Subgroups — C₂×#13128705 #16771272

Order 3328.

8622 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128705	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719264	C₂	1	2	yes	maximal, complemented
3	C₂×#11719386	C₂	1	2	yes	maximal, complemented
4	C₂×#11719539	C₂	1	2	yes	maximal, complemented
5	C₂×#11719304	C₂	1	2	yes	maximal, complemented
6	C₂×#11719317	C₂	1	2	yes	maximal, complemented
7	C₂×#11719259	C₂	1	2	yes	maximal, complemented
8	C₂×#11719381	C₂	1	2	yes	maximal, complemented
9	C₂×#11719534	C₂	1	2	yes	maximal, complemented
10	C₂×#11719324	C₂	1	2	yes	maximal, complemented
11	C₂×#11719267	C₂	1	2	yes	maximal, complemented
12	C₂×#11719312	C₂	1	2	yes	maximal, complemented
13	C₂×#11719433	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11719430	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#11719182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719421	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×D₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11719250	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×#6127	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
22	C₂²×#6131	C₂²	1	2	yes	complemented
23	C₂²×#6129	C₂²	1	2	yes	complemented
24	C₂²×D₄×D₁₃	C₂²	1	2	yes	—
25	C₂²×D₄×D₁₃	C₂²	1	2	yes	—
26	C₂²×D₄×D₁₃	C₂²	1	2	yes	—
27	C₂²×#6127	C₂²	1	1	yes	characteristic
28	C₂²×#6127	C₂²	1	2	yes	complemented
29	C₁₃×#532	C₂²	1	16	yes	complemented
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
33	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
37	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	#11719539	C₂²	1	32	yes	complemented
39	#11719534	C₂²	1	32	yes	complemented
40	C₂×#88201	C₂²	1	2	yes	complemented
41	C₂×#88200	C₂²	1	2	yes	—
42	C₂×Q₈×Dic₁₃	C₂²	1	2	yes	complemented
43	C₂×#88194	C₂²	1	2	yes	—
44	C₂×#88194	C₂²	1	2	yes	—
45	C₂×#88194	C₂²	1	2	yes	—
46	C₂×#88194	C₂²	1	4	yes	complemented
47	C₂×#88193	C₂²	1	4	yes	complemented
48	C₂×#88192	C₂²	1	2	yes	complemented
49	C₂×#88192	C₂²	1	4	yes	complemented
50	C₂×#88192	C₂²	1	2	yes	complemented
51	C₂×#88191	C₂²	1	4	yes	—
52	C₂×#88190	C₂²	1	2	yes	complemented
53	C₂×D₄×Dic₁₃	C₂²	1	2	yes	complemented
54	C₂×D₄×Dic₁₃	C₂²	1	2	yes	complemented
55	C₂×#88184	C₂²	1	4	yes	complemented
56	C₂×#88184	C₂²	1	2	yes	complemented
57	C₂×#88184	C₂²	1	2	yes	complemented
58	C₂×#88183	C₂²	1	4	yes	complemented
59	C₂×C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
60	C₂×C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
64	C₂²×#6103	C₂²	1	4	yes	—
65	C₂×#88180	C₂²	1	1	yes	characteristic, complemented
66	#11719433	C₂²	1	16	yes	complemented
67	#11719430	C₂²	1	16	yes	complemented
68	#11719421	C₂²	1	16	yes	complemented
69	D₁₃×#127	C₂²	1	16	yes	complemented
70	#11719386	C₂²	1	32	yes	complemented
71	#11719381	C₂²	1	32	yes	complemented
72	#11719324	C₂²	1	32	yes	complemented
73	#11719317	C₂²	1	32	yes	complemented
74	#11719312	C₂²	1	32	yes	complemented
75	#11719304	C₂²	1	32	yes	complemented
76	#11719267	C₂²	1	32	yes	complemented
77	#11719264	C₂²	1	32	yes	complemented
78	#11719259	C₂²	1	32	yes	complemented
79	#11719250	C₂²	1	32	yes	complemented
80	C₂×#88151	C₂²	1	2	yes	—
81	C₂×#88149	C₂²	1	2	yes	complemented
82	C₂×#88149	C₂²	1	2	yes	complemented
83	C₂×#88147	C₂²	1	2	yes	complemented
84	C₂×#88147	C₂²	1	2	yes	complemented
85	C₂×#88146	C₂²	1	2	yes	—
86	C₂×#88144	C₂²	1	2	yes	complemented
87	C₂×#88141	C₂²	1	2	yes	complemented
88	C₂×#88140	C₂²	1	4	yes	complemented
89	C₂×#88139	C₂²	1	4	yes	complemented
90	C₂×#88138	C₂²	1	4	yes	complemented
91	C₂×#88137	C₂²	1	4	yes	complemented
92	C₂×#88137	C₂²	1	4	yes	complemented
93	C₂×#88136	C₂²	1	4	yes	—
94	C₂×#88135	C₂²	1	4	yes	complemented
95	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
96	#11719182	C₂²	1	16	yes	complemented
97	C₂×#88129	C₂²	1	2	yes	complemented
98	C₂×#88128	C₂²	1	1	yes	characteristic
99	C₄×#6127	C₂²	1	16	yes	complemented
100	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
101	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
102	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
103	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
104	C₂×#88126	C₂²	1	1	yes	characteristic
105	C₂×#88126	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
107	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
108	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
111	C₂⁴×D₁₃	C₂³	1	4	yes	—
112	C₂×C₁₃×#41	—	4	8	no	—
113	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
114	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
123	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
124	C₂²×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
125	C₂²×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
126	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
