Subgroups — C₂×#13128799 #16771016

Order 3328.

8006 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128799	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719290	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719247	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11719268	C₂	1	2	yes	maximal, complemented
5	C₂×#11719410	C₂	1	4	yes	maximal, complemented
6	C₂×Q₈×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11719338	C₂	1	2	yes	maximal, complemented
8	C₂×#11719317	C₂	1	2	yes	maximal, complemented
9	C₂×#11719255	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11719239	C₂	1	2	yes	maximal, complemented
12	C₂×#11719362	C₂	1	4	yes	maximal, complemented
13	C₂×#11719182	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11719396	C₂	1	2	yes	maximal, complemented
15	C₂×D₁₃×#124	C₂	1	2	yes	maximal, complemented
16	C₂×#11719226	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×#6127	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×Q₈×D₁₃	C₂²	1	2	yes	complemented
20	C₂²×D₄×D₁₃	C₂²	1	2	yes	—
21	C₂²×#6127	C₂²	1	1	yes	characteristic
22	C₂²×#6127	C₂²	1	2	yes	complemented
23	C₂³×D₅₂	C₂²	1	2	yes	—
24	C₁₃×#529	C₂²	1	16	yes	complemented
25	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#88201	C₂²	1	2	yes	complemented
37	C₂×#88192	C₂²	1	4	yes	complemented
38	C₂×#88191	C₂²	1	4	yes	complemented
39	C₂×#88190	C₂²	1	2	yes	—
40	C₂×#88184	C₂²	1	2	yes	—
41	C₂×#88184	C₂²	1	2	yes	complemented
42	C₂×#88184	C₂²	1	2	yes	complemented
43	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
44	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
45	C₂×#88180	C₂²	1	1	yes	characteristic, complemented
46	C₂×#88180	C₂²	1	2	yes	complemented
47	C₂×#88178	C₂²	1	2	yes	complemented
48	#11719410	C₂²	1	64	yes	complemented
49	#11719396	C₂²	1	32	yes	complemented
50	D₁₃×#124	C₂²	1	32	yes	complemented
51	#11719362	C₂²	1	64	yes	complemented
52	#11719338	C₂²	1	32	yes	complemented
53	#11719317	C₂²	1	32	yes	complemented
54	#11719290	C₂²	1	16	yes	complemented
55	Q₈×D₅₂	C₂²	1	16	yes	complemented
56	#11719268	C₂²	1	32	yes	complemented
57	#11719255	C₂²	1	32	yes	complemented
58	D₄×D₅₂	C₂²	1	16	yes	complemented
59	#11719247	C₂²	1	16	yes	complemented
60	#11719239	C₂²	1	32	yes	complemented
61	#11719226	C₂²	1	32	yes	complemented
62	C₂×#88152	C₂²	1	4	yes	complemented
63	C₂×#88151	C₂²	1	2	yes	complemented
64	C₂×#88151	C₂²	1	4	yes	complemented
65	C₂×#88150	C₂²	1	4	yes	complemented
66	C₂×#88149	C₂²	1	2	yes	—
67	C₂×#88148	C₂²	1	4	yes	complemented
68	C₂×#88148	C₂²	1	4	yes	complemented
69	C₂×#88147	C₂²	1	4	yes	complemented
70	C₂×#88147	C₂²	1	4	yes	complemented
71	C₂×#88147	C₂²	1	2	yes	complemented
72	C₂×#88146	C₂²	1	4	yes	complemented
73	C₂×#88141	C₂²	1	2	yes	complemented
74	C₂×#88139	C₂²	1	4	yes	complemented
75	C₂×#88139	C₂²	1	4	yes	complemented
76	C₂×#88139	C₂²	1	4	yes	complemented
77	C₂×#88138	C₂²	1	4	yes	complemented
78	C₂×#88137	C₂²	1	4	yes	complemented
79	C₂×#88136	C₂²	1	4	yes	—
80	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
81	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
82	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
83	C₂×#88133	C₂²	1	4	yes	complemented
84	#11719182	C₂²	1	16	yes	complemented
85	C₂×#88129	C₂²	1	2	yes	complemented
86	C₂×#88129	C₂²	1	2	yes	complemented
87	C₂×#88128	C₂²	1	1	yes	characteristic
88	C₄×#6127	C₂²	1	16	yes	complemented
89	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
90	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
91	C₂×C₄×D₅₂	C₂²	1	2	yes	—
92	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
93	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
94	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
95	C₂×#88126	C₂²	1	2	yes	complemented
96	C₂×C₄²×D₁₃	C₂²	1	2	yes	complemented
97	C₂×#88123	C₂²	1	2	yes	complemented
98	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
101	C₂⁴×D₁₃	C₂³	1	4	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
110	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
111	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
112	C₂×Q₈×D₁₃	—	4	8	no	—
113	C₂×Q₈×D₁₃	C₂³	1	16	yes	complemented
