Subgroups — C₂×#13129352 #16770256

Order 3328.

8122 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129352	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719405	C₂	1	2	yes	maximal, complemented
3	C₂×#11719388	C₂	1	2	yes	maximal, complemented
4	C₂×#11719290	C₂	1	2	yes	maximal, complemented
5	C₂×#11719257	C₂	1	2	yes	maximal, complemented
6	C₂×#11719255	C₂	1	2	yes	maximal, complemented
7	C₂×#11719359	C₂	1	4	yes	maximal, complemented
8	C₂×D₄×D₅₂	C₂	1	2	yes	maximal, complemented
9	C₂×#11719239	C₂	1	2	yes	maximal, complemented
10	C₂×#11719349	C₂	1	2	yes	maximal, complemented
11	C₂×#11719409	C₂	1	4	yes	maximal, complemented
12	C₂×#11719230	C₂	1	2	yes	maximal, complemented
13	C₂×#11719310	C₂	1	2	yes	maximal, complemented
14	C₂×#11719182	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#88129	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
18	C₂²×#6127	C₂²	1	2	yes	complemented
19	C₂²×#6127	C₂²	1	2	yes	complemented
20	C₂³×D₅₂	C₂²	1	1	yes	characteristic
21	C₂³×D₅₂	C₂²	1	2	yes	complemented
22	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#529	C₂²	1	16	yes	complemented
24	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#88201	C₂²	1	4	yes	complemented
36	C₂×#88193	C₂²	1	4	yes	complemented
37	C₂×#88191	C₂²	1	4	yes	complemented
38	C₂×#88184	C₂²	1	2	yes	—
39	C₂×#88184	C₂²	1	2	yes	complemented
40	C₂×#88184	C₂²	1	2	yes	complemented
41	C₂²×#6103	C₂²	1	2	yes	complemented
42	C₂²×#6103	C₂²	1	2	yes	complemented
43	C₂×#88178	C₂²	1	2	yes	complemented
44	#11719409	C₂²	1	64	yes	complemented
45	#11719405	C₂²	1	32	yes	complemented
46	#11719388	C₂²	1	32	yes	complemented
47	#11719359	C₂²	1	64	yes	complemented
48	#11719349	C₂²	1	32	yes	complemented
49	#11719310	C₂²	1	32	yes	complemented
50	#11719290	C₂²	1	32	yes	complemented
51	#11719257	C₂²	1	32	yes	complemented
52	#11719255	C₂²	1	32	yes	complemented
53	D₄×D₅₂	C₂²	1	32	yes	complemented
54	#11719239	C₂²	1	32	yes	complemented
55	#11719230	C₂²	1	32	yes	complemented
56	C₂×#88152	C₂²	1	4	yes	complemented
57	C₂×#88150	C₂²	1	4	yes	complemented
58	C₂×#88150	C₂²	1	4	yes	complemented
59	C₂×#88149	C₂²	1	4	yes	complemented
60	C₂×#88149	C₂²	1	4	yes	complemented
61	C₂×#88149	C₂²	1	4	yes	complemented
62	C₂×#88148	C₂²	1	4	yes	complemented
63	C₂×#88148	C₂²	1	4	yes	complemented
64	C₂×#88148	C₂²	1	4	yes	complemented
65	C₂×#88147	C₂²	1	4	yes	complemented
66	C₂×#88139	C₂²	1	4	yes	complemented
67	C₂×#88139	C₂²	1	4	yes	complemented
68	C₂×#88138	C₂²	1	4	yes	complemented
69	C₂×#88137	C₂²	1	4	yes	complemented
70	C₂×#88136	C₂²	1	4	yes	complemented
71	C₂×#88136	C₂²	1	4	yes	complemented
72	C₂×#88136	C₂²	1	4	yes	complemented
73	C₂×#88136	C₂²	1	4	yes	complemented
74	C₂×#88135	C₂²	1	4	yes	complemented
75	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
76	#11719182	C₂²	1	16	yes	complemented
77	C₂×#88129	C₂²	1	2	yes	complemented
78	C₂×#88129	C₂²	1	2	yes	complemented
79	C₂×#88129	C₂²	1	2	yes	complemented
80	C₂×#88129	C₂²	1	2	yes	complemented
81	C₂×#88129	C₂²	1	2	yes	complemented
82	C₂×#88129	C₂²	1	2	yes	complemented
83	C₂×#88129	C₂²	1	16	yes	complemented
84	C₂×#88128	C₂²	1	2	yes	—
85	C₂×#88128	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
87	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
88	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
89	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
91	C₂⁴×D₁₃	C₂³	1	2	yes	—
92	C₂⁴×D₁₃	C₂³	1	4	yes	—
93	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
101	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
102	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
103	C₂³×Dic₁₃	C₂³	1	2	yes	—
104	C₂×D₄×D₁₃	—	4	16	no	—
105	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
106	C₂×#6127	—	4	8	no	—
107	C₂×#6127	—	4	8	no	—
108	C₂×#6127	C₂³	1	16	yes	complemented
109	C₂×#6127	C₂³	1	16	yes	complemented
110	C₂²×D₅₂	—	4	4	no	—
111	C₂²×D₅₂	—	4	8	no	—
112	C₂²×D₅₂	C₂³	1	2	yes	—
