Subgroups — C₂×#13128252 #16769717

Order 3328.

7994 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128252	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719224	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719287	C₂	1	2	yes	maximal, complemented
4	C₂×#11719239	C₂	1	2	yes	maximal, complemented
5	C₂×#11719240	C₂	1	2	yes	maximal, complemented
6	C₂×#11719267	C₂	1	2	yes	maximal, complemented
7	C₂×#11719265	C₂	1	4	yes	maximal, complemented
8	C₂×#11719538	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11719230	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11719535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11719182	C₂	1	2	yes	maximal, complemented
12	C₂×#11719253	C₂	1	2	yes	maximal, complemented
13	C₂×#11719285	C₂	1	2	yes	maximal, complemented
14	C₂×#11719184	C₂	1	2	yes	maximal, complemented
15	C₂×#11719252	C₂	1	4	yes	maximal, complemented
16	C₂×C₄×#6127	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×#6127	C₂²	1	1	yes	characteristic
21	C₂²×#6127	C₂²	1	4	yes	complemented
22	C₂³×D₅₂	C₂²	1	1	yes	characteristic
23	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
24	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
35	#11719538	C₂²	1	16	yes	complemented
36	#11719535	C₂²	1	16	yes	complemented
37	C₂×#88201	C₂²	1	2	yes	—
38	C₂×#88200	C₂²	1	2	yes	complemented
39	C₂×#88194	C₂²	1	2	yes	—
40	C₂×#88193	C₂²	1	4	yes	—
41	C₂×#88192	C₂²	1	2	yes	complemented
42	C₂×#88191	C₂²	1	4	yes	—
43	C₂×#88184	C₂²	1	2	yes	—
44	C₂×#88184	C₂²	1	2	yes	—
45	C₂×#88184	C₂²	1	4	yes	complemented
46	C₂×#88184	C₂²	1	2	yes	complemented
47	C₂×#88183	C₂²	1	4	yes	complemented
48	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
49	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
50	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
51	C₂²×#6103	C₂²	1	2	yes	—
52	C₂×#88180	C₂²	1	1	yes	characteristic
53	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
54	C₂×#88178	C₂²	1	2	yes	complemented
55	#11719287	C₂²	1	32	yes	complemented
56	#11719285	C₂²	1	32	yes	complemented
57	#11719267	C₂²	1	32	yes	complemented
58	#11719265	C₂²	1	64	yes	complemented
59	#11719253	C₂²	1	32	yes	complemented
60	#11719252	C₂²	1	64	yes	complemented
61	#11719240	C₂²	1	32	yes	complemented
62	#11719239	C₂²	1	32	yes	complemented
63	#11719230	C₂²	1	16	yes	complemented
64	#11719224	C₂²	1	16	yes	complemented
65	C₂×#88152	C₂²	1	4	yes	complemented
66	C₂×#88150	C₂²	1	4	yes	complemented
67	C₂×#88149	C₂²	1	2	yes	—
68	C₂×#88149	C₂²	1	2	yes	—
69	C₂×#88148	C₂²	1	4	yes	complemented
70	C₂×#88148	C₂²	1	4	yes	complemented
71	C₂×#88144	C₂²	1	2	yes	complemented
72	C₂×#88142	C₂²	1	2	yes	complemented
73	C₂×#88139	C₂²	1	4	yes	complemented
74	C₂×#88138	C₂²	1	4	yes	complemented
75	C₂×#88138	C₂²	1	4	yes	complemented
76	C₂×#88137	C₂²	1	4	yes	complemented
77	C₂×#88136	C₂²	1	4	yes	—
78	C₂×#88132	C₂²	1	4	yes	—
79	#11719184	C₂²	1	32	yes	complemented
80	C₂×#88130	C₂²	1	4	yes	complemented
81	#11719182	C₂²	1	32	yes	complemented
82	C₂×#88129	C₂²	1	2	yes	—
83	C₂×#88129	C₂²	1	4	yes	complemented
84	C₂×#88128	C₂²	1	2	yes	—
85	C₄×#6127	C₂²	1	16	yes	complemented
86	C₂×C₄×D₅₂	C₂²	1	2	yes	—
87	C₂×C₄×D₅₂	C₂²	1	2	yes	—
88	C₂×C₄×D₅₂	C₂²	1	2	yes	—
89	C₂×C₄×D₅₂	C₂²	1	2	yes	—
90	C₂×C₄×D₅₂	C₂²	1	16	yes	complemented
91	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
94	C₂×#88126	C₂²	1	2	yes	complemented
95	C₂×#88126	C₂²	1	4	yes	complemented
96	C₂×C₄²×D₁₃	C₂²	1	2	yes	complemented
97	C₂×#88124	C₂²	1	2	yes	complemented
98	C₂×#88123	C₂²	1	2	yes	complemented
99	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
101	C₂⁴×D₁₃	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	—	2	8	no	—
103	C₂×C₁₃×#41	C₂³	1	8	yes	—
104	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
114	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
115	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
116	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
117	C₂³×Dic₁₃	C₂³	1	2	yes	—
118	C₂×#6127	—	2	8	no	—
119	C₂×#6127	—	4	16	no	—
120	C₂×#6127	C₂³	1	8	yes	—