114	C₂×D₄×D₁₃	—	4	8	no	—
115	C₂×D₄×D₁₃	C₂³	1	16	yes	—
116	C₂×#6127	—	2	8	no	—
117	C₂×#6127	—	4	8	no	—
118	C₂×#6127	C₂³	1	8	yes	—
119	C₂×#6127	C₂³	1	16	yes	complemented
120	C₂²×D₅₂	—	2	16	no	—
121	C₂²×D₅₂	C₂³	1	2	yes	—
122	C₂²×D₅₂	C₂³	1	2	yes	—
123	C₂²×D₅₂	C₂³	1	4	yes	—
124	C₂²×D₅₂	C₂³	1	16	yes	—
125	C₂²×D₅₂	C₂³	1	2	yes	—
126	C₂²×D₅₂	C₂³	1	1	yes	characteristic
127	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
128	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
129	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
130	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
131	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
132	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
133	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
134	C₂²×Dic₂₆	C₂³	1	2	yes	—
135	C₂²×Dic₂₆	C₂³	1	4	yes	—
136	C₁₃×#126	C₂³	1	16	yes	complemented
137	C₁₃×#125	C₂³	1	8	yes	complemented
138	C₁₃×#124	C₂³	1	8	yes	—
139	C₁₃×#123	C₂³	1	16	yes	complemented
140	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
141	C₁₃×#121	C₂³	1	8	yes	—
142	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
143	C₄×D₄×C₁₃	C₂³	1	8	yes	—
144	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
145	C₁₃×#117	C₂³	1	16	yes	complemented
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
163	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
164	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
165	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
166	#88201	C₂³	1	16	yes	complemented
167	#88192	C₂³	1	32	yes	complemented
168	#88191	C₂³	1	32	yes	complemented
169	#88190	C₂³	1	16	yes	—
170	#88184	C₂³	1	16	yes	—
171	#88184	C₂³	1	16	yes	complemented
172	#88184	C₂³	1	16	yes	complemented
173	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	complemented
174	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	complemented
175	C₂×#6103	C₂³	1	2	yes	—
176	C₂×#6103	C₂³	1	2	yes	—
177	C₂×#6103	C₂³	1	4	yes	—
178	C₂×#6103	C₂³	1	4	yes	—
179	C₂×#6103	C₂³	1	4	yes	—
180	C₂×#6103	C₂³	1	4	yes	—
181	C₂×#6103	C₂³	1	4	yes	—
182	C₂×#6103	C₂³	1	4	yes	—
183	C₂×#6103	C₂³	1	4	yes	—
184	#88180	C₂³	1	8	yes	complemented
185	#88180	C₂³	1	16	yes	complemented
186	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
190	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
191	#88178	C₂³	1	16	yes	complemented
192	C₂×#6101	C₂³	1	2	yes	—
193	C₂×#6101	C₂³	1	2	yes	—
194	C₂×#6101	C₂³	1	4	yes	—
195	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
196	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
197	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
198	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
199	#88152	C₂³	1	32	yes	complemented
200	#88151	C₂³	1	16	yes	complemented
201	#88151	C₂³	1	32	yes	complemented
202	#88150	C₂³	1	32	yes	complemented
203	#88149	C₂³	1	16	yes	—
204	#88148	C₂³	1	32	yes	complemented
205	#88148	C₂³	1	32	yes	complemented
206	#88147	C₂³	1	32	yes	complemented
207	#88147	C₂³	1	32	yes	complemented
208	#88147	C₂³	1	16	yes	complemented
209	#88146	C₂³	1	32	yes	complemented
210	#88141	C₂³	1	16	yes	complemented
211	#88139	C₂³	1	32	yes	complemented
212	#88139	C₂³	1	32	yes	complemented
213	#88139	C₂³	1	32	yes	complemented
214	#88138	C₂³	1	32	yes	complemented
215	#88137	C₂³	1	32	yes	complemented
216	#88136	C₂³	1	32	yes	—
217	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
218	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
219	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
220	#88133	C₂³	1	32	yes	complemented
221	#88129	C₂³	1	16	yes	complemented
222	#88129	C₂³	1	16	yes	complemented
223	#88128	C₂³	1	8	yes	—
224	C₄×D₅₂	C₂³	1	8	yes	—
225	C₄×D₅₂	C₂³	1	8	yes	—
226	C₄×D₅₂	C₂³	1	16	yes	—
227	C₄×D₅₂	C₂³	1	16	yes	complemented
228	C₄×D₅₂	C₂³	1	16	yes	complemented
229	C₄×D₅₂	C₂³	1	16	yes	complemented
230	#88126	C₂³	1	16	yes	complemented
231	C₄²×D₁₃	C₂³	1	16	yes	complemented
232	#88123	C₂³	1	8	yes	complemented
233	#88123	C₂³	1	16	yes	complemented
234	C₄×Dic₂₆	C₂³	1	8	yes	complemented
235	C₄×Dic₂₆	C₂³	1	8	yes	complemented
236	C₂×#3514	—	13	1	no	maximal, Sylow