113	C₂²×D₅₂	C₂³	1	2	yes	—
114	C₂²×D₅₂	C₂³	1	2	yes	—
115	C₂²×D₅₂	C₂³	1	4	yes	—
116	C₂²×D₅₂	C₂³	1	4	yes	—
117	C₂²×D₅₂	C₂³	1	2	yes	—
118	C₂²×D₅₂	C₂³	1	2	yes	—
119	C₂²×D₅₂	C₂³	1	8	yes	—
120	C₂²×D₅₂	C₂³	1	4	yes	—
121	C₂²×D₅₂	C₂³	1	16	yes	complemented
122	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
123	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
124	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
125	C₂²×Dic₂₆	—	4	4	no	—
126	C₂²×Dic₂₆	C₂³	1	2	yes	—
127	C₂²×Dic₂₆	C₂³	1	2	yes	—
128	C₂²×Dic₂₆	C₂³	1	2	yes	—
129	C₂²×Dic₂₆	C₂³	1	8	yes	complemented
130	C₁₃×#126	C₂³	1	16	yes	complemented
131	C₁₃×#125	C₂³	1	8	yes	complemented
132	C₁₃×#124	C₂³	1	8	yes	complemented
133	C₁₃×#123	C₂³	1	16	yes	complemented
134	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
135	C₁₃×#121	C₂³	1	8	yes	—
136	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
137	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
138	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
139	C₁₃×#117	C₂³	1	16	yes	complemented
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
157	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
158	#88201	C₂³	1	32	yes	complemented
159	#88193	C₂³	1	32	yes	complemented
160	#88191	C₂³	1	32	yes	complemented
161	#88184	C₂³	1	16	yes	—
162	#88184	C₂³	1	16	yes	complemented
163	#88184	C₂³	1	16	yes	complemented
164	C₂×#6103	C₂³	1	4	yes	—
165	C₂×#6103	C₂³	1	4	yes	—
166	C₂×#6103	C₂³	1	4	yes	—
167	C₂×#6103	C₂³	1	4	yes	—
168	C₂×#6103	C₂³	1	4	yes	—
169	C₂×#6103	C₂³	1	4	yes	—
170	C₂×#6103	C₂³	1	4	yes	—
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	16	yes	complemented
175	C₂×#6103	C₂³	1	16	yes	complemented
176	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
178	#88178	C₂³	1	16	yes	complemented
179	C₂×#6101	C₂³	1	4	yes	—
180	C₂×#6101	C₂³	1	4	yes	—
181	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
182	#88152	C₂³	1	32	yes	complemented
183	#88150	C₂³	1	32	yes	complemented
184	#88150	C₂³	1	32	yes	complemented
185	#88149	C₂³	1	32	yes	complemented
186	#88149	C₂³	1	32	yes	complemented
187	#88149	C₂³	1	32	yes	complemented
188	#88148	C₂³	1	32	yes	complemented
189	#88148	C₂³	1	32	yes	complemented
190	#88148	C₂³	1	32	yes	complemented
191	#88147	C₂³	1	32	yes	complemented
192	#88139	C₂³	1	32	yes	complemented
193	#88139	C₂³	1	32	yes	complemented
194	#88138	C₂³	1	32	yes	complemented
195	#88137	C₂³	1	32	yes	complemented
196	#88136	C₂³	1	32	yes	complemented
197	#88136	C₂³	1	32	yes	complemented
198	#88136	C₂³	1	32	yes	complemented
199	#88136	C₂³	1	32	yes	complemented
200	#88135	C₂³	1	32	yes	complemented
201	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
202	#88129	C₂³	1	16	yes	complemented
203	#88129	C₂³	1	16	yes	complemented
204	#88129	C₂³	1	16	yes	complemented
205	#88129	C₂³	1	16	yes	complemented
206	#88129	C₂³	1	16	yes	complemented
207	#88129	C₂³	1	16	yes	complemented
208	#88128	C₂³	1	16	yes	—
209	#88128	C₂³	1	8	yes	complemented
210	C₄×D₅₂	C₂³	1	16	yes	complemented
211	C₄×D₅₂	C₂³	1	16	yes	complemented
212	C₄×D₅₂	C₂³	1	16	yes	complemented
213	#88123	C₂³	1	8	yes	complemented
214	C₄×Dic₂₆	C₂³	1	16	yes	complemented
215	C₂×#3558	—	13	1	no	maximal, Sylow
216	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
217	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₂³×D₁₃	—	2	8	no	—
219	C₂³×D₁₃	—	4	8	no	—
220	C₂³×D₁₃	—	4	4	no	—
221	C₂³×D₁₃	—	4	8	no	—
222	C₂³×D₁₃	—	4	8	no	—
223	C₂³×D₁₃	—	4	4	no	—
224	C₂³×D₁₃	C₂⁴	1	4	yes	—
225	C₂³×D₁₃	C₂⁴	1	4	yes	—
226	C₂³×D₁₃	C₂⁴	1	8	yes	—
227	C₂³×D₁₃	C₂⁴	1	16	yes	—
228	C₂×Q₈×C₁₃	—	4	2	no	—
229	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
230	C₂×D₄×C₁₃	—	2	8	no	—
231	C₂×D₄×C₁₃	—	4	2	no	—
232	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
233	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	2	4	no	—
236	C₂²×C₄×C₁₃	—	2	8	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₂²⋊D₁₃	—	2	16	no	—
