Subgroups — C₂×#13128675 #16770847

Order 3328.

8082 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128675	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719245	C₂	1	4	yes	maximal, complemented
3	C₂×#11719270	C₂	1	2	yes	maximal, complemented
4	C₂×#11719246	C₂	1	2	yes	maximal, complemented
5	C₂×#11719261	C₂	1	4	yes	maximal, complemented
6	C₂×#11719257	C₂	1	2	yes	maximal, complemented
7	C₂×#11719255	C₂	1	2	yes	maximal, complemented
8	C₂×#11719220	C₂	1	2	yes	maximal, complemented
9	C₂×#11719199	C₂	1	2	yes	maximal, complemented
10	C₂×#11719509	C₂	1	2	yes	maximal, complemented
11	C₂×#11719184	C₂	1	2	yes	maximal, complemented
12	C₂×#11719496	C₂	1	2	yes	maximal, complemented
13	C₂²×#88178	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#88184	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#11719191	C₂	1	2	yes	maximal, complemented
16	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
21	C₂²×#6127	C₂²	1	2	yes	complemented
22	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
23	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
28	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#88207	C₂²	1	4	yes	complemented
34	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
35	#11719509	C₂²	1	32	yes	complemented
36	C₂×#88193	C₂²	1	4	yes	complemented
37	C₂×#88193	C₂²	1	4	yes	complemented
38	C₂×#88191	C₂²	1	4	yes	—
39	C₂×#88189	C₂²	1	4	yes	—
40	#11719496	C₂²	1	32	yes	complemented
41	C₂×#88184	C₂²	1	2	yes	—
42	C₂×#88184	C₂²	1	2	yes	—
43	C₂×#88184	C₂²	1	2	yes	complemented
44	C₂×#88184	C₂²	1	2	yes	complemented
45	C₂×#88184	C₂²	1	2	yes	complemented
46	C₂×#88184	C₂²	1	16	yes	complemented
47	C₂×#88183	C₂²	1	4	yes	complemented
48	C₂×#88183	C₂²	1	4	yes	complemented
49	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
50	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
51	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
52	C₂²×#6103	C₂²	1	2	yes	complemented
53	C₂×#88180	C₂²	1	2	yes	complemented
54	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×#88178	C₂²	1	2	yes	complemented
57	C₂×#88178	C₂²	1	2	yes	complemented
58	C₂×#88178	C₂²	1	2	yes	complemented
59	C₂×#88178	C₂²	1	2	yes	complemented
60	C₂×#88178	C₂²	1	2	yes	complemented
61	C₂×#88178	C₂²	1	16	yes	complemented
62	C₂²×#6101	C₂²	1	2	yes	complemented
63	#11719270	C₂²	1	32	yes	complemented
64	#11719261	C₂²	1	64	yes	complemented
65	#11719257	C₂²	1	32	yes	complemented
66	#11719255	C₂²	1	32	yes	complemented
67	#11719246	C₂²	1	32	yes	complemented
68	#11719245	C₂²	1	64	yes	complemented
69	#11719220	C₂²	1	32	yes	complemented
70	C₂×#88152	C₂²	1	4	yes	complemented
71	C₂×#88150	C₂²	1	4	yes	complemented
72	C₂×#88148	C₂²	1	4	yes	complemented
73	C₂×#88143	C₂²	1	4	yes	complemented
74	#11719199	C₂²	1	32	yes	complemented
75	C₂×#88139	C₂²	1	4	yes	complemented
76	C₂×#88138	C₂²	1	4	yes	complemented
77	C₂×#88137	C₂²	1	4	yes	complemented
78	#11719191	C₂²	1	32	yes	complemented
79	C₂×#88135	C₂²	1	4	yes	complemented
80	C₂×#88135	C₂²	1	4	yes	complemented
81	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
82	C₂×#88133	C₂²	1	4	yes	complemented
83	C₂×#88131	C₂²	1	4	yes	complemented
84	#11719184	C₂²	1	32	yes	complemented
85	C₂×#88130	C₂²	1	4	yes	complemented
86	C₂×#88129	C₂²	1	2	yes	complemented
87	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
88	C₂×#88126	C₂²	1	4	yes	complemented
89	C₂×#88124	C₂²	1	2	yes	complemented
90	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
91	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
92	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
93	C₂⁴×D₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	—	2	8	no	—
95	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
98	C₂³×C₄×C₁₃	—	4	4	no	—
99	C₂³×C₄×C₁₃	—	4	4	no	—
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
113	C₂²×C₂²⋊D₁₃	—	2	16	no	—
114	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
115	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	—
116	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
