Subgroups — C₂×#13128400 #16769957

Order 3328.

7954 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128400	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719289	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719268	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11719284	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11719263	C₂	1	2	yes	maximal, complemented
6	C₂×#11719286	C₂	1	2	yes	maximal, complemented
7	C₂×#11719246	C₂	1	2	yes	maximal, complemented
8	C₂×#11719261	C₂	1	4	yes	maximal, complemented
9	C₂×#11719256	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11719255	C₂	1	2	yes	maximal, complemented
11	C₂×#11719175	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11719184	C₂	1	2	yes	maximal, complemented
13	C₂×#11719233	C₂	1	4	yes	maximal, complemented
14	C₂×#11719533	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×#6127	C₂	1	2	yes	maximal, complemented
16	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×D₁₃×#117	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×#6127	C₂²	1	2	yes	—
21	C₂³×D₅₂	C₂²	1	1	yes	characteristic
22	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
23	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
34	#11719533	C₂²	1	32	yes	complemented
35	C₂×#88200	C₂²	1	2	yes	complemented
36	C₂×#88200	C₂²	1	2	yes	complemented
37	C₂×#88192	C₂²	1	2	yes	complemented
38	C₂×#88192	C₂²	1	2	yes	complemented
39	C₂×#88191	C₂²	1	4	yes	—
40	C₂×#88189	C₂²	1	4	yes	—
41	C₂×#88184	C₂²	1	2	yes	—
42	C₂×#88183	C₂²	1	4	yes	complemented
43	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
44	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
45	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
46	C₂²×#6103	C₂²	1	2	yes	—
47	C₂×#88180	C₂²	1	2	yes	—
48	C₂×#88180	C₂²	1	2	yes	complemented
49	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
50	C₂×#88178	C₂²	1	2	yes	—
51	C₂×#88178	C₂²	1	2	yes	—
52	C₂×#88178	C₂²	1	2	yes	complemented
53	#11719289	C₂²	1	16	yes	complemented
54	#11719286	C₂²	1	32	yes	complemented
55	#11719284	C₂²	1	16	yes	complemented
56	#11719268	C₂²	1	16	yes	complemented
57	#11719263	C₂²	1	32	yes	complemented
58	#11719261	C₂²	1	64	yes	complemented
59	#11719256	C₂²	1	16	yes	complemented
60	#11719255	C₂²	1	32	yes	complemented
61	#11719246	C₂²	1	32	yes	complemented
62	#11719233	C₂²	1	64	yes	complemented
63	D₁₃×#117	C₂²	1	32	yes	complemented
64	C₂×#88152	C₂²	1	4	yes	complemented
65	C₂×#88150	C₂²	1	4	yes	complemented
66	C₂×#88148	C₂²	1	4	yes	—
67	C₂×#88146	C₂²	1	2	yes	complemented
68	C₂×#88146	C₂²	1	2	yes	complemented
69	C₂×C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
70	C₂×C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
71	C₂×#88143	C₂²	1	4	yes	complemented
72	C₂×#88139	C₂²	1	4	yes	complemented
73	C₂×#88138	C₂²	1	4	yes	—
74	C₂×#88137	C₂²	1	4	yes	complemented
75	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
76	C₂×#88133	C₂²	1	4	yes	complemented
77	C₂×#88131	C₂²	1	4	yes	—
78	#11719184	C₂²	1	32	yes	complemented
79	C₂×#88130	C₂²	1	4	yes	complemented
80	C₂×#88129	C₂²	1	2	yes	—
81	C₄×#6127	C₂²	1	32	yes	complemented
82	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
83	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
84	C₂×C₄×D₅₂	C₂²	1	2	yes	—
85	C₂×C₄×D₅₂	C₂²	1	2	yes	—
86	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
87	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
88	C₂×C₄×D₅₂	C₂²	1	2	yes	—
89	C₂×C₄×D₅₂	C₂²	1	16	yes	complemented
90	C₂×#88126	C₂²	1	4	yes	complemented
91	C₂×#88126	C₂²	1	4	yes	complemented
92	C₂×C₄²×D₁₃	C₂²	1	4	yes	complemented
93	#11719175	C₂²	1	16	yes	complemented
94	C₂×#88124	C₂²	1	2	yes	complemented
95	C₂×#88124	C₂²	1	2	yes	complemented
96	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
97	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
99	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
100	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
101	C₂⁴×D₁₃	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	—	2	8	no	—