237	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
238	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂³×D₁₃	—	2	16	no	—
240	C₂³×D₁₃	—	4	8	no	—
241	C₂³×D₁₃	—	4	8	no	—
242	C₂³×D₁₃	C₂⁴	1	4	yes	—
243	C₂³×D₁₃	C₂⁴	1	2	yes	—
244	C₂³×D₁₃	C₂⁴	1	16	yes	—
245	C₂×Q₈×C₁₃	—	2	4	no	—
246	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	4	4	no	—
249	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
251	C₂²×C₄×C₁₃	—	2	8	no	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	—	2	4	no	—
254	C₂²×C₄×C₁₃	—	4	2	no	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×C₂²⋊D₁₃	—	2	8	no	—
269	C₂×C₂²⋊D₁₃	—	4	8	no	—
270	C₂×C₂²⋊D₁₃	—	4	8	no	—
271	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
272	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
273	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
274	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
275	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
276	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
277	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
278	Q₈×D₁₃	—	4	32	no	—
279	D₄×D₁₃	—	4	32	no	—
280	#6127	—	2	32	no	—
281	#6127	—	4	32	no	—
282	C₂×D₅₂	—	2	16	no	—
283	C₂×D₅₂	—	2	8	no	—
284	C₂×D₅₂	—	2	8	no	—
285	C₂×D₅₂	—	2	64	no	—
286	C₂×D₅₂	—	4	4	no	—
287	C₂×D₅₂	#41	1	8	yes	complemented
288	C₂×D₅₂	C₂⁴	1	8	yes	—
289	C₂×D₅₂	C₂⁴	1	8	yes	—
290	C₂×D₅₂	C₂⁴	1	16	yes	—
291	C₂×D₅₂	C₂⁴	1	8	yes	—
292	C₂×D₅₂	C₂⁴	1	4	yes	—
293	C₂×C₄×D₁₃	—	2	8	no	—
294	C₂×C₄×D₁₃	—	2	8	no	—
295	C₂×C₄×D₁₃	—	4	4	no	—
296	C₂×C₄×D₁₃	—	4	8	no	—
297	C₂×C₄×D₁₃	—	4	8	no	—
298	C₂×C₄×D₁₃	—	4	8	no	—
299	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
300	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
301	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
302	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
303	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
304	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
305	C₂×Dic₂₆	—	2	4	no	—
306	C₂×Dic₂₆	—	2	8	no	—
307	C₂×Dic₂₆	—	4	8	no	—
308	C₂×Dic₂₆	C₂⁴	1	4	yes	—
309	C₂×Dic₂₆	C₂⁴	1	8	yes	—
310	C₂×Dic₂₆	C₂⁴	1	16	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
317	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
318	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
319	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
320	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
321	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
322	C₄²×C₁₃	C₂⁴	1	4	yes	—
323	C₄²×C₁₃	C₂⁴	1	4	yes	—
324	C₄²×C₁₃	C₂⁴	1	8	yes	—
325	C₄²×C₁₃	C₂⁴	1	4	yes	—
326	C₄²×C₁₃	C₂⁴	1	4	yes	—
327	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
328	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
329	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
330	#6103	C₂⁴	1	8	yes	—
331	#6103	C₂⁴	1	8	yes	—
332	#6103	C₂⁴	1	16	yes	—
333	#6103	C₂⁴	1	16	yes	—
334	#6103	C₂⁴	1	16	yes	—
335	#6103	C₂⁴	1	16	yes	—
336	#6103	C₂⁴	1	16	yes	—
337	#6103	C₂⁴	1	16	yes	—
338	#6103	C₂⁴	1	16	yes	—
339	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
340	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
341	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
342	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
343	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
344	#6101	C₂⁴	1	8	yes	—
345	#6101	C₂⁴	1	8	yes	—
346	#6101	C₂⁴	1	16	yes	—
347	C₄×Dic₁₃	C₂⁴	1	8	yes	—
348	C₄×Dic₁₃	C₂⁴	1	8	yes	—
349	C₄×Dic₁₃	C₂⁴	1	8	yes	—
350	C₄×Dic₁₃	C₂⁴	1	16	yes	—
351	#3514	—	13	32	no	—
352	C₂×#559	—	13	1	no	—
353	C₂×#556	—	13	1	no	—
354	C₂×#555	—	13	2	no	—
355	C₂×#551	—	13	4	no	—
356	C₂×D₄×Q₈	—	13	1	no	—
357	C₂×#548	—	13	2	no	—
358	C₂×#546	—	13	2	no	—
359	C₂×#546	—	13	2	no	—
360	C₂×D₄²	—	13	1	no	—
361	C₂×#542	—	13	2	no	—
362	C₂×#538	—	13	4	no	—
363	C₂×#532	—	13	1	no	—
364	C₂×#529	—	13	2	no	—
365	C₂×#529	D₁₃	1	1	yes	characteristic, complemented
366	C₂²×#124	—	13	2	no	—
367	C₂×#518	—	13	2	no	—
368	C₂×C₄×#41	—	13	1	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	4	no	—
371	C₂³×C₁₃	—	2	2	no	—
372	C₂³×C₁₃	—	2	4	no	—
373	C₂³×C₁₃	—	2	2	no	—
374	C₂³×C₁₃	—	2	4	no	—
375	C₂³×C₁₃	C₂⁵	1	4	yes	—
376	C₂³×C₁₃	C₂⁵	1	2	yes	—