117	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
118	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
119	C₂³×Dic₁₃	C₂³	1	2	yes	—
120	C₂³×Dic₁₃	C₂³	1	2	yes	—
121	C₂³×Dic₁₃	C₂³	1	2	yes	—
122	C₂×#6127	—	4	8	no	—
123	C₂×#6127	C₂³	1	16	yes	complemented
124	C₂²×D₅₂	—	4	4	no	—
125	C₂²×D₅₂	C₂³	1	2	yes	—
126	C₂²×D₅₂	C₂³	1	2	yes	—
127	C₂²×D₅₂	C₂³	1	8	yes	complemented
128	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
129	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
130	C₂²×Dic₂₆	—	4	4	no	—
131	C₂²×Dic₂₆	C₂³	1	2	yes	—
132	C₂²×Dic₂₆	C₂³	1	2	yes	—
133	C₂²×Dic₂₆	C₂³	1	8	yes	complemented
134	C₄×D₄×C₁₃	C₂³	1	16	yes	—
135	C₄×D₄×C₁₃	C₂³	1	16	yes	—
136	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
137	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
147	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
150	#88207	C₂³	1	32	yes	complemented
151	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
152	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
153	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
154	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	—
155	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
156	#88193	C₂³	1	32	yes	complemented
157	#88193	C₂³	1	32	yes	complemented
158	#88191	C₂³	1	32	yes	—
159	#88189	C₂³	1	32	yes	—
160	#88184	C₂³	1	16	yes	—
161	#88184	C₂³	1	16	yes	—
162	#88184	C₂³	1	16	yes	complemented
163	#88184	C₂³	1	16	yes	complemented
164	#88184	C₂³	1	16	yes	complemented
165	#88183	C₂³	1	32	yes	complemented
166	#88183	C₂³	1	32	yes	complemented
167	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
168	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
169	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
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	4	yes	—
175	C₂×#6103	C₂³	1	4	yes	—
176	C₂×#6103	C₂³	1	16	yes	complemented
177	#88180	C₂³	1	16	yes	complemented
178	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
179	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
181	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
182	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	complemented
183	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	complemented
184	#88178	C₂³	1	16	yes	complemented
185	#88178	C₂³	1	16	yes	complemented
186	#88178	C₂³	1	16	yes	complemented
187	#88178	C₂³	1	16	yes	complemented
188	#88178	C₂³	1	16	yes	complemented
189	C₂×#6101	C₂³	1	4	yes	—
190	C₂×#6101	C₂³	1	4	yes	—
191	C₂×#6101	C₂³	1	4	yes	—
192	C₂×#6101	C₂³	1	4	yes	—
193	C₂×#6101	C₂³	1	4	yes	—
194	C₂×#6101	C₂³	1	4	yes	—
195	C₂×#6101	C₂³	1	16	yes	complemented
196	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
197	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
198	#88152	C₂³	1	32	yes	complemented
199	#88150	C₂³	1	32	yes	complemented
200	#88148	C₂³	1	32	yes	complemented
201	#88143	C₂³	1	32	yes	complemented
202	#88139	C₂³	1	32	yes	complemented
203	#88138	C₂³	1	32	yes	complemented
204	#88137	C₂³	1	32	yes	complemented
205	#88135	C₂³	1	32	yes	complemented
206	#88135	C₂³	1	32	yes	complemented
207	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
208	#88133	C₂³	1	32	yes	complemented
209	#88131	C₂³	1	32	yes	complemented
210	#88130	C₂³	1	32	yes	complemented
211	#88129	C₂³	1	16	yes	complemented
212	C₄×D₅₂	C₂³	1	16	yes	complemented
213	#88126	C₂³	1	32	yes	complemented
214	#88124	C₂³	1	16	yes	complemented
215	C₄×Dic₂₆	C₂³	1	16	yes	complemented
216	C₂×#3505	—	13	1	no	maximal, Sylow
217	C₂⁴×C₁₃	—	2	4	no	—
218	C₂⁴×C₁₃	—	4	2	no	—
219	C₂⁴×C₁₃	—	4	2	no	—
220	C₂⁴×C₁₃	—	4	2	no	—
221	C₂⁴×C₁₃	—	4	2	no	—
222	C₂⁴×C₁₃	#41	1	8	yes	complemented
223	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
224	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
228	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
229	C₂³×D₁₃	—	2	8	no	—
230	C₂³×D₁₃	—	4	4	no	—
231	C₂³×D₁₃	—	4	4	no	—
232	C₂³×D₁₃	C₂⁴	1	4	yes	—
233	C₂³×D₁₃	C₂⁴	1	8	yes	—
234	C₂×D₄×C₁₃	—	2	8	no	—
235	C₂×D₄×C₁₃	—	2	8	no	—
236	C₂×D₄×C₁₃	—	2	32	no	—