103	C₂×C₁₃×#41	C₂³	1	8	yes	—
104	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
114	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
115	C₂³×Dic₁₃	C₂³	1	2	yes	—
116	C₂×#6127	—	2	16	no	—
117	C₂×#6127	C₂³	1	16	yes	—
118	C₂²×D₅₂	—	2	8	no	—
119	C₂²×D₅₂	C₂³	1	1	yes	characteristic
120	C₂²×D₅₂	C₂³	1	2	yes	—
121	C₂²×D₅₂	C₂³	1	8	yes	—
122	C₂²×D₅₂	C₂³	1	1	yes	characteristic
123	C₂²×C₄×D₁₃	—	2	16	no	—
124	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
125	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
126	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
127	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
128	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
129	C₂²×C₄×D₁₃	C₂³	1	16	yes	—
130	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
131	C₂²×Dic₂₆	C₂³	1	2	yes	—
132	C₂²×Dic₂₆	C₂³	1	2	yes	—
133	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
134	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
135	C₄×D₄×C₁₃	C₂³	1	16	yes	—
136	C₄×D₄×C₁₃	C₂³	1	16	yes	—
137	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
138	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
139	C₁₃×#117	C₂³	1	8	yes	—
140	C₁₃×#117	C₂³	1	16	yes	complemented
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
154	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
157	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
158	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
159	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
160	#88200	C₂³	1	16	yes	complemented
161	#88200	C₂³	1	16	yes	complemented
162	#88192	C₂³	1	16	yes	complemented
163	#88192	C₂³	1	16	yes	complemented
164	#88191	C₂³	1	32	yes	—
165	#88189	C₂³	1	32	yes	—
166	#88184	C₂³	1	16	yes	—
167	#88183	C₂³	1	32	yes	complemented
168	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
169	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
170	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
171	C₂×#6103	C₂³	1	2	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	2	yes	—
176	C₂×#6103	C₂³	1	2	yes	—
177	C₂×#6103	C₂³	1	2	yes	—
178	C₂×#6103	C₂³	1	16	yes	—
179	C₂×#6103	C₂³	1	4	yes	—
180	#88180	C₂³	1	16	yes	—
181	#88180	C₂³	1	16	yes	complemented
182	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
185	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
186	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
187	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
190	#88178	C₂³	1	16	yes	—
191	#88178	C₂³	1	16	yes	—
192	#88178	C₂³	1	16	yes	complemented
193	C₂×#6101	C₂³	1	4	yes	—
194	C₂×#6101	C₂³	1	4	yes	—
195	C₂×#6101	C₂³	1	4	yes	—
196	C₂×#6101	C₂³	1	4	yes	—
197	C₂×#6101	C₂³	1	4	yes	—
198	C₂×#6101	C₂³	1	4	yes	—
199	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
200	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
201	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
202	#88152	C₂³	1	32	yes	complemented
203	#88150	C₂³	1	32	yes	complemented
204	#88148	C₂³	1	32	yes	—
205	#88146	C₂³	1	16	yes	complemented
206	#88146	C₂³	1	16	yes	complemented
207	C₄⋊C₄×D₁₃	C₂³	1	16	yes	complemented
208	C₄⋊C₄×D₁₃	C₂³	1	16	yes	complemented
209	#88143	C₂³	1	32	yes	complemented
210	#88139	C₂³	1	32	yes	complemented
211	#88138	C₂³	1	32	yes	—
212	#88137	C₂³	1	32	yes	complemented
213	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	—
214	#88133	C₂³	1	32	yes	complemented
215	#88131	C₂³	1	32	yes	—
216	#88130	C₂³	1	32	yes	complemented
217	#88129	C₂³	1	16	yes	—
218	C₄×D₅₂	C₂³	1	8	yes	—
219	C₄×D₅₂	C₂³	1	8	yes	—
220	C₄×D₅₂	C₂³	1	16	yes	—
221	C₄×D₅₂	C₂³	1	8	yes	—
222	C₄×D₅₂	C₂³	1	16	yes	—
223	C₄×D₅₂	C₂³	1	8	yes	—
224	C₄×D₅₂	C₂³	1	16	yes	—
225	#88126	C₂³	1	32	yes	complemented
226	#88126	C₂³	1	32	yes	complemented
227	C₄²×D₁₃	C₂³	1	32	yes	complemented
228	#88124	C₂³	1	16	yes	complemented
229	#88124	C₂³	1	16	yes	complemented
230	#88123	C₂³	1	8	yes	complemented
231	#88123	C₂³	1	8	yes	complemented
232	C₄×Dic₂₆	C₂³	1	16	yes	complemented
233	C₄×Dic₂₆	C₂³	1	16	yes	complemented
