Subgroups — C₂×#13129359 #16770249

Order 3328.

8122 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129359	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719389	C₂	1	2	yes	maximal, complemented
3	C₂×#11719388	C₂	1	2	yes	maximal, complemented
4	C₂×#11719264	C₂	1	2	yes	maximal, complemented
5	C₂×#11719303	C₂	1	2	yes	maximal, complemented
6	C₂×#11719259	C₂	1	2	yes	maximal, complemented
7	C₂×#11719534	C₂	1	4	yes	maximal, complemented
8	C₂×#11719314	C₂	1	2	yes	maximal, complemented
9	C₂×#11719438	C₂	1	2	yes	maximal, complemented
10	C₂×#11719322	C₂	1	2	yes	maximal, complemented
11	C₂×#11719265	C₂	1	4	yes	maximal, complemented
12	C₂×#11719420	C₂	1	2	yes	maximal, complemented
13	C₂×#11719310	C₂	1	2	yes	maximal, complemented
14	C₂×#11719184	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#88129	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
18	C₂²×#6129	C₂²	1	2	yes	complemented
19	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
20	C₂²×D₄×D₁₃	C₂²	1	2	yes	complemented
21	C₂³×D₅₂	C₂²	1	1	yes	characteristic
22	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#532	C₂²	1	16	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
32	#11719534	C₂²	1	64	yes	complemented
33	C₂×#88201	C₂²	1	4	yes	complemented
34	C₂×#88200	C₂²	1	4	yes	complemented
35	C₂×#88194	C₂²	1	2	yes	—
36	C₂×#88193	C₂²	1	4	yes	complemented
37	C₂×#88193	C₂²	1	4	yes	complemented
38	C₂×#88193	C₂²	1	4	yes	complemented
39	C₂×#88191	C₂²	1	4	yes	complemented
40	C₂×#88191	C₂²	1	4	yes	complemented
41	C₂×#88191	C₂²	1	4	yes	complemented
42	C₂×#88190	C₂²	1	2	yes	complemented
43	C₂×D₄×Dic₁₃	C₂²	1	4	yes	complemented
44	C₂×#88184	C₂²	1	1	yes	characteristic
45	C₂×#88184	C₂²	1	4	yes	complemented
46	C₂×#88183	C₂²	1	2	yes	complemented
47	C₂×#88183	C₂²	1	4	yes	complemented
48	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
49	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
50	C₂²×#6103	C₂²	1	2	yes	complemented
51	C₂²×#6103	C₂²	1	4	yes	complemented
52	C₂²×#6103	C₂²	1	2	yes	complemented
53	C₂×#88178	C₂²	1	1	yes	characteristic, complemented
54	#11719438	C₂²	1	32	yes	complemented
55	#11719420	C₂²	1	32	yes	complemented
56	#11719389	C₂²	1	32	yes	complemented
57	#11719388	C₂²	1	32	yes	complemented
58	#11719322	C₂²	1	32	yes	complemented
59	#11719314	C₂²	1	32	yes	complemented
60	#11719310	C₂²	1	32	yes	complemented
61	#11719303	C₂²	1	32	yes	complemented
62	#11719265	C₂²	1	64	yes	complemented
63	#11719264	C₂²	1	32	yes	complemented
64	#11719259	C₂²	1	32	yes	complemented
65	C₂×#88152	C₂²	1	4	yes	complemented
66	C₂×#88151	C₂²	1	2	yes	complemented
67	C₂×#88149	C₂²	1	2	yes	—
68	C₂×#88148	C₂²	1	4	yes	complemented
69	C₂×#88147	C₂²	1	2	yes	complemented