377	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
378	C₂²×D₁₃	—	2	4	no	—
379	C₂²×D₁₃	—	2	4	no	—
380	C₂²×D₁₃	—	2	8	no	—
381	C₂²×D₁₃	—	2	8	no	—
382	C₂²×D₁₃	—	2	8	no	—
383	C₂²×D₁₃	—	2	32	no	—
384	C₂²×D₁₃	—	4	16	no	—
385	C₂²×D₁₃	—	4	16	no	—
386	C₂²×D₁₃	—	8	32	no	—
387	C₂²×D₁₃	C₂×#41	1	8	yes	—
388	C₂²×D₁₃	C₂⁵	1	8	yes	—
389	C₂²×D₁₃	C₂⁵	1	4	yes	—
390	Q₈×C₁₃	—	2	8	no	—
391	D₄×C₁₃	—	2	8	no	—
392	D₄×C₁₃	—	4	8	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	4	no	—
395	C₂×C₄×C₁₃	—	2	4	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	4	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	16	no	—
401	C₂×C₄×C₁₃	—	2	8	no	—
402	C₂×C₄×C₁₃	—	2	8	no	—
403	C₂×C₄×C₁₃	—	4	4	no	—
404	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
405	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
406	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
407	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
408	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
409	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
410	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
411	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
412	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
413	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
414	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
415	C₂²⋊D₁₃	—	2	16	no	—
416	C₂²⋊D₁₃	—	4	16	no	—
417	C₂²⋊D₁₃	—	4	16	no	—
418	C₂×Dic₁₃	—	2	4	no	—
419	C₂×Dic₁₃	—	2	8	no	—
420	C₂×Dic₁₃	—	2	4	no	—
421	C₂×Dic₁₃	—	2	4	no	—
422	C₂×Dic₁₃	C₂⁵	1	4	yes	—
423	C₂×Dic₁₃	C₂⁵	1	4	yes	—
424	C₂×Dic₁₃	C₂⁵	1	4	yes	—
425	C₂×Dic₁₃	C₂⁵	1	8	yes	—
426	D₅₂	—	2	32	no	—
427	D₅₂	—	2	16	no	—
428	D₅₂	—	2	16	no	—
429	D₅₂	—	4	8	no	—
430	D₅₂	C₂×#41	1	16	yes	complemented
431	C₄×D₁₃	—	2	16	no	—
432	C₄×D₁₃	—	2	16	no	—
433	C₄×D₁₃	—	4	8	no	—
434	C₄×D₁₃	—	4	16	no	—
435	C₄×D₁₃	—	4	16	no	—
436	C₄×D₁₃	—	4	16	no	—
437	Dic₂₆	—	2	8	no	—
438	Dic₂₆	—	2	16	no	—
439	Dic₂₆	—	4	16	no	—
440	C₂²×#41	—	13	1	no	—
441	C₂²×#41	—	13	2	no	—
442	C₂³×Q₈	—	13	2	no	—
443	C₂³×D₄	—	13	2	no	—
444	C₂³×D₄	—	13	2	no	—
445	#559	—	13	16	no	—
446	#556	—	13	16	no	—
447	#555	—	13	32	no	—
448	#551	—	13	64	no	—
449	D₄×Q₈	—	13	16	no	—
450	#548	—	13	32	no	—
451	#546	—	13	32	no	—
452	#546	—	13	32	no	—
453	D₄²	—	13	16	no	—
454	#542	—	13	32	no	—
455	#538	—	13	64	no	—
456	#532	—	13	16	no	—
457	C₂×C₄⋊Q₈	—	13	1	no	—
458	C₂×C₄⋊Q₈	—	13	2	no	—
459	C₂×#127	—	13	1	no	—
460	#529	—	13	32	no	—
461	#529	C₂×D₁₃	1	16	yes	complemented
462	C₂×#126	—	13	4	no	—
463	C₂×#126	—	13	4	no	—
464	C₂×#126	C₂×D₁₃	1	2	yes	complemented
465	C₂×#125	C₂×D₁₃	1	1	yes	characteristic, complemented
466	C₂×#124	—	13	2	no	—
467	C₂×#124	—	13	2	no	—
468	C₂×#124	—	13	32	no	—
469	C₂×#124	—	13	4	no	—
470	C₂×#124	—	13	4	no	—
471	C₂×#124	—	13	4	no	—
472	C₂×#124	—	13	2	no	—
473	C₂×#124	—	13	2	no	—
474	C₂×#124	C₂×D₁₃	1	1	yes	characteristic
475	C₂×#123	—	13	4	no	—
476	C₂×#123	—	13	4	no	—
477	C₂×#123	—	13	4	no	—
478	C₂×#123	C₂×D₁₃	1	2	yes	complemented
479	C₂×C₂²⋊Q₈	—	13	2	no	—
480	C₂×C₂²⋊Q₈	—	13	4	no	—
481	C₂×C₂²⋊Q₈	—	13	2	no	—
482	C₂×C₂²⋊Q₈	—	13	4	no	—
483	C₂×C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
484	C₂×#121	—	13	4	no	—
485	C₂×#121	—	13	2	no	—
486	C₂×#121	—	13	2	no	—
487	C₂×#121	—	13	2	no	—
488	C₂×#121	—	13	2	no	—
489	C₂×#121	—	13	4	no	—
490	C₂×#121	C₂×D₁₃	1	1	yes	characteristic
491	C₂×#120	—	13	4	no	—
492	C₂×#120	—	13	4	no	—
493	#518	—	13	32	no	—
494	C₄×#41	—	13	16	no	—
495	C₂×C₄×Q₈	—	13	2	no	—
496	C₂×C₄×Q₈	—	13	1	no	—
497	C₂×C₄×Q₈	—	13	1	no	—
498	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
499	C₂×C₄×D₄	—	13	2	no	—
500	C₂×C₄×D₄	—	13	2	no	—
501	C₂×C₄×D₄	—	13	4	no	—
502	C₂×C₄×D₄	—	13	4	no	—
503	C₂×C₄×D₄	—	13	2	no	—
504	C₂×C₄×D₄	—	13	1	no	—
505	C₂×C₄×D₄	—	13	1	no	—
506	C₂×C₄×D₄	—	13	2	no	—
507	C₂×C₄×D₄	—	13	2	no	—
508	C₂×C₄×D₄	—	13	2	no	—
509	C₂×C₄×D₄	—	13	2	no	—
510	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
511	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
512	C₂×#117	—	13	1	no	—
513	C₂×#117	—	13	2	no	—
514	C₂×#117	—	13	4	no	—
515	C₂×#117	—	13	2	no	—
516	C₂×#117	C₂×D₁₃	1	2	yes	complemented
517	C₂²×C₂²⋊C₄	—	13	4	no	—