234	C₄×Dic₂₆	C₂³	1	16	yes	complemented
235	C₂×#3475	—	13	1	no	maximal, Sylow
236	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
237	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂³×D₁₃	—	2	8	no	—
239	C₂³×D₁₃	—	2	8	no	—
240	C₂³×D₁₃	—	4	4	no	—
241	C₂³×D₁₃	C₂⁴	1	2	yes	—
242	C₂³×D₁₃	C₂⁴	1	8	yes	—
243	C₂³×D₁₃	C₂⁴	1	2	yes	—
244	C₁₃×#41	—	2	32	no	—
245	C₂×Q₈×C₁₃	—	2	4	no	—
246	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
247	C₂×D₄×C₁₃	—	2	8	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	—	2	8	no	—
253	C₂²×C₄×C₁₃	—	2	8	no	—
254	C₂²×C₄×C₁₃	—	4	2	no	—
255	C₂²×C₄×C₁₃	—	4	4	no	—
256	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×C₂²⋊D₁₃	—	2	16	no	—
273	C₂×C₂²⋊D₁₃	—	4	8	no	—
274	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
275	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
276	C₂²×Dic₁₃	—	2	8	no	—
277	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
278	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
279	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
280	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
281	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
282	#6127	—	2	64	no	—
283	C₂×D₅₂	—	2	8	no	—
284	C₂×D₅₂	—	2	4	no	—
285	C₂×D₅₂	—	2	32	no	—
286	C₂×D₅₂	#41	1	8	yes	complemented
287	C₂×D₅₂	C₂⁴	1	4	yes	—
288	C₂×D₅₂	C₂⁴	1	8	yes	—
289	C₂×D₅₂	C₂⁴	1	4	yes	—
290	C₂×C₄×D₁₃	—	2	16	no	—
291	C₂×C₄×D₁₃	—	2	8	no	—
292	C₂×C₄×D₁₃	—	2	8	no	—
293	C₂×C₄×D₁₃	—	2	8	no	—
294	C₂×C₄×D₁₃	—	2	8	no	—
295	C₂×C₄×D₁₃	—	2	64	no	—
296	C₂×C₄×D₁₃	—	4	8	no	—
297	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
298	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
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×Dic₂₆	—	2	8	no	—
304	C₂×Dic₂₆	—	4	4	no	—
305	C₂×Dic₂₆	C₂⁴	1	8	yes	—
306	C₂×Dic₂₆	C₂⁴	1	8	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
311	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
312	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
313	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
314	C₄²×C₁₃	C₂⁴	1	4	yes	—
315	C₄²×C₁₃	C₂⁴	1	4	yes	—
316	C₄²×C₁₃	C₂⁴	1	8	yes	—
317	C₄²×C₁₃	C₂⁴	1	4	yes	—
318	C₄²×C₁₃	C₂⁴	1	4	yes	—
319	C₄²×C₁₃	C₂⁴	1	8	yes	—
320	C₄²×C₁₃	C₂⁴	1	8	yes	—
321	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
322	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
323	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
324	#6103	C₂⁴	1	8	yes	—
325	#6103	C₂⁴	1	16	yes	—
326	#6103	C₂⁴	1	16	yes	—
327	#6103	C₂⁴	1	16	yes	—
328	#6103	C₂⁴	1	8	yes	—
329	#6103	C₂⁴	1	8	yes	—
330	#6103	C₂⁴	1	8	yes	—
331	#6103	C₂⁴	1	16	yes	—
332	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
333	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
334	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
335	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
336	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
337	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
338	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
339	#6101	C₂⁴	1	16	yes	—
340	#6101	C₂⁴	1	16	yes	—
341	#6101	C₂⁴	1	16	yes	—
342	#6101	C₂⁴	1	16	yes	—
343	#6101	C₂⁴	1	16	yes	—
344	#6101	C₂⁴	1	16	yes	—
345	C₄×Dic₁₃	C₂⁴	1	16	yes	—
346	C₄×Dic₁₃	C₂⁴	1	16	yes	—
347	C₄×Dic₁₃	C₂⁴	1	16	yes	—
348	#3475	—	13	32	no	—
349	C₂×#556	—	13	1	no	—
350	C₂×#555	—	13	1	no	—
351	C₂×#554	—	13	1	no	—
352	C₂×#553	—	13	2	no	—
353	C₂×#552	—	13	2	no	—
354	C₂×#552	—	13	2	no	—
355	C₂×#551	—	13	4	no	—
356	C₂×#547	—	13	1	no	—
357	C₂×#546	—	13	2	no	—
358	C₂×#533	—	13	1	no	—
359	C₂×#529	—	13	2	no	—
360	C₂×#529	—	13	4	no	—
361	C₂×#525	—	13	2	no	—
362	C₂×C₄×#41	—	13	2	no	—
363	C₂×C₄×#41	D₁₃	1	1	yes	characteristic, complemented
364	C₂²×C₄×D₄	—	13	1	no	—
365	C₂²×#117	—	13	2	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	—	2	4	no	—
369	C₂³×C₁₃	—	2	4	no	—
370	C₂³×C₁₃	—	2	4	no	—
371	C₂³×C₁₃	C₂×#41	1	4	yes	—
372	C₂³×C₁₃	C₂⁵	1	4	yes	—
373	C₂³×C₁₃	C₂⁵	1	2	yes	—
374	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
375	C₂²×D₁₃	—	2	4	no	—