237	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
239	C₂²×C₄×C₁₃	—	2	4	no	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	2	4	no	—
242	C₂²×C₄×C₁₃	—	2	8	no	—
243	C₂²×C₄×C₁₃	—	2	4	no	—
244	C₂²×C₄×C₁₃	—	4	16	no	—
245	C₂²×C₄×C₁₃	—	4	16	no	—
246	C₂²×C₄×C₁₃	—	4	2	no	—
247	C₂²×C₄×C₁₃	—	4	2	no	—
248	C₂²×C₄×C₁₃	—	4	2	no	—
249	C₂²×C₄×C₁₃	—	4	4	no	—
250	C₂²×C₄×C₁₃	—	4	2	no	—
251	C₂²×C₄×C₁₃	—	4	2	no	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	4	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	C₂×C₂²⋊D₁₃	—	2	16	no	—
271	C₂×C₂²⋊D₁₃	—	2	16	no	—
272	C₂×C₂²⋊D₁₃	—	2	64	no	—
273	C₂×C₂²⋊D₁₃	—	4	8	no	—
274	C₂×C₂²⋊D₁₃	—	4	8	no	—
275	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
276	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
277	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
278	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
279	C₂²×Dic₁₃	—	2	8	no	—
280	C₂²×Dic₁₃	—	4	4	no	—
281	C₂²×Dic₁₃	—	4	4	no	—
282	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
283	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
284	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
285	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
286	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
287	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
288	#6127	—	4	32	no	—
289	C₂×D₅₂	—	2	8	no	—
290	C₂×D₅₂	—	4	16	no	—
291	C₂×D₅₂	—	4	4	no	—
292	C₂×D₅₂	C₂⁴	1	8	yes	—
293	C₂×D₅₂	C₂⁴	1	8	yes	—
294	C₂×C₄×D₁₃	—	4	8	no	—
295	C₂×C₄×D₁₃	—	4	8	no	—
296	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
297	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
298	C₂×Dic₂₆	—	2	8	no	—
299	C₂×Dic₂₆	—	4	16	no	—
300	C₂×Dic₂₆	—	4	4	no	—
301	C₂×Dic₂₆	C₂⁴	1	8	yes	—
302	C₂×Dic₂₆	C₂⁴	1	8	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
305	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
306	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
307	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
308	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
309	C₄²×C₁₃	C₂⁴	1	8	yes	—
310	C₄²×C₁₃	C₂⁴	1	8	yes	—
311	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
312	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
313	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
314	C₂²⋊Dic₁₃	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	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
322	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
323	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
324	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
325	#6101	C₂⁴	1	16	yes	—
326	#6101	C₂⁴	1	16	yes	—
327	#6101	C₂⁴	1	16	yes	—
328	#6101	C₂⁴	1	16	yes	—
329	#6101	C₂⁴	1	16	yes	—
330	#6101	C₂⁴	1	16	yes	—
331	C₄×Dic₁₃	C₂⁴	1	16	yes	—
332	C₄×Dic₁₃	C₂⁴	1	16	yes	—
333	#3505	—	13	32	no	—
334	C₂×#553	—	13	2	no	—
335	C₂×#553	—	13	4	no	—
336	C₂×#552	—	13	2	no	—
337	C₂×#551	—	13	4	no	—
338	C₂×#548	—	13	2	no	—
339	C₂×#546	—	13	2	no	—
340	C₂×#539	—	13	2	no	—
341	C₂×#538	—	13	2	no	—
342	C₂×#534	—	13	2	no	—
343	C₂×#529	—	13	2	no	—
344	C₂×#525	—	13	2	no	—
345	C₂²×C₂²⋊Q₈	—	13	1	no	—
346	C₂²×#121	—	13	1	no	—
347	C₂×#518	—	13	2	no	—
348	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
349	C₂³×C₁₃	—	2	2	no	—
350	C₂³×C₁₃	—	2	2	no	—
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	8	no	—
356	C₂³×C₁₃	—	2	4	no	—
357	C₂³×C₁₃	—	2	4	no	—
358	C₂³×C₁₃	—	2	4	no	—
359	C₂³×C₁₃	—	4	4	no	—
360	C₂³×C₁₃	—	4	4	no	—
361	C₂³×C₁₃	—	4	16	no	—
362	C₂³×C₁₃	—	4	4	no	—
363	C₂³×C₁₃	—	4	4	no	—
364	C₂³×C₁₃	—	4	16	no	—
365	C₂³×C₁₃	C₂×#41	1	4	yes	—
366	C₂³×C₁₃	C₂×#41	1	4	yes	—
367	C₂³×C₁₃	C₂×#41	1	4	yes	—
368	C₂³×C₁₃	C₂×#41	1	16	yes	complemented
369	C₂³×C₁₃	C₂⁵	1	4	yes	—
370	C₂³×C₁₃	C₂⁵	1	2	yes	—
371	C₂³×C₁₃	C₂⁵	1	2	yes	—
372	C₂³×C₁₃	C₂⁵	1	2	yes	—
373	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
374	C₂²×D₁₃	—	2	8	no	—
375	C₂²×D₁₃	—	2	8	no	—
376	C₂²×D₁₃	—	2	8	no	—
377	C₂²×D₁₃	—	2	16	no	—
378	C₂²×D₁₃	—	4	8	no	—
379	C₂²×D₁₃	—	4	8	no	—
380	C₂²×D₁₃	—	8	16	no	—
381	C₂²×D₁₃	C₂⁵	1	8	yes	—
382	D₄×C₁₃	—	2	16	no	—