252	C₂×C₂²⋊D₁₃	—	4	8	no	—
253	C₂×C₂²⋊D₁₃	—	4	8	no	—
254	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
255	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
256	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
257	C₂²×Dic₁₃	—	4	4	no	—
258	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
259	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
260	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
261	D₄×D₁₃	—	4	64	no	—
262	#6127	—	4	32	no	—
263	#6127	—	4	32	no	—
264	C₂×D₅₂	—	2	8	no	—
265	C₂×D₅₂	—	2	8	no	—
266	C₂×D₅₂	—	4	16	no	—
267	C₂×D₅₂	—	4	32	no	—
268	C₂×D₅₂	—	4	4	no	—
269	C₂×D₅₂	—	4	8	no	—
270	C₂×D₅₂	—	4	4	no	—
271	C₂×D₅₂	—	4	8	no	—
272	C₂×D₅₂	—	4	4	no	—
273	C₂×D₅₂	—	4	8	no	—
274	C₂×D₅₂	C₂⁴	1	8	yes	—
275	C₂×D₅₂	C₂⁴	1	8	yes	—
276	C₂×D₅₂	C₂⁴	1	8	yes	—
277	C₂×D₅₂	C₂⁴	1	16	yes	—
278	C₂×D₅₂	C₂⁴	1	16	yes	—
279	C₂×D₅₂	C₂⁴	1	8	yes	—
280	C₂×D₅₂	C₂⁴	1	8	yes	—
281	C₂×D₅₂	C₂⁴	1	16	yes	—
282	C₂×C₄×D₁₃	—	4	8	no	—
283	C₂×C₄×D₁₃	—	4	8	no	—
284	C₂×C₄×D₁₃	—	4	8	no	—
285	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
286	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
287	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
288	C₂×Dic₂₆	—	2	8	no	—
289	C₂×Dic₂₆	—	4	16	no	—
290	C₂×Dic₂₆	—	4	4	no	—
291	C₂×Dic₂₆	—	4	4	no	—
292	C₂×Dic₂₆	C₂⁴	1	8	yes	—
293	C₂×Dic₂₆	C₂⁴	1	8	yes	—
294	C₂×Dic₂₆	C₂⁴	1	8	yes	—
295	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
296	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
297	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
298	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
301	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
302	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
303	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
304	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
305	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
306	C₄²×C₁₃	C₂⁴	1	8	yes	—
307	C₄²×C₁₃	C₂⁴	1	4	yes	—
308	C₄²×C₁₃	C₂⁴	1	4	yes	—
309	C₄²×C₁₃	C₂⁴	1	4	yes	—
310	C₄²×C₁₃	C₂⁴	1	4	yes	—
311	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
312	#6103	C₂⁴	1	16	yes	—
313	#6103	C₂⁴	1	16	yes	—
314	#6103	C₂⁴	1	16	yes	—
315	#6103	C₂⁴	1	16	yes	—
316	#6103	C₂⁴	1	16	yes	—
317	#6103	C₂⁴	1	16	yes	—
318	#6103	C₂⁴	1	16	yes	—
319	#6103	C₂⁴	1	16	yes	—
320	#6103	C₂⁴	1	16	yes	—
321	#6103	C₂⁴	1	16	yes	—
322	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
323	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
324	#6101	C₂⁴	1	16	yes	—
325	#6101	C₂⁴	1	16	yes	—
326	C₄×Dic₁₃	C₂⁴	1	16	yes	—
327	#3558	—	13	32	no	—
328	C₂×#562	—	13	2	no	—
329	C₂×H(3,𝔽₄)	—	13	2	no	—
330	C₂×#559	—	13	2	no	—
331	C₂×#548	—	13	2	no	—
332	C₂×#546	—	13	4	no	—
333	C₂×#546	—	13	2	no	—
334	C₂×D₄²	—	13	2	no	—
335	C₂×#542	—	13	2	no	—
336	C₂×#538	—	13	4	no	—
337	C₂×#538	—	13	2	no	—
338	C₂×#535	—	13	2	no	—
339	C₂×#534	—	13	2	no	—
340	C₂×#532	—	13	1	no	—
341	C₂×#529	D₁₃	1	1	yes	characteristic, complemented
342	C₂²×#124	—	13	1	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	4	no	—
346	C₂³×C₁₃	—	2	4	no	—
347	C₂³×C₁₃	—	2	4	no	—
348	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
349	C₂³×C₁₃	C₂⁵	1	4	yes	—
350	C₂³×C₁₃	C₂⁵	1	2	yes	—
351	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
352	C₂²×D₁₃	—	2	8	no	—
353	C₂²×D₁₃	—	2	8	no	—
354	C₂²×D₁₃	—	2	8	no	—
355	C₂²×D₁₃	—	2	8	no	—
356	C₂²×D₁₃	—	2	8	no	—
357	C₂²×D₁₃	—	2	8	no	—
358	C₂²×D₁₃	—	2	16	no	—
359	C₂²×D₁₃	—	4	16	no	—
360	C₂²×D₁₃	—	4	8	no	—
361	C₂²×D₁₃	—	4	16	no	—
362	C₂²×D₁₃	—	4	16	no	—
363	C₂²×D₁₃	—	4	8	no	—
364	C₂²×D₁₃	—	8	16	no	—
365	C₂²×D₁₃	—	8	32	no	—
366	C₂²×D₁₃	C₂⁵	1	8	yes	—
367	C₂²×D₁₃	C₂⁵	1	8	yes	—
368	Q₈×C₁₃	—	4	4	no	—
369	D₄×C₁₃	—	2	16	no	—
370	D₄×C₁₃	—	4	4	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	4	no	—
375	C₂×C₄×C₁₃	—	2	4	no	—
376	C₂×C₄×C₁₃	—	2	8	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	4	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	8	no	—