127	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
128	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
129	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
130	C₂³×Dic₁₃	C₂³	1	4	yes	—
131	C₂×#6131	—	4	8	no	—
132	C₂×#6131	C₂³	1	16	yes	complemented
133	C₂×#6129	—	4	8	no	—
134	C₂×#6129	C₂³	1	16	yes	complemented
135	C₂×D₄×D₁₃	—	2	16	no	—
136	C₂×D₄×D₁₃	—	4	8	no	—
137	C₂×D₄×D₁₃	—	4	8	no	—
138	C₂×D₄×D₁₃	C₂³	1	16	yes	—
139	C₂×D₄×D₁₃	C₂³	1	16	yes	—
140	C₂×D₄×D₁₃	C₂³	1	16	yes	—
141	C₂×#6127	—	2	8	no	—
142	C₂×#6127	—	4	8	no	—
143	C₂×#6127	C₂³	1	8	yes	—
144	C₂×#6127	C₂³	1	16	yes	complemented
145	C₂²×D₅₂	C₂³	1	1	yes	characteristic
146	C₂²×D₅₂	C₂³	1	2	yes	—
147	C₂²×D₅₂	C₂³	1	2	yes	—
148	C₂²×D₅₂	C₂³	1	2	yes	—
149	C₂²×D₅₂	C₂³	1	4	yes	—
150	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
151	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
152	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
153	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
154	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
155	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
156	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
157	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
158	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
159	C₂²×Dic₂₆	C₂³	1	2	yes	—
160	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
161	C₁₃×#127	C₂³	1	8	yes	—
162	C₁₃×#124	C₂³	1	16	yes	complemented
163	C₁₃×#121	C₂³	1	16	yes	complemented
164	C₁₃×#121	C₂³	1	16	yes	complemented
165	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
166	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
176	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
177	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
178	C₂×C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
180	#88201	C₂³	1	16	yes	complemented
181	#88200	C₂³	1	16	yes	—
182	Q₈×Dic₁₃	C₂³	1	16	yes	complemented
183	#88194	C₂³	1	16	yes	—
184	#88194	C₂³	1	16	yes	—
185	#88194	C₂³	1	16	yes	—
186	#88194	C₂³	1	32	yes	complemented
187	#88193	C₂³	1	32	yes	complemented
188	#88192	C₂³	1	16	yes	complemented
189	#88192	C₂³	1	32	yes	complemented
190	#88192	C₂³	1	16	yes	complemented
191	#88191	C₂³	1	32	yes	—
192	#88190	C₂³	1	16	yes	complemented
193	D₄×Dic₁₃	C₂³	1	16	yes	complemented
194	D₄×Dic₁₃	C₂³	1	16	yes	complemented
195	#88184	C₂³	1	16	yes	complemented
196	#88184	C₂³	1	16	yes	complemented
197	#88184	C₂³	1	32	yes	complemented
198	#88183	C₂³	1	32	yes	complemented
199	C₄×C₂²⋊D₁₃	C₂³	1	8	yes	—
200	C₄×C₂²⋊D₁₃	C₂³	1	8	yes	—
201	C₄×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
202	C₄×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
203	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
204	C₂×#6103	C₂³	1	1	yes	characteristic
205	C₂×#6103	C₂³	1	1	yes	characteristic
206	C₂×#6103	C₂³	1	1	yes	characteristic
207	C₂×#6103	C₂³	1	1	yes	characteristic
208	C₂×#6103	C₂³	1	4	yes	—
209	C₂×#6103	C₂³	1	4	yes	—
210	C₂×#6103	C₂³	1	4	yes	—
211	C₂×#6103	C₂³	1	4	yes	—
212	C₂×#6103	C₂³	1	4	yes	—
213	C₂×#6103	C₂³	1	32	yes	—
214	#88180	C₂³	1	8	yes	complemented
215	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
218	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
219	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
220	C₂×#6101	C₂³	1	1	yes	characteristic
221	C₂×#6101	C₂³	1	1	yes	characteristic
222	C₂×#6101	C₂³	1	1	yes	characteristic
223	C₂×#6101	C₂³	1	1	yes	characteristic
224	C₂×#6101	C₂³	1	4	yes	—
225	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
228	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
229	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
230	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
231	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
232	#88151	C₂³	1	16	yes	—
233	#88149	C₂³	1	16	yes	complemented
234	#88149	C₂³	1	16	yes	complemented
235	#88147	C₂³	1	16	yes	complemented
236	#88147	C₂³	1	16	yes	complemented
237	#88146	C₂³	1	16	yes	—
238	#88144	C₂³	1	16	yes	complemented
239	#88141	C₂³	1	16	yes	complemented
240	#88140	C₂³	1	32	yes	complemented
241	#88139	C₂³	1	32	yes	complemented
242	#88138	C₂³	1	32	yes	complemented
243	#88137	C₂³	1	32	yes	complemented
244	#88137	C₂³	1	32	yes	complemented
245	#88136	C₂³	1	32	yes	—
246	#88135	C₂³	1	32	yes	complemented
247	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	—
248	#88129	C₂³	1	16	yes	complemented
249	#88128	C₂³	1	8	yes	—
250	C₄×D₅₂	C₂³	1	8	yes	—
251	C₄×D₅₂	C₂³	1	8	yes	—
252	C₄×D₅₂	C₂³	1	16	yes	complemented
253	C₄×D₅₂	C₂³	1	16	yes	complemented
254	#88126	C₂³	1	8	yes	—
255	#88126	C₂³	1	8	yes	complemented
256	C₄²×D₁₃	C₂³	1	8	yes	—
257	C₄²×D₁₃	C₂³	1	8	yes	complemented
258	#88123	C₂³	1	8	yes	complemented
259	C₄×Dic₂₆	C₂³	1	8	yes	complemented
