #11719530	C₂²	semidirect
35. C₂×#88201	C₂²	semidirect
36. C₂×#88198	C₂²	semidirect
38. C₂×#88193	C₂²	semidirect
39. C₂×#88192	C₂²	semidirect
42. C₂×#88191	C₂²	semidirect
45. C₂×#88189	C₂²	semidirect
46. C₂×#88189	C₂²	semidirect
47. #11719496	C₂²	semidirect
50. C₂×#88184	C₂²	semidirect
51. C₂×#88183	C₂²	semidirect
52. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
53. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
54. C₂×#88180	C₂²	semidirect
55. C₂×#88180	C₂²	semidirect
56. C₂×#88180	C₂²	semidirect
57. C₂×#88178	C₂²	semidirect
58. C₂×#88178	C₂²	semidirect
59. C₂×#88178	C₂²	semidirect
60. #11719369	C₂²	semidirect
61. #11719364	C₂²	semidirect
62. #11719345	C₂²	semidirect
63. #11719318	C₂²	semidirect
64. #11719300	C₂²	semidirect
65. #11719299	C₂²	semidirect
66. #11719268	C₂²	semidirect
67. #11719257	C₂²	semidirect
68. #11719255	C₂²	semidirect
69. #11719247	C₂²	semidirect
70. #11719239	C₂²	semidirect
71. C₂×#88152	C₂²	semidirect
72. C₂×#88150	C₂²	semidirect
73. C₂×#88150	C₂²	semidirect
74. C₂×#88148	C₂²	semidirect
75. C₂×#88146	C₂²	semidirect
76. C₂×#88141	C₂²	semidirect
77. C₂×#88139	C₂²	semidirect
78. C₂×#88139	C₂²	semidirect
79. C₂×#88139	C₂²	semidirect
80. C₂×#88139	C₂²	semidirect
82. C₂×#88137	C₂²	semidirect
83. C₂×#88135	C₂²	semidirect
84. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
85. C₂×#88133	C₂²	semidirect
86. C₂×#88133	C₂²	semidirect
87. C₂×#88129	C₂²	semidirect
88. C₂×C₄×D₅₂	C₂²	semidirect
89. C₂×#88123	C₂²	semidirect
90. C₂×C₄×Dic₂₆	C₂²	semidirect
108. C₂³×C₄×C₁₃	C₂³	semidirect
119. C₂²×D₅₂	C₂³	semidirect
126. C₂²×Dic₂₆	C₂³	semidirect
128. C₁₃×#123	C₂³	semidirect
129. C₁₃×C₂²⋊Q₈	C₂³	semidirect
132. C₁₃×#120	C₂³	semidirect
134. C₄×D₄×C₁₃	C₂³	semidirect
135. C₁₃×#117	C₂³	semidirect
146. #88207	C₂³	semidirect
153. #88201	C₂³	semidirect
154. #88198	C₂³	semidirect
156. #88193	C₂³	semidirect
157. #88192	C₂³	semidirect
160. #88191	C₂³	semidirect
163. #88189	C₂³	semidirect
164. #88189	C₂³	semidirect
167. #88184	C₂³	semidirect
168. #88183	C₂³	semidirect
169. C₄×C₂²⋊D₁₃	C₂³	semidirect
170. C₄×C₂²⋊D₁₃	C₂³	semidirect
177. #88180	C₂³	semidirect
178. #88180	C₂³	semidirect
179. #88180	C₂³	semidirect
183. #88178	C₂³	semidirect
184. #88178	C₂³	semidirect
185. #88178	C₂³	semidirect
194. #88152	C₂³	semidirect
195. #88150	C₂³	semidirect
196. #88150	C₂³	semidirect
197. #88148	C₂³	semidirect
198. #88146	C₂³	semidirect
199. #88141	C₂³	semidirect
200. #88139	C₂³	semidirect
201. #88139	C₂³	semidirect
202. #88139	C₂³	semidirect
203. #88139	C₂³	semidirect
205. #88137	C₂³	semidirect
206. #88135	C₂³	semidirect
207. C₂²⋊C₄×D₁₃	C₂³	semidirect
208. #88133	C₂³	semidirect
209. #88133	C₂³	semidirect
210. #88129	C₂³	semidirect
211. C₄×D₅₂	C₂³	semidirect
212. #88123	C₂³	semidirect
213. C₄×Dic₂₆	C₂³	semidirect
337. C₂×#525	D₁₃	semidirect
410. C₂⁴×C₄	C₂×D₁₃	semidirect
439. #525	C₂×D₁₃	semidirect
446. C₂×#123	C₂×D₁₃	semidirect
452. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
465. C₂×#120	C₂×D₁₃	semidirect
473. C₂×C₄×D₄	C₂×D₁₃	semidirect
478. C₂×#117	C₂×D₁₃	semidirect
547. C₂³×C₄	C₂²×D₁₃	semidirect
568. #123	C₂²×D₁₃	semidirect
574. C₂²⋊Q₈	C₂²×D₁₃	semidirect
587. #120	C₂²×D₁₃	semidirect
595. C₄×D₄	C₂²×D₁₃	semidirect
600. #117	C₂²×D₁₃	semidirect
639. C₂×C₁₃	#3540	semidirect
750. C₁₃	C₂×#3540	semidirect
856. C₂	#13129111	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129111	2
C₂×#11719299	2
C₂×#11719300	2
C₂×#11719369	2
C₂×#11719247	2
C₂×#11719268	2
C₂×#11719364	2
C₂×#11719257	2
C₂×#11719255	2
C₂×#11719239	2
C₂×#11719345	2
C₂×#11719318	2
C₂×#11719530	2
C₂×#11719535	2
C₂×#11719496	2
C₂×C₁₃×#525	2
C₂×#3540	13

Subgroups — C2×#13129111 #16770210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129111 #16770210