383	D₄×C₁₃	—	2	16	no	—
384	C₂×C₄×C₁₃	—	2	8	no	—
385	C₂×C₄×C₁₃	—	2	4	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	4	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	4	no	—
391	C₂×C₄×C₁₃	—	2	8	no	—
392	C₂×C₄×C₁₃	—	2	8	no	—
393	C₂×C₄×C₁₃	—	2	16	no	—
394	C₂×C₄×C₁₃	—	2	8	no	—
395	C₂×C₄×C₁₃	—	4	4	no	—
396	C₂×C₄×C₁₃	—	4	4	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	4	8	no	—
399	C₂×C₄×C₁₃	—	4	4	no	—
400	C₂×C₄×C₁₃	—	4	4	no	—
401	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
402	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
403	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
404	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
405	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
406	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
407	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
408	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
409	C₂²⋊D₁₃	—	2	32	no	—
410	C₂²⋊D₁₃	—	2	32	no	—
411	C₂²⋊D₁₃	—	4	16	no	—
412	C₂²⋊D₁₃	—	4	16	no	—
413	C₂×Dic₁₃	—	2	16	no	—
414	C₂×Dic₁₃	—	2	8	no	—
415	C₂×Dic₁₃	—	2	8	no	—
416	C₂×Dic₁₃	—	2	8	no	—
417	C₂×Dic₁₃	—	4	8	no	—
418	C₂×Dic₁₃	—	4	8	no	—
419	C₂×Dic₁₃	C₂⁵	1	8	yes	—
420	C₂×Dic₁₃	C₂⁵	1	8	yes	—
421	C₂×Dic₁₃	C₂⁵	1	8	yes	—
422	D₅₂	—	2	16	no	—
423	D₅₂	—	4	8	no	—
424	C₄×D₁₃	—	4	16	no	—
425	C₄×D₁₃	—	4	16	no	—
426	Dic₂₆	—	2	16	no	—
427	Dic₂₆	—	4	8	no	—
428	C₂²×#41	—	13	2	no	—
429	C₂³×Q₈	—	13	1	no	—
430	C₂³×D₄	—	13	2	no	—
431	C₂³×D₄	—	13	1	no	—
432	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
433	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
434	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
435	#553	—	13	64	no	—
436	#553	—	13	32	no	—
437	#552	—	13	32	no	—
438	#551	—	13	64	no	—
439	#548	—	13	32	no	—
440	#546	—	13	32	no	—
441	#539	—	13	32	no	—
442	#538	—	13	32	no	—
443	#534	—	13	32	no	—
444	#529	—	13	32	no	—
445	C₂×#126	—	13	4	no	—
446	C₂×#126	—	13	4	no	—
447	C₂×#126	—	13	4	no	—
448	C₂×#125	—	13	4	no	—
449	C₂×#125	—	13	2	no	—
450	C₂×#124	—	13	4	no	—
451	C₂×#124	—	13	2	no	—
452	#525	—	13	32	no	—
453	C₂×#123	—	13	4	no	—
454	C₂×#123	—	13	4	no	—
455	C₂×#123	—	13	4	no	—
456	C₂×#123	—	13	4	no	—
457	C₂×#123	—	13	4	no	—
458	C₂×C₂²⋊Q₈	—	13	2	no	—
459	C₂×C₂²⋊Q₈	—	13	2	no	—
460	C₂×C₂²⋊Q₈	—	13	2	no	—
461	C₂×C₂²⋊Q₈	—	13	2	no	—
462	C₂×C₂²⋊Q₈	—	13	16	no	—
463	C₂×C₂²⋊Q₈	—	13	2	no	—
464	C₂×C₂²⋊Q₈	—	13	4	no	—
465	C₂×#121	—	13	4	no	—
466	C₂×#121	—	13	4	no	—
467	C₂×#121	—	13	2	no	—
468	C₂×#121	—	13	2	no	—
469	C₂×#121	—	13	2	no	—
470	C₂×#121	—	13	2	no	—
471	C₂×#121	—	13	16	no	—
472	C₂×#121	—	13	2	no	—
473	C₂×#121	—	13	4	no	—
474	C₂×#120	—	13	4	no	—
475	C₂×#120	—	13	4	no	—
476	#518	—	13	32	no	—
477	C₂×C₄×Q₈	—	13	2	no	—
478	C₂×C₄×D₄	—	13	4	no	—
479	C₂×C₄×D₄	—	13	4	no	—
480	C₂×C₄×D₄	—	13	4	no	—
481	C₂×C₄×D₄	—	13	4	no	—
482	C₂×C₄×D₄	—	13	4	no	—
483	C₂×C₄×D₄	—	13	2	no	—
484	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
485	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
486	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
487	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
488	C₂×C₄×D₄	C₂×D₁₃	1	16	yes	complemented
489	C₂×#117	—	13	2	no	—
490	C₂×#117	—	13	4	no	—
491	C₂×#117	—	13	4	no	—
492	C₂²×C₄⋊C₄	—	13	2	no	—
493	C₂²×C₄⋊C₄	—	13	1	no	—
494	C₂²×C₄⋊C₄	—	13	1	no	—
495	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
496	C₂²×C₂²⋊C₄	—	13	2	no	—
497	C₂²×C₂²⋊C₄	—	13	2	no	—
498	C₂²×C₂²⋊C₄	—	13	4	no	—
499	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
500	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
501	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
502	C₂²×C₁₃	—	2	2	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	2	8	no	—
509	C₂²×C₁₃	—	2	8	no	—
510	C₂²×C₁₃	—	2	8	no	—
511	C₂²×C₁₃	—	2	4	no	—
512	C₂²×C₁₃	—	2	4	no	—
513	C₂²×C₁₃	—	2	4	no	—
514	C₂²×C₁₃	—	4	16	no	—
515	C₂²×C₁₃	—	4	16	no	—
516	C₂²×C₁₃	—	4	8	no	—
517	C₂²×C₁₃	C₂²×#41	1	4	yes	—
518	C₂²×C₁₃	C₂²×#41	1	4	yes	—
519	C₂²×C₁₃	C₂²×#41	1	4	yes	—
520	C₂²×C₁₃	C₂²×#41	1	2	yes	—