260	C₄×Dic₂₆	C₂³	1	8	yes	complemented
261	C₂×#3508	—	13	1	no	maximal, Sylow
262	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
263	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂³×D₁₃	—	2	16	no	—
265	C₂³×D₁₃	—	4	8	no	—
266	C₂³×D₁₃	—	4	8	no	—
267	C₂³×D₁₃	C₂⁴	1	4	yes	—
268	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
269	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
270	C₂³×D₁₃	C₂⁴	1	16	yes	—
271	C₁₃×#41	—	4	32	no	—
272	C₂×Q₈×C₁₃	—	2	8	no	—
273	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
274	C₂×D₄×C₁₃	—	2	8	no	—
275	C₂×D₄×C₁₃	—	2	8	no	—
276	C₂×D₄×C₁₃	—	2	8	no	—
277	C₂×D₄×C₁₃	—	4	8	no	—
278	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
279	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
280	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
281	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
282	C₂²×C₄×C₁₃	—	2	4	no	—
283	C₂²×C₄×C₁₃	—	2	4	no	—
284	C₂²×C₄×C₁₃	—	2	4	no	—
285	C₂²×C₄×C₁₃	—	4	8	no	—
286	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂×C₂²⋊D₁₃	—	2	4	no	—
298	C₂×C₂²⋊D₁₃	—	2	4	no	—
299	C₂×C₂²⋊D₁₃	—	2	16	no	—
300	C₂×C₂²⋊D₁₃	—	4	8	no	—
301	C₂×C₂²⋊D₁₃	—	4	8	no	—
302	C₂×C₂²⋊D₁₃	—	4	8	no	—
303	C₂×C₂²⋊D₁₃	—	4	8	no	—
304	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
305	C₂×C₂²⋊D₁₃	C₂⁴	1	4	yes	—
306	C₂×C₂²⋊D₁₃	C₂⁴	1	4	yes	—
307	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
308	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
309	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
310	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
311	C₂²×Dic₁₃	—	4	8	no	—
312	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
313	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
314	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
315	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
316	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
317	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
318	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
319	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
320	#6131	—	4	32	no	—
321	#6129	—	4	32	no	—
322	D₄×D₁₃	—	2	64	no	—
323	D₄×D₁₃	—	4	32	no	—
324	D₄×D₁₃	—	4	32	no	—
325	#6127	—	2	32	no	—
326	#6127	—	4	32	no	—
327	C₂×D₅₂	—	2	4	no	—
328	C₂×D₅₂	—	2	8	no	—
329	C₂×D₅₂	—	2	8	no	—
330	C₂×D₅₂	—	2	8	no	—
331	C₂×D₅₂	—	4	8	no	—
332	C₂×D₅₂	C₂⁴	1	4	yes	—
333	C₂×D₅₂	C₂⁴	1	8	yes	—
334	C₂×D₅₂	C₂⁴	1	8	yes	—
335	C₂×D₅₂	C₂⁴	1	8	yes	—
336	C₂×D₅₂	C₂⁴	1	16	yes	—
337	C₂×C₄×D₁₃	—	2	4	no	—
338	C₂×C₄×D₁₃	—	2	4	no	—
339	C₂×C₄×D₁₃	—	2	4	no	—
340	C₂×C₄×D₁₃	—	2	4	no	—
341	C₂×C₄×D₁₃	—	2	4	no	—
342	C₂×C₄×D₁₃	—	4	8	no	—
343	C₂×C₄×D₁₃	—	4	8	no	—
344	C₂×C₄×D₁₃	#41	1	8	yes	complemented
345	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
346	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
347	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
348	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
349	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
350	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
351	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
352	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
353	C₂×Dic₂₆	—	2	8	no	—
354	C₂×Dic₂₆	—	2	4	no	—
355	C₂×Dic₂₆	C₂⁴	1	4	yes	—
356	C₂×Dic₂₆	C₂⁴	1	8	yes	—
357	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
358	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
359	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
360	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
361	C₄²×C₁₃	C₂⁴	1	4	yes	—
362	C₄²×C₁₃	C₂⁴	1	4	yes	—
363	C₄²×C₁₃	C₂⁴	1	4	yes	—
364	C₄²×C₁₃	C₂⁴	1	4	yes	—
365	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
366	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
367	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
368	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
369	#6103	C₂⁴	1	4	yes	—
370	#6103	C₂⁴	1	4	yes	—
371	#6103	C₂⁴	1	4	yes	—
372	#6103	C₂⁴	1	4	yes	—
373	#6103	C₂⁴	1	16	yes	—
374	#6103	C₂⁴	1	16	yes	—
375	#6103	C₂⁴	1	16	yes	—
376	#6103	C₂⁴	1	16	yes	—
377	#6103	C₂⁴	1	16	yes	—
378	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
379	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
380	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
381	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
382	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
383	#6101	C₂⁴	1	4	yes	—
384	#6101	C₂⁴	1	4	yes	—
385	#6101	C₂⁴	1	4	yes	—
386	#6101	C₂⁴	1	4	yes	—
387	#6101	C₂⁴	1	16	yes	—
388	C₄×Dic₁₃	C₂⁴	1	4	yes	—
389	C₄×Dic₁₃	C₂⁴	1	4	yes	—
390	C₄×Dic₁₃	C₂⁴	1	4	yes	—
391	C₄×Dic₁₃	C₂⁴	1	4	yes	—
392	C₄×Dic₁₃	C₂⁴	1	4	yes	—
393	C₄×Dic₁₃	C₂⁴	1	4	yes	—
394	C₄×Dic₁₃	C₂⁴	1	16	yes	—
395	#3508	—	13	32	no	—
396	C₂×#559	—	13	2	no	—
397	C₂×#559	—	13	2	no	—