70	C₂×#88141	C₂²	1	2	yes	complemented
71	C₂×#88140	C₂²	1	4	yes	complemented
72	C₂×#88139	C₂²	1	4	yes	complemented
73	C₂×#88139	C₂²	1	4	yes	complemented
74	C₂×#88138	C₂²	1	4	yes	complemented
75	C₂×#88137	C₂²	1	4	yes	complemented
76	C₂×#88136	C₂²	1	4	yes	complemented
77	C₂×#88136	C₂²	1	4	yes	complemented
78	C₂×#88132	C₂²	1	4	yes	complemented
79	#11719184	C₂²	1	16	yes	complemented
80	C₂×#88130	C₂²	1	2	yes	complemented
81	C₂×#88129	C₂²	1	2	yes	complemented
82	C₂×#88129	C₂²	1	2	yes	complemented
83	C₂×#88129	C₂²	1	2	yes	complemented
84	C₂×#88129	C₂²	1	2	yes	complemented
85	C₂×#88129	C₂²	1	1	yes	characteristic, complemented
86	C₂×#88129	C₂²	1	16	yes	complemented
87	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
88	C₂×#88126	C₂²	1	2	yes	complemented
89	C₂×#88124	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₁₃	C₂³	1	2	yes	—
92	C₂⁴×D₁₃	C₂³	1	4	yes	—
93	C₂×C₁₃×#41	—	4	8	no	—
94	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
95	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
104	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
105	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
106	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
108	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
109	C₂³×Dic₁₃	C₂³	1	4	yes	—
110	C₂³×Dic₁₃	C₂³	1	2	yes	—
111	C₂×#6129	—	4	8	no	—
112	C₂×#6129	C₂³	1	16	yes	complemented
113	C₂×D₄×D₁₃	—	4	8	no	—
114	C₂×D₄×D₁₃	—	4	16	no	—
115	C₂×D₄×D₁₃	C₂³	1	16	yes	complemented
116	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
117	C₂²×D₅₂	—	4	4	no	—
118	C₂²×D₅₂	C₂³	1	2	yes	—
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	4	yes	—
123	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
124	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
125	C₂²×Dic₂₆	—	4	4	no	—
126	C₂²×Dic₂₆	C₂³	1	2	yes	—
127	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
128	C₂²×Dic₂₆	C₂³	1	2	yes	—
129	C₂²×Dic₂₆	C₂³	1	8	yes	complemented
130	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
131	C₁₃×#127	C₂³	1	8	yes	complemented
132	C₁₃×#124	C₂³	1	16	yes	complemented
133	C₁₃×#121	C₂³	1	16	yes	complemented
134	C₁₃×#121	C₂³	1	16	yes	complemented
135	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
136	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
146	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
147	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
148	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
149	#88201	C₂³	1	32	yes	complemented
150	#88200	C₂³	1	32	yes	complemented
151	#88194	C₂³	1	16	yes	—
152	#88193	C₂³	1	32	yes	complemented
153	#88193	C₂³	1	32	yes	complemented
154	#88193	C₂³	1	32	yes	complemented