376	C₂²×D₁₃	—	2	4	no	—
377	C₂²×D₁₃	—	2	16	no	—
378	C₂²×D₁₃	—	2	4	no	—
379	C₂²×D₁₃	—	2	4	no	—
380	C₂²×D₁₃	—	2	4	no	—
381	C₂²×D₁₃	—	2	16	no	—
382	C₂²×D₁₃	—	4	8	no	—
383	C₂²×D₁₃	—	4	32	no	—
384	C₂²×D₁₃	C₂×#41	1	8	yes	—
385	C₂²×D₁₃	C₂⁵	1	4	yes	—
386	C₂²×D₁₃	C₂⁵	1	4	yes	—
387	Q₈×C₁₃	—	2	8	no	—
388	D₄×C₁₃	—	2	16	no	—
389	D₄×C₁₃	—	2	8	no	—
390	C₂×C₄×C₁₃	—	2	4	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	4	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	4	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	8	no	—
397	C₂×C₄×C₁₃	—	2	16	no	—
398	C₂×C₄×C₁₃	—	2	16	no	—
399	C₂×C₄×C₁₃	—	4	4	no	—
400	C₂×C₄×C₁₃	—	4	8	no	—
401	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
402	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
403	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
404	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
405	C₂×C₄×C₁₃	C₂⁵	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	4	yes	—
410	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
411	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
412	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
413	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
414	C₂²⋊D₁₃	—	2	32	no	—
415	C₂²⋊D₁₃	—	4	16	no	—
416	C₂×Dic₁₃	—	2	8	no	—
417	C₂×Dic₁₃	—	2	16	no	—
418	C₂×Dic₁₃	—	2	4	no	—
419	C₂×Dic₁₃	—	2	4	no	—
420	C₂×Dic₁₃	—	2	8	no	—
421	C₂×Dic₁₃	C₂⁵	1	4	yes	—
422	C₂×Dic₁₃	C₂⁵	1	8	yes	—
423	C₂×Dic₁₃	C₂⁵	1	8	yes	—
424	C₂×Dic₁₃	C₂⁵	1	4	yes	—
425	D₅₂	—	2	16	no	—
426	D₅₂	—	2	8	no	—
427	D₅₂	C₂×#41	1	16	yes	complemented
428	C₄×D₁₃	—	2	32	no	—
429	C₄×D₁₃	—	2	16	no	—
430	C₄×D₁₃	—	2	16	no	—
431	C₄×D₁₃	—	2	16	no	—
432	C₄×D₁₃	—	2	16	no	—
433	C₄×D₁₃	—	4	16	no	—
434	Dic₂₆	—	2	16	no	—
435	Dic₂₆	—	4	8	no	—
436	C₂²×#41	—	13	2	no	—
437	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
438	C₂³×D₄	—	13	1	no	—
439	C₂⁴×C₄	—	13	2	no	—
440	#556	—	13	16	no	—
441	#555	—	13	16	no	—
442	#554	—	13	16	no	—
443	#553	—	13	32	no	—
444	#552	—	13	32	no	—
445	#552	—	13	32	no	—
446	#551	—	13	64	no	—
447	#547	—	13	16	no	—
448	#546	—	13	32	no	—
449	#533	—	13	16	no	—
450	C₂×C₄⋊Q₈	—	13	1	no	—
451	C₂×C₄⋊Q₈	—	13	1	no	—
452	#529	—	13	64	no	—
453	#529	—	13	32	no	—
454	C₂×#126	—	13	4	no	—
455	C₂×#126	—	13	4	no	—
456	C₂×#126	—	13	4	no	—
457	C₂×#125	—	13	4	no	—
458	C₂×#125	—	13	2	no	—
459	C₂×#125	—	13	2	no	—
460	C₂×#124	—	13	4	no	—
461	C₂×#124	—	13	2	no	—
462	#525	—	13	32	no	—
463	C₂×#123	—	13	4	no	—
464	C₂×#123	—	13	4	no	—
465	C₂×#123	—	13	4	no	—
466	C₂×#123	—	13	4	no	—
467	C₂×C₂²⋊Q₈	—	13	2	no	—
468	C₂×C₂²⋊Q₈	—	13	2	no	—
469	C₂×C₂²⋊Q₈	—	13	2	no	—
470	C₂×C₂²⋊Q₈	—	13	2	no	—
471	C₂×C₂²⋊Q₈	—	13	2	no	—
472	C₂×C₂²⋊Q₈	—	13	4	no	—
473	C₂×#121	—	13	2	no	—
474	C₂×#121	—	13	2	no	—
475	C₂×#121	—	13	2	no	—
476	C₂×#121	—	13	4	no	—
477	C₂×#120	—	13	4	no	—
478	C₄×#41	—	13	32	no	—
479	C₄×#41	C₂×D₁₃	1	16	yes	complemented
480	C₂×C₄×Q₈	—	13	2	no	—
481	C₂×C₄×Q₈	—	13	2	no	—
482	C₂×C₄×Q₈	—	13	2	no	—
483	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
484	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
485	C₂×C₄×D₄	—	13	4	no	—
486	C₂×C₄×D₄	—	13	4	no	—
487	C₂×C₄×D₄	—	13	4	no	—
488	C₂×C₄×D₄	—	13	1	no	—
489	C₂×C₄×D₄	—	13	2	no	—
490	C₂×C₄×D₄	—	13	1	no	—
491	C₂×C₄×D₄	—	13	1	no	—
492	C₂×C₄×D₄	—	13	2	no	—
493	C₂×C₄×D₄	—	13	1	no	—
494	C₂×C₄×D₄	—	13	2	no	—
495	C₂×C₄×D₄	—	13	16	no	—
496	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
497	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
498	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
499	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
500	C₂×#117	—	13	2	no	—
501	C₂×#117	—	13	2	no	—
502	C₂×#117	—	13	32	no	—
503	C₂×#117	—	13	2	no	—
504	C₂×#117	—	13	2	no	—
505	C₂×#117	—	13	4	no	—
506	C₂×#117	—	13	4	no	—
507	C₂×#117	—	13	4	no	—
508	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
509	C₂×#117	C₂×D₁₃	1	2	yes	complemented
510	C₂²×C₄⋊C₄	—	13	1	no	—
511	C₂²×C₄⋊C₄	—	13	2	no	—
512	C₂²×C₄⋊C₄	—	13	2	no	—
513	C₂²×C₂²⋊C₄	—	13	2	no	—
514	C₂²×C₂²⋊C₄	—	13	4	no	—