398	C₂×#550	—	13	2	no	—
399	C₂×#550	—	13	2	no	—
400	C₂×#546	—	13	2	no	—
401	C₂×#546	—	13	2	no	—
402	C₂×#546	—	13	2	no	—
403	C₂×#546	—	13	2	no	—
404	C₂×#540	—	13	2	no	—
405	C₂×#540	—	13	2	no	—
406	C₂×#535	—	13	2	no	—
407	C₂×#533	—	13	1	no	—
408	C₂×#532	—	13	1	no	—
409	C₂×#532	—	13	1	no	—
410	C₂×#532	—	13	1	no	—
411	C₂×#532	D₁₃	1	1	yes	characteristic, complemented
412	C₂²×#127	—	13	1	no	—
413	C₂×#518	—	13	2	no	—
414	C₂×C₄×#41	—	13	1	no	—
415	C₂³×C₁₃	—	2	2	no	—
416	C₂³×C₁₃	—	2	8	no	—
417	C₂³×C₁₃	—	2	8	no	—
418	C₂³×C₁₃	—	2	2	no	—
419	C₂³×C₁₃	—	2	8	no	—
420	C₂³×C₁₃	—	2	2	no	—
421	C₂³×C₁₃	C₂⁵	1	8	yes	—
422	C₂³×C₁₃	C₂⁵	1	2	yes	—
423	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
424	C₂²×D₁₃	—	2	2	no	—
425	C₂²×D₁₃	—	2	2	no	—
426	C₂²×D₁₃	—	2	2	no	—
427	C₂²×D₁₃	—	2	8	no	—
428	C₂²×D₁₃	—	2	2	no	—
429	C₂²×D₁₃	—	2	2	no	—
430	C₂²×D₁₃	—	2	8	no	—
431	C₂²×D₁₃	—	2	8	no	—
432	C₂²×D₁₃	—	2	32	no	—
433	C₂²×D₁₃	—	4	16	no	—
434	C₂²×D₁₃	—	4	16	no	—
435	C₂²×D₁₃	—	8	32	no	—
436	C₂²×D₁₃	C₂×#41	1	4	yes	—
437	C₂²×D₁₃	C₂⁵	1	8	yes	—
438	C₂²×D₁₃	C₂⁵	1	2	yes	—
439	C₂²×D₁₃	C₂⁵	1	2	yes	—
440	Q₈×C₁₃	—	2	16	no	—
441	D₄×C₁₃	—	2	16	no	—
442	D₄×C₁₃	—	2	16	no	—
443	D₄×C₁₃	—	2	16	no	—
444	D₄×C₁₃	—	4	16	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	8	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	8	no	—
450	C₂×C₄×C₁₃	—	2	8	no	—
451	C₂×C₄×C₁₃	—	2	8	no	—
452	C₂×C₄×C₁₃	—	4	16	no	—
453	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
454	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
455	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
456	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
457	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
458	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
459	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
460	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
461	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
462	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
463	C₂²⋊D₁₃	—	2	8	no	—
464	C₂²⋊D₁₃	—	2	8	no	—
465	C₂²⋊D₁₃	—	2	32	no	—
466	C₂²⋊D₁₃	—	4	16	no	—
467	C₂²⋊D₁₃	—	4	16	no	—
468	C₂²⋊D₁₃	—	4	16	no	—
469	C₂²⋊D₁₃	—	4	16	no	—
470	C₂×Dic₁₃	—	2	2	no	—
471	C₂×Dic₁₃	—	2	8	no	—
472	C₂×Dic₁₃	—	2	2	no	—
473	C₂×Dic₁₃	—	2	2	no	—
474	C₂×Dic₁₃	—	2	2	no	—
475	C₂×Dic₁₃	—	2	2	no	—
476	C₂×Dic₁₃	—	4	16	no	—
477	C₂×Dic₁₃	C₂×#41	1	4	yes	—
478	C₂×Dic₁₃	C₂⁵	1	2	yes	—
479	C₂×Dic₁₃	C₂⁵	1	2	yes	—
480	C₂×Dic₁₃	C₂⁵	1	2	yes	—
481	C₂×Dic₁₃	C₂⁵	1	2	yes	—
482	C₂×Dic₁₃	C₂⁵	1	2	yes	—
483	C₂×Dic₁₃	C₂⁵	1	8	yes	—
484	C₂×Dic₁₃	C₂⁵	1	2	yes	—
485	D₅₂	—	2	8	no	—
486	D₅₂	—	2	16	no	—
487	D₅₂	—	2	16	no	—
488	D₅₂	—	2	16	no	—
489	D₅₂	—	4	16	no	—
490	C₄×D₁₃	—	2	8	no	—
491	C₄×D₁₃	—	2	8	no	—
492	C₄×D₁₃	—	2	8	no	—
493	C₄×D₁₃	—	2	8	no	—
494	C₄×D₁₃	—	2	8	no	—
495	C₄×D₁₃	—	4	16	no	—
496	C₄×D₁₃	—	4	16	no	—
497	C₄×D₁₃	C₂×#41	1	16	yes	complemented
498	Dic₂₆	—	2	16	no	—
499	Dic₂₆	—	2	8	no	—
500	C₂²×#41	—	13	2	no	—
501	C₂²×#41	—	13	2	no	—
502	C₂²×#41	—	13	1	no	—
503	C₂²×#41	—	13	2	no	—
504	C₂²×#41	C₂×D₁₃	1	2	yes	complemented
505	C₂³×D₄	—	13	2	no	—
506	C₂³×D₄	—	13	2	no	—
507	C₂³×D₄	—	13	2	no	—
508	#559	—	13	32	no	—
509	#559	—	13	32	no	—
510	#550	—	13	32	no	—
511	#550	—	13	32	no	—
512	#546	—	13	32	no	—
513	#546	—	13	32	no	—
514	#546	—	13	32	no	—
515	#546	—	13	32	no	—
516	#540	—	13	32	no	—
517	#540	—	13	32	no	—
518	#535	—	13	32	no	—
519	#533	—	13	16	no	—
520	#532	—	13	16	no	—
521	#532	—	13	16	no	—
522	#532	—	13	16	no	—
523	#532	C₂×D₁₃	1	16	yes	complemented
524	C₂×C₄⋊Q₈	—	13	1	no	—
525	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
526	C₂×#127	—	13	2	no	—
527	C₂×#127	—	13	2	no	—
528	C₂×#127	—	13	2	no	—
529	C₂×#127	—	13	4	no	—
530	C₂×#127	—	13	16	no	—
531	C₂×#127	—	13	1	no	—
532	C₂×#127	C₂×D₁₃	1	1	yes	characteristic
533	C₂×#125	—	13	2	no	—
534	C₂×#124	—	13	2	no	—
535	C₂×#124	—	13	2	no	—
536	C₂×#124	—	13	4	no	—
537	C₂×#124	—	13	2	no	—
538	C₂×#124	C₂×D₁₃	1	2	yes	complemented
539	C₂×#123	—	13	4	no	—
540	C₂×#123	—	13	4	no	—
541	C₂×#123	—	13	4	no	—
542	C₂×#123	—	13	4	no	—
543	C₂×C₂²⋊Q₈	—	13	2	no	—
544	C₂×C₂²⋊Q₈	—	13	2	no	—
545	C₂×#121	—	13	2	no	—
546	C₂×#121	—	13	2	no	—
547	C₂×#121	—	13	4	no	—
548	C₂×#121	—	13	4	no	—
549	C₂×#121	—	13	2	no	—
550	C₂×#121	—	13	2	no	—
551	C₂×#121	—	13	4	no	—
552	C₂×#121	—	13	2	no	—
553	C₂×#121	—	13	2	no	—
554	C₂×#121	—	13	4	no	—
555	C₂×#121	C₂×D₁₃	1	2	yes	complemented
556	C₂×#121	C₂×D₁₃	1	2	yes	complemented
557	C₂×#120	—	13	4	no	—
558	C₂×#120	—	13	4	no	—
559	#518	—	13	32	no	—
560	C₄×#41	—	13	16	no	—
561	C₂×C₄×Q₈	—	13	2	no	—
562	C₂×C₄×Q₈	—	13	2	no	—
563	C₂×C₄×Q₈	—	13	1	no	—
564	C₂×C₄×Q₈	—	13	1	no	—
565	C₂×C₄×D₄	—	13	2	no	—
566	C₂×C₄×D₄	—	13	2	no	—
567	C₂×C₄×D₄	—	13	1	no	—
568	C₂×C₄×D₄	—	13	1	no	—
569	C₂×C₄×D₄	—	13	1	no	—
570	C₂×C₄×D₄	—	13	1	no	—