518	C₂²×C₂²⋊C₄	—	13	4	no	—
519	C₂²×C₂²⋊C₄	—	13	4	no	—
520	C₂²×C₄²	—	13	2	no	—
521	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
522	C₂²×C₁₃	—	2	2	no	—
523	C₂²×C₁₃	—	2	4	no	—
524	C₂²×C₁₃	—	2	2	no	—
525	C₂²×C₁₃	—	2	4	no	—
526	C₂²×C₁₃	—	2	2	no	—
527	C₂²×C₁₃	—	2	4	no	—
528	C₂²×C₁₃	—	4	8	no	—
529	C₂²×C₁₃	—	4	4	no	—
530	C₂²×C₁₃	C₂²×#41	1	2	yes	—
531	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
532	C₂²×C₁₃	#585	1	2	yes	—
533	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
534	C₂×D₁₃	—	2	4	no	—
535	C₂×D₁₃	—	2	4	no	—
536	C₂×D₁₃	—	2	16	no	—
537	C₂×D₁₃	—	2	8	no	—
538	C₂×D₁₃	—	2	8	no	—
539	C₂×D₁₃	—	2	8	no	—
540	C₂×D₁₃	—	4	16	no	—
541	C₂×D₁₃	—	8	32	no	—
542	C₂×D₁₃	C₂²×#41	1	8	yes	—
543	C₄×C₁₃	—	2	2	no	—
544	C₄×C₁₃	—	2	4	no	—
545	C₄×C₁₃	—	2	4	no	—
546	C₄×C₁₃	—	2	2	no	—
547	C₄×C₁₃	—	2	2	no	—
548	C₄×C₁₃	—	2	4	no	—
549	C₄×C₁₃	—	2	2	no	—
550	C₄×C₁₃	C₂²×#41	1	4	yes	—
551	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
552	Dic₁₃	—	2	4	no	—
553	Dic₁₃	—	2	8	no	—
554	Dic₁₃	—	2	4	no	—
555	Dic₁₃	—	2	4	no	—
556	C₂⁵	—	13	4	no	—
557	C₂×#41	—	13	8	no	—
558	C₂×#41	—	13	16	no	—
559	C₂×#41	—	26	8	no	—
560	C₂×#41	—	52	8	no	—
561	C₂²×Q₈	—	13	16	no	—
562	C₂²×Q₈	—	13	1	no	—
563	C₂²×Q₈	—	13	2	no	—
564	C₂²×Q₈	—	13	4	no	—
565	C₂²×Q₈	—	52	8	no	—
566	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
567	C₂²×D₄	—	13	2	no	—
568	C₂²×D₄	—	13	4	no	—
569	C₂²×D₄	—	13	4	no	—
570	C₂²×D₄	—	13	16	no	—
571	C₂²×D₄	—	13	1	no	—
572	C₂²×D₄	—	13	4	no	—
573	C₂²×D₄	—	13	2	no	—
574	C₂²×D₄	—	13	2	no	—
575	C₂²×D₄	—	13	16	no	—
576	C₂²×D₄	—	13	2	no	—
577	C₂²×D₄	—	26	16	no	—
578	C₂²×D₄	—	52	8	no	—
579	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
580	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
581	C₂³×C₄	—	13	2	no	—
582	C₂³×C₄	—	13	2	no	—
583	C₂³×C₄	—	13	2	no	—
584	C₂³×C₄	—	13	4	no	—
585	C₂³×C₄	—	13	4	no	—
586	C₂³×C₄	—	13	4	no	—
587	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
588	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
589	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
590	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
591	C₄⋊Q₈	—	13	8	no	—
592	C₄⋊Q₈	—	13	16	no	—
593	#127	—	13	8	no	—
594	#126	—	13	32	no	—
595	#126	—	13	32	no	—
596	#126	C₂²×D₁₃	1	16	yes	complemented
597	#125	C₂²×D₁₃	1	8	yes	complemented
598	#124	—	13	16	no	—
599	#124	—	13	16	no	—
600	#124	—	13	32	no	—
601	#124	—	13	32	no	—
602	#124	—	13	32	no	—
603	#124	—	13	16	no	—
604	#124	—	13	16	no	—
605	#124	C₂²×D₁₃	1	8	yes	—
606	#123	—	13	32	no	—
607	#123	—	13	32	no	—
608	#123	—	13	32	no	—
609	#123	C₂²×D₁₃	1	16	yes	complemented
610	C₂²⋊Q₈	—	13	16	no	—
611	C₂²⋊Q₈	—	13	16	no	—
612	C₂²⋊Q₈	—	13	32	no	—
613	C₂²⋊Q₈	—	13	32	no	—
614	C₂²⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
615	#121	—	13	32	no	—
616	#121	—	13	16	no	—
617	#121	—	13	16	no	—
618	#121	—	13	16	no	—
619	#121	—	13	16	no	—
620	#121	—	13	32	no	—
621	#121	C₂²×D₁₃	1	8	yes	—
622	#120	—	13	32	no	—
623	#120	—	13	32	no	—
624	C₄×Q₈	—	13	16	no	—
625	C₄×Q₈	—	13	8	no	—
626	C₄×Q₈	—	13	8	no	—
627	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
628	C₄×D₄	—	13	16	no	—
629	C₄×D₄	—	13	16	no	—
630	C₄×D₄	—	13	32	no	—
631	C₄×D₄	—	13	32	no	—
632	C₄×D₄	—	13	16	no	—
633	C₄×D₄	—	13	8	no	—
634	C₄×D₄	—	13	8	no	—
635	C₄×D₄	—	13	16	no	—
636	C₄×D₄	—	13	16	no	—
637	C₄×D₄	—	13	16	no	—
638	C₄×D₄	—	13	16	no	—
639	C₄×D₄	C₂²×D₁₃	1	8	yes	—
640	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
641	#117	—	13	8	no	—
642	#117	—	13	16	no	—
643	#117	—	13	32	no	—
644	#117	—	13	16	no	—
645	#117	C₂²×D₁₃	1	16	yes	complemented
646	C₂×C₄⋊C₄	—	13	1	no	—
647	C₂×C₄⋊C₄	—	13	2	no	—
648	C₂×C₄⋊C₄	—	13	1	no	—
649	C₂×C₄⋊C₄	—	13	2	no	—
650	C₂×C₄⋊C₄	—	13	2	no	—
651	C₂×C₄⋊C₄	—	13	4	no	—
652	C₂×C₄⋊C₄	—	13	2	no	—
653	C₂×C₄⋊C₄	—	13	4	no	—
654	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
660	C₂×C₂²⋊C₄	—	13	4	no	—
661	C₂×C₂²⋊C₄	—	13	4	no	—
662	C₂×C₂²⋊C₄	—	13	2	no	—
663	C₂×C₂²⋊C₄	—	13	2	no	—
664	C₂×C₂²⋊C₄	—	13	4	no	—
665	C₂×C₂²⋊C₄	—	13	4	no	—
666	C₂×C₂²⋊C₄	—	13	4	no	—
667	C₂×C₂²⋊C₄	—	13	4	no	—
668	C₂×C₂²⋊C₄	—	13	4	no	—
669	C₂×C₂²⋊C₄	—	13	2	no	—
670	C₂×C₂²⋊C₄	—	13	4	no	—
671	C₂×C₂²⋊C₄	—	13	4	no	—