121	C₂×#6127	C₂³	1	32	yes	complemented
122	C₂²×D₅₂	—	2	8	no	—
123	C₂²×D₅₂	C₂³	1	2	yes	—
124	C₂²×D₅₂	C₂³	1	2	yes	—
125	C₂²×D₅₂	C₂³	1	1	yes	characteristic
126	C₂²×D₅₂	C₂³	1	8	yes	—
127	C₂²×D₅₂	C₂³	1	4	yes	—
128	C₂²×D₅₂	C₂³	1	4	yes	—
129	C₂²×C₄×D₁₃	—	4	8	no	—
130	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
132	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
133	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
134	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
135	C₂²×C₄×D₁₃	C₂³	1	16	yes	—
136	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
137	C₂²×Dic₂₆	C₂³	1	4	yes	—
138	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
139	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
140	C₄×D₄×C₁₃	C₂³	1	16	yes	—
141	C₄×D₄×C₁₃	C₂³	1	16	yes	—
142	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
143	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
144	C₁₃×#117	C₂³	1	8	yes	—
145	C₁₃×#117	C₂³	1	16	yes	complemented
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
162	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
164	#88201	C₂³	1	16	yes	—
165	#88200	C₂³	1	16	yes	complemented
166	#88194	C₂³	1	16	yes	—
167	#88193	C₂³	1	32	yes	—
168	#88192	C₂³	1	16	yes	complemented
169	#88191	C₂³	1	32	yes	—
170	#88184	C₂³	1	16	yes	—
171	#88184	C₂³	1	16	yes	—
172	#88184	C₂³	1	16	yes	complemented
173	#88184	C₂³	1	32	yes	complemented
174	#88183	C₂³	1	32	yes	complemented
175	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	—
176	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	—
177	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
178	C₂×#6103	C₂³	1	2	yes	—
179	C₂×#6103	C₂³	1	2	yes	—
180	C₂×#6103	C₂³	1	4	yes	—
181	C₂×#6103	C₂³	1	4	yes	—
182	C₂×#6103	C₂³	1	4	yes	—
183	C₂×#6103	C₂³	1	4	yes	—
184	C₂×#6103	C₂³	1	16	yes	—
185	C₂×#6103	C₂³	1	4	yes	—
186	C₂×#6103	C₂³	1	4	yes	—
187	C₂×#6103	C₂³	1	4	yes	—
188	#88180	C₂³	1	8	yes	—
189	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
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	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
195	#88178	C₂³	1	16	yes	complemented
196	C₂×#6101	C₂³	1	2	yes	—
197	C₂×#6101	C₂³	1	2	yes	—
198	C₂×#6101	C₂³	1	4	yes	—
199	C₂×#6101	C₂³	1	4	yes	—
200	C₂×#6101	C₂³	1	4	yes	—
201	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
202	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
203	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
204	#88152	C₂³	1	32	yes	complemented
205	#88150	C₂³	1	32	yes	complemented
206	#88149	C₂³	1	16	yes	—
207	#88149	C₂³	1	16	yes	—
208	#88148	C₂³	1	32	yes	complemented
209	#88148	C₂³	1	32	yes	complemented
210	#88144	C₂³	1	16	yes	complemented
211	#88142	C₂³	1	16	yes	complemented
212	#88139	C₂³	1	32	yes	complemented
213	#88138	C₂³	1	32	yes	complemented
214	#88138	C₂³	1	32	yes	complemented
215	#88137	C₂³	1	32	yes	complemented
216	#88136	C₂³	1	32	yes	—
217	#88132	C₂³	1	32	yes	—
218	#88130	C₂³	1	32	yes	complemented
219	#88129	C₂³	1	16	yes	—
220	#88129	C₂³	1	32	yes	complemented
221	#88128	C₂³	1	16	yes	—
222	C₄×D₅₂	C₂³	1	16	yes	—
223	C₄×D₅₂	C₂³	1	16	yes	—
224	C₄×D₅₂	C₂³	1	16	yes	—
225	C₄×D₅₂	C₂³	1	16	yes	—
226	C₄×D₅₂	C₂³	1	8	yes	complemented
227	C₄×D₅₂	C₂³	1	8	yes	complemented
228	C₄×D₅₂	C₂³	1	32	yes	complemented
229	#88126	C₂³	1	16	yes	complemented
230	#88126	C₂³	1	32	yes	complemented
231	C₄²×D₁₃	C₂³	1	16	yes	complemented
232	#88124	C₂³	1	16	yes	complemented
233	#88123	C₂³	1	16	yes	complemented
234	C₄×Dic₂₆	C₂³	1	8	yes	complemented
235	C₄×Dic₂₆	C₂³	1	8	yes	complemented
236	C₂×#3460	—	13	1	no	maximal, Sylow
237	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
238	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂³×D₁₃	—	2	8	no	—
240	C₂³×D₁₃	—	4	4	no	—
241	C₂³×D₁₃	—	4	4	no	—
242	C₂³×D₁₃	C₂⁴	1	4	yes	—
243	C₂³×D₁₃	C₂⁴	1	2	yes	—
244	C₂³×D₁₃	C₂⁴	1	8	yes	—
245	C₁₃×#41	—	2	32	no	—
246	C₂×Q₈×C₁₃	—	2	4	no	—
247	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
248	C₂×D₄×C₁₃	—	2	8	no	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