571	C₂×C₄×D₄	—	13	4	no	—
572	C₂×C₄×D₄	—	13	2	no	—
573	C₂×C₄×D₄	—	13	2	no	—
574	C₂×C₄×D₄	—	13	4	no	—
575	C₂×C₄×D₄	—	13	1	no	—
576	C₂×C₄×D₄	—	13	1	no	—
577	C₂×C₄×D₄	—	13	2	no	—
578	C₂×C₄×D₄	—	13	2	no	—
579	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
580	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
581	C₂×#117	—	13	1	no	—
582	C₂×#117	—	13	2	no	—
583	C₂×#117	—	13	1	no	—
584	C₂×#117	—	13	1	no	—
585	C₂²×C₂²⋊C₄	—	13	4	no	—
586	C₂²×C₂²⋊C₄	—	13	4	no	—
587	C₂²×C₄²	—	13	1	no	—
588	C₂²×C₄²	—	13	1	no	—
589	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
590	C₂²×C₁₃	—	2	2	no	—
591	C₂²×C₁₃	—	2	8	no	—
592	C₂²×C₁₃	—	2	8	no	—
593	C₂²×C₁₃	—	2	2	no	—
594	C₂²×C₁₃	—	2	8	no	—
595	C₂²×C₁₃	—	2	2	no	—
596	C₂²×C₁₃	—	4	16	no	—
597	C₂²×C₁₃	—	4	4	no	—
598	C₂²×C₁₃	C₂²×#41	1	2	yes	—
599	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
600	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
601	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
602	C₂×D₁₃	—	2	2	no	—
603	C₂×D₁₃	—	2	2	no	—
604	C₂×D₁₃	—	2	8	no	—
605	C₂×D₁₃	—	2	2	no	—
606	C₂×D₁₃	—	2	8	no	—
607	C₂×D₁₃	—	2	2	no	—
608	C₂×D₁₃	—	2	2	no	—
609	C₂×D₁₃	—	2	8	no	—
610	C₂×D₁₃	—	2	8	no	—
611	C₂×D₁₃	—	4	4	no	—
612	C₂×D₁₃	—	4	16	no	—
613	C₂×D₁₃	—	8	32	no	—
614	C₂×D₁₃	C₂²×#41	1	4	yes	—
615	C₄×C₁₃	—	2	2	no	—
616	C₄×C₁₃	—	2	2	no	—
617	C₄×C₁₃	—	2	8	no	—
618	C₄×C₁₃	—	2	2	no	—
619	C₄×C₁₃	C₂²×#41	1	4	yes	—
620	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
621	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
622	Dic₁₃	—	2	2	no	—
623	Dic₁₃	—	2	8	no	—
624	Dic₁₃	—	2	2	no	—
625	Dic₁₃	—	2	2	no	—
626	Dic₁₃	—	2	2	no	—
627	Dic₁₃	—	2	2	no	—
628	Dic₁₃	C₂²×#41	1	4	yes	—
629	C₂⁵	—	13	4	no	—
630	C₂×#41	—	4	8	no	—
631	C₂×#41	—	13	16	no	—
632	C₂×#41	—	13	16	no	—
633	C₂×#41	—	13	8	no	—
634	C₂×#41	—	13	16	no	—
635	C₂×#41	—	26	8	no	—
636	C₂×#41	—	52	8	no	—
637	C₂×#41	—	52	8	no	—
638	C₂×#41	—	52	8	no	—
639	C₂×#41	C₂²×D₁₃	1	16	yes	complemented
640	C₂²×Q₈	—	13	1	no	—
641	C₂²×Q₈	—	13	2	no	—
642	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
643	C₂²×D₄	—	13	1	no	—
644	C₂²×D₄	—	13	4	no	—
645	C₂²×D₄	—	13	1	no	—
646	C₂²×D₄	—	13	4	no	—
647	C₂²×D₄	—	13	4	no	—
648	C₂²×D₄	—	13	4	no	—
649	C₂²×D₄	—	13	4	no	—
650	C₂²×D₄	—	13	16	no	—
651	C₂²×D₄	—	13	16	no	—
652	C₂²×D₄	—	13	16	no	—
653	C₂²×D₄	—	13	1	no	—
654	C₂²×D₄	—	13	2	no	—
655	C₂²×D₄	—	13	2	no	—
656	C₂²×D₄	—	13	2	no	—
657	C₂²×D₄	—	13	4	no	—
658	C₂²×D₄	—	26	16	no	—
659	C₂²×D₄	—	52	8	no	—
660	C₂²×D₄	—	52	8	no	—
661	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
662	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
663	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
664	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
665	C₂³×C₄	—	13	1	no	—
666	C₂³×C₄	—	13	4	no	—
667	C₂³×C₄	—	13	1	no	—
668	C₂³×C₄	—	13	1	no	—
669	C₂³×C₄	—	13	1	no	—
670	C₂³×C₄	—	13	1	no	—
671	C₂³×C₄	—	13	1	no	—
672	C₂³×C₄	—	13	4	no	—
673	C₂³×C₄	—	13	4	no	—
674	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
675	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
676	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
677	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
678	C₄⋊Q₈	—	13	8	no	—
679	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
680	#127	—	13	16	no	—
681	#127	—	13	16	no	—
682	#127	—	13	16	no	—
683	#127	—	13	32	no	—
684	#127	—	13	8	no	—
685	#127	C₂²×D₁₃	1	8	yes	—
686	#125	—	13	16	no	—
687	#124	—	13	16	no	—
688	#124	—	13	16	no	—
689	#124	—	13	32	no	—
690	#124	—	13	16	no	—
691	#124	C₂²×D₁₃	1	16	yes	complemented
692	#123	—	13	32	no	—
693	#123	—	13	32	no	—
694	#123	—	13	32	no	—
695	#123	—	13	32	no	—
696	C₂²⋊Q₈	—	13	16	no	—
697	C₂²⋊Q₈	—	13	16	no	—
698	#121	—	13	16	no	—
699	#121	—	13	16	no	—
700	#121	—	13	32	no	—
701	#121	—	13	32	no	—
702	#121	—	13	16	no	—
703	#121	—	13	16	no	—
704	#121	—	13	32	no	—
705	#121	—	13	16	no	—
706	#121	—	13	16	no	—
707	#121	—	13	32	no	—
708	#121	C₂²×D₁₃	1	16	yes	complemented
709	#121	C₂²×D₁₃	1	16	yes	complemented
710	#120	—	13	32	no	—
711	#120	—	13	32	no	—
712	C₄×Q₈	—	13	16	no	—
713	C₄×Q₈	—	13	16	no	—
714	C₄×Q₈	—	13	8	no	—
715	C₄×Q₈	—	13	8	no	—
716	C₄×D₄	—	13	16	no	—
717	C₄×D₄	—	13	16	no	—
718	C₄×D₄	—	13	8	no	—
719	C₄×D₄	—	13	8	no	—
720	C₄×D₄	—	13	8	no	—
721	C₄×D₄	—	13	8	no	—
722	C₄×D₄	—	13	32	no	—
723	C₄×D₄	—	13	16	no	—
724	C₄×D₄	—	13	16	no	—
725	C₄×D₄	—	13	32	no	—
726	C₄×D₄	—	13	8	no	—
727	C₄×D₄	—	13	8	no	—
728	C₄×D₄	—	13	16	no	—
729	C₄×D₄	—	13	16	no	—
730	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
731	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
732	#117	—	13	8	no	—
733	#117	—	13	16	no	—
734	#117	—	13	8	no	—
735	#117	—	13	8	no	—
736	C₂×C₄⋊C₄	—	13	1	no	—
737	C₂×C₄⋊C₄	—	13	1	no	—
738	C₂×C₄⋊C₄	—	13	2	no	—
739	C₂×C₄⋊C₄	—	13	1	no	—