155	#88191	C₂³	1	32	yes	complemented
156	#88191	C₂³	1	32	yes	complemented
157	#88191	C₂³	1	32	yes	complemented
158	#88190	C₂³	1	16	yes	complemented
159	D₄×Dic₁₃	C₂³	1	32	yes	complemented
160	#88184	C₂³	1	8	yes	—
161	#88184	C₂³	1	32	yes	complemented
162	#88183	C₂³	1	16	yes	complemented
163	#88183	C₂³	1	32	yes	complemented
164	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	complemented
165	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
166	C₂×#6103	C₂³	1	2	yes	—
167	C₂×#6103	C₂³	1	2	yes	—
168	C₂×#6103	C₂³	1	2	yes	—
169	C₂×#6103	C₂³	1	4	yes	—
170	C₂×#6103	C₂³	1	4	yes	—
171	C₂×#6103	C₂³	1	4	yes	—
172	C₂×#6103	C₂³	1	4	yes	—
173	C₂×#6103	C₂³	1	2	yes	—
174	C₂×#6103	C₂³	1	4	yes	—
175	C₂×#6103	C₂³	1	4	yes	—
176	C₂×#6103	C₂³	1	4	yes	—
177	C₂×#6103	C₂³	1	16	yes	complemented
178	C₂×#6103	C₂³	1	16	yes	complemented
179	C₂×#6103	C₂³	1	32	yes	complemented
180	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
183	#88178	C₂³	1	8	yes	complemented
184	C₂×#6101	C₂³	1	2	yes	—
185	C₂×#6101	C₂³	1	2	yes	—
186	C₂×#6101	C₂³	1	2	yes	—
187	C₂×#6101	C₂³	1	2	yes	—
188	C₂×#6101	C₂³	1	4	yes	—
189	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
190	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
191	#88152	C₂³	1	32	yes	complemented
192	#88151	C₂³	1	16	yes	complemented
193	#88149	C₂³	1	16	yes	—
194	#88148	C₂³	1	32	yes	complemented
195	#88147	C₂³	1	16	yes	complemented
196	#88141	C₂³	1	16	yes	complemented
197	#88140	C₂³	1	32	yes	complemented
198	#88139	C₂³	1	32	yes	complemented
199	#88139	C₂³	1	32	yes	complemented
200	#88138	C₂³	1	32	yes	complemented
201	#88137	C₂³	1	32	yes	complemented
202	#88136	C₂³	1	32	yes	complemented
203	#88136	C₂³	1	32	yes	complemented
204	#88132	C₂³	1	32	yes	complemented
205	#88130	C₂³	1	16	yes	complemented
206	#88129	C₂³	1	16	yes	complemented
207	#88129	C₂³	1	16	yes	complemented
208	#88129	C₂³	1	16	yes	complemented
209	#88129	C₂³	1	16	yes	complemented
210	#88129	C₂³	1	8	yes	complemented
211	C₄×D₅₂	C₂³	1	8	yes	complemented
212	#88126	C₂³	1	16	yes	complemented
213	#88124	C₂³	1	8	yes	complemented
214	C₄×Dic₂₆	C₂³	1	8	yes	complemented
215	C₂×#3558	—	13	1	no	maximal, Sylow
216	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
217	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₂³×D₁₃	—	2	8	no	—
219	C₂³×D₁₃	—	4	4	no	—
220	C₂³×D₁₃	—	4	8	no	—
221	C₂³×D₁₃	—	4	8	no	—
222	C₂³×D₁₃	—	4	8	no	—
223	C₂³×D₁₃	—	4	4	no	—
224	C₂³×D₁₃	C₂⁴	1	2	yes	—
225	C₂³×D₁₃	C₂⁴	1	4	yes	—
226	C₂³×D₁₃	C₂⁴	1	8	yes	—
227	C₂³×D₁₃	C₂⁴	1	16	yes	—
228	C₁₃×#41	—	4	32	no	—
229	C₂×Q₈×C₁₃	—	4	4	no	—
230	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
231	C₂×D₄×C₁₃	—	2	16	no	—
232	C₂×D₄×C₁₃	—	2	8	no	—
233	C₂×D₄×C₁₃	—	4	4	no	—