251	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₁₃	—	2	8	no	—
253	C₂²×C₄×C₁₃	—	2	4	no	—
254	C₂²×C₄×C₁₃	—	2	8	no	—
255	C₂²×C₄×C₁₃	—	4	2	no	—
256	C₂²×C₄×C₁₃	—	4	4	no	—
257	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×C₂²⋊D₁₃	—	2	8	no	—
274	C₂×C₂²⋊D₁₃	—	4	8	no	—
275	C₂×C₂²⋊D₁₃	—	4	8	no	—
276	C₂×C₂²⋊D₁₃	—	4	8	no	—
277	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
278	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
279	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
280	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
281	C₂²×Dic₁₃	—	4	4	no	—
282	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
283	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
284	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
285	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
286	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
287	#6127	—	2	32	no	—
288	#6127	—	4	64	no	—
289	C₂×D₅₂	—	2	8	no	—
290	C₂×D₅₂	—	2	8	no	—
291	C₂×D₅₂	—	2	4	no	—
292	C₂×D₅₂	—	2	32	no	—
293	C₂×D₅₂	—	4	8	no	—
294	C₂×D₅₂	—	4	8	no	—
295	C₂×D₅₂	C₂⁴	1	8	yes	—
296	C₂×D₅₂	C₂⁴	1	8	yes	—
297	C₂×D₅₂	C₂⁴	1	4	yes	—
298	C₂×D₅₂	C₂⁴	1	16	yes	—
299	C₂×D₅₂	C₂⁴	1	16	yes	—
300	C₂×C₄×D₁₃	—	2	8	no	—
301	C₂×C₄×D₁₃	—	2	16	no	—
302	C₂×C₄×D₁₃	—	2	8	no	—
303	C₂×C₄×D₁₃	—	4	32	no	—
304	C₂×C₄×D₁₃	—	4	8	no	—
305	C₂×C₄×D₁₃	—	4	4	no	—
306	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
307	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
308	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
309	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
310	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
311	C₂×Dic₂₆	—	2	4	no	—
312	C₂×Dic₂₆	—	4	8	no	—
313	C₂×Dic₂₆	C₂⁴	1	4	yes	—
314	C₂×Dic₂₆	C₂⁴	1	16	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
319	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
320	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
321	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
322	C₄²×C₁₃	C₂⁴	1	4	yes	—
323	C₄²×C₁₃	C₂⁴	1	4	yes	—
324	C₄²×C₁₃	C₂⁴	1	8	yes	—
325	C₄²×C₁₃	C₂⁴	1	4	yes	—
326	C₄²×C₁₃	C₂⁴	1	4	yes	—
327	C₄²×C₁₃	C₂⁴	1	8	yes	—
328	C₄²×C₁₃	C₂⁴	1	8	yes	—
329	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
330	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
331	#6103	C₂⁴	1	8	yes	—
332	#6103	C₂⁴	1	8	yes	—
333	#6103	C₂⁴	1	16	yes	—
334	#6103	C₂⁴	1	16	yes	—
335	#6103	C₂⁴	1	16	yes	—
336	#6103	C₂⁴	1	16	yes	—
337	#6103	C₂⁴	1	16	yes	—
338	#6103	C₂⁴	1	16	yes	—
339	#6103	C₂⁴	1	16	yes	—
340	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
341	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
342	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
343	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
344	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
345	#6101	C₂⁴	1	8	yes	—
346	#6101	C₂⁴	1	8	yes	—
347	#6101	C₂⁴	1	16	yes	—
348	#6101	C₂⁴	1	16	yes	—
349	#6101	C₂⁴	1	16	yes	—
350	C₄×Dic₁₃	C₂⁴	1	8	yes	—
351	C₄×Dic₁₃	C₂⁴	1	8	yes	—
352	C₄×Dic₁₃	C₂⁴	1	8	yes	—
353	#3460	—	13	32	no	—
354	C₂×#544	—	13	1	no	—
355	C₂×#542	—	13	2	no	—
356	C₂×#542	—	13	2	no	—
357	C₂×#540	—	13	2	no	—
358	C₂×#540	—	13	2	no	—
359	C₂×#538	—	13	4	no	—
360	C₂×#537	—	13	1	no	—
361	C₂×#535	—	13	1	no	—
362	C₂×#535	—	13	1	no	—
363	C₂×#532	—	13	2	no	—
364	C₂×#532	—	13	2	no	—
365	C₂×#529	—	13	2	no	—
366	C₂×#529	—	13	2	no	—
367	C₂×#525	—	13	4	no	—
368	C₂×C₄×#41	—	13	1	no	—
369	C₂×C₄×#41	D₁₃	1	1	yes	characteristic, complemented
370	C₂²×C₄×D₄	—	13	1	no	—
371	C₂³×C₁₃	—	2	2	no	—
372	C₂³×C₁₃	—	2	2	no	—
373	C₂³×C₁₃	—	2	4	no	—
374	C₂³×C₁₃	—	2	4	no	—
375	C₂³×C₁₃	—	2	4	no	—
376	C₂³×C₁₃	C₂×#41	1	4	yes	—
377	C₂³×C₁₃	C₂⁵	1	4	yes	—
378	C₂³×C₁₃	C₂⁵	1	2	yes	—
379	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
380	C₂²×D₁₃	—	2	4	no	—
381	C₂²×D₁₃	—	2	16	no	—
382	C₂²×D₁₃	—	2	8	no	—
383	C₂²×D₁₃	—	2	8	no	—
384	C₂²×D₁₃	—	2	4	no	—
385	C₂²×D₁₃	—	2	4	no	—
386	C₂²×D₁₃	—	2	8	no	—
387	C₂²×D₁₃	—	4	8	no	—
388	C₂²×D₁₃	—	4	8	no	—
389	C₂²×D₁₃	—	4	32	no	—
390	C₂²×D₁₃	C₂⁵	1	8	yes	—