515	C₂²×C₄²	—	13	4	no	—
516	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
517	C₂²×C₄²	C₂×D₁₃	1	2	yes	complemented
518	C₂²×C₁₃	—	2	2	no	—
519	C₂²×C₁₃	—	2	2	no	—
520	C₂²×C₁₃	—	2	8	no	—
521	C₂²×C₁₃	—	2	4	no	—
522	C₂²×C₁₃	—	2	4	no	—
523	C₂²×C₁₃	—	2	4	no	—
524	C₂²×C₁₃	—	4	8	no	—
525	C₂²×C₁₃	C₂²×#41	1	4	yes	—
526	C₂²×C₁₃	C₂²×#41	1	2	yes	—
527	C₂²×C₁₃	C₂²×#41	1	2	yes	—
528	C₂²×C₁₃	#585	1	2	yes	—
529	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
530	C₂×D₁₃	—	2	4	no	—
531	C₂×D₁₃	—	2	4	no	—
532	C₂×D₁₃	—	2	16	no	—
533	C₂×D₁₃	—	2	4	no	—
534	C₂×D₁₃	—	2	4	no	—
535	C₂×D₁₃	—	2	4	no	—
536	C₂×D₁₃	—	4	32	no	—
537	C₂×D₁₃	—	4	8	no	—
538	C₂×D₁₃	C₂²×#41	1	8	yes	—
539	C₄×C₁₃	—	2	4	no	—
540	C₄×C₁₃	—	2	2	no	—
541	C₄×C₁₃	—	2	4	no	—
542	C₄×C₁₃	—	2	2	no	—
543	C₄×C₁₃	—	2	4	no	—
544	C₄×C₁₃	—	2	2	no	—
545	C₄×C₁₃	C₂²×#41	1	4	yes	—
546	C₄×C₁₃	C₂²×#41	1	4	yes	—
547	C₄×C₁₃	C₂²×#41	1	4	yes	—
548	Dic₁₃	—	2	8	no	—
549	Dic₁₃	—	2	4	no	—
550	Dic₁₃	—	2	4	no	—
551	Dic₁₃	—	2	8	no	—
552	C₂⁵	—	13	2	no	—
553	C₂×#41	—	2	8	no	—
554	C₂×#41	—	13	16	no	—
555	C₂×#41	—	26	16	no	—
556	C₂×#41	C₂²×D₁₃	1	8	yes	—
557	C₂²×Q₈	—	13	2	no	—
558	C₂²×Q₈	—	13	2	no	—
559	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
560	C₂²×D₄	—	13	4	no	—
561	C₂²×D₄	—	13	4	no	—
562	C₂²×D₄	—	13	1	no	—
563	C₂²×D₄	—	13	2	no	—
564	C₂²×D₄	—	13	1	no	—
565	C₂²×D₄	—	13	8	no	—
566	C₂²×D₄	—	26	8	no	—
567	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
568	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
569	C₂³×C₄	—	13	2	no	—
570	C₂³×C₄	—	13	4	no	—
571	C₂³×C₄	—	13	2	no	—
572	C₂³×C₄	—	13	2	no	—
573	C₂³×C₄	—	13	16	no	—
574	C₂³×C₄	—	13	2	no	—
575	C₂³×C₄	—	13	2	no	—
576	C₂³×C₄	—	13	4	no	—
577	C₂³×C₄	—	26	16	no	—
578	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
579	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
580	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
581	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
582	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
583	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
584	C₄⋊Q₈	—	13	8	no	—
585	C₄⋊Q₈	—	13	8	no	—
586	#126	—	13	32	no	—
587	#126	—	13	32	no	—
588	#126	—	13	32	no	—
589	#125	—	13	32	no	—
590	#125	—	13	16	no	—
591	#125	—	13	16	no	—
592	#124	—	13	32	no	—
593	#124	—	13	16	no	—
594	#123	—	13	32	no	—
595	#123	—	13	32	no	—
596	#123	—	13	32	no	—
597	#123	—	13	32	no	—
598	C₂²⋊Q₈	—	13	16	no	—
599	C₂²⋊Q₈	—	13	16	no	—
600	C₂²⋊Q₈	—	13	16	no	—
601	C₂²⋊Q₈	—	13	16	no	—
602	C₂²⋊Q₈	—	13	16	no	—
603	C₂²⋊Q₈	—	13	32	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	C₄×Q₈	—	13	16	no	—
610	C₄×Q₈	—	13	16	no	—
611	C₄×Q₈	—	13	16	no	—
612	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
613	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
614	C₄×D₄	—	13	32	no	—
615	C₄×D₄	—	13	32	no	—
616	C₄×D₄	—	13	32	no	—
617	C₄×D₄	—	13	8	no	—
618	C₄×D₄	—	13	8	no	—
619	C₄×D₄	—	13	16	no	—
620	C₄×D₄	—	13	8	no	—
621	C₄×D₄	—	13	16	no	—
622	C₄×D₄	—	13	8	no	—
623	C₄×D₄	—	13	16	no	—
624	C₄×D₄	C₂²×D₁₃	1	16	yes	—
625	C₄×D₄	C₂²×D₁₃	1	16	yes	—
626	C₄×D₄	C₂²×D₁₃	1	8	yes	complemented
627	C₄×D₄	C₂²×D₁₃	1	8	yes	complemented
628	#117	—	13	16	no	—
629	#117	—	13	16	no	—
630	#117	—	13	16	no	—
631	#117	—	13	16	no	—
632	#117	—	13	32	no	—
633	#117	—	13	32	no	—
634	#117	—	13	32	no	—
635	#117	C₂²×D₁₃	1	8	yes	—
636	#117	C₂²×D₁₃	1	16	yes	complemented
637	C₂×C₄⋊C₄	—	13	1	no	—
638	C₂×C₄⋊C₄	—	13	2	no	—
639	C₂×C₄⋊C₄	—	13	2	no	—
640	C₂×C₄⋊C₄	—	13	4	no	—
641	C₂×C₄⋊C₄	—	13	4	no	—
642	C₂×C₄⋊C₄	—	13	1	no	—
643	C₂×C₄⋊C₄	—	13	2	no	—
644	C₂×C₄⋊C₄	—	13	8	no	—
645	C₂×C₄⋊C₄	—	13	2	no	—
646	C₂×C₄⋊C₄	—	13	4	no	—
647	C₂×C₄⋊C₄	—	13	4	no	—
648	C₂×C₄⋊C₄	—	13	4	no	—
649	C₂×C₄⋊C₄	—	13	4	no	—
650	C₂×C₄⋊C₄	—	13	2	no	—
651	C₂×C₄⋊C₄	—	13	16	no	—
652	C₂×C₄⋊C₄	—	13	16	no	—
653	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
657	C₂×C₂²⋊C₄	—	13	4	no	—
658	C₂×C₂²⋊C₄	—	13	4	no	—
659	C₂×C₂²⋊C₄	—	13	4	no	—
660	C₂×C₂²⋊C₄	—	13	2	no	—
661	C₂×C₂²⋊C₄	—	13	4	no	—
662	C₂×C₂²⋊C₄	—	13	4	no	—
663	C₂×C₂²⋊C₄	—	13	2	no	—