672	C₂×C₂²⋊C₄	—	13	32	no	—
673	C₂×C₂²⋊C₄	—	13	32	no	—
674	C₂×C₂²⋊C₄	—	13	32	no	—
675	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
680	C₂×C₄²	—	13	2	no	—
681	C₂×C₄²	—	13	4	no	—
682	C₂×C₄²	—	13	2	no	—
683	C₂×C₄²	—	13	2	no	—
684	C₂×C₄²	—	13	16	no	—
685	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
686	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
687	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
688	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
689	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
690	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
691	C₂×C₁₃	—	4	4	no	—
692	C₂×C₁₃	—	4	2	no	—
693	C₂×C₁₃	#3514	1	4	yes	complemented
694	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
695	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
697	D₁₃	—	2	8	no	—
698	D₁₃	—	4	8	no	—
699	C₂⁴	—	13	2	no	—
700	C₂⁴	—	13	4	no	—
701	C₂⁴	—	13	16	no	—
702	C₂⁴	—	26	16	no	—
703	C₂⁴	—	52	8	no	—
704	C₂⁴	—	52	8	no	—
705	C₂⁴	C₂³×D₁₃	1	2	yes	—
706	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
707	#41	—	26	32	no	—
708	#41	—	52	32	no	—
709	C₂×Q₈	—	2	4	no	—
710	C₂×Q₈	—	13	4	no	—
711	C₂×Q₈	—	13	8	no	—
712	C₂×Q₈	—	13	16	no	—
713	C₂×Q₈	—	26	4	no	—
714	C₂×Q₈	—	26	8	no	—
715	C₂×Q₈	—	52	8	no	—
716	C₂×Q₈	—	52	32	no	—
717	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	13	8	no	—
721	C₂×D₄	—	13	16	no	—
722	C₂×D₄	—	13	16	no	—
723	C₂×D₄	—	13	8	no	—
724	C₂×D₄	—	13	4	no	—
725	C₂×D₄	—	13	16	no	—
726	C₂×D₄	—	13	8	no	—
727	C₂×D₄	—	13	8	no	—
728	C₂×D₄	—	13	8	no	—
729	C₂×D₄	—	26	64	no	—
730	C₂×D₄	—	26	16	no	—
731	C₂×D₄	—	26	8	no	—
732	C₂×D₄	—	26	8	no	—
733	C₂×D₄	—	26	8	no	—
734	C₂×D₄	—	52	4	no	—
735	C₂×D₄	—	52	32	no	—
736	C₂×D₄	—	52	8	no	—
737	C₂×D₄	—	52	8	no	—
738	C₂×D₄	C₂³×D₁₃	1	4	yes	—
739	C₂×D₄	C₂³×D₁₃	1	8	yes	—
740	C₂²×C₄	—	2	8	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	13	2	no	—
745	C₂²×C₄	—	13	2	no	—
746	C₂²×C₄	—	13	2	no	—
747	C₂²×C₄	—	13	4	no	—
748	C₂²×C₄	—	13	8	no	—
749	C₂²×C₄	—	13	8	no	—
750	C₂²×C₄	—	13	8	no	—
751	C₂²×C₄	—	13	16	no	—
752	C₂²×C₄	—	13	16	no	—
753	C₂²×C₄	—	13	16	no	—
754	C₂²×C₄	—	26	8	no	—
755	C₂²×C₄	—	26	8	no	—
756	C₂²×C₄	—	52	8	no	—
757	C₂²×C₄	—	52	8	no	—
758	C₂²×C₄	—	52	4	no	—
759	C₂²×C₄	—	52	8	no	—
760	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
761	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
762	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
763	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
764	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
765	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
766	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
769	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
770	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
771	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
772	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
773	C₄⋊C₄	—	13	4	no	—
774	C₄⋊C₄	—	13	8	no	—
775	C₄⋊C₄	—	13	4	no	—
776	C₄⋊C₄	—	13	8	no	—
777	C₄⋊C₄	—	13	8	no	—
778	C₄⋊C₄	—	13	16	no	—
779	C₄⋊C₄	—	13	8	no	—
780	C₄⋊C₄	—	13	16	no	—
781	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
782	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
783	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
784	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
785	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
786	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
787	C₂²⋊C₄	—	13	16	no	—
788	C₂²⋊C₄	—	13	16	no	—
789	C₂²⋊C₄	—	13	8	no	—
790	C₂²⋊C₄	—	13	8	no	—
791	C₂²⋊C₄	—	13	16	no	—
792	C₂²⋊C₄	—	13	16	no	—
793	C₂²⋊C₄	—	13	16	no	—
794	C₂²⋊C₄	—	13	16	no	—
795	C₂²⋊C₄	—	13	16	no	—
796	C₂²⋊C₄	—	13	8	no	—
797	C₂²⋊C₄	—	13	16	no	—
798	C₂²⋊C₄	—	13	16	no	—
799	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
800	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
801	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
802	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
803	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
804	C₄²	—	13	8	no	—
805	C₄²	—	13	8	no	—
806	C₄²	—	13	8	no	—
807	C₄²	—	13	16	no	—
808	C₄²	C₂³×D₁₃	1	4	yes	—