391	C₂²×D₁₃	C₂⁵	1	4	yes	—
392	Q₈×C₁₃	—	2	8	no	—
393	D₄×C₁₃	—	2	16	no	—
394	D₄×C₁₃	—	2	8	no	—
395	C₂×C₄×C₁₃	—	2	4	no	—
396	C₂×C₄×C₁₃	—	2	4	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	4	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	16	no	—
402	C₂×C₄×C₁₃	—	2	8	no	—
403	C₂×C₄×C₁₃	—	2	16	no	—
404	C₂×C₄×C₁₃	—	4	4	no	—
405	C₂×C₄×C₁₃	—	4	8	no	—
406	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
407	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
408	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
409	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
410	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
411	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
412	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
413	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
414	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
415	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
416	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
417	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
418	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
419	C₂²⋊D₁₃	—	2	16	no	—
420	C₂²⋊D₁₃	—	4	16	no	—
421	C₂²⋊D₁₃	—	4	16	no	—
422	C₂²⋊D₁₃	—	4	16	no	—
423	C₂×Dic₁₃	—	2	4	no	—
424	C₂×Dic₁₃	—	2	4	no	—
425	C₂×Dic₁₃	—	2	8	no	—
426	C₂×Dic₁₃	—	2	4	no	—
427	C₂×Dic₁₃	—	4	8	no	—
428	C₂×Dic₁₃	C₂⁵	1	4	yes	—
429	C₂×Dic₁₃	C₂⁵	1	4	yes	—
430	C₂×Dic₁₃	C₂⁵	1	4	yes	—
431	C₂×Dic₁₃	C₂⁵	1	8	yes	—
432	D₅₂	—	2	16	no	—
433	D₅₂	—	2	16	no	—
434	D₅₂	—	2	8	no	—
435	D₅₂	—	4	16	no	—
436	D₅₂	—	4	16	no	—
437	C₄×D₁₃	—	2	16	no	—
438	C₄×D₁₃	—	2	32	no	—
439	C₄×D₁₃	—	2	16	no	—
440	C₄×D₁₃	—	4	16	no	—
441	C₄×D₁₃	—	4	8	no	—
442	Dic₂₆	—	2	8	no	—
443	Dic₂₆	—	4	16	no	—
444	C₂²×#41	—	13	1	no	—
445	C₂²×#41	—	13	4	no	—
446	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
447	C₂³×D₄	—	13	1	no	—
448	C₂⁴×C₄	—	13	2	no	—
449	#544	—	13	16	no	—
450	#542	—	13	32	no	—
451	#542	—	13	32	no	—
452	#540	—	13	32	no	—
453	#540	—	13	32	no	—
454	#538	—	13	64	no	—
455	#537	—	13	16	no	—
456	#535	—	13	16	no	—
457	#535	—	13	16	no	—
458	#532	—	13	32	no	—
459	#532	—	13	32	no	—
460	C₂×C₄⋊Q₈	—	13	2	no	—
461	C₂×C₄⋊Q₈	—	13	2	no	—
462	C₂×#127	—	13	2	no	—
463	C₂×#127	—	13	2	no	—
464	#529	—	13	32	no	—
465	#529	—	13	32	no	—
466	C₂×#126	—	13	4	no	—
467	C₂×#126	—	13	4	no	—
468	C₂×#125	—	13	2	no	—
469	C₂×#125	—	13	2	no	—
470	C₂×#124	—	13	2	no	—
471	C₂×#124	—	13	4	no	—
472	C₂×#124	—	13	2	no	—
473	C₂×#124	—	13	4	no	—
474	#525	—	13	64	no	—
475	C₂×#123	—	13	4	no	—
476	C₂×#123	—	13	4	no	—
477	C₂×#123	—	13	4	no	—
478	C₂×#123	—	13	4	no	—
479	C₂×C₂²⋊Q₈	—	13	2	no	—
480	C₂×C₂²⋊Q₈	—	13	2	no	—
481	C₂×C₂²⋊Q₈	—	13	4	no	—
482	C₂×C₂²⋊Q₈	—	13	4	no	—
483	C₂×#121	—	13	2	no	—
484	C₂×#121	—	13	4	no	—
485	C₂×#121	—	13	2	no	—
486	C₂×#121	—	13	2	no	—
487	C₂×#121	—	13	2	no	—
488	C₂×#121	—	13	4	no	—
489	C₂×#121	—	13	2	no	—
490	C₂×#121	—	13	2	no	—
491	C₂×#121	—	13	4	no	—
492	C₂×#121	—	13	4	no	—
493	C₂×#120	—	13	4	no	—
494	C₂×#120	—	13	4	no	—
495	C₄×#41	—	13	16	no	—
496	C₄×#41	C₂×D₁₃	1	16	yes	complemented
497	C₂×C₄×Q₈	—	13	1	no	—
498	C₂×C₄×Q₈	—	13	1	no	—
499	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
500	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
501	C₂×C₄×D₄	—	13	2	no	—
502	C₂×C₄×D₄	—	13	2	no	—
503	C₂×C₄×D₄	—	13	4	no	—
504	C₂×C₄×D₄	—	13	2	no	—
505	C₂×C₄×D₄	—	13	2	no	—
506	C₂×C₄×D₄	—	13	2	no	—
507	C₂×C₄×D₄	—	13	2	no	—
508	C₂×C₄×D₄	—	13	16	no	—
509	C₂×C₄×D₄	—	13	1	no	—
510	C₂×C₄×D₄	—	13	1	no	—
511	C₂×C₄×D₄	—	13	4	no	—
512	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
513	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
514	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
515	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
516	C₂×#117	—	13	1	no	—
517	C₂×#117	—	13	2	no	—
518	C₂×#117	—	13	4	no	—
519	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
520	C₂×#117	C₂×D₁₃	1	2	yes	complemented
521	C₂²×C₄⋊C₄	—	13	1	no	—
522	C₂²×C₂²⋊C₄	—	13	2	no	—
523	C₂²×C₄²	—	13	2	no	—
524	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