664	C₂×C₂²⋊C₄	—	13	2	no	—
665	C₂×C₂²⋊C₄	—	13	2	no	—
666	C₂×C₂²⋊C₄	—	13	16	no	—
667	C₂×C₂²⋊C₄	—	13	4	no	—
668	C₂×C₂²⋊C₄	—	13	4	no	—
669	C₂×C₂²⋊C₄	—	13	32	no	—
670	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
673	C₂×C₄²	—	13	4	no	—
674	C₂×C₄²	—	13	4	no	—
675	C₂×C₄²	—	13	4	no	—
676	C₂×C₄²	—	13	32	no	—
677	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
678	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
679	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
680	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
681	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
682	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
683	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
684	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
685	C₂×C₄²	C₂²×D₁₃	1	16	yes	complemented
686	C₂×C₁₃	—	2	4	no	—
687	C₂×C₁₃	—	4	4	no	—
688	C₂×C₁₃	#3475	1	4	yes	complemented
689	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
690	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
691	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
692	D₁₃	—	2	8	no	—
693	D₁₃	—	4	4	no	—
694	C₂⁴	—	13	2	no	—
695	C₂⁴	—	13	2	no	—
696	C₂⁴	—	13	8	no	—
697	C₂⁴	—	26	8	no	—
698	C₂⁴	—	26	8	no	—
699	C₂⁴	—	52	4	no	—
700	C₂⁴	C₂³×D₁₃	1	2	yes	—
701	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
702	#41	—	2	32	no	—
703	#41	—	26	64	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	13	8	no	—
706	C₂×Q₈	—	13	8	no	—
707	C₂×Q₈	—	26	8	no	—
708	C₂×Q₈	—	52	4	no	—
709	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
710	C₂×D₄	—	2	8	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	13	16	no	—
713	C₂×D₄	—	13	16	no	—
714	C₂×D₄	—	13	8	no	—
715	C₂×D₄	—	13	4	no	—
716	C₂×D₄	—	13	8	no	—
717	C₂×D₄	—	13	4	no	—
718	C₂×D₄	—	26	32	no	—
719	C₂×D₄	—	26	8	no	—
720	C₂×D₄	—	26	16	no	—
721	C₂×D₄	—	26	4	no	—
722	C₂×D₄	—	52	8	no	—
723	C₂×D₄	C₂³×D₁₃	1	8	yes	—
724	C₂×D₄	C₂³×D₁₃	1	4	yes	—
725	C₂²×C₄	—	2	8	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	8	no	—
728	C₂²×C₄	—	4	4	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	13	2	no	—
731	C₂²×C₄	—	13	4	no	—
732	C₂²×C₄	—	13	4	no	—
733	C₂²×C₄	—	13	2	no	—
734	C₂²×C₄	—	13	8	no	—
735	C₂²×C₄	—	13	8	no	—
736	C₂²×C₄	—	13	16	no	—
737	C₂²×C₄	—	13	8	no	—
738	C₂²×C₄	—	13	8	no	—
739	C₂²×C₄	—	13	8	no	—
740	C₂²×C₄	—	13	16	no	—
741	C₂²×C₄	—	26	16	no	—
742	C₂²×C₄	—	26	8	no	—
743	C₂²×C₄	—	26	8	no	—
744	C₂²×C₄	—	26	8	no	—
745	C₂²×C₄	—	26	8	no	—
746	C₂²×C₄	—	26	8	no	—
747	C₂²×C₄	—	26	64	no	—
748	C₂²×C₄	—	52	8	no	—
749	C₂²×C₄	#6127	1	8	yes	complemented
750	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
751	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
752	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
753	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
754	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
755	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
756	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
757	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
758	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
759	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
760	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
761	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
762	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
763	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
764	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
765	C₄⋊C₄	—	13	4	no	—
766	C₄⋊C₄	—	13	8	no	—
767	C₄⋊C₄	—	13	8	no	—
768	C₄⋊C₄	—	13	16	no	—
769	C₄⋊C₄	—	13	16	no	—
770	C₄⋊C₄	—	13	4	no	—
771	C₄⋊C₄	—	13	8	no	—
772	C₄⋊C₄	—	13	8	no	—
773	C₄⋊C₄	—	13	16	no	—
774	C₄⋊C₄	—	13	16	no	—
775	C₄⋊C₄	—	13	16	no	—
776	C₄⋊C₄	—	13	16	no	—
777	C₄⋊C₄	—	13	8	no	—
778	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
779	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
780	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
781	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
782	C₂²⋊C₄	—	13	16	no	—