234	C₂×D₄×C₁₃	—	4	4	no	—
235	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
236	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
237	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
239	C₂²×C₄×C₁₃	—	2	4	no	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	8	no	—
243	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₂²⋊D₁₃	—	2	8	no	—
255	C₂×C₂²⋊D₁₃	—	4	8	no	—
256	C₂×C₂²⋊D₁₃	—	4	8	no	—
257	C₂×C₂²⋊D₁₃	—	4	8	no	—
258	C₂×C₂²⋊D₁₃	—	4	8	no	—
259	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
260	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
261	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
262	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
263	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
264	C₂²×Dic₁₃	—	4	4	no	—
265	C₂²×Dic₁₃	—	4	8	no	—
266	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
267	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
268	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
269	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
270	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
271	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
272	#6129	—	4	32	no	—
273	D₄×D₁₃	—	4	32	no	—
274	D₄×D₁₃	—	4	64	no	—
275	C₂×D₅₂	—	2	8	no	—
276	C₂×D₅₂	—	4	16	no	—
277	C₂×D₅₂	—	4	4	no	—
278	C₂×D₅₂	—	4	2	no	—
279	C₂×D₅₂	—	4	8	no	—
280	C₂×D₅₂	C₂⁴	1	8	yes	—
281	C₂×D₅₂	C₂⁴	1	4	yes	—
282	C₂×D₅₂	C₂⁴	1	8	yes	—
283	C₂×D₅₂	C₂⁴	1	16	yes	—
284	C₂×C₄×D₁₃	—	2	8	no	—
285	C₂×C₄×D₁₃	—	4	8	no	—
286	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
287	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
288	C₂×Dic₂₆	—	2	8	no	—
289	C₂×Dic₂₆	—	4	16	no	—
290	C₂×Dic₂₆	—	4	4	no	—
291	C₂×Dic₂₆	—	4	2	no	—
292	C₂×Dic₂₆	C₂⁴	1	8	yes	—
293	C₂×Dic₂₆	C₂⁴	1	4	yes	—
294	C₂×Dic₂₆	C₂⁴	1	8	yes	—
295	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
296	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
297	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
298	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
299	C₄²×C₁₃	C₂⁴	1	4	yes	—
300	C₄²×C₁₃	C₂⁴	1	4	yes	—
301	C₄²×C₁₃	C₂⁴	1	4	yes	—
302	C₄²×C₁₃	C₂⁴	1	4	yes	—
303	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
304	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
305	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
306	#6103	C₂⁴	1	8	yes	—
307	#6103	C₂⁴	1	8	yes	—
308	#6103	C₂⁴	1	8	yes	—
309	#6103	C₂⁴	1	16	yes	—
310	#6103	C₂⁴	1	16	yes	—
311	#6103	C₂⁴	1	16	yes	—
312	#6103	C₂⁴	1	16	yes	—
313	#6103	C₂⁴	1	8	yes	—
314	#6103	C₂⁴	1	16	yes	—
315	#6103	C₂⁴	1	16	yes	—
316	#6103	C₂⁴	1	16	yes	—
317	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