525	C₂²×C₄²	C₂×D₁₃	1	2	yes	complemented
526	C₂²×C₁₃	—	2	2	no	—
527	C₂²×C₁₃	—	2	2	no	—
528	C₂²×C₁₃	—	2	8	no	—
529	C₂²×C₁₃	—	2	4	no	—
530	C₂²×C₁₃	—	2	4	no	—
531	C₂²×C₁₃	—	2	4	no	—
532	C₂²×C₁₃	—	4	8	no	—
533	C₂²×C₁₃	C₂²×#41	1	4	yes	—
534	C₂²×C₁₃	C₂²×#41	1	2	yes	—
535	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
536	C₂²×C₁₃	#585	1	2	yes	—
537	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
538	C₂×D₁₃	—	2	4	no	—
539	C₂×D₁₃	—	2	8	no	—
540	C₂×D₁₃	—	2	8	no	—
541	C₂×D₁₃	—	2	4	no	—
542	C₂×D₁₃	—	2	4	no	—
543	C₂×D₁₃	—	2	8	no	—
544	C₂×D₁₃	—	4	32	no	—
545	C₂×D₁₃	—	4	8	no	—
546	C₂×D₁₃	—	4	16	no	—
547	C₄×C₁₃	—	2	4	no	—
548	C₄×C₁₃	—	2	4	no	—
549	C₄×C₁₃	—	2	2	no	—
550	C₄×C₁₃	—	2	2	no	—
551	C₄×C₁₃	—	2	4	no	—
552	C₄×C₁₃	—	2	2	no	—
553	C₄×C₁₃	C₂²×#41	1	4	yes	—
554	C₄×C₁₃	C₂²×#41	1	4	yes	—
555	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
556	Dic₁₃	—	2	4	no	—
557	Dic₁₃	—	2	4	no	—
558	Dic₁₃	—	2	8	no	—
559	Dic₁₃	—	2	4	no	—
560	C₂⁵	—	13	2	no	—
561	C₂×#41	—	2	8	no	—
562	C₂×#41	—	13	8	no	—
563	C₂×#41	—	13	32	no	—
564	C₂×#41	—	26	8	no	—
565	C₂×#41	—	52	16	no	—
566	C₂×#41	C₂²×D₁₃	1	8	yes	—
567	C₂²×Q₈	—	13	1	no	—
568	C₂²×Q₈	—	13	4	no	—
569	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
570	C₂²×D₄	—	13	2	no	—
571	C₂²×D₄	—	13	4	no	—
572	C₂²×D₄	—	13	4	no	—
573	C₂²×D₄	—	13	4	no	—
574	C₂²×D₄	—	13	2	no	—
575	C₂²×D₄	—	13	2	no	—
576	C₂²×D₄	—	13	1	no	—
577	C₂²×D₄	—	13	8	no	—
578	C₂²×D₄	—	13	4	no	—
579	C₂²×D₄	—	13	4	no	—
580	C₂²×D₄	—	26	8	no	—
581	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
582	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
583	C₂³×C₄	—	13	2	no	—
584	C₂³×C₄	—	13	2	no	—
585	C₂³×C₄	—	13	4	no	—
586	C₂³×C₄	—	13	2	no	—
587	C₂³×C₄	—	13	2	no	—
588	C₂³×C₄	—	13	4	no	—
589	C₂³×C₄	—	13	16	no	—
590	C₂³×C₄	—	52	8	no	—
591	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
592	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
593	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
594	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
595	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
596	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
597	C₄⋊Q₈	—	13	16	no	—
598	C₄⋊Q₈	—	13	16	no	—
599	#127	—	13	16	no	—
600	#127	—	13	16	no	—
601	#126	—	13	32	no	—
602	#126	—	13	32	no	—
603	#125	—	13	16	no	—
604	#125	—	13	16	no	—
605	#124	—	13	16	no	—
606	#124	—	13	32	no	—
607	#124	—	13	16	no	—
608	#124	—	13	32	no	—
609	#123	—	13	32	no	—
610	#123	—	13	32	no	—
611	#123	—	13	32	no	—
612	#123	—	13	32	no	—
613	C₂²⋊Q₈	—	13	16	no	—
614	C₂²⋊Q₈	—	13	16	no	—
615	C₂²⋊Q₈	—	13	32	no	—
616	C₂²⋊Q₈	—	13	32	no	—
617	#121	—	13	32	no	—
618	#121	—	13	16	no	—
619	#121	—	13	16	no	—
620	#121	—	13	16	no	—
621	#121	—	13	16	no	—
622	#121	—	13	32	no	—
623	#121	—	13	16	no	—
624	#121	—	13	16	no	—
625	#121	—	13	32	no	—
626	#121	—	13	32	no	—
627	#120	—	13	32	no	—
628	#120	—	13	32	no	—
629	C₄×Q₈	—	13	8	no	—
630	C₄×Q₈	—	13	8	no	—
631	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
632	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
633	C₄×D₄	—	13	16	no	—
634	C₄×D₄	—	13	16	no	—
635	C₄×D₄	—	13	32	no	—
636	C₄×D₄	—	13	16	no	—
637	C₄×D₄	—	13	16	no	—
638	C₄×D₄	—	13	16	no	—
639	C₄×D₄	—	13	16	no	—
640	C₄×D₄	—	13	8	no	—
641	C₄×D₄	—	13	8	no	—
642	C₄×D₄	—	13	32	no	—
643	C₄×D₄	C₂²×D₁₃	1	16	yes	—
644	C₄×D₄	C₂²×D₁₃	1	16	yes	—
645	C₄×D₄	C₂²×D₁₃	1	8	yes	complemented
646	C₄×D₄	C₂²×D₁₃	1	8	yes	complemented
647	#117	—	13	8	no	—
648	#117	—	13	16	no	—
649	#117	—	13	32	no	—
650	#117	C₂²×D₁₃	1	8	yes	—
651	#117	C₂²×D₁₃	1	16	yes	complemented
652	C₂×C₄⋊C₄	—	13	2	no	—
653	C₂×C₄⋊C₄	—	13	2	no	—
654	C₂×C₄⋊C₄	—	13	8	no	—
655	C₂×C₄⋊C₄	—	13	1	no	—
656	C₂×C₄⋊C₄	—	13	1	no	—
657	C₂×C₄⋊C₄	—	13	2	no	—
658	C₂×C₄⋊C₄	—	13	2	no	—
659	C₂×C₄⋊C₄	—	13	4	no	—
660	C₂×C₄⋊C₄	—	13	4	no	—
661	C₂×C₄⋊C₄	—	13	4	no	—
662	C₂×C₄⋊C₄	—	13	4	no	—
663	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
666	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
667	C₂×C₂²⋊C₄	—	13	2	no	—
668	C₂×C₂²⋊C₄	—	13	4	no	—
669	C₂×C₂²⋊C₄	—	13	4	no	—