740	C₂×C₄⋊C₄	—	13	1	no	—
741	C₂×C₄⋊C₄	—	13	1	no	—
742	C₂×C₄⋊C₄	—	13	1	no	—
743	C₂×C₄⋊C₄	—	13	2	no	—
744	C₂×C₄⋊C₄	—	13	4	no	—
745	C₂×C₄⋊C₄	—	13	4	no	—
746	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
747	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
748	C₂×C₂²⋊C₄	—	13	4	no	—
749	C₂×C₂²⋊C₄	—	13	1	no	—
750	C₂×C₂²⋊C₄	—	13	1	no	—
751	C₂×C₂²⋊C₄	—	13	4	no	—
752	C₂×C₂²⋊C₄	—	13	1	no	—
753	C₂×C₂²⋊C₄	—	13	1	no	—
754	C₂×C₂²⋊C₄	—	13	4	no	—
755	C₂×C₂²⋊C₄	—	13	4	no	—
756	C₂×C₂²⋊C₄	—	13	4	no	—
757	C₂×C₂²⋊C₄	—	13	32	no	—
758	C₂×C₂²⋊C₄	—	13	1	no	—
759	C₂×C₂²⋊C₄	—	13	1	no	—
760	C₂×C₂²⋊C₄	—	13	4	no	—
761	C₂×C₂²⋊C₄	—	13	4	no	—
762	C₂×C₂²⋊C₄	—	13	32	no	—
763	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
764	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
765	C₂×C₄²	—	13	1	no	—
766	C₂×C₄²	—	13	1	no	—
767	C₂×C₄²	—	13	4	no	—
768	C₂×C₄²	—	13	1	no	—
769	C₂×C₄²	—	13	1	no	—
770	C₂×C₄²	—	13	1	no	—
771	C₂×C₄²	—	13	1	no	—
772	C₂×C₄²	—	13	8	no	—
773	C₂×C₄²	—	13	8	no	—
774	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
775	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
776	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
777	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
778	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
779	C₂×C₁₃	—	4	8	no	—
780	C₂×C₁₃	—	4	2	no	—
781	C₂×C₁₃	#3508	1	4	yes	complemented
782	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
783	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
784	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
785	D₁₃	—	2	4	no	—
786	D₁₃	—	4	2	no	—
787	D₁₃	—	4	8	no	—
788	C₂⁴	—	13	1	no	—
789	C₂⁴	—	13	4	no	—
790	C₂⁴	—	13	1	no	—
791	C₂⁴	—	13	16	no	—
792	C₂⁴	—	26	16	no	—
793	C₂⁴	—	52	8	no	—
794	C₂⁴	—	52	8	no	—
795	C₂⁴	C₂³×D₁₃	1	4	yes	—
796	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
797	#41	—	4	32	no	—
798	#41	—	26	32	no	—
799	#41	—	52	32	no	—
800	#41	—	52	32	no	—
801	#41	—	52	32	no	—
802	C₂×Q₈	—	2	8	no	—
803	C₂×Q₈	—	13	4	no	—
804	C₂×Q₈	—	13	8	no	—
805	C₂×Q₈	—	26	4	no	—
806	C₂×Q₈	—	26	8	no	—
807	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
808	C₂×D₄	—	2	8	no	—
809	C₂×D₄	—	2	8	no	—
810	C₂×D₄	—	2	8	no	—
811	C₂×D₄	—	4	8	no	—
812	C₂×D₄	—	13	4	no	—
813	C₂×D₄	—	13	16	no	—
814	C₂×D₄	—	13	4	no	—
815	C₂×D₄	—	13	16	no	—
816	C₂×D₄	—	13	16	no	—
817	C₂×D₄	—	13	16	no	—
818	C₂×D₄	—	13	16	no	—
819	C₂×D₄	—	13	4	no	—
820	C₂×D₄	—	13	8	no	—
821	C₂×D₄	—	13	8	no	—
822	C₂×D₄	—	13	8	no	—
823	C₂×D₄	—	13	16	no	—
824	C₂×D₄	—	26	4	no	—
825	C₂×D₄	—	26	64	no	—
826	C₂×D₄	—	26	16	no	—
827	C₂×D₄	—	26	4	no	—
828	C₂×D₄	—	26	4	no	—
829	C₂×D₄	—	26	8	no	—
830	C₂×D₄	—	26	8	no	—
831	C₂×D₄	—	26	8	no	—
832	C₂×D₄	—	52	8	no	—
833	C₂×D₄	—	52	32	no	—
834	C₂×D₄	—	52	32	no	—
835	C₂×D₄	—	52	8	no	—
836	C₂×D₄	—	52	8	no	—
837	C₂×D₄	—	52	8	no	—
838	C₂×D₄	—	52	8	no	—
839	C₂×D₄	C₂³×D₁₃	1	8	yes	—
840	C₂×D₄	C₂³×D₁₃	1	8	yes	—
841	C₂×D₄	C₂³×D₁₃	1	8	yes	—
842	C₂×D₄	C₂³×D₁₃	1	16	yes	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	2	4	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	4	8	no	—
847	C₂²×C₄	—	13	1	no	—
848	C₂²×C₄	—	13	8	no	—
849	C₂²×C₄	—	13	4	no	—
850	C₂²×C₄	—	13	1	no	—
851	C₂²×C₄	—	13	1	no	—
852	C₂²×C₄	—	13	1	no	—
853	C₂²×C₄	—	13	1	no	—
854	C₂²×C₄	—	13	1	no	—
855	C₂²×C₄	—	13	4	no	—
856	C₂²×C₄	—	13	16	no	—
857	C₂²×C₄	—	13	4	no	—
858	C₂²×C₄	—	13	4	no	—
859	C₂²×C₄	—	13	4	no	—
860	C₂²×C₄	—	13	4	no	—
861	C₂²×C₄	—	13	4	no	—
862	C₂²×C₄	—	13	16	no	—
863	C₂²×C₄	—	13	16	no	—
864	C₂²×C₄	—	26	4	no	—
865	C₂²×C₄	—	26	4	no	—
866	C₂²×C₄	—	26	4	no	—
867	C₂²×C₄	—	26	4	no	—
868	C₂²×C₄	—	26	4	no	—
869	C₂²×C₄	—	52	8	no	—
870	C₂²×C₄	—	52	8	no	—
871	C₂²×C₄	—	52	8	no	—
872	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
873	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
874	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
875	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
876	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
877	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
878	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
879	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
880	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
881	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
882	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
883	C₄⋊C₄	—	13	4	no	—
884	C₄⋊C₄	—	13	4	no	—
885	C₄⋊C₄	—	13	8	no	—
886	C₄⋊C₄	—	13	4	no	—
887	C₄⋊C₄	—	13	4	no	—
888	C₄⋊C₄	—	13	4	no	—
889	C₄⋊C₄	—	13	4	no	—
890	C₄⋊C₄	—	13	8	no	—
891	C₄⋊C₄	—	13	16	no	—
892	C₄⋊C₄	—	13	16	no	—
893	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
894	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
895	C₂²⋊C₄	—	13	16	no	—
896	C₂²⋊C₄	—	13	4	no	—
897	C₂²⋊C₄	—	13	4	no	—
898	C₂²⋊C₄	—	13	16	no	—
899	C₂²⋊C₄	—	13	4	no	—
