Subgroups — C₂×#13128868 #16770914

Order 3328.

8774 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128868	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719268	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719248	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11719219	C₂	1	2	yes	maximal, complemented
5	C₂×#11719270	C₂	1	2	yes	maximal, complemented
6	C₂×#11719258	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11719255	C₂	1	2	yes	maximal, complemented
8	C₂×#11719195	C₂	1	4	yes	maximal, complemented
9	C₂×D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₄×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
11	C₂×#11719267	C₂	1	2	yes	maximal, complemented
12	C₂×#11719265	C₂	1	4	yes	maximal, complemented
13	C₂×#11719182	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11719184	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#11719496	C₂	1	2	yes	maximal, complemented
16	C₂²×#88184	C₂	1	2	yes	maximal, complemented
17	C₂×#11719250	C₂	1	2	yes	maximal, complemented
18	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
21	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
22	C₂²×D₄×D₁₃	C₂²	1	2	yes	—
23	C₂²×#6127	C₂²	1	2	yes	complemented
24	C₂²×#6127	C₂²	1	2	yes	complemented
25	C₂³×D₅₂	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
32	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#88207	C₂²	1	4	yes	complemented
37	C₂×#88194	C₂²	1	2	yes	complemented
38	C₂×#88193	C₂²	1	4	yes	complemented
39	D₄×C₂²⋊D₁₃	C₂²	1	32	yes	complemented
40	C₂×#88192	C₂²	1	2	yes	complemented
41	C₂×#88191	C₂²	1	4	yes	complemented
42	C₂×D₄×Dic₁₃	C₂²	1	2	yes	—
43	#11719496	C₂²	1	32	yes	complemented
44	C₂×#88184	C₂²	1	1	yes	characteristic
45	C₂×#88184	C₂²	1	4	yes	complemented
46	C₂×#88184	C₂²	1	2	yes	complemented
47	C₂×#88184	C₂²	1	2	yes	complemented
48	C₂×#88184	C₂²	1	4	yes	complemented
49	C₂×#88184	C₂²	1	2	yes	complemented
50	C₂×#88184	C₂²	1	2	yes	complemented
51	C₂×#88184	C₂²	1	2	yes	complemented
52	C₂×#88184	C₂²	1	32	yes	complemented
53	C₂×#88183	C₂²	1	4	yes	complemented
54	C₂×#88183	C₂²	1	2	yes	complemented
55	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
56	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
57	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
58	C₂²×#6103	C₂²	1	4	yes	complemented
59	C₂×#88180	C₂²	1	2	yes	complemented
60	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
61	C₂×#88178	C₂²	1	2	yes	complemented
62	C₂×#88178	C₂²	1	1	yes	characteristic, complemented
63	#11719270	C₂²	1	32	yes	complemented
64	#11719268	C₂²	1	16	yes	complemented
65	#11719267	C₂²	1	32	yes	complemented
66	#11719265	C₂²	1	64	yes	complemented
67	#11719258	C₂²	1	16	yes	complemented
68	#11719255	C₂²	1	32	yes	complemented
69	D₄×D₅₂	C₂²	1	16	yes	complemented
70	#11719250	C₂²	1	32	yes	complemented
71	#11719248	C₂²	1	16	yes	complemented
72	#11719219	C₂²	1	32	yes	complemented
73	C₂×#88152	C₂²	1	4	yes	complemented
74	C₂×#88149	C₂²	1	2	yes	complemented
75	C₂×#88148	C₂²	1	4	yes	complemented
76	C₂×#88147	C₂²	1	2	yes	complemented
77	C₂×#88146	C₂²	1	2	yes	complemented
78	C₂×#88144	C₂²	1	2	yes	complemented
79	C₂×#88139	C₂²	1	4	yes	complemented
80	#11719195	C₂²	1	64	yes	complemented
81	C₂×#88138	C₂²	1	4	yes	complemented
82	C₂×#88138	C₂²	1	4	yes	complemented
83	C₂×#88137	C₂²	1	4	yes	complemented
84	C₂×#88136	C₂²	1	4	yes	complemented
85	C₂×#88135	C₂²	1	4	yes	complemented
86	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
87	C₂×#88132	C₂²	1	4	yes	complemented
88	#11719184	C₂²	1	16	yes	complemented
89	C₂×#88130	C₂²	1	2	yes	complemented
90	#11719182	C₂²	1	16	yes	complemented
91	C₂×#88129	C₂²	1	1	yes	characteristic, complemented
92	C₂×#88129	C₂²	1	2	yes	complemented
93	C₂×#88128	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
95	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
97	C₂×#88126	C₂²	1	2	yes	complemented
98	C₂×#88124	C₂²	1	1	yes	characteristic, complemented
99	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₁₃	C₂³	1	2	yes	—
102	C₂⁴×D₁₃	C₂³	1	4	yes	—
103	C₂²×D₄×C₁₃	—	2	8	no	—
104	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
105	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
107	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	—	4	8	no	—
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	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	16	yes	complemented
118	C₂²×C₂²⋊D₁₃	—	4	16	no	—
119	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