521	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
522	C₂²×C₁₃	#585	1	2	yes	—
523	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
524	C₂×D₁₃	—	2	8	no	—
525	C₂×D₁₃	—	2	8	no	—
526	C₂×D₁₃	—	2	8	no	—
527	C₂×D₁₃	—	4	16	no	—
528	C₂×D₁₃	—	8	16	no	—
529	C₄×C₁₃	—	2	4	no	—
530	C₄×C₁₃	—	2	2	no	—
531	C₄×C₁₃	—	2	4	no	—
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	2	no	—
534	C₄×C₁₃	—	2	4	no	—
535	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
536	Dic₁₃	—	2	8	no	—
537	Dic₁₃	—	2	8	no	—
538	Dic₁₃	—	2	8	no	—
539	C₂⁵	—	13	2	no	—
540	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
541	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
542	C₂×#41	—	13	16	no	—
543	C₂×#41	—	52	8	no	—
544	C₂²×Q₈	—	13	2	no	—
545	C₂²×Q₈	—	13	2	no	—
546	C₂²×Q₈	—	13	8	no	—
547	C₂²×Q₈	—	52	4	no	—
548	C₂²×D₄	—	2	8	no	—
549	C₂²×D₄	—	13	4	no	—
550	C₂²×D₄	—	13	4	no	—
551	C₂²×D₄	—	13	16	no	—
552	C₂²×D₄	—	13	4	no	—
553	C₂²×D₄	—	13	4	no	—
554	C₂²×D₄	—	13	2	no	—
555	C₂²×D₄	—	13	2	no	—
556	C₂²×D₄	—	13	8	no	—
557	C₂²×D₄	—	26	16	no	—
558	C₂²×D₄	—	52	4	no	—
559	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
560	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
561	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
562	C₂³×C₄	—	4	4	no	—
563	C₂³×C₄	—	4	4	no	—
564	C₂³×C₄	—	13	2	no	—
565	C₂³×C₄	—	13	2	no	—
566	C₂³×C₄	—	13	2	no	—
567	C₂³×C₄	—	13	4	no	—
568	C₂³×C₄	—	13	4	no	—
569	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
570	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
571	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
572	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
573	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
574	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
575	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
576	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
577	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
578	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
579	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
580	C₂³×C₄	C₂²×D₁₃	1	8	yes	—
581	C₂³×C₄	C₂²×D₁₃	1	8	yes	complemented
582	#126	—	13	32	no	—
583	#126	—	13	32	no	—
584	#126	—	13	32	no	—
585	#125	—	13	32	no	—
586	#125	—	13	16	no	—
587	#124	—	13	32	no	—
588	#124	—	13	16	no	—
589	#123	—	13	32	no	—
590	#123	—	13	32	no	—
591	#123	—	13	32	no	—
592	#123	—	13	32	no	—
593	#123	—	13	32	no	—
594	C₂²⋊Q₈	—	13	16	no	—
595	C₂²⋊Q₈	—	13	16	no	—
596	C₂²⋊Q₈	—	13	16	no	—
597	C₂²⋊Q₈	—	13	16	no	—
598	C₂²⋊Q₈	—	13	16	no	—
599	C₂²⋊Q₈	—	13	32	no	—
600	#121	—	13	32	no	—
601	#121	—	13	32	no	—
602	#121	—	13	16	no	—
603	#121	—	13	16	no	—
604	#121	—	13	16	no	—
605	#121	—	13	16	no	—
606	#121	—	13	16	no	—
607	#121	—	13	32	no	—
608	#120	—	13	32	no	—
609	#120	—	13	32	no	—
610	C₄×Q₈	—	13	16	no	—
611	C₄×D₄	—	13	32	no	—
612	C₄×D₄	—	13	32	no	—
613	C₄×D₄	—	13	32	no	—
614	C₄×D₄	—	13	32	no	—
615	C₄×D₄	—	13	32	no	—
616	C₄×D₄	—	13	16	no	—
617	C₄×D₄	C₂²×D₁₃	1	16	yes	—
618	C₄×D₄	C₂²×D₁₃	1	16	yes	—
619	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
620	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
621	#117	—	13	16	no	—
622	#117	—	13	32	no	—
623	#117	—	13	32	no	—
624	C₂×C₄⋊C₄	—	13	2	no	—
625	C₂×C₄⋊C₄	—	13	4	no	—
626	C₂×C₄⋊C₄	—	13	2	no	—
627	C₂×C₄⋊C₄	—	13	2	no	—
628	C₂×C₄⋊C₄	—	13	8	no	—
629	C₂×C₄⋊C₄	—	13	4	no	—
630	C₂×C₄⋊C₄	—	13	2	no	—
631	C₂×C₄⋊C₄	—	13	16	no	—
632	C₂×C₄⋊C₄	—	13	8	no	—
633	C₂×C₄⋊C₄	—	13	4	no	—
634	C₂×C₄⋊C₄	—	13	4	no	—
635	C₂×C₄⋊C₄	—	13	4	no	—
636	C₂×C₄⋊C₄	—	13	4	no	—
637	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂²×D₁₃	1	8	yes	complemented
640	C₂×C₂²⋊C₄	—	13	4	no	—
641	C₂×C₂²⋊C₄	—	13	4	no	—
642	C₂×C₂²⋊C₄	—	13	16	no	—
643	C₂×C₂²⋊C₄	—	13	4	no	—
644	C₂×C₂²⋊C₄	—	13	4	no	—
645	C₂×C₂²⋊C₄	—	13	4	no	—
646	C₂×C₂²⋊C₄	—	13	4	no	—
647	C₂×C₂²⋊C₄	—	13	4	no	—
648	C₂×C₂²⋊C₄	—	13	4	no	—
649	C₂×C₂²⋊C₄	—	13	16	no	—
650	C₂×C₂²⋊C₄	—	13	4	no	—
651	C₂×C₂²⋊C₄	—	13	4	no	—
652	C₂×C₂²⋊C₄	—	13	32	no	—
653	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
656	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	complemented