318	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
319	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
320	#6101	C₂⁴	1	8	yes	—
321	#6101	C₂⁴	1	8	yes	—
322	#6101	C₂⁴	1	8	yes	—
323	#6101	C₂⁴	1	8	yes	—
324	#6101	C₂⁴	1	16	yes	—
325	C₄×Dic₁₃	C₂⁴	1	8	yes	—
326	C₄×Dic₁₃	C₂⁴	1	16	yes	—
327	#3558	—	13	32	no	—
328	C₂×#562	—	13	2	no	—
329	C₂×H(3,𝔽₄)	—	13	2	no	—
330	C₂×#559	—	13	2	no	—
331	C₂×#548	—	13	2	no	—
332	C₂×#546	—	13	4	no	—
333	C₂×#546	—	13	2	no	—
334	C₂×D₄²	—	13	2	no	—
335	C₂×#542	—	13	2	no	—
336	C₂×#538	—	13	2	no	—
337	C₂×#538	—	13	4	no	—
338	C₂×#535	—	13	2	no	—
339	C₂×#534	—	13	2	no	—
340	C₂×#532	D₁₃	1	1	yes	characteristic, complemented
341	C₂×#529	—	13	1	no	—
342	C₂²×#124	—	13	1	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	8	no	—
346	C₂³×C₁₃	—	2	8	no	—
347	C₂³×C₁₃	—	2	8	no	—
348	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
349	C₂³×C₁₃	C₂⁵	1	8	yes	—
350	C₂³×C₁₃	C₂⁵	1	2	yes	—
351	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
352	C₂²×D₁₃	—	2	4	no	—
353	C₂²×D₁₃	—	2	8	no	—
354	C₂²×D₁₃	—	2	8	no	—
355	C₂²×D₁₃	—	2	4	no	—
356	C₂²×D₁₃	—	2	4	no	—
357	C₂²×D₁₃	—	2	8	no	—
358	C₂²×D₁₃	—	2	16	no	—
359	C₂²×D₁₃	—	4	8	no	—
360	C₂²×D₁₃	—	4	16	no	—
361	C₂²×D₁₃	—	4	16	no	—
362	C₂²×D₁₃	—	4	16	no	—
363	C₂²×D₁₃	—	4	8	no	—
364	C₂²×D₁₃	—	8	16	no	—
365	C₂²×D₁₃	—	8	32	no	—
366	C₂²×D₁₃	C₂⁵	1	4	yes	—
367	C₂²×D₁₃	C₂⁵	1	8	yes	—
368	Q₈×C₁₃	—	4	8	no	—
369	D₄×C₁₃	—	2	32	no	—
370	D₄×C₁₃	—	2	16	no	—
371	D₄×C₁₃	—	4	8	no	—
372	D₄×C₁₃	—	4	8	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	8	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	8	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	8	no	—
381	C₂×C₄×C₁₃	—	4	4	no	—
382	C₂×C₄×C₁₃	—	4	16	no	—
383	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
384	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
385	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
386	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
387	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
388	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
389	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
390	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
391	C₂²⋊D₁₃	—	2	16	no	—
392	C₂²⋊D₁₃	—	4	16	no	—
393	C₂²⋊D₁₃	—	4	16	no	—
394	C₂²⋊D₁₃	—	4	16	no	—
395	C₂²⋊D₁₃	—	4	16	no	—
396	C₂×Dic₁₃	—	2	8	no	—
397	C₂×Dic₁₃	—	2	4	no	—
398	C₂×Dic₁₃	—	2	4	no	—
399	C₂×Dic₁₃	—	2	4	no	—
400	C₂×Dic₁₃	—	4	8	no	—
401	C₂×Dic₁₃	—	4	16	no	—
402	C₂×Dic₁₃	C₂⁵	1	4	yes	—
403	C₂×Dic₁₃	C₂⁵	1	4	yes	—
404	C₂×Dic₁₃	C₂⁵	1	8	yes	—
405	C₂×Dic₁₃	C₂⁵	1	4	yes	—
406	D₅₂	—	2	16	no	—
407	D₅₂	—	4	8	no	—
408	D₅₂	—	4	4	no	—
409	D₅₂	—	4	16	no	—
410	C₄×D₁₃	—	2	16	no	—
411	C₄×D₁₃	—	4	16	no	—
412	Dic₂₆	—	2	16	no	—