120	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
121	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
122	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
123	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
124	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
125	C₂²×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
126	C₂³×Dic₁₃	C₂³	1	4	yes	—
127	C₂×D₄×D₁₃	—	2	16	no	—
128	C₂×D₄×D₁₃	C₂³	1	16	yes	—
129	C₂×#6127	—	4	8	no	—
130	C₂×#6127	—	4	8	no	—
131	C₂×#6127	C₂³	1	16	yes	complemented
132	C₂×#6127	C₂³	1	16	yes	complemented
133	C₂²×D₅₂	—	4	8	no	—
134	C₂²×D₅₂	C₂³	1	2	yes	—
135	C₂²×D₅₂	C₂³	1	2	yes	—
136	C₂²×D₅₂	C₂³	1	1	yes	characteristic
137	C₂²×D₅₂	C₂³	1	2	yes	—
138	C₂²×D₅₂	C₂³	1	4	yes	—
139	C₂²×D₅₂	C₂³	1	16	yes	complemented
140	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
141	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
142	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
143	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
144	C₂²×Dic₂₆	C₂³	1	2	yes	—
145	C₄×D₄×C₁₃	C₂³	1	8	yes	—
146	C₄×D₄×C₁₃	C₂³	1	8	yes	—
147	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
148	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
149	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
150	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
165	#88207	C₂³	1	32	yes	complemented
166	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
167	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
168	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
169	#88194	C₂³	1	16	yes	complemented
170	#88193	C₂³	1	32	yes	complemented
171	#88192	C₂³	1	16	yes	complemented
172	#88191	C₂³	1	32	yes	complemented
173	D₄×Dic₁₃	C₂³	1	16	yes	—
174	#88184	C₂³	1	8	yes	—
175	#88184	C₂³	1	16	yes	complemented
176	#88184	C₂³	1	16	yes	complemented
177	#88184	C₂³	1	32	yes	complemented
178	#88184	C₂³	1	16	yes	complemented
179	#88184	C₂³	1	16	yes	complemented
180	#88184	C₂³	1	32	yes	complemented
181	#88184	C₂³	1	16	yes	complemented
182	#88183	C₂³	1	16	yes	complemented
183	#88183	C₂³	1	32	yes	complemented
184	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	complemented
185	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
186	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
187	C₂×#6103	C₂³	1	2	yes	—
188	C₂×#6103	C₂³	1	2	yes	—
189	C₂×#6103	C₂³	1	4	yes	—
190	C₂×#6103	C₂³	1	4	yes	—
191	C₂×#6103	C₂³	1	2	yes	—
192	C₂×#6103	C₂³	1	2	yes	—
193	C₂×#6103	C₂³	1	4	yes	—
194	C₂×#6103	C₂³	1	4	yes	—
195	C₂×#6103	C₂³	1	4	yes	—
196	C₂×#6103	C₂³	1	32	yes	complemented
197	#88180	C₂³	1	16	yes	complemented
198	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
200	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
201	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
203	C₂×C₄⋊Dic₁₃	C₂³	1	16	yes	complemented
204	#88178	C₂³	1	8	yes	complemented
205	#88178	C₂³	1	16	yes	complemented
206	C₂×#6101	C₂³	1	2	yes	—
207	C₂×#6101	C₂³	1	2	yes	—
208	C₂×#6101	C₂³	1	2	yes	—
209	C₂×#6101	C₂³	1	2	yes	—
210	C₂×#6101	C₂³	1	4	yes	—
211	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
212	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
213	#88152	C₂³	1	32	yes	complemented
214	#88149	C₂³	1	16	yes	complemented
215	#88148	C₂³	1	32	yes	complemented
216	#88147	C₂³	1	16	yes	complemented
217	#88146	C₂³	1	16	yes	complemented
218	#88144	C₂³	1	16	yes	complemented
219	#88139	C₂³	1	32	yes	complemented
220	#88138	C₂³	1	32	yes	complemented
221	#88138	C₂³	1	32	yes	complemented
222	#88137	C₂³	1	32	yes	complemented
223	#88136	C₂³	1	32	yes	complemented
224	#88135	C₂³	1	32	yes	complemented
225	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
226	#88132	C₂³	1	32	yes	complemented
227	#88130	C₂³	1	16	yes	complemented
228	#88129	C₂³	1	16	yes	complemented
229	#88129	C₂³	1	8	yes	complemented
230	#88128	C₂³	1	8	yes	complemented
231	C₄×D₅₂	C₂³	1	16	yes	complemented
232	C₄×D₅₂	C₂³	1	16	yes	complemented
233	C₄×D₅₂	C₂³	1	8	yes	complemented
234	#88126	C₂³	1	16	yes	complemented
235	#88124	C₂³	1	8	yes	complemented
236	#88123	C₂³	1	8	yes	complemented
237	C₄×Dic₂₆	C₂³	1	8	yes	complemented
238	C₂×#3519	—	13	1	no	maximal, Sylow
239	C₂⁴×C₁₃	—	2	8	no	—
240	C₂⁴×C₁₃	—	2	8	no	—
241	C₂⁴×C₁₃	—	4	4	no	—
242	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
243	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
244	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
245	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂³×D₁₃	—	2	16	no	—