783	C₂²⋊C₄	—	13	16	no	—
784	C₂²⋊C₄	—	13	16	no	—
785	C₂²⋊C₄	—	13	8	no	—
786	C₂²⋊C₄	—	13	16	no	—
787	C₂²⋊C₄	—	13	16	no	—
788	C₂²⋊C₄	—	13	8	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	C₂³×D₁₃	1	8	yes	—
794	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
795	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
796	C₄²	—	13	16	no	—
797	C₄²	—	13	16	no	—
798	C₄²	—	13	16	no	—
799	C₄²	C₂³×D₁₃	1	8	yes	—
800	C₄²	C₂³×D₁₃	1	4	yes	—
801	C₄²	C₂³×D₁₃	1	4	yes	—
802	C₄²	C₂³×D₁₃	1	4	yes	—
803	C₄²	C₂³×D₁₃	1	4	yes	—
804	C₄²	C₂³×D₁₃	1	8	yes	—
805	C₄²	C₂³×D₁₃	1	8	yes	—
806	C₁₃	C₂×#3475	1	1	yes	characteristic, complemented, Sylow
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	2	4	no	—
811	C₂³	—	2	4	no	—
812	C₂³	—	13	8	no	—
813	C₂³	—	13	4	no	—
814	C₂³	—	13	4	no	—
815	C₂³	—	26	16	no	—
816	C₂³	—	26	4	no	—
817	C₂³	—	26	4	no	—
818	C₂³	—	26	16	no	—
819	C₂³	—	26	4	no	—
820	C₂³	—	26	4	no	—
821	C₂³	—	26	4	no	—
822	C₂³	—	52	8	no	—
823	C₂³	—	52	32	no	—
824	C₂³	C₂×#6127	1	4	yes	—
825	C₂³	C₂⁴×D₁₃	1	4	yes	—
826	C₂³	C₂⁴×D₁₃	1	2	yes	—
827	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
828	Q₈	—	2	8	no	—
829	Q₈	—	26	16	no	—
830	Q₈	—	52	8	no	—
831	D₄	—	2	16	no	—
832	D₄	—	2	8	no	—
833	D₄	—	13	16	no	—
834	D₄	—	26	16	no	—
835	D₄	—	26	32	no	—
836	D₄	—	26	8	no	—
837	D₄	—	52	16	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	16	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	16	no	—
847	C₂×C₄	—	4	8	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	13	4	no	—
850	C₂×C₄	—	13	8	no	—
851	C₂×C₄	—	13	8	no	—
852	C₂×C₄	—	13	4	no	—
853	C₂×C₄	—	26	32	no	—
854	C₂×C₄	—	26	16	no	—
855	C₂×C₄	—	26	4	no	—
856	C₂×C₄	—	26	4	no	—
857	C₂×C₄	—	26	8	no	—
858	C₂×C₄	—	26	8	no	—
859	C₂×C₄	—	26	16	no	—
860	C₂×C₄	—	26	16	no	—
861	C₂×C₄	—	26	16	no	—
862	C₂×C₄	—	26	16	no	—
863	C₂×C₄	—	52	16	no	—
864	C₂×C₄	C₂×#6127	1	4	yes	—
865	C₂×C₄	C₂×#6127	1	4	yes	—
866	C₂×C₄	C₂×#6127	1	16	yes	complemented
867	C₂×C₄	#41×D₁₃	1	4	yes	—
868	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
869	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
870	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
871	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
872	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
873	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
874	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
875	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
876	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	8	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	4	8	no	—
884	C₂²	—	13	8	no	—
885	C₂²	—	26	4	no	—
886	C₂²	—	26	4	no	—
887	C₂²	—	26	16	no	—
888	C₂²	—	26	4	no	—
889	C₂²	—	26	4	no	—
890	C₂²	—	26	4	no	—
891	C₂²	—	52	32	no	—
892	C₂²	—	52	8	no	—
893	C₂²	C₂²×#6127	1	4	yes	—
894	C₂²	C₂²×#6127	1	2	yes	—
895	C₂²	C₂×#41×D₁₃	1	2	yes	—
896	C₂²	#11719648	1	2	yes	—
897	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
898	C₄	—	2	4	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	4	no	—
903	C₄	—	2	2	no	—
904	C₄	—	26	8	no	—
905	C₄	—	26	4	no	—
906	C₄	—	26	4	no	—
907	C₄	—	26	8	no	—
908	C₄	C₂²×#6127	1	4	yes	—
909	C₄	C₂²×#6127	1	4	yes	—
910	C₄	C₂×#41×D₁₃	1	4	yes	—
911	C₂	—	2	4	no	—
912	C₂	—	4	4	no	—
913	C₂	—	26	8	no	—
914	C₂	—	52	4	no	—
915	C₂	#13128400	1	4	yes	direct product factor
916	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic
917	C₂	C₂³×#6127	1	1	yes	characteristic
918	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₄×C₁₃×#41	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×C₄×#41	D₁₃
hypocenter	C₁₃	C₂×#3475
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #13128400	C₂	direct (N × H)
2. C₂×#11719289	C₂	semidirect
3. C₂×#11719268	C₂	semidirect
4. C₂×#11719284	C₂	semidirect
5. C₂×#11719263	C₂	semidirect
6. C₂×#11719286	C₂	semidirect
7. C₂×#11719246	C₂	semidirect
8. C₂×#11719261	C₂	semidirect
9. C₂×#11719256	C₂	semidirect
10. C₂×#11719255	C₂	semidirect
11. C₂×#11719175	C₂	semidirect
12. C₂×#11719184	C₂	semidirect
13. C₂×#11719233	C₂	semidirect