381	C₂×C₄×C₁₃	—	2	16	no	—
382	C₂×C₄×C₁₃	—	4	4	no	—
383	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
384	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
385	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
386	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
387	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
388	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
389	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
390	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
391	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
392	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
393	C₂²⋊D₁₃	—	2	32	no	—
394	C₂²⋊D₁₃	—	4	16	no	—
395	C₂²⋊D₁₃	—	4	16	no	—
396	C₂×Dic₁₃	—	2	8	no	—
397	C₂×Dic₁₃	—	2	8	no	—
398	C₂×Dic₁₃	—	4	8	no	—
399	C₂×Dic₁₃	C₂⁵	1	8	yes	—
400	C₂×Dic₁₃	C₂⁵	1	8	yes	—
401	D₅₂	—	2	16	no	—
402	D₅₂	—	2	16	no	—
403	D₅₂	—	4	8	no	—
404	D₅₂	—	4	16	no	—
405	D₅₂	—	4	8	no	—
406	D₅₂	—	4	16	no	—
407	D₅₂	—	4	8	no	—
408	D₅₂	—	4	16	no	—
409	C₄×D₁₃	—	4	16	no	—
410	C₄×D₁₃	—	4	16	no	—
411	C₄×D₁₃	—	4	16	no	—
412	Dic₂₆	—	2	16	no	—
413	Dic₂₆	—	4	8	no	—
414	Dic₂₆	—	4	8	no	—
415	C₂²×#41	—	13	2	no	—
416	C₂²×#41	—	13	2	no	—
417	C₂³×Q₈	—	13	1	no	—
418	C₂³×D₄	—	13	4	no	—
419	C₂³×D₄	—	13	1	no	—
420	C₂³×D₄	—	13	2	no	—
421	#562	—	13	32	no	—
422	H(3,𝔽₄)	—	13	32	no	—
423	#559	—	13	32	no	—
424	#548	—	13	32	no	—
425	#546	—	13	64	no	—
426	#546	—	13	32	no	—
427	D₄²	—	13	32	no	—
428	#542	—	13	32	no	—
429	#538	—	13	64	no	—
430	#538	—	13	32	no	—
431	#535	—	13	32	no	—
432	#534	—	13	32	no	—
433	#532	—	13	16	no	—
434	C₂×C₄⋊Q₈	—	13	1	no	—
435	C₂×#127	—	13	2	no	—
436	C₂×#127	—	13	1	no	—
437	#529	C₂×D₁₃	1	16	yes	complemented
438	C₂×#126	—	13	4	no	—
439	C₂×#126	C₂×D₁₃	1	2	yes	complemented
440	C₂×#125	C₂×D₁₃	1	1	yes	characteristic, complemented
441	C₂×#124	—	13	4	no	—
442	C₂×#124	—	13	4	no	—
443	C₂×#124	—	13	4	no	—
444	C₂×#124	—	13	2	no	—
445	C₂×#124	—	13	2	no	—
446	C₂×#124	—	13	2	no	—
447	C₂×#124	—	13	2	no	—
448	C₂×#124	—	13	2	no	—
449	C₂×#124	—	13	2	no	—
450	C₂×#124	—	13	16	no	—
451	C₂×#124	C₂×D₁₃	1	1	yes	characteristic, complemented
452	C₂×#123	—	13	4	no	—
453	C₂×#123	—	13	4	no	—
454	C₂×#123	—	13	4	no	—
455	C₂×#123	—	13	4	no	—
456	C₂×#123	C₂×D₁₃	1	2	yes	complemented
457	C₂×C₂²⋊Q₈	—	13	2	no	—
458	C₂×C₂²⋊Q₈	—	13	4	no	—
459	C₂×C₂²⋊Q₈	—	13	4	no	—
460	C₂×C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
461	C₂×#121	—	13	4	no	—
462	C₂×#121	—	13	2	no	—
463	C₂×#121	—	13	2	no	—
464	C₂×#121	—	13	2	no	—
465	C₂×#121	—	13	4	no	—
466	C₂×#121	—	13	4	no	—
467	C₂×#121	—	13	4	no	—
468	C₂×#121	—	13	4	no	—
469	C₂×#121	C₂×D₁₃	1	1	yes	characteristic
470	C₂×#120	—	13	4	no	—
471	C₂×#120	—	13	4	no	—
472	C₂×#120	—	13	4	no	—
473	C₂×#120	—	13	4	no	—
474	C₂×#120	—	13	4	no	—
475	C₂×C₄×Q₈	—	13	2	no	—
476	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
477	C₂×C₄×D₄	—	13	4	no	—
478	C₂×C₄×D₄	—	13	4	no	—
479	C₂×C₄×D₄	—	13	2	no	—
480	C₂×C₄×D₄	—	13	2	no	—
481	C₂×C₄×D₄	—	13	2	no	—
482	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
483	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
484	C₂×#117	C₂×D₁₃	1	2	yes	complemented
485	C₂²×C₂²⋊C₄	—	13	2	no	—
486	C₂²×C₂²⋊C₄	—	13	2	no	—
487	C₂²×C₂²⋊C₄	—	13	4	no	—
488	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
489	C₂²×C₁₃	—	2	2	no	—
490	C₂²×C₁₃	—	2	2	no	—
491	C₂²×C₁₃	—	2	8	no	—
492	C₂²×C₁₃	—	2	4	no	—
493	C₂²×C₁₃	—	2	4	no	—
494	C₂²×C₁₃	—	2	4	no	—
495	C₂²×C₁₃	—	4	8	no	—
496	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
497	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
498	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
499	C₂²×C₁₃	#585	1	2	yes	—
500	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
501	C₂×D₁₃	—	2	8	no	—
502	C₂×D₁₃	—	2	8	no	—
503	C₂×D₁₃	—	2	8	no	—
504	C₂×D₁₃	—	2	8	no	—
505	C₂×D₁₃	—	2	8	no	—
506	C₂×D₁₃	—	2	8	no	—
507	C₂×D₁₃	—	4	16	no	—
508	C₂×D₁₃	—	4	16	no	—