413	Dic₂₆	—	4	8	no	—
414	Dic₂₆	—	4	4	no	—
415	C₂²×#41	—	13	2	no	—
416	C₂²×#41	C₂×D₁₃	1	2	yes	complemented
417	C₂³×Q₈	—	13	1	no	—
418	C₂³×D₄	—	13	4	no	—
419	C₂³×D₄	—	13	2	no	—
420	C₂³×D₄	—	13	1	no	—
421	#562	—	13	32	no	—
422	H(3,𝔽₄)	—	13	32	no	—
423	#559	—	13	32	no	—
424	#548	—	13	32	no	—
425	#546	—	13	64	no	—
426	#546	—	13	32	no	—
427	D₄²	—	13	32	no	—
428	#542	—	13	32	no	—
429	#538	—	13	32	no	—
430	#538	—	13	64	no	—
431	#535	—	13	32	no	—
432	#534	—	13	32	no	—
433	#532	C₂×D₁₃	1	16	yes	complemented
434	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
435	C₂×#127	—	13	2	no	—
436	C₂×#127	C₂×D₁₃	1	1	yes	characteristic, complemented
437	#529	—	13	16	no	—
438	C₂×#126	—	13	4	no	—
439	C₂×#126	—	13	2	no	—
440	C₂×#125	—	13	1	no	—
441	C₂×#124	—	13	4	no	—
442	C₂×#124	—	13	2	no	—
443	C₂×#124	—	13	4	no	—
444	C₂×#124	—	13	4	no	—
445	C₂×#124	—	13	2	no	—
446	C₂×#124	—	13	2	no	—
447	C₂×#124	—	13	2	no	—
448	C₂×#124	—	13	2	no	—
449	C₂×#124	—	13	1	no	—
450	C₂×#124	—	13	16	no	—
451	C₂×#124	C₂×D₁₃	1	2	yes	complemented
452	C₂×#123	—	13	2	no	—
453	C₂×#123	—	13	4	no	—
454	C₂×#123	—	13	4	no	—
455	C₂×#123	—	13	4	no	—
456	C₂×#123	—	13	4	no	—
457	C₂×C₂²⋊Q₈	—	13	4	no	—
458	C₂×C₂²⋊Q₈	—	13	1	no	—
459	C₂×C₂²⋊Q₈	—	13	2	no	—
460	C₂×C₂²⋊Q₈	—	13	4	no	—
461	C₂×#121	—	13	4	no	—
462	C₂×#121	—	13	4	no	—
463	C₂×#121	—	13	4	no	—
464	C₂×#121	—	13	1	no	—
465	C₂×#121	—	13	4	no	—
466	C₂×#121	—	13	2	no	—
467	C₂×#121	—	13	4	no	—
468	C₂×#121	C₂×D₁₃	1	2	yes	complemented
469	C₂×#121	C₂×D₁₃	1	2	yes	complemented
470	C₂×#120	—	13	4	no	—
471	C₂×#120	—	13	4	no	—
472	C₂×#120	—	13	4	no	—
473	C₂×#120	—	13	4	no	—
474	C₂×#120	—	13	4	no	—
475	C₂×C₄×Q₈	—	13	2	no	—
476	C₂×C₄×Q₈	—	13	1	no	—
477	C₂×C₄×D₄	—	13	4	no	—
478	C₂×C₄×D₄	—	13	2	no	—
479	C₂×C₄×D₄	—	13	4	no	—
480	C₂×C₄×D₄	—	13	2	no	—
481	C₂×C₄×D₄	—	13	1	no	—
482	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
483	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
484	C₂×#117	—	13	2	no	—
485	C₂²×C₂²⋊C₄	—	13	2	no	—
486	C₂²×C₂²⋊C₄	—	13	2	no	—
487	C₂²×C₂²⋊C₄	—	13	4	no	—
488	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
489	C₂²×C₁₃	—	2	2	no	—
490	C₂²×C₁₃	—	2	2	no	—
491	C₂²×C₁₃	—	2	8	no	—
492	C₂²×C₁₃	—	2	8	no	—
493	C₂²×C₁₃	—	2	8	no	—
494	C₂²×C₁₃	—	2	8	no	—
495	C₂²×C₁₃	—	4	16	no	—
496	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
497	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
498	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
499	C₂²×C₁₃	#585	1	2	yes	—
500	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
501	C₂×D₁₃	—	2	4	no	—
502	C₂×D₁₃	—	2	8	no	—
503	C₂×D₁₃	—	2	8	no	—
504	C₂×D₁₃	—	2	4	no	—
505	C₂×D₁₃	—	2	4	no	—
506	C₂×D₁₃	—	2	8	no	—
507	C₂×D₁₃	—	4	8	no	—