14. C₂×#11719533	C₂	semidirect
15. C₂×C₄×#6127	C₂	semidirect
16. C₂²×C₄×D₅₂	C₂	semidirect
17. C₂×D₁₃×#117	C₂	semidirect
18. C₂×C₄×C₁₃×#41	C₂	semidirect
23. C₄×C₁₃×#41	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂×C₁₃×#117	C₂²	semidirect
33. C₂²×C₄²×C₁₃	C₂²	semidirect
34. #11719533	C₂²	semidirect
35. C₂×#88200	C₂²	semidirect
36. C₂×#88200	C₂²	semidirect
37. C₂×#88192	C₂²	semidirect
38. C₂×#88192	C₂²	semidirect
42. C₂×#88183	C₂²	semidirect
43. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
44. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
45. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
48. C₂×#88180	C₂²	semidirect
52. C₂×#88178	C₂²	semidirect
53. #11719289	C₂²	semidirect
54. #11719286	C₂²	semidirect
55. #11719284	C₂²	semidirect
56. #11719268	C₂²	semidirect
57. #11719263	C₂²	semidirect
58. #11719261	C₂²	semidirect
59. #11719256	C₂²	semidirect
60. #11719255	C₂²	semidirect
61. #11719246	C₂²	semidirect
62. #11719233	C₂²	semidirect
63. D₁₃×#117	C₂²	semidirect
64. C₂×#88152	C₂²	semidirect
65. C₂×#88150	C₂²	semidirect
67. C₂×#88146	C₂²	semidirect
68. C₂×#88146	C₂²	semidirect
69. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
70. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
71. C₂×#88143	C₂²	semidirect
72. C₂×#88139	C₂²	semidirect
74. C₂×#88137	C₂²	semidirect
76. C₂×#88133	C₂²	semidirect
78. #11719184	C₂²	semidirect
79. C₂×#88130	C₂²	semidirect
81. C₄×#6127	C₂²	semidirect
89. C₂×C₄×D₅₂	C₂²	semidirect
90. C₂×#88126	C₂²	semidirect
91. C₂×#88126	C₂²	semidirect
92. C₂×C₄²×D₁₃	C₂²	semidirect
93. #11719175	C₂²	semidirect
94. C₂×#88124	C₂²	semidirect
95. C₂×#88124	C₂²	semidirect
96. C₂×#88123	C₂²	semidirect
97. C₂×#88123	C₂²	semidirect
98. C₂×C₄×Dic₂₆	C₂²	semidirect
99. C₂×C₄×Dic₂₆	C₂²	semidirect
100. C₂×C₄×Dic₂₆	C₂²	semidirect
133. C₄×Q₈×C₁₃	C₂³	semidirect
134. C₄×Q₈×C₁₃	C₂³	semidirect
137. C₄×D₄×C₁₃	C₂³	semidirect
138. C₄×D₄×C₁₃	C₂³	semidirect
140. C₁₃×#117	C₂³	semidirect
156. C₂×C₄²×C₁₃	C₂³	semidirect
160. #88200	C₂³	semidirect
161. #88200	C₂³	semidirect
162. #88192	C₂³	semidirect
163. #88192	C₂³	semidirect
167. #88183	C₂³	semidirect
168. C₄×C₂²⋊D₁₃	C₂³	semidirect
169. C₄×C₂²⋊D₁₃	C₂³	semidirect
170. C₄×C₂²⋊D₁₃	C₂³	semidirect
181. #88180	C₂³	semidirect
192. #88178	C₂³	semidirect
202. #88152	C₂³	semidirect
203. #88150	C₂³	semidirect
205. #88146	C₂³	semidirect
206. #88146	C₂³	semidirect
207. C₄⋊C₄×D₁₃	C₂³	semidirect
208. C₄⋊C₄×D₁₃	C₂³	semidirect
209. #88143	C₂³	semidirect
210. #88139	C₂³	semidirect
212. #88137	C₂³	semidirect
214. #88133	C₂³	semidirect
216. #88130	C₂³	semidirect
225. #88126	C₂³	semidirect
226. #88126	C₂³	semidirect
227. C₄²×D₁₃	C₂³	semidirect
228. #88124	C₂³	semidirect
229. #88124	C₂³	semidirect
230. #88123	C₂³	semidirect
231. #88123	C₂³	semidirect
232. C₄×Dic₂₆	C₂³	semidirect
233. C₄×Dic₂₆	C₂³	semidirect
234. C₄×Dic₂₆	C₂³	semidirect
256. C₂²×C₄×C₁₃	#41	semidirect
286. C₂×D₅₂	#41	semidirect
363. C₂×C₄×#41	D₁₃	semidirect
404. C₂×C₄×C₁₃	C₂×#41	semidirect
427. D₅₂	C₂×#41	semidirect
479. C₄×#41	C₂×D₁₃	semidirect
483. C₂×C₄×Q₈	C₂×D₁₃	semidirect
484. C₂×C₄×Q₈	C₂×D₁₃	semidirect
498. C₂×C₄×D₄	C₂×D₁₃	semidirect
499. C₂×C₄×D₄	C₂×D₁₃	semidirect
509. C₂×#117	C₂×D₁₃	semidirect
517. C₂²×C₄²	C₂×D₁₃	semidirect
612. C₄×Q₈	C₂²×D₁₃	semidirect
613. C₄×Q₈	C₂²×D₁₃	semidirect
626. C₄×D₄	C₂²×D₁₃	semidirect
627. C₄×D₄	C₂²×D₁₃	semidirect
636. #117	C₂²×D₁₃	semidirect
685. C₂×C₄²	C₂²×D₁₃	semidirect
688. C₂×C₁₃	#3475	semidirect
749. C₂²×C₄	#6127	semidirect
806. C₁₃	C₂×#3475	semidirect
866. C₂×C₄	C₂×#6127	semidirect
915. C₂	#13128400	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128400	2
C₂×#11719289	2
C₂×#11719268	2
C₂×#11719284	2
C₂×#11719263	2
C₂×#11719286	2
C₂×#11719246	2
C₂×#11719261	2
C₂×#11719256	2
C₂×#11719255	2
C₂×#11719175	2
C₂×#11719184	2
C₂×#11719233	2
C₂×#11719533	2
C₂×C₄×#6127	2
C₂²×C₄×D₅₂	2
C₂×D₁₃×#117	2
C₂×C₄×C₁₃×#41	2
C₂×#3475	13

Subgroups — C2×#13128400 #16769957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128400 #16769957