509	C₂×D₁₃	—	8	16	no	—
510	C₂×D₁₃	—	8	32	no	—
511	C₄×C₁₃	—	2	2	no	—
512	C₄×C₁₃	—	2	2	no	—
513	C₄×C₁₃	—	2	2	no	—
514	C₄×C₁₃	—	2	4	no	—
515	C₄×C₁₃	—	2	4	no	—
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	—	2	4	no	—
518	C₄×C₁₃	—	2	2	no	—
519	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
520	Dic₁₃	—	2	8	no	—
521	Dic₁₃	—	2	8	no	—
522	C₂⁵	—	13	2	no	—
523	C₂⁵	—	13	4	no	—
524	C₂×#41	—	13	16	no	—
525	C₂×#41	—	13	16	no	—
526	C₂×#41	—	52	8	no	—
527	C₂×#41	—	52	8	no	—
528	C₂²×Q₈	—	13	2	no	—
529	C₂²×Q₈	—	13	2	no	—
530	C₂²×Q₈	—	13	2	no	—
531	C₂²×Q₈	—	13	8	no	—
532	C₂²×Q₈	—	52	4	no	—
533	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
534	C₂²×D₄	—	13	4	no	—
535	C₂²×D₄	—	13	4	no	—
536	C₂²×D₄	—	13	4	no	—
537	C₂²×D₄	—	13	32	no	—
538	C₂²×D₄	—	13	2	no	—
539	C₂²×D₄	—	13	2	no	—
540	C₂²×D₄	—	13	4	no	—
541	C₂²×D₄	—	13	2	no	—
542	C₂²×D₄	—	13	2	no	—
543	C₂²×D₄	—	13	2	no	—
544	C₂²×D₄	—	13	4	no	—
545	C₂²×D₄	—	13	4	no	—
546	C₂²×D₄	—	13	8	no	—
547	C₂²×D₄	—	13	16	no	—
548	C₂²×D₄	—	52	4	no	—
549	C₂²×D₄	—	52	8	no	—
550	C₂²×D₄	—	52	16	no	—
551	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
552	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
553	C₂³×C₄	—	13	2	no	—
554	C₂³×C₄	—	13	4	no	—
555	C₂³×C₄	—	13	4	no	—
556	C₂³×C₄	—	13	4	no	—
557	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
558	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
559	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
560	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
561	C₄⋊Q₈	—	13	8	no	—
562	#127	—	13	8	no	—
563	#127	—	13	16	no	—
564	#126	—	13	32	no	—
565	#126	C₂²×D₁₃	1	16	yes	complemented
566	#125	C₂²×D₁₃	1	8	yes	complemented
567	#124	—	13	32	no	—
568	#124	—	13	32	no	—
569	#124	—	13	32	no	—
570	#124	—	13	16	no	—
571	#124	—	13	16	no	—
572	#124	—	13	16	no	—
573	#124	—	13	16	no	—
574	#124	—	13	16	no	—
575	#124	—	13	16	no	—
576	#124	C₂²×D₁₃	1	8	yes	complemented
577	#123	—	13	32	no	—
578	#123	—	13	32	no	—
579	#123	—	13	32	no	—
580	#123	—	13	32	no	—
581	#123	C₂²×D₁₃	1	16	yes	complemented
582	C₂²⋊Q₈	—	13	16	no	—
583	C₂²⋊Q₈	—	13	32	no	—
584	C₂²⋊Q₈	—	13	32	no	—
585	C₂²⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
586	#121	—	13	32	no	—
587	#121	—	13	16	no	—
588	#121	—	13	16	no	—
589	#121	—	13	16	no	—
590	#121	—	13	32	no	—
591	#121	—	13	32	no	—
592	#121	—	13	32	no	—
593	#121	—	13	32	no	—
594	#121	C₂²×D₁₃	1	8	yes	—
595	#120	—	13	32	no	—
596	#120	—	13	32	no	—
597	#120	—	13	32	no	—
598	#120	—	13	32	no	—
599	#120	—	13	32	no	—
600	C₄×Q₈	—	13	16	no	—
601	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
602	C₄×D₄	—	13	32	no	—
603	C₄×D₄	—	13	32	no	—
604	C₄×D₄	—	13	16	no	—
605	C₄×D₄	—	13	16	no	—
606	C₄×D₄	—	13	16	no	—
607	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
608	C₄×D₄	C₂²×D₁₃	1	8	yes	complemented
609	#117	C₂²×D₁₃	1	16	yes	complemented
610	C₂×C₄⋊C₄	—	13	2	no	—
611	C₂×C₄⋊C₄	—	13	4	no	—
612	C₂×C₄⋊C₄	—	13	2	no	—
613	C₂×C₄⋊C₄	—	13	4	no	—
614	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	4	no	—
624	C₂×C₂²⋊C₄	—	13	4	no	—
625	C₂×C₂²⋊C₄	—	13	4	no	—
626	C₂×C₂²⋊C₄	—	13	16	no	—
627	C₂×C₂²⋊C₄	—	13	16	no	—
628	C₂×C₂²⋊C₄	—	13	4	no	—
629	C₂×C₂²⋊C₄	—	13	4	no	—
630	C₂×C₂²⋊C₄	—	13	4	no	—
631	C₂×C₂²⋊C₄	—	13	4	no	—
632	C₂×C₂²⋊C₄	—	13	4	no	—
633	C₂×C₂²⋊C₄	—	13	32	no	—
634	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
639	C₂×C₄²	—	13	4	no	—
640	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
641	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
642	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
644	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
645	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
646	C₂×C₁₃	—	2	4	no	—
647	C₂×C₁₃	—	4	4	no	—
648	C₂×C₁₃	#3558	1	4	yes	complemented
649	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
650	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
651	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