670	C₂×C₂²⋊C₄	—	13	4	no	—
671	C₂×C₂²⋊C₄	—	13	16	no	—
672	C₂×C₂²⋊C₄	—	13	2	no	—
673	C₂×C₂²⋊C₄	—	13	2	no	—
674	C₂×C₂²⋊C₄	—	13	4	no	—
675	C₂×C₂²⋊C₄	—	13	4	no	—
676	C₂×C₂²⋊C₄	—	13	4	no	—
677	C₂×C₂²⋊C₄	—	13	4	no	—
678	C₂×C₂²⋊C₄	—	13	4	no	—
679	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
682	C₂×C₄²	—	13	2	no	—
683	C₂×C₄²	—	13	2	no	—
684	C₂×C₄²	—	13	2	no	—
685	C₂×C₄²	—	13	16	no	—
686	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
687	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
688	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
689	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
690	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
691	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
692	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
693	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
694	C₂×C₄²	C₂²×D₁₃	1	16	yes	complemented
695	C₂×C₁₃	—	2	4	no	—
696	C₂×C₁₃	—	4	4	no	—
697	C₂×C₁₃	#3460	1	4	yes	complemented
698	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
699	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
700	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
701	D₁₃	—	4	4	no	—
702	D₁₃	—	4	8	no	—
703	C₂⁴	—	13	4	no	—
704	C₂⁴	—	13	2	no	—
705	C₂⁴	—	13	8	no	—
706	C₂⁴	—	26	8	no	—
707	C₂⁴	—	52	4	no	—
708	C₂⁴	—	52	4	no	—
709	C₂⁴	C₂³×D₁₃	1	2	yes	—
710	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
711	#41	—	2	32	no	—
712	#41	—	26	32	no	—
713	#41	—	52	64	no	—
714	C₂×Q₈	—	2	4	no	—
715	C₂×Q₈	—	13	4	no	—
716	C₂×Q₈	—	13	16	no	—
717	C₂×Q₈	—	26	4	no	—
718	C₂×Q₈	—	52	8	no	—
719	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
720	C₂×D₄	—	2	8	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	13	8	no	—
723	C₂×D₄	—	13	16	no	—
724	C₂×D₄	—	13	16	no	—
725	C₂×D₄	—	13	16	no	—
726	C₂×D₄	—	13	8	no	—
727	C₂×D₄	—	13	8	no	—
728	C₂×D₄	—	13	4	no	—
729	C₂×D₄	—	13	16	no	—
730	C₂×D₄	—	13	16	no	—
731	C₂×D₄	—	26	8	no	—
732	C₂×D₄	—	26	8	no	—
733	C₂×D₄	—	26	8	no	—
734	C₂×D₄	—	26	4	no	—
735	C₂×D₄	—	26	32	no	—
736	C₂×D₄	—	52	8	no	—
737	C₂×D₄	—	52	8	no	—
738	C₂×D₄	—	52	8	no	—
739	C₂×D₄	—	52	8	no	—
740	C₂×D₄	—	52	8	no	—
741	C₂×D₄	C₂³×D₁₃	1	8	yes	—
742	C₂×D₄	C₂³×D₁₃	1	4	yes	—
743	C₂²×C₄	—	2	8	no	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	2	8	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	4	no	—
748	C₂²×C₄	—	13	2	no	—
749	C₂²×C₄	—	13	2	no	—
750	C₂²×C₄	—	13	2	no	—
751	C₂²×C₄	—	13	4	no	—
752	C₂²×C₄	—	13	8	no	—
753	C₂²×C₄	—	13	8	no	—
754	C₂²×C₄	—	13	8	no	—
755	C₂²×C₄	—	13	16	no	—
756	C₂²×C₄	—	13	8	no	—
757	C₂²×C₄	—	13	16	no	—
758	C₂²×C₄	—	26	8	no	—
759	C₂²×C₄	—	26	16	no	—
760	C₂²×C₄	—	26	8	no	—
761	C₂²×C₄	—	52	32	no	—
762	C₂²×C₄	—	52	8	no	—
763	C₂²×C₄	—	52	4	no	—
764	C₂²×C₄	—	52	4	no	—
765	C₂²×C₄	#6127	1	8	yes	complemented
766	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
769	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
770	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
771	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
772	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
773	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
774	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
775	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
776	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
777	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
778	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
779	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
780	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
781	C₄⋊C₄	—	13	8	no	—
782	C₄⋊C₄	—	13	8	no	—
783	C₄⋊C₄	—	13	4	no	—
784	C₄⋊C₄	—	13	4	no	—
785	C₄⋊C₄	—	13	8	no	—
786	C₄⋊C₄	—	13	8	no	—
787	C₄⋊C₄	—	13	16	no	—
788	C₄⋊C₄	—	13	16	no	—
789	C₄⋊C₄	—	13	16	no	—
790	C₄⋊C₄	—	13	16	no	—
791	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
792	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
793	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
794	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
795	C₂²⋊C₄	—	13	8	no	—