247	C₂³×D₁₃	—	4	8	no	—
248	C₂³×D₁₃	—	4	8	no	—
249	C₂³×D₁₃	C₂⁴	1	2	yes	—
250	C₂³×D₁₃	C₂⁴	1	4	yes	—
251	C₂³×D₁₃	C₂⁴	1	16	yes	—
252	C₂×D₄×C₁₃	—	2	8	no	—
253	C₂×D₄×C₁₃	—	2	32	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	#41	1	8	yes	complemented
256	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
257	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₁₃	—	2	4	no	—
260	C₂²×C₄×C₁₃	—	2	4	no	—
261	C₂²×C₄×C₁₃	—	2	8	no	—
262	C₂²×C₄×C₁₃	—	2	8	no	—
263	C₂²×C₄×C₁₃	—	2	4	no	—
264	C₂²×C₄×C₁₃	—	4	32	no	—
265	C₂²×C₄×C₁₃	—	4	4	no	—
266	C₂²×C₄×C₁₃	—	4	4	no	—
267	C₂²×C₄×C₁₃	—	4	4	no	—
268	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×C₂²⋊D₁₃	—	2	16	no	—
285	C₂×C₂²⋊D₁₃	—	2	16	no	—
286	C₂×C₂²⋊D₁₃	—	2	8	no	—
287	C₂×C₂²⋊D₁₃	—	4	8	no	—
288	C₂×C₂²⋊D₁₃	—	4	8	no	—
289	C₂×C₂²⋊D₁₃	—	4	8	no	—
290	C₂×C₂²⋊D₁₃	—	4	64	no	—
291	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
292	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
293	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
294	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
295	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
296	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
297	C₂²×Dic₁₃	—	4	8	no	—
298	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
299	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
300	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
301	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
302	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
303	D₄×D₁₃	—	2	64	no	—
304	#6127	—	4	32	no	—
305	#6127	—	4	32	no	—
306	C₂×D₅₂	—	2	8	no	—
307	C₂×D₅₂	—	2	4	no	—
308	C₂×D₅₂	—	2	8	no	—
309	C₂×D₅₂	—	4	32	no	—
310	C₂×D₅₂	—	4	8	no	—
311	C₂×D₅₂	—	4	4	no	—
312	C₂×D₅₂	C₂⁴	1	8	yes	—
313	C₂×D₅₂	C₂⁴	1	8	yes	—
314	C₂×D₅₂	C₂⁴	1	4	yes	—
315	C₂×D₅₂	C₂⁴	1	8	yes	—
316	C₂×D₅₂	C₂⁴	1	16	yes	—
317	C₂×C₄×D₁₃	—	2	8	no	—
318	C₂×C₄×D₁₃	—	4	8	no	—
319	C₂×C₄×D₁₃	—	4	8	no	—
320	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
321	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
322	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
323	C₂×Dic₂₆	—	2	4	no	—
324	C₂×Dic₂₆	—	4	4	no	—
325	C₂×Dic₂₆	C₂⁴	1	4	yes	—
326	C₂×Dic₂₆	C₂⁴	1	8	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
330	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
331	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
332	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₄²×C₁₃	C₂⁴	1	4	yes	—
335	C₄²×C₁₃	C₂⁴	1	4	yes	—
336	C₄²×C₁₃	C₂⁴	1	4	yes	—
337	C₄²×C₁₃	C₂⁴	1	4	yes	—
338	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
339	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
340	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
341	#6103	C₂⁴	1	8	yes	—
342	#6103	C₂⁴	1	8	yes	—
343	#6103	C₂⁴	1	16	yes	—
344	#6103	C₂⁴	1	16	yes	—
345	#6103	C₂⁴	1	8	yes	—
346	#6103	C₂⁴	1	8	yes	—
347	#6103	C₂⁴	1	16	yes	—
348	#6103	C₂⁴	1	16	yes	—
349	#6103	C₂⁴	1	16	yes	—
350	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
351	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
352	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
353	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
354	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
355	#6101	C₂⁴	1	8	yes	—
356	#6101	C₂⁴	1	8	yes	—
357	#6101	C₂⁴	1	8	yes	—
358	#6101	C₂⁴	1	8	yes	—
359	#6101	C₂⁴	1	16	yes	—
360	C₄×Dic₁₃	C₂⁴	1	8	yes	—
361	C₄×Dic₁₃	C₂⁴	1	16	yes	—
362	#3519	—	13	32	no	—
363	C₂×#555	—	13	1	no	—
364	C₂×#554	—	13	1	no	—
365	C₂×#553	—	13	2	no	—
366	C₂×#553	—	13	2	no	—
367	C₂×#550	—	13	1	no	—
368	C₂×#546	—	13	2	no	—
369	C₂×#546	—	13	4	no	—
370	C₂×D₄²	—	13	2	no	—
371	C₂×D₄²	—	13	1	no	—
372	C₂×#540	—	13	2	no	—
373	C₂×#538	—	13	4	no	—
374	C₂×#532	—	13	1	no	—
375	C₂×#529	—	13	1	no	—
376	C₂×#525	—	13	2	no	—
377	C₂²×#121	—	13	2	no	—
378	C₂×#518	—	13	2	no	—
379	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	4	no	—
382	C₂³×C₁₃	—	2	2	no	—
383	C₂³×C₁₃	—	2	4	no	—
384	C₂³×C₁₃	—	2	16	no	—
385	C₂³×C₁₃	—	2	4	no	—
386	C₂³×C₁₃	—	2	16	no	—
387	C₂³×C₁₃	—	2	4	no	—
388	C₂³×C₁₃	—	2	4	no	—
389	C₂³×C₁₃	—	4	8	no	—
390	C₂³×C₁₃	—	4	32	no	—
391	C₂³×C₁₃	C₂×#41	1	8	yes	—
392	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
393	C₂³×C₁₃	C₂⁵	1	4	yes	—
394	C₂³×C₁₃	C₂⁵	1	4	yes	—
395	C₂³×C₁₃	C₂⁵	1	2	yes	—
396	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
397	C₂²×D₁₃	—	2	4	no	—
398	C₂²×D₁₃	—	2	8	no	—
399	C₂²×D₁₃	—	2	8	no	—
400	C₂²×D₁₃	—	2	8	no	—