652	D₁₃	—	4	8	no	—
653	D₁₃	—	4	8	no	—
654	C₂⁴	—	13	4	no	—
655	C₂⁴	—	13	4	no	—
656	C₂⁴	—	13	8	no	—
657	C₂⁴	—	13	16	no	—
658	C₂⁴	—	26	8	no	—
659	C₂⁴	—	52	4	no	—
660	C₂⁴	—	52	8	no	—
661	C₂⁴	—	52	8	no	—
662	C₂⁴	—	52	4	no	—
663	C₂⁴	—	52	8	no	—
664	C₂⁴	C₂³×D₁₃	1	2	yes	—
665	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
666	#41	—	52	32	no	—
667	#41	—	52	32	no	—
668	C₂×Q₈	—	4	2	no	—
669	C₂×Q₈	—	13	8	no	—
670	C₂×Q₈	—	13	8	no	—
671	C₂×Q₈	—	13	8	no	—
672	C₂×Q₈	—	26	8	no	—
673	C₂×Q₈	—	52	4	no	—
674	C₂×Q₈	—	52	4	no	—
675	C₂×Q₈	—	52	16	no	—
676	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
677	C₂×D₄	—	2	8	no	—
678	C₂×D₄	—	4	2	no	—
679	C₂×D₄	—	13	16	no	—
680	C₂×D₄	—	13	16	no	—
681	C₂×D₄	—	13	16	no	—
682	C₂×D₄	—	13	8	no	—
683	C₂×D₄	—	13	8	no	—
684	C₂×D₄	—	13	16	no	—
685	C₂×D₄	—	13	8	no	—
686	C₂×D₄	—	13	8	no	—
687	C₂×D₄	—	13	8	no	—
688	C₂×D₄	—	13	16	no	—
689	C₂×D₄	—	13	16	no	—
690	C₂×D₄	—	26	16	no	—
691	C₂×D₄	—	26	8	no	—
692	C₂×D₄	—	26	8	no	—
693	C₂×D₄	—	52	16	no	—
694	C₂×D₄	—	52	32	no	—
695	C₂×D₄	—	52	8	no	—
696	C₂×D₄	—	52	4	no	—
697	C₂×D₄	—	52	8	no	—
698	C₂×D₄	—	52	4	no	—
699	C₂×D₄	—	52	4	no	—
700	C₂×D₄	—	52	8	no	—
701	C₂×D₄	—	52	8	no	—
702	C₂×D₄	—	52	8	no	—
703	C₂×D₄	—	52	64	no	—
704	C₂×D₄	C₂³×D₁₃	1	8	yes	—
705	C₂×D₄	C₂³×D₁₃	1	4	yes	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	8	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	13	4	no	—
711	C₂²×C₄	—	13	4	no	—
712	C₂²×C₄	—	13	8	no	—
713	C₂²×C₄	—	13	16	no	—
714	C₂²×C₄	—	13	16	no	—
715	C₂²×C₄	—	13	16	no	—
716	C₂²×C₄	—	52	8	no	—
717	C₂²×C₄	—	52	8	no	—
718	C₂²×C₄	—	52	8	no	—
719	C₂²×C₄	—	52	4	no	—
720	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
721	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
722	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
723	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
724	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
727	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
728	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
729	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
730	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
731	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
732	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
733	C₄⋊C₄	—	13	8	no	—
734	C₄⋊C₄	—	13	16	no	—
735	C₄⋊C₄	—	13	8	no	—
736	C₄⋊C₄	—	13	16	no	—
737	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
738	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
739	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
740	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
741	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
742	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
743	C₂²⋊C₄	—	13	16	no	—
744	C₂²⋊C₄	—	13	16	no	—
745	C₂²⋊C₄	—	13	16	no	—
746	C₂²⋊C₄	—	13	16	no	—
747	C₂²⋊C₄	—	13	16	no	—
748	C₂²⋊C₄	—	13	16	no	—
749	C₂²⋊C₄	—	13	16	no	—
750	C₂²⋊C₄	—	13	16	no	—
751	C₂²⋊C₄	—	13	16	no	—
752	C₂²⋊C₄	—	13	16	no	—
753	C₂²⋊C₄	—	13	16	no	—
754	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
755	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
756	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
757	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
758	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
759	C₄²	—	13	16	no	—
760	C₄²	C₂³×D₁₃	1	4	yes	—
761	C₄²	C₂³×D₁₃	1	4	yes	—
762	C₄²	C₂³×D₁₃	1	4	yes	—
763	C₄²	C₂³×D₁₃	1	4	yes	—
764	C₄²	C₂³×D₁₃	1	8	yes	—
765	C₁₃	C₂×#3558	1	1	yes	characteristic, complemented, Sylow
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	2	4	no	—
770	C₂³	—	2	4	no	—
771	C₂³	—	13	8	no	—
772	C₂³	—	13	8	no	—
773	C₂³	—	26	8	no	—
774	C₂³	—	26	8	no	—
775	C₂³	—	26	8	no	—
776	C₂³	—	26	8	no	—
777	C₂³	—	26	8	no	—
778	C₂³	—	26	8	no	—
779	C₂³	—	26	16	no	—
780	C₂³	—	52	8	no	—
781	C₂³	—	52	16	no	—
782	C₂³	—	52	16	no	—
783	C₂³	—	52	8	no	—
784	C₂³	—	52	16	no	—
785	C₂³	—	104	16	no	—