796	C₂²⋊C₄	—	13	16	no	—
797	C₂²⋊C₄	—	13	16	no	—
798	C₂²⋊C₄	—	13	16	no	—
799	C₂²⋊C₄	—	13	8	no	—
800	C₂²⋊C₄	—	13	8	no	—
801	C₂²⋊C₄	—	13	16	no	—
802	C₂²⋊C₄	—	13	16	no	—
803	C₂²⋊C₄	—	13	16	no	—
804	C₂²⋊C₄	—	13	16	no	—
805	C₂²⋊C₄	—	13	16	no	—
806	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
807	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
808	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
809	C₄²	—	13	8	no	—
810	C₄²	—	13	8	no	—
811	C₄²	—	13	8	no	—
812	C₄²	C₂³×D₁₃	1	4	yes	—
813	C₄²	C₂³×D₁₃	1	4	yes	—
814	C₄²	C₂³×D₁₃	1	4	yes	—
815	C₄²	C₂³×D₁₃	1	4	yes	—
816	C₄²	C₂³×D₁₃	1	8	yes	—
817	C₄²	C₂³×D₁₃	1	8	yes	—
818	C₄²	C₂³×D₁₃	1	8	yes	—
819	C₁₃	C₂×#3460	1	1	yes	characteristic, complemented, Sylow
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	4	no	—
823	C₂³	—	2	4	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	13	8	no	—
826	C₂³	—	13	4	no	—
827	C₂³	—	26	4	no	—
828	C₂³	—	26	16	no	—
829	C₂³	—	26	8	no	—
830	C₂³	—	26	8	no	—
831	C₂³	—	26	4	no	—
832	C₂³	—	26	4	no	—
833	C₂³	—	26	8	no	—
834	C₂³	—	52	8	no	—
835	C₂³	—	52	8	no	—
836	C₂³	—	52	32	no	—
837	C₂³	C₂×#6127	1	4	yes	—
838	C₂³	C₂⁴×D₁₃	1	4	yes	—
839	C₂³	C₂⁴×D₁₃	1	2	yes	—
840	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
841	Q₈	—	2	8	no	—
842	Q₈	—	26	8	no	—
843	Q₈	—	52	16	no	—
844	D₄	—	2	16	no	—
845	D₄	—	2	8	no	—
846	D₄	—	26	16	no	—
847	D₄	—	26	16	no	—
848	D₄	—	26	16	no	—
849	D₄	—	26	8	no	—
850	D₄	—	52	16	no	—
851	D₄	—	52	16	no	—
852	D₄	—	52	16	no	—
853	D₄	—	52	16	no	—
854	D₄	—	52	16	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	4	no	—
861	C₂×C₄	—	2	16	no	—
862	C₂×C₄	—	2	8	no	—
863	C₂×C₄	—	2	16	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	13	4	no	—
867	C₂×C₄	—	13	4	no	—
868	C₂×C₄	—	13	4	no	—
869	C₂×C₄	—	13	8	no	—
870	C₂×C₄	—	26	4	no	—
871	C₂×C₄	—	26	8	no	—
872	C₂×C₄	—	26	4	no	—
873	C₂×C₄	—	26	4	no	—
874	C₂×C₄	—	26	16	no	—
875	C₂×C₄	—	26	32	no	—
876	C₂×C₄	—	26	16	no	—
877	C₂×C₄	—	52	8	no	—
878	C₂×C₄	—	52	16	no	—
879	C₂×C₄	—	52	8	no	—
880	C₂×C₄	C₂×#6127	1	4	yes	—
881	C₂×C₄	C₂×#6127	1	4	yes	—
882	C₂×C₄	C₂×#6127	1	16	yes	complemented
883	C₂×C₄	#88256	1	4	yes	—
884	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
885	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
886	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
887	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
888	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
889	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
890	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
891	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
892	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
893	C₂²	—	2	8	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	4	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	4	8	no	—
900	C₂²	—	26	4	no	—
901	C₂²	—	26	8	no	—
902	C₂²	—	26	8	no	—
903	C₂²	—	26	4	no	—
904	C₂²	—	26	4	no	—
905	C₂²	—	26	8	no	—
906	C₂²	—	52	32	no	—
907	C₂²	—	52	8	no	—
908	C₂²	—	52	16	no	—
909	C₂²	C₂²×#6127	1	4	yes	—
910	C₂²	C₂²×#6127	1	2	yes	—
911	C₂²	C₂×#88256	1	2	yes	—
912	C₂²	#11719648	1	2	yes	—
913	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
914	C₄	—	2	4	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	4	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	4	no	—
920	C₄	—	26	4	no	—
921	C₄	—	26	8	no	—
922	C₄	—	26	4	no	—
923	C₄	—	26	4	no	—
924	C₄	C₂²×#6127	1	4	yes	—
925	C₄	C₂²×#6127	1	4	yes	—
926	C₄	C₂×#88256	1	4	yes	—
927	C₂	—	2	4	no	—
928	C₂	—	4	4	no	—
929	C₂	—	52	8	no	—
930	C₂	—	52	4	no	—
931	C₂	#13128252	1	4	yes	direct product factor
932	C₂	C₂³×#6127	1	1	yes	characteristic
933	C₂	C₂²×#88256	1	1	yes	characteristic
934	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₄×C₁₃×#41	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×C₄×#41	D₁₃
hypocenter	C₁₃	C₂×#3460
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #13128252	C₂	direct (N × H)
2. C₂×#11719224	C₂	semidirect
3. C₂×#11719287	C₂	semidirect
4. C₂×#11719239	C₂	semidirect
5. C₂×#11719240	C₂	semidirect
6. C₂×#11719267	C₂	semidirect