401	C₂²×D₁₃	—	2	4	no	—
402	C₂²×D₁₃	—	2	4	no	—
403	C₂²×D₁₃	—	2	32	no	—
404	C₂²×D₁₃	—	4	16	no	—
405	C₂²×D₁₃	—	4	16	no	—
406	C₂²×D₁₃	—	8	32	no	—
407	C₂²×D₁₃	C₂⁵	1	4	yes	—
408	C₂²×D₁₃	C₂⁵	1	8	yes	—
409	D₄×C₁₃	—	2	16	no	—
410	D₄×C₁₃	—	2	8	no	—
411	D₄×C₁₃	C₂×#41	1	16	yes	complemented
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	4	no	—
416	C₂×C₄×C₁₃	—	2	4	no	—
417	C₂×C₄×C₁₃	—	2	8	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	8	no	—
420	C₂×C₄×C₁₃	—	2	16	no	—
421	C₂×C₄×C₁₃	—	2	16	no	—
422	C₂×C₄×C₁₃	—	2	8	no	—
423	C₂×C₄×C₁₃	—	4	8	no	—
424	C₂×C₄×C₁₃	—	4	8	no	—
425	C₂×C₄×C₁₃	—	4	8	no	—
426	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
427	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
428	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
429	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
430	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
431	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
432	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
433	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
434	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
435	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
436	C₂²⋊D₁₃	—	2	32	no	—
437	C₂²⋊D₁₃	—	2	32	no	—
438	C₂²⋊D₁₃	—	2	16	no	—
439	C₂²⋊D₁₃	—	4	16	no	—
440	C₂²⋊D₁₃	—	4	16	no	—
441	C₂²⋊D₁₃	—	4	16	no	—
442	C₂×Dic₁₃	—	2	4	no	—
443	C₂×Dic₁₃	—	2	4	no	—
444	C₂×Dic₁₃	—	2	8	no	—
445	C₂×Dic₁₃	—	2	4	no	—
446	C₂×Dic₁₃	—	4	16	no	—
447	C₂×Dic₁₃	C₂⁵	1	4	yes	—
448	C₂×Dic₁₃	C₂⁵	1	4	yes	—
449	C₂×Dic₁₃	C₂⁵	1	4	yes	—
450	C₂×Dic₁₃	C₂⁵	1	8	yes	—
451	D₅₂	—	2	16	no	—
452	D₅₂	—	2	8	no	—
453	D₅₂	—	2	16	no	—
454	D₅₂	—	4	16	no	—
455	D₅₂	—	4	8	no	—
456	C₄×D₁₃	—	2	16	no	—
457	C₄×D₁₃	—	4	16	no	—
458	C₄×D₁₃	—	4	16	no	—
459	Dic₂₆	—	2	8	no	—
460	Dic₂₆	—	4	8	no	—
461	C₂²×#41	—	13	2	no	—
462	C₂²×#41	—	13	2	no	—
463	C₂³×D₄	—	13	4	no	—
464	C₂³×D₄	—	13	2	no	—
465	C₂³×D₄	—	13	2	no	—
466	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
467	C₂⁴×C₄	C₂×D₁₃	1	2	yes	complemented
468	#555	—	13	16	no	—
469	#554	—	13	16	no	—
470	#553	—	13	32	no	—
471	#553	—	13	32	no	—
472	#550	—	13	16	no	—
473	#546	—	13	32	no	—
474	#546	—	13	64	no	—
475	D₄²	—	13	32	no	—
476	D₄²	—	13	16	no	—
477	#540	—	13	32	no	—
478	#538	—	13	64	no	—
479	#532	—	13	16	no	—
480	C₂×C₄⋊Q₈	—	13	1	no	—
481	C₂×#127	—	13	2	no	—
482	C₂×#127	—	13	1	no	—
483	#529	—	13	16	no	—
484	C₂×#126	—	13	4	no	—
485	C₂×#126	—	13	2	no	—
486	C₂×#125	—	13	2	no	—
487	C₂×#125	—	13	1	no	—
488	C₂×#124	—	13	4	no	—
489	C₂×#124	—	13	1	no	—
490	C₂×#124	—	13	2	no	—
491	#525	—	13	32	no	—
492	C₂×#123	—	13	4	no	—
493	C₂×#123	—	13	2	no	—
494	C₂×#123	—	13	4	no	—
495	C₂×#123	—	13	4	no	—
496	C₂×C₂²⋊Q₈	—	13	1	no	—
497	C₂×C₂²⋊Q₈	—	13	2	no	—
498	C₂×C₂²⋊Q₈	—	13	4	no	—
499	C₂×#121	—	13	2	no	—
500	C₂×#121	—	13	4	no	—
501	C₂×#121	—	13	1	no	—
502	C₂×#121	—	13	2	no	—
503	C₂×#121	—	13	4	no	—
504	C₂×#121	—	13	4	no	—
505	C₂×#121	—	13	2	no	—
506	C₂×#121	—	13	2	no	—
507	C₂×#121	—	13	2	no	—
508	C₂×#121	—	13	2	no	—
509	C₂×#121	—	13	32	no	—
510	C₂×#121	—	13	2	no	—
511	C₂×#121	—	13	4	no	—
512	C₂×#121	—	13	4	no	—
513	C₂×#120	—	13	4	no	—
514	C₂×#120	—	13	4	no	—
515	C₂×#120	—	13	4	no	—
516	#518	—	13	32	no	—
517	C₂×C₄×Q₈	—	13	1	no	—
518	C₂×C₄×D₄	—	13	2	no	—
519	C₂×C₄×D₄	—	13	4	no	—
520	C₂×C₄×D₄	—	13	4	no	—
521	C₂×C₄×D₄	—	13	2	no	—
522	C₂×C₄×D₄	—	13	2	no	—
523	C₂×C₄×D₄	—	13	4	no	—
524	C₂×C₄×D₄	—	13	2	no	—
525	C₂×C₄×D₄	—	13	1	no	—
526	C₂×C₄×D₄	—	13	2	no	—
527	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
528	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
529	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
530	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
531	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
532	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
533	C₂×C₄×D₄	C₂×D₁₃	1	16	yes	complemented
534	C₂×#117	—	13	2	no	—
535	C₂×#117	—	13	2	no	—
536	C₂×#117	—	13	2	no	—
537	C₂²×C₄⋊C₄	—	13	2	no	—
538	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
539	C₂²×C₂²⋊C₄	—	13	4	no	—
540	C₂²×C₂²⋊C₄	—	13	4	no	—
541	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
542	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
543	C₂²×C₁₃	—	2	2	no	—
544	C₂²×C₁₃	—	2	4	no	—
545	C₂²×C₁₃	—	2	2	no	—
546	C₂²×C₁₃	—	2	4	no	—
547	C₂²×C₁₃	—	2	16	no	—
548	C₂²×C₁₃	—	2	8	no	—
549	C₂²×C₁₃	—	2	4	no	—
550	C₂²×C₁₃	—	2	4	no	—
551	C₂²×C₁₃	—	2	4	no	—
552	C₂²×C₁₃	—	4	32	no	—
553	C₂²×C₁₃	—	4	8	no	—
554	C₂²×C₁₃	C₂²×#41	1	8	yes	—
555	C₂²×C₁₃	C₂²×#41	1	2	yes	—