809	C₄²	C₂³×D₁₃	1	4	yes	—
810	C₄²	C₂³×D₁₃	1	4	yes	—
811	C₄²	C₂³×D₁₃	1	4	yes	—
812	C₄²	C₂³×D₁₃	1	8	yes	—
813	C₁₃	C₂×#3514	1	1	yes	characteristic, complemented, Sylow
814	C₂³	—	2	2	no	—
815	C₂³	—	2	4	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	4	no	—
820	C₂³	—	13	8	no	—
821	C₂³	—	13	4	no	—
822	C₂³	—	13	8	no	—
823	C₂³	—	26	32	no	—
824	C₂³	—	26	4	no	—
825	C₂³	—	26	4	no	—
826	C₂³	—	26	8	no	—
827	C₂³	—	26	8	no	—
828	C₂³	—	26	8	no	—
829	C₂³	—	52	16	no	—
830	C₂³	—	52	16	no	—
831	C₂³	—	104	32	no	—
832	C₂³	C₂⁴×D₁₃	1	4	yes	—
833	C₂³	C₂⁴×D₁₃	1	2	yes	—
834	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
835	Q₈	—	2	8	no	—
836	Q₈	—	26	8	no	—
837	Q₈	—	26	16	no	—
838	Q₈	—	52	16	no	—
839	D₄	—	2	8	no	—
840	D₄	—	4	8	no	—
841	D₄	—	13	16	no	—
842	D₄	—	26	32	no	—
843	D₄	—	26	16	no	—
844	D₄	—	26	16	no	—
845	D₄	—	26	16	no	—
846	D₄	—	52	8	no	—
847	D₄	—	52	16	no	—
848	D₄	—	52	16	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	16	no	—
857	C₂×C₄	—	2	8	no	—
858	C₂×C₄	—	2	8	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	13	4	no	—
861	C₂×C₄	—	13	4	no	—
862	C₂×C₄	—	13	4	no	—
863	C₂×C₄	—	13	8	no	—
864	C₂×C₄	—	26	16	no	—
865	C₂×C₄	—	26	4	no	—
866	C₂×C₄	—	26	4	no	—
867	C₂×C₄	—	26	8	no	—
868	C₂×C₄	—	26	4	no	—
869	C₂×C₄	—	26	16	no	—
870	C₂×C₄	—	52	8	no	—
871	C₂×C₄	—	52	16	no	—
872	C₂×C₄	—	52	16	no	—
873	C₂×C₄	—	52	16	no	—
874	C₂×C₄	#41×D₁₃	1	4	yes	—
875	C₂×C₄	#88256	1	4	yes	—
876	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
877	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
878	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
879	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
880	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
881	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
882	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
883	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
884	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	4	4	no	—
892	C₂²	—	4	8	no	—
893	C₂²	—	13	8	no	—
894	C₂²	—	26	16	no	—
895	C₂²	—	26	4	no	—
896	C₂²	—	26	4	no	—
897	C₂²	—	26	8	no	—
898	C₂²	—	26	8	no	—
899	C₂²	—	26	8	no	—
900	C₂²	—	52	16	no	—
901	C₂²	—	104	32	no	—
902	C₂²	C₂×#41×D₁₃	1	2	yes	—
903	C₂²	C₂×#88256	1	2	yes	—
904	C₂²	#11719648	1	2	yes	—
905	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
906	C₄	—	2	2	no	—
907	C₄	—	2	4	no	—
908	C₄	—	2	2	no	—
909	C₄	—	2	4	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	4	no	—
913	C₄	—	26	4	no	—
914	C₄	—	26	4	no	—
915	C₄	—	26	8	no	—
916	C₄	—	26	4	no	—
917	C₄	C₂×#41×D₁₃	1	4	yes	—
918	C₄	C₂×#88256	1	4	yes	—
919	C₂	—	4	4	no	—
920	C₂	—	4	2	no	—
921	C₂	—	26	8	no	—
922	C₂	—	52	8	no	—
923	C₂	#13128799	1	4	yes	direct product factor
924	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic
925	C₂	C₂²×#88256	1	1	yes	characteristic
926	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#529	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#529	D₁₃
hypocenter	C₁₃	C₂×#3514
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #13128799	C₂	direct (N × H)
2. C₂×#11719290	C₂	semidirect
3. C₂×#11719247	C₂	semidirect
4. C₂×#11719268	C₂	semidirect
5. C₂×#11719410	C₂	semidirect
6. C₂×Q₈×D₅₂	C₂	semidirect
7. C₂×#11719338	C₂	semidirect
8. C₂×#11719317	C₂	semidirect
9. C₂×#11719255	C₂	semidirect
10. C₂×D₄×D₅₂	C₂	semidirect
11. C₂×#11719239	C₂	semidirect
12. C₂×#11719362	C₂	semidirect
13. C₂×#11719182	C₂	semidirect
14. C₂×#11719396	C₂	semidirect
15. C₂×D₁₃×#124	C₂	semidirect
16. C₂×#11719226	C₂	semidirect
17. C₂×C₄×#6127	C₂	semidirect
18. C₂×C₁₃×#529	C₂	semidirect
19. C₂²×Q₈×D₁₃	C₂²	semidirect
22. C₂²×#6127	C₂²	semidirect
24. C₁₃×#529	C₂²	semidirect
25. C₂×C₁₃×#126	C₂²	semidirect
26. C₂×C₁₃×#125	C₂²	semidirect
28. C₂×C₁₃×#123	C₂²	semidirect
29. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₁₃×#117	C₂²	semidirect
35. C₂²×C₄²×C₁₃	C₂²	semidirect
36. C₂×#88201	C₂²	semidirect
37. C₂×#88192	C₂²	semidirect
38. C₂×#88191	C₂²	semidirect
41. C₂×#88184	C₂²	semidirect
42. C₂×#88184	C₂²	semidirect
43. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
44. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
45. C₂×#88180	C₂²	semidirect