7. C₂×#11719265	C₂	semidirect
8. C₂×#11719538	C₂	semidirect
9. C₂×#11719230	C₂	semidirect
10. C₂×#11719535	C₂	semidirect
11. C₂×#11719182	C₂	semidirect
12. C₂×#11719253	C₂	semidirect
13. C₂×#11719285	C₂	semidirect
14. C₂×#11719184	C₂	semidirect
15. C₂×#11719252	C₂	semidirect
16. C₂×C₄×#6127	C₂	semidirect
17. C₂²×C₄×D₅₂	C₂	semidirect
18. C₂×C₄×C₁₃×#41	C₂	semidirect
21. C₂²×#6127	C₂²	semidirect
24. C₄×C₁₃×#41	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃	C₂²	semidirect
32. C₂×C₁₃×#117	C₂²	semidirect
34. C₂²×C₄²×C₁₃	C₂²	semidirect
35. #11719538	C₂²	semidirect
36. #11719535	C₂²	semidirect
38. C₂×#88200	C₂²	semidirect
41. C₂×#88192	C₂²	semidirect
45. C₂×#88184	C₂²	semidirect
46. C₂×#88184	C₂²	semidirect
47. C₂×#88183	C₂²	semidirect
50. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
54. C₂×#88178	C₂²	semidirect
55. #11719287	C₂²	semidirect
56. #11719285	C₂²	semidirect
57. #11719267	C₂²	semidirect
58. #11719265	C₂²	semidirect
59. #11719253	C₂²	semidirect
60. #11719252	C₂²	semidirect
61. #11719240	C₂²	semidirect
62. #11719239	C₂²	semidirect
63. #11719230	C₂²	semidirect
64. #11719224	C₂²	semidirect
65. C₂×#88152	C₂²	semidirect
66. C₂×#88150	C₂²	semidirect
69. C₂×#88148	C₂²	semidirect
70. C₂×#88148	C₂²	semidirect
71. C₂×#88144	C₂²	semidirect
72. C₂×#88142	C₂²	semidirect
73. C₂×#88139	C₂²	semidirect
74. C₂×#88138	C₂²	semidirect
75. C₂×#88138	C₂²	semidirect
76. C₂×#88137	C₂²	semidirect
79. #11719184	C₂²	semidirect
80. C₂×#88130	C₂²	semidirect
81. #11719182	C₂²	semidirect
83. C₂×#88129	C₂²	semidirect
85. C₄×#6127	C₂²	semidirect
90. C₂×C₄×D₅₂	C₂²	semidirect
91. C₂×C₄×D₅₂	C₂²	semidirect
92. C₂×C₄×D₅₂	C₂²	semidirect
93. C₂×C₄×D₅₂	C₂²	semidirect
94. C₂×#88126	C₂²	semidirect
95. C₂×#88126	C₂²	semidirect
96. C₂×C₄²×D₁₃	C₂²	semidirect
97. C₂×#88124	C₂²	semidirect
98. C₂×#88123	C₂²	semidirect
99. C₂×C₄×Dic₂₆	C₂²	semidirect
100. C₂×C₄×Dic₂₆	C₂²	semidirect
121. C₂×#6127	C₂³	semidirect
138. C₄×Q₈×C₁₃	C₂³	semidirect
139. C₄×Q₈×C₁₃	C₂³	semidirect
142. C₄×D₄×C₁₃	C₂³	semidirect
143. C₄×D₄×C₁₃	C₂³	semidirect
145. C₁₃×#117	C₂³	semidirect
161. C₂×C₄²×C₁₃	C₂³	semidirect
165. #88200	C₂³	semidirect
168. #88192	C₂³	semidirect
172. #88184	C₂³	semidirect
173. #88184	C₂³	semidirect
174. #88183	C₂³	semidirect
177. C₄×C₂²⋊D₁₃	C₂³	semidirect
195. #88178	C₂³	semidirect
204. #88152	C₂³	semidirect
205. #88150	C₂³	semidirect
208. #88148	C₂³	semidirect
209. #88148	C₂³	semidirect
210. #88144	C₂³	semidirect
211. #88142	C₂³	semidirect
212. #88139	C₂³	semidirect
213. #88138	C₂³	semidirect
214. #88138	C₂³	semidirect
215. #88137	C₂³	semidirect
218. #88130	C₂³	semidirect
220. #88129	C₂³	semidirect
226. C₄×D₅₂	C₂³	semidirect
227. C₄×D₅₂	C₂³	semidirect
228. C₄×D₅₂	C₂³	semidirect
229. #88126	C₂³	semidirect
230. #88126	C₂³	semidirect
231. C₄²×D₁₃	C₂³	semidirect
232. #88124	C₂³	semidirect
233. #88123	C₂³	semidirect
234. C₄×Dic₂₆	C₂³	semidirect
235. C₄×Dic₂₆	C₂³	semidirect
257. C₂²×C₄×C₁₃	#41	semidirect
369. C₂×C₄×#41	D₁₃	semidirect
408. C₂×C₄×C₁₃	C₂×#41	semidirect
496. C₄×#41	C₂×D₁₃	semidirect
499. C₂×C₄×Q₈	C₂×D₁₃	semidirect
500. C₂×C₄×Q₈	C₂×D₁₃	semidirect
514. C₂×C₄×D₄	C₂×D₁₃	semidirect
515. C₂×C₄×D₄	C₂×D₁₃	semidirect
520. C₂×#117	C₂×D₁₃	semidirect
525. C₂²×C₄²	C₂×D₁₃	semidirect
631. C₄×Q₈	C₂²×D₁₃	semidirect
632. C₄×Q₈	C₂²×D₁₃	semidirect
645. C₄×D₄	C₂²×D₁₃	semidirect
646. C₄×D₄	C₂²×D₁₃	semidirect
651. #117	C₂²×D₁₃	semidirect
694. C₂×C₄²	C₂²×D₁₃	semidirect
697. C₂×C₁₃	#3460	semidirect
765. C₂²×C₄	#6127	semidirect
819. C₁₃	C₂×#3460	semidirect
882. C₂×C₄	C₂×#6127	semidirect
931. C₂	#13128252	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128252	2
C₂×#11719224	2
C₂×#11719287	2
C₂×#11719239	2
C₂×#11719240	2
C₂×#11719267	2
C₂×#11719265	2
C₂×#11719538	2
C₂×#11719230	2
C₂×#11719535	2
C₂×#11719182	2
C₂×#11719253	2
C₂×#11719285	2
C₂×#11719184	2
C₂×#11719252	2
C₂×C₄×#6127	2
C₂²×C₄×D₅₂	2
C₂×C₄×C₁₃×#41	2
C₂×#3460	13

Subgroups — C2×#13128252 #16769717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128252 #16769717