900	C₂²⋊C₄	—	13	4	no	—
901	C₂²⋊C₄	—	13	16	no	—
902	C₂²⋊C₄	—	13	16	no	—
903	C₂²⋊C₄	—	13	16	no	—
904	C₂²⋊C₄	—	13	4	no	—
905	C₂²⋊C₄	—	13	4	no	—
906	C₂²⋊C₄	—	13	16	no	—
907	C₂²⋊C₄	—	13	16	no	—
908	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
909	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
910	C₄²	—	13	4	no	—
911	C₄²	—	13	4	no	—
912	C₄²	—	13	4	no	—
913	C₄²	—	13	4	no	—
914	C₄²	—	13	4	no	—
915	C₄²	—	13	4	no	—
916	C₄²	—	13	16	no	—
917	C₄²	C₂³×D₁₃	1	4	yes	—
918	C₄²	C₂³×D₁₃	1	4	yes	—
919	C₄²	C₂³×D₁₃	1	4	yes	—
920	C₄²	C₂³×D₁₃	1	4	yes	—
921	C₁₃	C₂×#3508	1	1	yes	characteristic, complemented, Sylow
922	C₂³	—	2	2	no	—
923	C₂³	—	2	8	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	8	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	8	no	—
928	C₂³	—	13	4	no	—
929	C₂³	—	13	2	no	—
930	C₂³	—	13	8	no	—
931	C₂³	—	13	2	no	—
932	C₂³	—	26	32	no	—
933	C₂³	—	26	2	no	—
934	C₂³	—	26	2	no	—
935	C₂³	—	26	2	no	—
936	C₂³	—	26	8	no	—
937	C₂³	—	26	2	no	—
938	C₂³	—	26	8	no	—
939	C₂³	—	26	2	no	—
940	C₂³	—	26	8	no	—
941	C₂³	—	52	16	no	—
942	C₂³	—	52	16	no	—
943	C₂³	—	104	32	no	—
944	C₂³	C₂⁴×D₁₃	1	8	yes	—
945	C₂³	C₂⁴×D₁₃	1	2	yes	—
946	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
947	Q₈	—	2	16	no	—
948	Q₈	—	26	8	no	—
949	Q₈	—	26	16	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	16	no	—
953	D₄	—	4	16	no	—
954	D₄	—	26	8	no	—
955	D₄	—	26	32	no	—
956	D₄	—	26	8	no	—
957	D₄	—	26	8	no	—
958	D₄	—	26	16	no	—
959	D₄	—	26	16	no	—
960	D₄	—	26	16	no	—
961	D₄	—	52	16	no	—
962	D₄	—	52	16	no	—
963	D₄	—	52	16	no	—
964	D₄	—	52	16	no	—
965	D₄	—	52	16	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	8	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	8	no	—
971	C₂×C₄	—	2	8	no	—
972	C₂×C₄	—	2	8	no	—
973	C₂×C₄	—	4	16	no	—
974	C₂×C₄	—	13	4	no	—
975	C₂×C₄	—	13	2	no	—
976	C₂×C₄	—	13	16	no	—
977	C₂×C₄	—	13	2	no	—
978	C₂×C₄	—	13	2	no	—
979	C₂×C₄	—	13	2	no	—
980	C₂×C₄	—	13	2	no	—
981	C₂×C₄	—	13	2	no	—
982	C₂×C₄	—	13	8	no	—
983	C₂×C₄	—	26	2	no	—
984	C₂×C₄	—	26	2	no	—
985	C₂×C₄	—	26	2	no	—
986	C₂×C₄	—	26	2	no	—
987	C₂×C₄	—	26	2	no	—
988	C₂×C₄	—	26	8	no	—
989	C₂×C₄	—	26	8	no	—
990	C₂×C₄	—	26	8	no	—
991	C₂×C₄	—	26	8	no	—
992	C₂×C₄	—	26	8	no	—
993	C₂×C₄	—	26	8	no	—
994	C₂×C₄	—	52	16	no	—
995	C₂×C₄	—	52	16	no	—
996	C₂×C₄	—	52	16	no	—
997	C₂×C₄	#88251	1	4	yes	—
998	C₂×C₄	#41×D₁₃	1	4	yes	—
999	C₂×C₄	#88256	1	4	yes	—
1000	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
1001	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1002	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1003	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1004	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1005	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1006	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	8	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	8	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	8	no	—
1013	C₂²	—	4	4	no	—
1014	C₂²	—	4	16	no	—
1015	C₂²	—	13	4	no	—
1016	C₂²	—	26	8	no	—
1017	C₂²	—	26	2	no	—
1018	C₂²	—	26	2	no	—
1019	C₂²	—	26	2	no	—
1020	C₂²	—	26	8	no	—
1021	C₂²	—	26	2	no	—
1022	C₂²	—	26	8	no	—
1023	C₂²	—	26	2	no	—
1024	C₂²	—	26	8	no	—
1025	C₂²	—	52	4	no	—
1026	C₂²	—	52	16	no	—
1027	C₂²	—	104	32	no	—
1028	C₂²	C₂×#88251	1	2	yes	—
1029	C₂²	C₂×#41×D₁₃	1	2	yes	—
1030	C₂²	C₂×#88256	1	2	yes	—
1031	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	8	no	—
1035	C₄	—	2	2	no	—
1036	C₄	—	13	4	no	—
1037	C₄	—	26	2	no	—
1038	C₄	—	26	2	no	—
1039	C₄	—	26	2	no	—
1040	C₄	—	26	2	no	—
1041	C₄	—	26	2	no	—
1042	C₄	—	26	8	no	—
1043	C₄	C₂×#88251	1	4	yes	—
1044	C₄	C₂×#41×D₁₃	1	4	yes	—
1045	C₄	C₂×#88256	1	4	yes	—
1046	C₂	—	4	8	no	—
1047	C₂	—	4	2	no	—
1048	C₂	—	26	4	no	—
1049	C₂	—	52	8	no	—
1050	C₂	—	52	2	no	—
1051	C₂	#13128705	1	4	yes	direct product factor
1052	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic
1053	C₂	C₂²×#88251	1	1	yes	characteristic
1054	C₂	C₂²×#88256	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#532	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#532	D₁₃
hypocenter	C₁₃	C₂×#3508
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #13128705	C₂	direct (N × H)
2. C₂×#11719264	C₂	semidirect
3. C₂×#11719386	C₂	semidirect
4. C₂×#11719539	C₂	semidirect
5. C₂×#11719304	C₂	semidirect
6. C₂×#11719317	C₂	semidirect
7. C₂×#11719259	C₂	semidirect
8. C₂×#11719381	C₂	semidirect
9. C₂×#11719534	C₂	semidirect
10. C₂×#11719324	C₂	semidirect
11. C₂×#11719267	C₂	semidirect
12. C₂×#11719312	C₂	semidirect
13. C₂×#11719433	C₂	semidirect
14. C₂×#11719430	C₂	semidirect
15. C₂×#11719182	C₂	semidirect
16. C₂×#11719421	C₂	semidirect
17. C₂×D₁₃×#127	C₂	semidirect
18. C₂×#11719250	C₂	semidirect
19. C₂×C₄×#6127	C₂	semidirect
20. C₂×C₁₃×#532	C₂	semidirect