659	C₂×C₄²	—	13	4	no	—
660	C₂×C₄²	—	13	4	no	—
661	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
662	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
663	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
664	C₂×C₁₃	—	2	4	no	—
665	C₂×C₁₃	—	2	4	no	—
666	C₂×C₁₃	—	2	4	no	—
667	C₂×C₁₃	—	4	4	no	—
668	C₂×C₁₃	#3505	1	4	yes	complemented
669	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
670	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
672	D₁₃	—	4	8	no	—
673	C₂⁴	—	2	4	no	—
674	C₂⁴	—	4	2	no	—
675	C₂⁴	—	4	2	no	—
676	C₂⁴	—	4	2	no	—
677	C₂⁴	—	4	2	no	—
678	C₂⁴	—	13	4	no	—
679	C₂⁴	—	13	8	no	—
680	C₂⁴	—	26	8	no	—
681	C₂⁴	—	52	4	no	—
682	C₂⁴	—	52	4	no	—
683	C₂⁴	#6127	1	8	yes	complemented
684	C₂⁴	C₂³×D₁₃	1	2	yes	—
685	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
686	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
687	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
688	C₂⁴	C₂³×D₁₃	1	4	yes	—
689	C₂⁴	C₂³×D₁₃	1	4	yes	—
690	#41	—	52	32	no	—
691	C₂×Q₈	—	13	8	no	—
692	C₂×Q₈	—	13	8	no	—
693	C₂×Q₈	—	26	8	no	—
694	C₂×Q₈	—	52	4	no	—
695	C₂×Q₈	—	52	16	no	—
696	C₂×D₄	—	2	8	no	—
697	C₂×D₄	—	2	8	no	—
698	C₂×D₄	—	2	32	no	—
699	C₂×D₄	—	13	16	no	—
700	C₂×D₄	—	13	16	no	—
701	C₂×D₄	—	13	16	no	—
702	C₂×D₄	—	13	16	no	—
703	C₂×D₄	—	13	8	no	—
704	C₂×D₄	—	13	8	no	—
705	C₂×D₄	—	26	16	no	—
706	C₂×D₄	—	26	16	no	—
707	C₂×D₄	—	26	64	no	—
708	C₂×D₄	—	26	8	no	—
709	C₂×D₄	—	52	16	no	—
710	C₂×D₄	—	52	4	no	—
711	C₂×D₄	—	52	8	no	—
712	C₂×D₄	—	52	8	no	—
713	C₂×D₄	C₂³×D₁₃	1	8	yes	—
714	C₂×D₄	C₂³×D₁₃	1	8	yes	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	8	no	—
720	C₂²×C₄	—	4	16	no	—
721	C₂²×C₄	—	4	16	no	—
722	C₂²×C₄	—	4	4	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	13	8	no	—
729	C₂²×C₄	—	13	4	no	—
730	C₂²×C₄	—	13	4	no	—
731	C₂²×C₄	—	13	4	no	—
732	C₂²×C₄	—	13	8	no	—
733	C₂²×C₄	—	13	8	no	—
734	C₂²×C₄	—	13	16	no	—
735	C₂²×C₄	—	13	16	no	—
736	C₂²×C₄	—	26	8	no	—
737	C₂²×C₄	—	52	8	no	—
738	C₂²×C₄	—	52	8	no	—
739	C₂²×C₄	—	52	4	no	—
740	C₂²×C₄	—	52	4	no	—
741	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
742	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
743	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
744	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
745	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
746	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
747	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
748	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
749	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
750	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
751	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
752	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
753	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
754	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
755	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
756	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
757	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
758	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
759	C₄⋊C₄	—	13	8	no	—
760	C₄⋊C₄	—	13	16	no	—
761	C₄⋊C₄	—	13	8	no	—
762	C₄⋊C₄	—	13	8	no	—
763	C₄⋊C₄	—	13	16	no	—
764	C₄⋊C₄	—	13	8	no	—
765	C₄⋊C₄	—	13	16	no	—
766	C₄⋊C₄	—	13	16	no	—
767	C₄⋊C₄	—	13	16	no	—
768	C₄⋊C₄	—	13	16	no	—
769	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
770	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
771	C₂²⋊C₄	—	13	16	no	—
772	C₂²⋊C₄	—	13	16	no	—
773	C₂²⋊C₄	—	13	16	no	—
774	C₂²⋊C₄	—	13	16	no	—
775	C₂²⋊C₄	—	13	16	no	—
776	C₂²⋊C₄	—	13	16	no	—
777	C₂²⋊C₄	—	13	16	no	—
778	C₂²⋊C₄	—	13	16	no	—
779	C₂²⋊C₄	—	13	16	no	—
780	C₂²⋊C₄	—	13	16	no	—
781	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
782	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
783	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
784	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
785	C₄²	—	13	16	no	—
786	C₄²	—	13	16	no	—
787	C₄²	C₂³×D₁₃	1	8	yes	—