556	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
557	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
558	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
559	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
560	C₂×D₁₃	—	2	4	no	—
561	C₂×D₁₃	—	2	8	no	—
562	C₂×D₁₃	—	2	8	no	—
563	C₂×D₁₃	—	2	8	no	—
564	C₂×D₁₃	—	2	4	no	—
565	C₂×D₁₃	—	2	4	no	—
566	C₂×D₁₃	—	4	16	no	—
567	C₂×D₁₃	—	4	8	no	—
568	C₂×D₁₃	—	8	32	no	—
569	C₄×C₁₃	—	2	2	no	—
570	C₄×C₁₃	—	2	2	no	—
571	C₄×C₁₃	—	2	2	no	—
572	C₄×C₁₃	—	2	4	no	—
573	C₄×C₁₃	—	2	4	no	—
574	C₄×C₁₃	—	2	2	no	—
575	C₄×C₁₃	C₂²×#41	1	4	yes	—
576	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
577	Dic₁₃	—	2	4	no	—
578	Dic₁₃	—	2	4	no	—
579	Dic₁₃	—	2	8	no	—
580	Dic₁₃	—	2	4	no	—
581	C₂⁵	—	13	4	no	—
582	C₂⁵	C₂²×D₁₃	1	2	yes	—
583	C₂×#41	—	13	16	no	—
584	C₂×#41	—	13	16	no	—
585	C₂×#41	—	52	8	no	—
586	C₂×#41	—	52	8	no	—
587	C₂²×Q₈	—	13	1	no	—
588	C₂²×Q₈	—	13	2	no	—
589	C₂²×D₄	—	2	8	no	—
590	C₂²×D₄	—	13	4	no	—
591	C₂²×D₄	—	13	4	no	—
592	C₂²×D₄	—	13	2	no	—
593	C₂²×D₄	—	13	4	no	—
594	C₂²×D₄	—	13	4	no	—
595	C₂²×D₄	—	13	4	no	—
596	C₂²×D₄	—	13	32	no	—
597	C₂²×D₄	—	13	16	no	—
598	C₂²×D₄	—	13	2	no	—
599	C₂²×D₄	—	13	1	no	—
600	C₂²×D₄	—	13	2	no	—
601	C₂²×D₄	—	13	2	no	—
602	C₂²×D₄	—	13	4	no	—
603	C₂²×D₄	—	13	16	no	—
604	C₂²×D₄	—	26	16	no	—
605	C₂²×D₄	—	52	8	no	—
606	C₂²×D₄	—	52	16	no	—
607	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
608	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
609	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
610	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
611	C₂³×C₄	—	4	8	no	—
612	C₂³×C₄	—	13	4	no	—
613	C₂³×C₄	—	13	2	no	—
614	C₂³×C₄	—	13	4	no	—
615	C₂³×C₄	—	13	4	no	—
616	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
617	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
618	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
619	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
620	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
621	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
622	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
623	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
624	C₂³×C₄	C₂²×D₁₃	1	16	yes	complemented
625	C₄⋊Q₈	—	13	8	no	—
626	#127	—	13	16	no	—
627	#127	—	13	8	no	—
628	#126	—	13	32	no	—
629	#126	—	13	16	no	—
630	#125	—	13	16	no	—
631	#125	—	13	8	no	—
632	#124	—	13	32	no	—
633	#124	—	13	8	no	—
634	#124	—	13	16	no	—
635	#123	—	13	32	no	—
636	#123	—	13	16	no	—
637	#123	—	13	32	no	—
638	#123	—	13	32	no	—
639	C₂²⋊Q₈	—	13	8	no	—
640	C₂²⋊Q₈	—	13	16	no	—
641	C₂²⋊Q₈	—	13	32	no	—
642	#121	—	13	32	no	—
643	#121	—	13	16	no	—
644	#121	—	13	8	no	—
645	#121	—	13	16	no	—
646	#121	—	13	32	no	—
647	#121	—	13	32	no	—
648	#121	—	13	16	no	—
649	#121	—	13	16	no	—
650	#121	—	13	16	no	—
651	#121	—	13	16	no	—
652	#121	—	13	16	no	—
653	#121	—	13	32	no	—
654	#121	—	13	32	no	—
655	#120	—	13	32	no	—
656	#120	—	13	32	no	—
657	#120	—	13	32	no	—
658	C₄×Q₈	—	13	8	no	—
659	C₄×D₄	—	13	16	no	—
660	C₄×D₄	—	13	32	no	—
661	C₄×D₄	—	13	32	no	—
662	C₄×D₄	—	13	16	no	—
663	C₄×D₄	—	13	16	no	—
664	C₄×D₄	—	13	32	no	—
665	C₄×D₄	—	13	16	no	—
666	C₄×D₄	—	13	8	no	—
667	C₄×D₄	—	13	16	no	—
668	C₄×D₄	C₂²×D₁₃	1	8	yes	—
669	C₄×D₄	C₂²×D₁₃	1	8	yes	—
670	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
671	C₄×D₄	C₂²×D₁₃	1	8	yes	complemented
672	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
673	C₄×D₄	C₂²×D₁₃	1	8	yes	complemented
674	#117	—	13	16	no	—
675	#117	—	13	16	no	—
676	#117	—	13	16	no	—
677	C₂×C₄⋊C₄	—	13	1	no	—
678	C₂×C₄⋊C₄	—	13	2	no	—
679	C₂×C₄⋊C₄	—	13	4	no	—
680	C₂×C₄⋊C₄	—	13	16	no	—
681	C₂×C₄⋊C₄	—	13	1	no	—
682	C₂×C₄⋊C₄	—	13	2	no	—
683	C₂×C₄⋊C₄	—	13	2	no	—
684	C₂×C₄⋊C₄	—	13	2	no	—
685	C₂×C₄⋊C₄	—	13	2	no	—
686	C₂×C₄⋊C₄	—	13	4	no	—
687	C₂×C₄⋊C₄	—	13	2	no	—
688	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
691	C₂×C₄⋊C₄	C₂²×D₁₃	1	8	yes	complemented
692	C₂×C₂²⋊C₄	—	13	4	no	—
693	C₂×C₂²⋊C₄	—	13	4	no	—
694	C₂×C₂²⋊C₄	—	13	2	no	—
695	C₂×C₂²⋊C₄	—	13	2	no	—
696	C₂×C₂²⋊C₄	—	13	4	no	—
697	C₂×C₂²⋊C₄	—	13	2	no	—
698	C₂×C₂²⋊C₄	—	13	4	no	—
699	C₂×C₂²⋊C₄	—	13	4	no	—
700	C₂×C₂²⋊C₄	—	13	32	no	—
701	C₂×C₂²⋊C₄	—	13	2	no	—
702	C₂×C₂²⋊C₄	—	13	2	no	—
703	C₂×C₂²⋊C₄	—	13	4	no	—
704	C₂×C₂²⋊C₄	—	13	4	no	—
705	C₂×C₂²⋊C₄	—	13	32	no	—
706	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂²×D₁₃	1	16	yes	complemented
711	C₂×C₄²	—	13	4	no	—
712	C₂×C₄²	—	13	2	no	—
713	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