786	C₂³	—	104	32	no	—
787	C₂³	#88256	1	4	yes	—
788	C₂³	C₂⁴×D₁₃	1	4	yes	—
789	C₂³	C₂⁴×D₁₃	1	2	yes	—
790	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
791	Q₈	—	4	4	no	—
792	Q₈	—	26	16	no	—
793	Q₈	—	52	8	no	—
794	Q₈	—	52	8	no	—
795	D₄	—	2	16	no	—
796	D₄	—	4	4	no	—
797	D₄	—	26	32	no	—
798	D₄	—	26	16	no	—
799	D₄	—	26	16	no	—
800	D₄	—	52	8	no	—
801	D₄	—	52	16	no	—
802	D₄	—	52	16	no	—
803	D₄	—	52	8	no	—
804	D₄	—	52	16	no	—
805	D₄	—	52	8	no	—
806	D₄	—	52	16	no	—
807	D₄	—	52	16	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	8	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	8	no	—
818	C₂×C₄	—	2	16	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	13	8	no	—
821	C₂×C₄	—	13	8	no	—
822	C₂×C₄	—	26	8	no	—
823	C₂×C₄	—	26	8	no	—
824	C₂×C₄	—	52	16	no	—
825	C₂×C₄	—	52	16	no	—
826	C₂×C₄	—	52	16	no	—
827	C₂×C₄	—	52	8	no	—
828	C₂×C₄	#88256	1	4	yes	—
829	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
830	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
831	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
832	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
833	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
834	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
835	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
836	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
837	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
838	C₂²	—	2	8	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	2	4	no	—
844	C₂²	—	4	8	no	—
845	C₂²	—	26	8	no	—
846	C₂²	—	26	8	no	—
847	C₂²	—	26	8	no	—
848	C₂²	—	26	8	no	—
849	C₂²	—	26	8	no	—
850	C₂²	—	26	8	no	—
851	C₂²	—	52	16	no	—
852	C₂²	—	52	16	no	—
853	C₂²	—	104	16	no	—
854	C₂²	—	104	32	no	—
855	C₂²	C₂×#88256	1	4	yes	—
856	C₂²	C₂×#88256	1	2	yes	—
857	C₂²	C₂×#88256	1	2	yes	—
858	C₂²	#11719648	1	2	yes	—
859	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
860	C₄	—	2	2	no	—
861	C₄	—	2	4	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	4	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	4	no	—
868	C₄	—	26	8	no	—
869	C₄	—	26	8	no	—
870	C₄	C₂×#88256	1	4	yes	—
871	C₂	—	2	4	no	—
872	C₂	—	4	4	no	—
873	C₂	—	52	8	no	—
874	C₂	—	52	8	no	—
875	C₂	#13129352	1	4	yes	direct product factor
876	C₂	C₂²×#88256	1	1	yes	characteristic
877	C₂	C₂²×#88256	1	1	yes	characteristic
878	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#529	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#529	D₁₃
hypocenter	C₁₃	C₂×#3558
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #13129352	C₂	direct (N × H)
2. C₂×#11719405	C₂	semidirect
3. C₂×#11719388	C₂	semidirect
4. C₂×#11719290	C₂	semidirect
5. C₂×#11719257	C₂	semidirect
6. C₂×#11719255	C₂	semidirect
7. C₂×#11719359	C₂	semidirect
8. C₂×D₄×D₅₂	C₂	semidirect
9. C₂×#11719239	C₂	semidirect
10. C₂×#11719349	C₂	semidirect
11. C₂×#11719409	C₂	semidirect
12. C₂×#11719230	C₂	semidirect
13. C₂×#11719310	C₂	semidirect
14. C₂×#11719182	C₂	semidirect
15. C₂²×#88129	C₂	semidirect
16. C₂×C₁₃×#529	C₂	semidirect
17. C₂²×D₄×D₁₃	C₂²	semidirect
18. C₂²×#6127	C₂²	semidirect
19. C₂²×#6127	C₂²	semidirect
21. C₂³×D₅₂	C₂²	semidirect
22. C₂³×Dic₂₆	C₂²	semidirect
23. C₁₃×#529	C₂²	semidirect
24. C₂×C₁₃×#126	C₂²	semidirect
25. C₂×C₁₃×#125	C₂²	semidirect
26. C₂×C₁₃×#124	C₂²	semidirect
27. C₂×C₁₃×#123	C₂²	semidirect
28. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₂×C₁₃×#117	C₂²	semidirect
34. C₂²×C₄²×C₁₃	C₂²	semidirect
35. C₂×#88201	C₂²	semidirect
36. C₂×#88193	C₂²	semidirect
37. C₂×#88191	C₂²	semidirect
39. C₂×#88184	C₂²	semidirect
40. C₂×#88184	C₂²	semidirect
41. C₂²×#6103	C₂²	semidirect
42. C₂²×#6103	C₂²	semidirect
43. C₂×#88178	C₂²	semidirect
44. #11719409	C₂²	semidirect
45. #11719405	C₂²	semidirect
46. #11719388	C₂²	semidirect
47. #11719359	C₂²	semidirect
48. #11719349	C₂²	semidirect
49. #11719310	C₂²	semidirect
50. #11719290	C₂²	semidirect
51. #11719257	C₂²	semidirect