46. C₂×#88180	C₂²	semidirect
47. C₂×#88178	C₂²	semidirect
48. #11719410	C₂²	semidirect
49. #11719396	C₂²	semidirect
50. D₁₃×#124	C₂²	semidirect
51. #11719362	C₂²	semidirect
52. #11719338	C₂²	semidirect
53. #11719317	C₂²	semidirect
54. #11719290	C₂²	semidirect
55. Q₈×D₅₂	C₂²	semidirect
56. #11719268	C₂²	semidirect
57. #11719255	C₂²	semidirect
58. D₄×D₅₂	C₂²	semidirect
59. #11719247	C₂²	semidirect
60. #11719239	C₂²	semidirect
61. #11719226	C₂²	semidirect
62. C₂×#88152	C₂²	semidirect
63. C₂×#88151	C₂²	semidirect
64. C₂×#88151	C₂²	semidirect
65. C₂×#88150	C₂²	semidirect
67. C₂×#88148	C₂²	semidirect
68. C₂×#88148	C₂²	semidirect
69. C₂×#88147	C₂²	semidirect
70. C₂×#88147	C₂²	semidirect
71. C₂×#88147	C₂²	semidirect
72. C₂×#88146	C₂²	semidirect
73. C₂×#88141	C₂²	semidirect
74. C₂×#88139	C₂²	semidirect
75. C₂×#88139	C₂²	semidirect
76. C₂×#88139	C₂²	semidirect
77. C₂×#88138	C₂²	semidirect
78. C₂×#88137	C₂²	semidirect
80. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
81. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
82. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
83. C₂×#88133	C₂²	semidirect
84. #11719182	C₂²	semidirect
85. C₂×#88129	C₂²	semidirect
86. C₂×#88129	C₂²	semidirect
88. C₄×#6127	C₂²	semidirect
92. C₂×C₄×D₅₂	C₂²	semidirect
93. C₂×C₄×D₅₂	C₂²	semidirect
94. C₂×C₄×D₅₂	C₂²	semidirect
95. C₂×#88126	C₂²	semidirect
96. C₂×C₄²×D₁₃	C₂²	semidirect
97. C₂×#88123	C₂²	semidirect
98. C₂×#88123	C₂²	semidirect
99. C₂×C₄×Dic₂₆	C₂²	semidirect
100. C₂×C₄×Dic₂₆	C₂²	semidirect
113. C₂×Q₈×D₁₃	C₂³	semidirect
119. C₂×#6127	C₂³	semidirect
136. C₁₃×#126	C₂³	semidirect
137. C₁₃×#125	C₂³	semidirect
139. C₁₃×#123	C₂³	semidirect
140. C₁₃×C₂²⋊Q₈	C₂³	semidirect
142. C₄×Q₈×C₁₃	C₂³	semidirect
144. C₄×D₄×C₁₃	C₂³	semidirect
145. C₁₃×#117	C₂³	semidirect
162. C₂×C₄²×C₁₃	C₂³	semidirect
166. #88201	C₂³	semidirect
167. #88192	C₂³	semidirect
168. #88191	C₂³	semidirect
171. #88184	C₂³	semidirect
172. #88184	C₂³	semidirect
173. C₄×C₂²⋊D₁₃	C₂³	semidirect
174. C₄×C₂²⋊D₁₃	C₂³	semidirect
184. #88180	C₂³	semidirect
185. #88180	C₂³	semidirect
191. #88178	C₂³	semidirect
199. #88152	C₂³	semidirect
200. #88151	C₂³	semidirect
201. #88151	C₂³	semidirect
202. #88150	C₂³	semidirect
204. #88148	C₂³	semidirect
205. #88148	C₂³	semidirect
206. #88147	C₂³	semidirect
207. #88147	C₂³	semidirect
208. #88147	C₂³	semidirect
209. #88146	C₂³	semidirect
210. #88141	C₂³	semidirect
211. #88139	C₂³	semidirect
212. #88139	C₂³	semidirect
213. #88139	C₂³	semidirect
214. #88138	C₂³	semidirect
215. #88137	C₂³	semidirect
217. C₂²⋊C₄×D₁₃	C₂³	semidirect
218. C₂²⋊C₄×D₁₃	C₂³	semidirect
219. C₂²⋊C₄×D₁₃	C₂³	semidirect
220. #88133	C₂³	semidirect
221. #88129	C₂³	semidirect
222. #88129	C₂³	semidirect
227. C₄×D₅₂	C₂³	semidirect
228. C₄×D₅₂	C₂³	semidirect
229. C₄×D₅₂	C₂³	semidirect
230. #88126	C₂³	semidirect
231. C₄²×D₁₃	C₂³	semidirect
232. #88123	C₂³	semidirect
233. #88123	C₂³	semidirect
234. C₄×Dic₂₆	C₂³	semidirect
235. C₄×Dic₂₆	C₂³	semidirect
287. C₂×D₅₂	#41	semidirect
365. C₂×#529	D₁₃	semidirect
430. D₅₂	C₂×#41	semidirect
461. #529	C₂×D₁₃	semidirect
464. C₂×#126	C₂×D₁₃	semidirect
465. C₂×#125	C₂×D₁₃	semidirect
478. C₂×#123	C₂×D₁₃	semidirect
483. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
498. C₂×C₄×Q₈	C₂×D₁₃	semidirect
511. C₂×C₄×D₄	C₂×D₁₃	semidirect
516. C₂×#117	C₂×D₁₃	semidirect
521. C₂²×C₄²	C₂×D₁₃	semidirect
596. #126	C₂²×D₁₃	semidirect
597. #125	C₂²×D₁₃	semidirect
609. #123	C₂²×D₁₃	semidirect
614. C₂²⋊Q₈	C₂²×D₁₃	semidirect
627. C₄×Q₈	C₂²×D₁₃	semidirect
640. C₄×D₄	C₂²×D₁₃	semidirect
645. #117	C₂²×D₁₃	semidirect
690. C₂×C₄²	C₂²×D₁₃	semidirect
693. C₂×C₁₃	#3514	semidirect
813. C₁₃	C₂×#3514	semidirect
923. C₂	#13128799	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128799	2
C₂×#11719290	2
C₂×#11719247	2
C₂×#11719268	2
C₂×#11719410	2
C₂×Q₈×D₅₂	2
C₂×#11719338	2
C₂×#11719317	2
C₂×#11719255	2
C₂×D₄×D₅₂	2
C₂×#11719239	2
C₂×#11719362	2
C₂×#11719182	2
C₂×#11719396	2
C₂×D₁₃×#124	2
C₂×#11719226	2
C₂×C₄×#6127	2
C₂×C₁₃×#529	2
C₂×#3514	13

Subgroups — C2×#13128799 #16771016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128799 #16771016