714	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
715	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
716	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
717	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
718	C₂×C₁₃	—	2	8	no	—
719	C₂×C₁₃	—	2	4	no	—
720	C₂×C₁₃	—	4	4	no	—
721	C₂×C₁₃	#3519	1	4	yes	complemented
722	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
723	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
724	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
725	D₁₃	—	4	8	no	—
726	D₁₃	—	4	4	no	—
727	C₂⁴	—	2	8	no	—
728	C₂⁴	—	2	8	no	—
729	C₂⁴	—	4	4	no	—
730	C₂⁴	—	13	2	no	—
731	C₂⁴	—	13	4	no	—
732	C₂⁴	—	13	16	no	—
733	C₂⁴	—	26	16	no	—
734	C₂⁴	—	52	8	no	—
735	C₂⁴	—	52	8	no	—
736	C₂⁴	C₂³×D₁₃	1	2	yes	—
737	C₂⁴	C₂³×D₁₃	1	8	yes	—
738	C₂⁴	C₂³×D₁₃	1	2	yes	—
739	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
740	#41	—	52	32	no	—
741	#41	—	52	32	no	—
742	C₂×Q₈	—	13	4	no	—
743	C₂×Q₈	—	13	8	no	—
744	C₂×Q₈	—	26	4	no	—
745	C₂×Q₈	—	52	4	no	—
746	C₂×D₄	—	2	8	no	—
747	C₂×D₄	—	2	32	no	—
748	C₂×D₄	—	2	4	no	—
749	C₂×D₄	—	13	16	no	—
750	C₂×D₄	—	13	16	no	—
751	C₂×D₄	—	13	8	no	—
752	C₂×D₄	—	13	16	no	—
753	C₂×D₄	—	13	16	no	—
754	C₂×D₄	—	13	16	no	—
755	C₂×D₄	—	13	8	no	—
756	C₂×D₄	—	13	4	no	—
757	C₂×D₄	—	13	8	no	—
758	C₂×D₄	—	13	8	no	—
759	C₂×D₄	—	13	16	no	—
760	C₂×D₄	—	26	16	no	—
761	C₂×D₄	—	26	8	no	—
762	C₂×D₄	—	26	16	no	—
763	C₂×D₄	—	26	64	no	—
764	C₂×D₄	—	26	8	no	—
765	C₂×D₄	—	26	4	no	—
766	C₂×D₄	—	26	8	no	—
767	C₂×D₄	—	52	32	no	—
768	C₂×D₄	—	52	8	no	—
769	C₂×D₄	—	52	4	no	—
770	C₂×D₄	—	52	8	no	—
771	C₂×D₄	—	52	8	no	—
772	C₂×D₄	—	52	8	no	—
773	C₂×D₄	—	52	64	no	—
774	C₂×D₄	#6127	1	8	yes	complemented
775	C₂×D₄	C₂³×D₁₃	1	8	yes	—
776	C₂×D₄	C₂³×D₁₃	1	4	yes	—
777	C₂×D₄	C₂³×D₁₃	1	4	yes	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	8	no	—
782	C₂²×C₄	—	2	8	no	—
783	C₂²×C₄	—	4	32	no	—
784	C₂²×C₄	—	4	4	no	—
785	C₂²×C₄	—	4	4	no	—
786	C₂²×C₄	—	4	4	no	—
787	C₂²×C₄	—	13	2	no	—
788	C₂²×C₄	—	13	2	no	—
789	C₂²×C₄	—	13	4	no	—
790	C₂²×C₄	—	13	2	no	—
791	C₂²×C₄	—	13	16	no	—
792	C₂²×C₄	—	13	8	no	—
793	C₂²×C₄	—	13	16	no	—
794	C₂²×C₄	—	13	16	no	—
795	C₂²×C₄	—	26	8	no	—
796	C₂²×C₄	—	52	8	no	—
797	C₂²×C₄	—	52	8	no	—
798	C₂²×C₄	—	52	8	no	—
799	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
800	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
801	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
802	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
803	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
804	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
805	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
806	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
807	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
808	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
809	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
810	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
811	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
812	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
813	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
814	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
815	C₄⋊C₄	—	13	4	no	—
816	C₄⋊C₄	—	13	8	no	—
817	C₄⋊C₄	—	13	16	no	—
818	C₄⋊C₄	—	13	4	no	—
819	C₄⋊C₄	—	13	8	no	—
820	C₄⋊C₄	—	13	8	no	—
821	C₄⋊C₄	—	13	8	no	—
822	C₄⋊C₄	—	13	8	no	—
823	C₄⋊C₄	—	13	16	no	—
824	C₄⋊C₄	—	13	8	no	—
825	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
826	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
827	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
828	C₂²⋊C₄	—	13	16	no	—
829	C₂²⋊C₄	—	13	16	no	—
830	C₂²⋊C₄	—	13	8	no	—
831	C₂²⋊C₄	—	13	8	no	—
832	C₂²⋊C₄	—	13	16	no	—
833	C₂²⋊C₄	—	13	8	no	—
834	C₂²⋊C₄	—	13	16	no	—
835	C₂²⋊C₄	—	13	16	no	—
836	C₂²⋊C₄	—	13	8	no	—
837	C₂²⋊C₄	—	13	8	no	—
838	C₂²⋊C₄	—	13	16	no	—
839	C₂²⋊C₄	—	13	16	no	—
840	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
841	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
842	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
843	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
844	C₄²	—	13	16	no	—
845	C₄²	—	13	8	no	—
846	C₄²	C₂³×D₁₃	1	4	yes	—
847	C₄²	C₂³×D₁₃	1	4	yes	—
848	C₄²	C₂³×D₁₃	1	4	yes	—
849	C₄²	C₂³×D₁₃	1	4	yes	—
850	C₁₃	C₂×#3519	1	1	yes	characteristic, complemented, Sylow
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	4	no	—
854	C₂³	—	2	4	no	—
855	C₂³	—	2	16	no	—
856	C₂³	—	2	4	no	—