52. #11719255	C₂²	semidirect
53. D₄×D₅₂	C₂²	semidirect
54. #11719239	C₂²	semidirect
55. #11719230	C₂²	semidirect
56. C₂×#88152	C₂²	semidirect
57. C₂×#88150	C₂²	semidirect
58. C₂×#88150	C₂²	semidirect
59. C₂×#88149	C₂²	semidirect
60. C₂×#88149	C₂²	semidirect
61. C₂×#88149	C₂²	semidirect
62. C₂×#88148	C₂²	semidirect
63. C₂×#88148	C₂²	semidirect
64. C₂×#88148	C₂²	semidirect
65. C₂×#88147	C₂²	semidirect
66. C₂×#88139	C₂²	semidirect
67. C₂×#88139	C₂²	semidirect
68. C₂×#88138	C₂²	semidirect
69. C₂×#88137	C₂²	semidirect
70. C₂×#88136	C₂²	semidirect
71. C₂×#88136	C₂²	semidirect
72. C₂×#88136	C₂²	semidirect
73. C₂×#88136	C₂²	semidirect
74. C₂×#88135	C₂²	semidirect
75. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
76. #11719182	C₂²	semidirect
77. C₂×#88129	C₂²	semidirect
78. C₂×#88129	C₂²	semidirect
79. C₂×#88129	C₂²	semidirect
80. C₂×#88129	C₂²	semidirect
81. C₂×#88129	C₂²	semidirect
82. C₂×#88129	C₂²	semidirect
83. C₂×#88129	C₂²	semidirect
85. C₂×#88128	C₂²	semidirect
86. C₂×C₄×D₅₂	C₂²	semidirect
87. C₂×C₄×D₅₂	C₂²	semidirect
88. C₂×C₄×D₅₂	C₂²	semidirect
89. C₂×#88123	C₂²	semidirect
90. C₂×C₄×Dic₂₆	C₂²	semidirect
105. C₂×D₄×D₁₃	C₂³	semidirect
108. C₂×#6127	C₂³	semidirect
109. C₂×#6127	C₂³	semidirect
121. C₂²×D₅₂	C₂³	semidirect
129. C₂²×Dic₂₆	C₂³	semidirect
130. C₁₃×#126	C₂³	semidirect
131. C₁₃×#125	C₂³	semidirect
132. C₁₃×#124	C₂³	semidirect
133. C₁₃×#123	C₂³	semidirect
134. C₁₃×C₂²⋊Q₈	C₂³	semidirect
136. C₄×Q₈×C₁₃	C₂³	semidirect
137. C₄×D₄×C₁₃	C₂³	semidirect
138. C₄×D₄×C₁₃	C₂³	semidirect
139. C₁₃×#117	C₂³	semidirect
156. C₂×C₄²×C₁₃	C₂³	semidirect
158. #88201	C₂³	semidirect
159. #88193	C₂³	semidirect
160. #88191	C₂³	semidirect
162. #88184	C₂³	semidirect
163. #88184	C₂³	semidirect
174. C₂×#6103	C₂³	semidirect
175. C₂×#6103	C₂³	semidirect
178. #88178	C₂³	semidirect
182. #88152	C₂³	semidirect
183. #88150	C₂³	semidirect
184. #88150	C₂³	semidirect
185. #88149	C₂³	semidirect
186. #88149	C₂³	semidirect
187. #88149	C₂³	semidirect
188. #88148	C₂³	semidirect
189. #88148	C₂³	semidirect
190. #88148	C₂³	semidirect
191. #88147	C₂³	semidirect
192. #88139	C₂³	semidirect
193. #88139	C₂³	semidirect
194. #88138	C₂³	semidirect
195. #88137	C₂³	semidirect
196. #88136	C₂³	semidirect
197. #88136	C₂³	semidirect
198. #88136	C₂³	semidirect
199. #88136	C₂³	semidirect
200. #88135	C₂³	semidirect
201. C₂²⋊C₄×D₁₃	C₂³	semidirect
202. #88129	C₂³	semidirect
203. #88129	C₂³	semidirect
204. #88129	C₂³	semidirect
205. #88129	C₂³	semidirect
206. #88129	C₂³	semidirect
207. #88129	C₂³	semidirect
209. #88128	C₂³	semidirect
210. C₄×D₅₂	C₂³	semidirect
211. C₄×D₅₂	C₂³	semidirect
212. C₄×D₅₂	C₂³	semidirect
213. #88123	C₂³	semidirect
214. C₄×Dic₂₆	C₂³	semidirect
341. C₂×#529	D₁₃	semidirect
437. #529	C₂×D₁₃	semidirect
439. C₂×#126	C₂×D₁₃	semidirect
440. C₂×#125	C₂×D₁₃	semidirect
451. C₂×#124	C₂×D₁₃	semidirect
456. C₂×#123	C₂×D₁₃	semidirect
460. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
476. C₂×C₄×Q₈	C₂×D₁₃	semidirect
482. C₂×C₄×D₄	C₂×D₁₃	semidirect
483. C₂×C₄×D₄	C₂×D₁₃	semidirect
484. C₂×#117	C₂×D₁₃	semidirect
488. C₂²×C₄²	C₂×D₁₃	semidirect
565. #126	C₂²×D₁₃	semidirect
566. #125	C₂²×D₁₃	semidirect
576. #124	C₂²×D₁₃	semidirect
581. #123	C₂²×D₁₃	semidirect
585. C₂²⋊Q₈	C₂²×D₁₃	semidirect
601. C₄×Q₈	C₂²×D₁₃	semidirect
607. C₄×D₄	C₂²×D₁₃	semidirect
608. C₄×D₄	C₂²×D₁₃	semidirect
609. #117	C₂²×D₁₃	semidirect
645. C₂×C₄²	C₂²×D₁₃	semidirect
648. C₂×C₁₃	#3558	semidirect
765. C₁₃	C₂×#3558	semidirect
875. C₂	#13129352	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129352	2
C₂×#11719405	2
C₂×#11719388	2
C₂×#11719290	2
C₂×#11719257	2
C₂×#11719255	2
C₂×#11719359	2
C₂×D₄×D₅₂	2
C₂×#11719239	2
C₂×#11719349	2
C₂×#11719409	2
C₂×#11719230	2
C₂×#11719310	2
C₂×#11719182	2
C₂²×#88129	2
C₂×C₁₃×#529	2
C₂×#3558	13

Subgroups — C2×#13129352 #16770256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129352 #16770256