788	C₄²	C₂³×D₁₃	1	8	yes	—
789	C₁₃	C₂×#3505	1	1	yes	characteristic, complemented, Sylow
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	8	no	—
797	C₂³	—	2	4	no	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	4	4	no	—
801	C₂³	—	4	4	no	—
802	C₂³	—	4	16	no	—
803	C₂³	—	4	4	no	—
804	C₂³	—	4	4	no	—
805	C₂³	—	4	16	no	—
806	C₂³	—	13	8	no	—
807	C₂³	—	26	8	no	—
808	C₂³	—	26	8	no	—
809	C₂³	—	26	8	no	—
810	C₂³	—	26	16	no	—
811	C₂³	—	52	8	no	—
812	C₂³	—	52	8	no	—
813	C₂³	—	104	16	no	—
814	C₂³	C₂×#6127	1	4	yes	—
815	C₂³	C₂×#6127	1	4	yes	—
816	C₂³	C₂×#6127	1	4	yes	—
817	C₂³	C₂×#6127	1	16	yes	complemented
818	C₂³	C₂⁴×D₁₃	1	4	yes	—
819	C₂³	C₂⁴×D₁₃	1	2	yes	—
820	C₂³	C₂⁴×D₁₃	1	2	yes	—
821	C₂³	C₂⁴×D₁₃	1	2	yes	—
822	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
823	Q₈	—	26	16	no	—
824	Q₈	—	52	8	no	—
825	D₄	—	2	16	no	—
826	D₄	—	2	16	no	—
827	D₄	—	26	32	no	—
828	D₄	—	26	32	no	—
829	D₄	—	26	16	no	—
830	D₄	—	52	8	no	—
831	D₄	—	52	16	no	—
832	D₄	—	52	16	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	8	no	—
842	C₂×C₄	—	2	8	no	—
843	C₂×C₄	—	2	16	no	—
844	C₂×C₄	—	4	8	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	13	8	no	—
851	C₂×C₄	—	13	8	no	—
852	C₂×C₄	—	13	8	no	—
853	C₂×C₄	—	26	16	no	—
854	C₂×C₄	—	26	8	no	—
855	C₂×C₄	—	26	8	no	—
856	C₂×C₄	—	26	8	no	—
857	C₂×C₄	—	52	16	no	—
858	C₂×C₄	—	52	16	no	—
859	C₂×C₄	—	52	8	no	—
860	C₂×C₄	—	52	8	no	—
861	C₂×C₄	#88251	1	4	yes	—
862	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
863	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
864	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
865	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
866	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
867	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
868	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	8	no	—
876	C₂²	—	2	8	no	—
877	C₂²	—	2	8	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	4	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	4	16	no	—
882	C₂²	—	4	16	no	—
883	C₂²	—	4	8	no	—
884	C₂²	—	26	8	no	—
885	C₂²	—	26	8	no	—
886	C₂²	—	26	8	no	—
887	C₂²	—	52	16	no	—
888	C₂²	—	104	16	no	—
889	C₂²	C₂²×#6127	1	4	yes	—
890	C₂²	C₂²×#6127	1	4	yes	—
891	C₂²	C₂²×#6127	1	4	yes	—
892	C₂²	C₂²×#6127	1	2	yes	—
893	C₂²	C₂×#88251	1	2	yes	—
894	C₂²	#11719648	1	2	yes	—
895	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
896	C₄	—	2	4	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	4	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	4	no	—
902	C₄	—	26	8	no	—
903	C₄	—	26	8	no	—
904	C₄	—	26	8	no	—
905	C₄	C₂×#88251	1	4	yes	—
906	C₂	—	2	4	no	—
907	C₂	—	2	4	no	—
908	C₂	—	2	4	no	—
909	C₂	—	4	4	no	—
910	C₂	—	52	8	no	—
911	C₂	#13128675	1	4	yes	direct product factor
912	C₂	C₂³×#6127	1	1	yes	characteristic
913	C₂	C₂²×#88251	1	1	yes	characteristic
914	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂×#3505
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #13128675	C₂	direct (N × H)
2. C₂×#11719245	C₂	semidirect
3. C₂×#11719270	C₂	semidirect
4. C₂×#11719246	C₂	semidirect
5. C₂×#11719261	C₂	semidirect
6. C₂×#11719257	C₂	semidirect
7. C₂×#11719255	C₂	semidirect
8. C₂×#11719220	C₂	semidirect
9. C₂×#11719199	C₂	semidirect
10. C₂×#11719509	C₂	semidirect
11. C₂×#11719184	C₂	semidirect
12. C₂×#11719496	C₂	semidirect
13. C₂²×#88178	C₂	semidirect
14. C₂²×#88184	C₂	semidirect
15. C₂×#11719191	C₂	semidirect
16. C₂²×C₄×D₄×C₁₃	C₂	semidirect
19. C₂⁴×C₄×C₁₃	C₂²	semidirect
21. C₂²×#6127	C₂²	semidirect
22. C₂³×D₅₂	C₂²	semidirect
23. C₂³×Dic₂₆	C₂²	semidirect
26. C₂×C₄×D₄×C₁₃	C₂²	semidirect
27. C₂×C₄×D₄×C₁₃	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
31. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
32. C₂²×C₄²×C₁₃	C₂²	semidirect
33. C₂×#88207	C₂²	semidirect
35. #11719509	C₂²	semidirect
36. C₂×#88193	C₂²	semidirect
37. C₂×#88193	C₂²	semidirect
40. #11719496	C₂²	semidirect
43. C₂×#88184	C₂²	semidirect
44. C₂×#88184	C₂²	semidirect
45. C₂×#88184	C₂²	semidirect
46. C₂×#88184	C₂²	semidirect
47. C₂×#88183	C₂²	semidirect