857	C₂³	—	2	4	no	—
858	C₂³	—	2	16	no	—
859	C₂³	—	2	4	no	—
860	C₂³	—	4	8	no	—
861	C₂³	—	4	32	no	—
862	C₂³	—	13	4	no	—
863	C₂³	—	13	8	no	—
864	C₂³	—	26	4	no	—
865	C₂³	—	26	8	no	—
866	C₂³	—	26	8	no	—
867	C₂³	—	26	4	no	—
868	C₂³	—	26	8	no	—
869	C₂³	—	26	4	no	—
870	C₂³	—	26	32	no	—
871	C₂³	—	52	16	no	—
872	C₂³	—	52	16	no	—
873	C₂³	—	104	32	no	—
874	C₂³	C₂×#6127	1	8	yes	—
875	C₂³	#88256	1	4	yes	—
876	C₂³	C₂⁴×D₁₃	1	4	yes	—
877	C₂³	C₂⁴×D₁₃	1	4	yes	—
878	C₂³	C₂⁴×D₁₃	1	2	yes	—
879	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
880	Q₈	—	26	8	no	—
881	Q₈	—	52	8	no	—
882	D₄	—	2	16	no	—
883	D₄	—	2	8	no	—
884	D₄	—	26	32	no	—
885	D₄	—	26	16	no	—
886	D₄	—	26	32	no	—
887	D₄	—	26	16	no	—
888	D₄	—	26	8	no	—
889	D₄	—	26	16	no	—
890	D₄	—	52	16	no	—
891	D₄	—	52	8	no	—
892	D₄	—	52	16	no	—
893	D₄	—	52	16	no	—
894	D₄	—	52	16	no	—
895	D₄	C₂×#6127	1	16	yes	complemented
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	4	no	—
899	C₂×C₄	—	2	4	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	8	no	—
903	C₂×C₄	—	2	8	no	—
904	C₂×C₄	—	2	8	no	—
905	C₂×C₄	—	2	16	no	—
906	C₂×C₄	—	2	16	no	—
907	C₂×C₄	—	4	8	no	—
908	C₂×C₄	—	4	8	no	—
909	C₂×C₄	—	4	8	no	—
910	C₂×C₄	—	13	4	no	—
911	C₂×C₄	—	13	4	no	—
912	C₂×C₄	—	13	8	no	—
913	C₂×C₄	—	13	4	no	—
914	C₂×C₄	—	26	4	no	—
915	C₂×C₄	—	26	4	no	—
916	C₂×C₄	—	26	4	no	—
917	C₂×C₄	—	26	8	no	—
918	C₂×C₄	—	26	16	no	—
919	C₂×C₄	—	52	16	no	—
920	C₂×C₄	—	52	16	no	—
921	C₂×C₄	—	52	16	no	—
922	C₂×C₄	C₂×#6127	1	4	yes	—
923	C₂×C₄	#88251	1	4	yes	—
924	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
925	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
926	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
927	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
928	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
929	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
930	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
931	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	8	no	—
934	C₂²	—	2	16	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	4	no	—
940	C₂²	—	2	4	no	—
941	C₂²	—	4	32	no	—
942	C₂²	—	4	8	no	—
943	C₂²	—	26	4	no	—
944	C₂²	—	26	8	no	—
945	C₂²	—	26	8	no	—
946	C₂²	—	26	4	no	—
947	C₂²	—	26	8	no	—
948	C₂²	—	26	4	no	—
949	C₂²	—	52	16	no	—
950	C₂²	—	52	8	no	—
951	C₂²	—	104	32	no	—
952	C₂²	C₂²×#6127	1	8	yes	—
953	C₂²	C₂²×#6127	1	2	yes	—
954	C₂²	C₂×#88251	1	2	yes	—
955	C₂²	C₂×#88256	1	4	yes	—
956	C₂²	C₂×#88256	1	2	yes	—
957	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	4	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	26	4	no	—
965	C₄	—	26	4	no	—
966	C₄	—	26	4	no	—
967	C₄	—	26	8	no	—
968	C₄	C₂²×#6127	1	4	yes	—
969	C₄	C₂×#88251	1	4	yes	—
970	C₂	—	2	4	no	—
971	C₂	—	2	8	no	—
972	C₂	—	4	4	no	—
973	C₂	—	52	4	no	—
974	C₂	—	52	8	no	—
975	C₂	#13128868	1	4	yes	direct product factor
976	C₂	C₂³×#6127	1	1	yes	characteristic
977	C₂	C₂²×#88251	1	1	yes	characteristic
978	C₂	C₂²×#88256	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×#3519
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. #13128868	C₂	direct (N × H)
2. C₂×#11719268	C₂	semidirect
3. C₂×#11719248	C₂	semidirect
4. C₂×#11719219	C₂	semidirect
5. C₂×#11719270	C₂	semidirect
6. C₂×#11719258	C₂	semidirect
7. C₂×#11719255	C₂	semidirect
8. C₂×#11719195	C₂	semidirect
9. C₂×D₄×D₅₂	C₂	semidirect
10. C₂×D₄×C₂²⋊D₁₃	C₂	semidirect
11. C₂×#11719267	C₂	semidirect
12. C₂×#11719265	C₂	semidirect
13. C₂×#11719182	C₂	semidirect
14. C₂×#11719184	C₂	semidirect
15. C₂×#11719496	C₂	semidirect
16. C₂²×#88184	C₂	semidirect
17. C₂×#11719250	C₂	semidirect
18. C₂²×C₄×D₄×C₁₃	C₂	semidirect
20. C₂⁴×C₄×C₁₃	C₂²	semidirect
21. C₂³×C₂²⋊D₁₃	C₂²	semidirect
23. C₂²×#6127	C₂²	semidirect
24. C₂²×#6127	C₂²	semidirect
25. C₂³×D₅₂	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
34. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
35. C₂²×C₄²×C₁₃	C₂²	semidirect
36. C₂×#88207	C₂²	semidirect
37. C₂×#88194	C₂²	semidirect
38. C₂×#88193	C₂²	semidirect
39. D₄×C₂²⋊D₁₃	C₂²	semidirect
40. C₂×#88192	C₂²	semidirect
41. C₂×#88191	C₂²	semidirect
43. #11719496	C₂²	semidirect
45. C₂×#88184	C₂²	semidirect
46. C₂×#88184	C₂²	semidirect
47. C₂×#88184	C₂²	semidirect
48. C₂×#88184	C₂²	semidirect
49. C₂×#88184	C₂²	semidirect
50. C₂×#88184	C₂²	semidirect
51. C₂×#88184	C₂²	semidirect
52. C₂×#88184	C₂²	semidirect
53. C₂×#88183	C₂²	semidirect
54. C₂×#88183	C₂²	semidirect
55. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
56. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
57. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
58. C₂²×#6103	C₂²	semidirect
59. C₂×#88180	C₂²	semidirect
60. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
61. C₂×#88178	C₂²	semidirect
62. C₂×#88178	C₂²	semidirect
63. #11719270	C₂²	semidirect
64. #11719268	C₂²	semidirect
65. #11719267	C₂²	semidirect
66. #11719265	C₂²	semidirect
67. #11719258	C₂²	semidirect
68. #11719255	C₂²	semidirect
69. D₄×D₅₂	C₂²	semidirect
70. #11719250	C₂²	semidirect
71. #11719248	C₂²	semidirect
72. #11719219	C₂²	semidirect
73. C₂×#88152	C₂²	semidirect
74. C₂×#88149	C₂²	semidirect
75. C₂×#88148	C₂²	semidirect
76. C₂×#88147	C₂²	semidirect
77. C₂×#88146	C₂²	semidirect
78. C₂×#88144	C₂²	semidirect
79. C₂×#88139	C₂²	semidirect
80. #11719195	C₂²	semidirect
81. C₂×#88138	C₂²	semidirect
82. C₂×#88138	C₂²	semidirect
83. C₂×#88137	C₂²	semidirect
84. C₂×#88136	C₂²	semidirect
85. C₂×#88135	C₂²	semidirect
86. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
87. C₂×#88132	C₂²	semidirect
88. #11719184	C₂²	semidirect
89. C₂×#88130	C₂²	semidirect
90. #11719182	C₂²	semidirect
91. C₂×#88129	C₂²	semidirect
92. C₂×#88129	C₂²	semidirect
93. C₂×#88128	C₂²	semidirect
94. C₂×C₄×D₅₂	C₂²	semidirect
95. C₂×C₄×D₅₂	C₂²	semidirect
96. C₂×C₄×D₅₂	C₂²	semidirect
97. C₂×#88126	C₂²	semidirect
98. C₂×#88124	C₂²	semidirect
99. C₂×#88123	C₂²	semidirect
100. C₂×C₄×Dic₂₆	C₂²	semidirect
117. C₂³×C₄×C₁₃	C₂³	semidirect
125. C₂²×C₂²⋊D₁₃	C₂³	semidirect
131. C₂×#6127	C₂³	semidirect
132. C₂×#6127	C₂³	semidirect
139. C₂²×D₅₂	C₂³	semidirect
147. C₄×D₄×C₁₃	C₂³	semidirect
148. C₄×D₄×C₁₃	C₂³	semidirect
149. C₄×D₄×C₁₃	C₂³	semidirect
150. C₄×D₄×C₁₃	C₂³	semidirect
154. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
159. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
164. C₂×C₄²×C₁₃	C₂³	semidirect
165. #88207	C₂³	semidirect
169. #88194	C₂³	semidirect
170. #88193	C₂³	semidirect
171. #88192	C₂³	semidirect
172. #88191	C₂³	semidirect
175. #88184	C₂³	semidirect
176. #88184	C₂³	semidirect
177. #88184	C₂³	semidirect
178. #88184	C₂³	semidirect
179. #88184	C₂³	semidirect
180. #88184	C₂³	semidirect
181. #88184	C₂³	semidirect
182. #88183	C₂³	semidirect
183. #88183	C₂³	semidirect
184. C₄×C₂²⋊D₁₃	C₂³	semidirect
185. C₄×C₂²⋊D₁₃	C₂³	semidirect
186. C₄×C₂²⋊D₁₃	C₂³	semidirect
196. C₂×#6103	C₂³	semidirect
197. #88180	C₂³	semidirect
203. C₂×C₄⋊Dic₁₃	C₂³	semidirect
204. #88178	C₂³	semidirect
205. #88178	C₂³	semidirect
213. #88152	C₂³	semidirect
214. #88149	C₂³	semidirect
215. #88148	C₂³	semidirect
216. #88147	C₂³	semidirect
217. #88146	C₂³	semidirect
218. #88144	C₂³	semidirect
219. #88139	C₂³	semidirect
220. #88138	C₂³	semidirect
221. #88138	C₂³	semidirect
222. #88137	C₂³	semidirect
223. #88136	C₂³	semidirect
224. #88135	C₂³	semidirect
225. C₂²⋊C₄×D₁₃	C₂³	semidirect
226. #88132	C₂³	semidirect
227. #88130	C₂³	semidirect
228. #88129	C₂³	semidirect
229. #88129	C₂³	semidirect
230. #88128	C₂³	semidirect
231. C₄×D₅₂	C₂³	semidirect
232. C₄×D₅₂	C₂³	semidirect
233. C₄×D₅₂	C₂³	semidirect
234. #88126	C₂³	semidirect
235. #88124	C₂³	semidirect
236. #88123	C₂³	semidirect
237. C₄×Dic₂₆	C₂³	semidirect
255. C₂×D₄×C₁₃	#41	semidirect
379. C₂²×C₄×D₄	D₁₃	semidirect
411. D₄×C₁₃	C₂×#41	semidirect
467. C₂⁴×C₄	C₂×D₁₃	semidirect
529. C₂×C₄×D₄	C₂×D₁₃	semidirect
530. C₂×C₄×D₄	C₂×D₁₃	semidirect
531. C₂×C₄×D₄	C₂×D₁₃	semidirect
532. C₂×C₄×D₄	C₂×D₁₃	semidirect
533. C₂×C₄×D₄	C₂×D₁₃	semidirect
538. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
541. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
542. C₂²×C₄²	C₂×D₁₃	semidirect
624. C₂³×C₄	C₂²×D₁₃	semidirect
670. C₄×D₄	C₂²×D₁₃	semidirect
671. C₄×D₄	C₂²×D₁₃	semidirect
672. C₄×D₄	C₂²×D₁₃	semidirect
673. C₄×D₄	C₂²×D₁₃	semidirect
691. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
710. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
717. C₂×C₄²	C₂²×D₁₃	semidirect
721. C₂×C₁₃	#3519	semidirect
774. C₂×D₄	#6127	semidirect
850. C₁₃	C₂×#3519	semidirect
895. D₄	C₂×#6127	semidirect
975. C₂	#13128868	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128868	2
C₂×#11719268	2
C₂×#11719248	2
C₂×#11719219	2
C₂×#11719270	2
C₂×#11719258	2
C₂×#11719255	2
C₂×#11719195	2
C₂×D₄×D₅₂	2
C₂×D₄×C₂²⋊D₁₃	2
C₂×#11719267	2
C₂×#11719265	2
C₂×#11719182	2
C₂×#11719184	2
C₂×#11719496	2
C₂²×#88184	2
C₂×#11719250	2
C₂²×C₄×D₄×C₁₃	2
C₂×#3519	13

Subgroups — C2×#13128868 #16770914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128868 #16770914