21. C₂²×C₁₃×#41	C₂²	semidirect
22. C₂²×#6131	C₂²	semidirect
23. C₂²×#6129	C₂²	semidirect
28. C₂²×#6127	C₂²	semidirect
29. C₁₃×#532	C₂²	semidirect
30. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
32. C₂×C₁₃×#124	C₂²	semidirect
33. C₂×C₁₃×#121	C₂²	semidirect
34. C₂×C₁₃×#121	C₂²	semidirect
35. C₂×C₄×D₄×C₁₃	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃	C₂²	semidirect
37. C₂²×C₄²×C₁₃	C₂²	semidirect
38. #11719539	C₂²	semidirect
39. #11719534	C₂²	semidirect
40. C₂×#88201	C₂²	semidirect
42. C₂×Q₈×Dic₁₃	C₂²	semidirect
46. C₂×#88194	C₂²	semidirect
47. C₂×#88193	C₂²	semidirect
48. C₂×#88192	C₂²	semidirect
49. C₂×#88192	C₂²	semidirect
50. C₂×#88192	C₂²	semidirect
52. C₂×#88190	C₂²	semidirect
53. C₂×D₄×Dic₁₃	C₂²	semidirect
54. C₂×D₄×Dic₁₃	C₂²	semidirect
55. C₂×#88184	C₂²	semidirect
56. C₂×#88184	C₂²	semidirect
57. C₂×#88184	C₂²	semidirect
58. C₂×#88183	C₂²	semidirect
61. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
62. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
63. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
65. C₂×#88180	C₂²	semidirect
66. #11719433	C₂²	semidirect
67. #11719430	C₂²	semidirect
68. #11719421	C₂²	semidirect
69. D₁₃×#127	C₂²	semidirect
70. #11719386	C₂²	semidirect
71. #11719381	C₂²	semidirect
72. #11719324	C₂²	semidirect
73. #11719317	C₂²	semidirect
74. #11719312	C₂²	semidirect
75. #11719304	C₂²	semidirect
76. #11719267	C₂²	semidirect
77. #11719264	C₂²	semidirect
78. #11719259	C₂²	semidirect
79. #11719250	C₂²	semidirect
81. C₂×#88149	C₂²	semidirect
82. C₂×#88149	C₂²	semidirect
83. C₂×#88147	C₂²	semidirect
84. C₂×#88147	C₂²	semidirect
86. C₂×#88144	C₂²	semidirect
87. C₂×#88141	C₂²	semidirect
88. C₂×#88140	C₂²	semidirect
89. C₂×#88139	C₂²	semidirect
90. C₂×#88138	C₂²	semidirect
91. C₂×#88137	C₂²	semidirect
92. C₂×#88137	C₂²	semidirect
94. C₂×#88135	C₂²	semidirect
96. #11719182	C₂²	semidirect
97. C₂×#88129	C₂²	semidirect
99. C₄×#6127	C₂²	semidirect
102. C₂×C₄×D₅₂	C₂²	semidirect
103. C₂×C₄×D₅₂	C₂²	semidirect
105. C₂×#88126	C₂²	semidirect
107. C₂×C₄²×D₁₃	C₂²	semidirect
108. C₂×#88123	C₂²	semidirect
109. C₂×C₄×Dic₂₆	C₂²	semidirect
110. C₂×C₄×Dic₂₆	C₂²	semidirect
113. C₂×C₁₃×#41	C₂³	semidirect
132. C₂×#6131	C₂³	semidirect
134. C₂×#6129	C₂³	semidirect
144. C₂×#6127	C₂³	semidirect
160. C₁₃×C₄⋊Q₈	C₂³	semidirect
162. C₁₃×#124	C₂³	semidirect
163. C₁₃×#121	C₂³	semidirect
164. C₁₃×#121	C₂³	semidirect
165. C₄×D₄×C₁₃	C₂³	semidirect
166. C₄×D₄×C₁₃	C₂³	semidirect
175. C₂×C₄²×C₁₃	C₂³	semidirect
180. #88201	C₂³	semidirect
182. Q₈×Dic₁₃	C₂³	semidirect
186. #88194	C₂³	semidirect
187. #88193	C₂³	semidirect
188. #88192	C₂³	semidirect
189. #88192	C₂³	semidirect
190. #88192	C₂³	semidirect
192. #88190	C₂³	semidirect
193. D₄×Dic₁₃	C₂³	semidirect
194. D₄×Dic₁₃	C₂³	semidirect
195. #88184	C₂³	semidirect
196. #88184	C₂³	semidirect
197. #88184	C₂³	semidirect
198. #88183	C₂³	semidirect
201. C₄×C₂²⋊D₁₃	C₂³	semidirect
202. C₄×C₂²⋊D₁₃	C₂³	semidirect
203. C₄×C₂²⋊D₁₃	C₂³	semidirect
214. #88180	C₂³	semidirect
233. #88149	C₂³	semidirect
234. #88149	C₂³	semidirect
235. #88147	C₂³	semidirect
236. #88147	C₂³	semidirect
238. #88144	C₂³	semidirect
239. #88141	C₂³	semidirect
240. #88140	C₂³	semidirect
241. #88139	C₂³	semidirect
242. #88138	C₂³	semidirect
243. #88137	C₂³	semidirect
244. #88137	C₂³	semidirect
246. #88135	C₂³	semidirect
248. #88129	C₂³	semidirect
252. C₄×D₅₂	C₂³	semidirect
253. C₄×D₅₂	C₂³	semidirect
255. #88126	C₂³	semidirect
257. C₄²×D₁₃	C₂³	semidirect
258. #88123	C₂³	semidirect
259. C₄×Dic₂₆	C₂³	semidirect
260. C₄×Dic₂₆	C₂³	semidirect
344. C₂×C₄×D₁₃	#41	semidirect
411. C₂×#532	D₁₃	semidirect
497. C₄×D₁₃	C₂×#41	semidirect
504. C₂²×#41	C₂×D₁₃	semidirect
523. #532	C₂×D₁₃	semidirect
525. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
538. C₂×#124	C₂×D₁₃	semidirect
555. C₂×#121	C₂×D₁₃	semidirect
556. C₂×#121	C₂×D₁₃	semidirect
579. C₂×C₄×D₄	C₂×D₁₃	semidirect
580. C₂×C₄×D₄	C₂×D₁₃	semidirect
589. C₂²×C₄²	C₂×D₁₃	semidirect
639. C₂×#41	C₂²×D₁₃	semidirect
679. C₄⋊Q₈	C₂²×D₁₃	semidirect
691. #124	C₂²×D₁₃	semidirect
708. #121	C₂²×D₁₃	semidirect
709. #121	C₂²×D₁₃	semidirect
730. C₄×D₄	C₂²×D₁₃	semidirect
731. C₄×D₄	C₂²×D₁₃	semidirect
778. C₂×C₄²	C₂²×D₁₃	semidirect
781. C₂×C₁₃	#3508	semidirect
921. C₁₃	C₂×#3508	semidirect
1051. C₂	#13128705	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128705	2
C₂×#11719264	2
C₂×#11719386	2
C₂×#11719539	2
C₂×#11719304	2
C₂×#11719317	2
C₂×#11719259	2
C₂×#11719381	2
C₂×#11719534	2
C₂×#11719324	2
C₂×#11719267	2
C₂×#11719312	2
C₂×#11719433	2
C₂×#11719430	2
C₂×#11719182	2
C₂×#11719421	2
C₂×D₁₃×#127	2
C₂×#11719250	2
C₂×C₄×#6127	2
C₂×C₁₃×#532	2
C₂×#3508	13

Subgroups — C2×#13128705 #16771272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128705 #16771272