48. C₂×#88183	C₂²	semidirect
49. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
50. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
51. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
52. C₂²×#6103	C₂²	semidirect
53. C₂×#88180	C₂²	semidirect
54. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
55. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
56. C₂×#88178	C₂²	semidirect
57. C₂×#88178	C₂²	semidirect
58. C₂×#88178	C₂²	semidirect
59. C₂×#88178	C₂²	semidirect
60. C₂×#88178	C₂²	semidirect
61. C₂×#88178	C₂²	semidirect
62. C₂²×#6101	C₂²	semidirect
63. #11719270	C₂²	semidirect
64. #11719261	C₂²	semidirect
65. #11719257	C₂²	semidirect
66. #11719255	C₂²	semidirect
67. #11719246	C₂²	semidirect
68. #11719245	C₂²	semidirect
69. #11719220	C₂²	semidirect
70. C₂×#88152	C₂²	semidirect
71. C₂×#88150	C₂²	semidirect
72. C₂×#88148	C₂²	semidirect
73. C₂×#88143	C₂²	semidirect
74. #11719199	C₂²	semidirect
75. C₂×#88139	C₂²	semidirect
76. C₂×#88138	C₂²	semidirect
77. C₂×#88137	C₂²	semidirect
78. #11719191	C₂²	semidirect
79. C₂×#88135	C₂²	semidirect
80. C₂×#88135	C₂²	semidirect
81. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
82. C₂×#88133	C₂²	semidirect
83. C₂×#88131	C₂²	semidirect
84. #11719184	C₂²	semidirect
85. C₂×#88130	C₂²	semidirect
86. C₂×#88129	C₂²	semidirect
87. C₂×C₄×D₅₂	C₂²	semidirect
88. C₂×#88126	C₂²	semidirect
89. C₂×#88124	C₂²	semidirect
90. C₂×C₄×Dic₂₆	C₂²	semidirect
112. C₂³×C₄×C₁₃	C₂³	semidirect
123. C₂×#6127	C₂³	semidirect
127. C₂²×D₅₂	C₂³	semidirect
133. C₂²×Dic₂₆	C₂³	semidirect
136. C₄×D₄×C₁₃	C₂³	semidirect
137. C₄×D₄×C₁₃	C₂³	semidirect
140. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
146. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
149. C₂×C₄²×C₁₃	C₂³	semidirect
150. #88207	C₂³	semidirect
156. #88193	C₂³	semidirect
157. #88193	C₂³	semidirect
162. #88184	C₂³	semidirect
163. #88184	C₂³	semidirect
164. #88184	C₂³	semidirect
165. #88183	C₂³	semidirect
166. #88183	C₂³	semidirect
167. C₄×C₂²⋊D₁₃	C₂³	semidirect
168. C₄×C₂²⋊D₁₃	C₂³	semidirect
169. C₄×C₂²⋊D₁₃	C₂³	semidirect
176. C₂×#6103	C₂³	semidirect
177. #88180	C₂³	semidirect
182. C₂×C₄⋊Dic₁₃	C₂³	semidirect
183. C₂×C₄⋊Dic₁₃	C₂³	semidirect
184. #88178	C₂³	semidirect
185. #88178	C₂³	semidirect
186. #88178	C₂³	semidirect
187. #88178	C₂³	semidirect
188. #88178	C₂³	semidirect
195. C₂×#6101	C₂³	semidirect
198. #88152	C₂³	semidirect
199. #88150	C₂³	semidirect
200. #88148	C₂³	semidirect
201. #88143	C₂³	semidirect
202. #88139	C₂³	semidirect
203. #88138	C₂³	semidirect
204. #88137	C₂³	semidirect
205. #88135	C₂³	semidirect
206. #88135	C₂³	semidirect
207. C₂²⋊C₄×D₁₃	C₂³	semidirect
208. #88133	C₂³	semidirect
209. #88131	C₂³	semidirect
210. #88130	C₂³	semidirect
211. #88129	C₂³	semidirect
212. C₄×D₅₂	C₂³	semidirect
213. #88126	C₂³	semidirect
214. #88124	C₂³	semidirect
215. C₄×Dic₂₆	C₂³	semidirect
222. C₂⁴×C₁₃	#41	semidirect
348. C₂²×C₄×D₄	D₁₃	semidirect
368. C₂³×C₁₃	C₂×#41	semidirect
434. C₂⁴×C₄	C₂×D₁₃	semidirect
486. C₂×C₄×D₄	C₂×D₁₃	semidirect
487. C₂×C₄×D₄	C₂×D₁₃	semidirect
488. C₂×C₄×D₄	C₂×D₁₃	semidirect
495. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
500. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
501. C₂²×C₄²	C₂×D₁₃	semidirect
581. C₂³×C₄	C₂²×D₁₃	semidirect
619. C₄×D₄	C₂²×D₁₃	semidirect
620. C₄×D₄	C₂²×D₁₃	semidirect
639. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
658. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
663. C₂×C₄²	C₂²×D₁₃	semidirect
668. C₂×C₁₃	#3505	semidirect
683. C₂⁴	#6127	semidirect
789. C₁₃	C₂×#3505	semidirect
817. C₂³	C₂×#6127	semidirect
911. C₂	#13128675	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128675	2
C₂×#11719245	2
C₂×#11719270	2
C₂×#11719246	2
C₂×#11719261	2
C₂×#11719257	2
C₂×#11719255	2
C₂×#11719220	2
C₂×#11719199	2
C₂×#11719509	2
C₂×#11719184	2
C₂×#11719496	2
C₂²×#88178	2
C₂²×#88184	2
C₂×#11719191	2
C₂²×C₄×D₄×C₁₃	2
C₂×#3505	13

Subgroups — C2×#13128675 #16770847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128675 #16770847