508	C₂×D₁₃	—	4	16	no	—
509	C₂×D₁₃	—	8	16	no	—
510	C₂×D₁₃	—	8	32	no	—
511	C₄×C₁₃	—	2	2	no	—
512	C₄×C₁₃	—	2	8	no	—
513	C₄×C₁₃	—	2	2	no	—
514	C₄×C₁₃	—	2	2	no	—
515	C₄×C₁₃	—	2	2	no	—
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
518	Dic₁₃	—	2	8	no	—
519	Dic₁₃	—	2	4	no	—
520	Dic₁₃	—	2	4	no	—
521	Dic₁₃	—	2	4	no	—
522	C₂⁵	—	13	2	no	—
523	C₂⁵	—	13	4	no	—
524	C₂×#41	—	4	8	no	—
525	C₂×#41	—	13	16	no	—
526	C₂×#41	—	52	8	no	—
527	C₂×#41	C₂²×D₁₃	1	16	yes	complemented
528	C₂²×Q₈	—	13	2	no	—
529	C₂²×Q₈	—	13	1	no	—
530	C₂²×Q₈	—	13	2	no	—
531	C₂²×Q₈	—	13	8	no	—
532	C₂²×Q₈	—	52	4	no	—
533	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
534	C₂²×D₄	—	13	2	no	—
535	C₂²×D₄	—	13	4	no	—
536	C₂²×D₄	—	13	4	no	—
537	C₂²×D₄	—	13	4	no	—
538	C₂²×D₄	—	13	4	no	—
539	C₂²×D₄	—	13	32	no	—
540	C₂²×D₄	—	13	16	no	—
541	C₂²×D₄	—	13	2	no	—
542	C₂²×D₄	—	13	1	no	—
543	C₂²×D₄	—	13	4	no	—
544	C₂²×D₄	—	13	2	no	—
545	C₂²×D₄	—	13	8	no	—
546	C₂²×D₄	—	52	4	no	—
547	C₂²×D₄	—	52	8	no	—
548	C₂²×D₄	—	52	16	no	—
549	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
550	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
551	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
552	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
553	C₂³×C₄	—	13	2	no	—
554	C₂³×C₄	—	13	4	no	—
555	C₂³×C₄	—	13	2	no	—
556	C₂³×C₄	—	13	4	no	—
557	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
558	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
559	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
560	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
561	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
562	#127	—	13	16	no	—
563	#127	C₂²×D₁₃	1	8	yes	complemented
564	#126	—	13	32	no	—
565	#126	—	13	16	no	—
566	#125	—	13	8	no	—
567	#124	—	13	32	no	—
568	#124	—	13	16	no	—
569	#124	—	13	32	no	—
570	#124	—	13	32	no	—
571	#124	—	13	16	no	—
572	#124	—	13	16	no	—
573	#124	—	13	16	no	—
574	#124	—	13	16	no	—
575	#124	—	13	8	no	—
576	#124	C₂²×D₁₃	1	16	yes	complemented
577	#123	—	13	16	no	—
578	#123	—	13	32	no	—
579	#123	—	13	32	no	—
580	#123	—	13	32	no	—
581	#123	—	13	32	no	—
582	C₂²⋊Q₈	—	13	32	no	—
583	C₂²⋊Q₈	—	13	8	no	—
584	C₂²⋊Q₈	—	13	16	no	—
585	C₂²⋊Q₈	—	13	32	no	—
586	#121	—	13	32	no	—
587	#121	—	13	32	no	—
588	#121	—	13	32	no	—
589	#121	—	13	8	no	—
590	#121	—	13	32	no	—
591	#121	—	13	16	no	—
592	#121	—	13	32	no	—
593	#121	C₂²×D₁₃	1	16	yes	complemented
594	#121	C₂²×D₁₃	1	16	yes	complemented
595	#120	—	13	32	no	—
596	#120	—	13	32	no	—
597	#120	—	13	32	no	—
598	#120	—	13	32	no	—
599	#120	—	13	32	no	—
600	C₄×Q₈	—	13	16	no	—
601	C₄×Q₈	—	13	8	no	—
602	C₄×D₄	—	13	32	no	—
603	C₄×D₄	—	13	16	no	—
604	C₄×D₄	—	13	32	no	—
605	C₄×D₄	—	13	16	no	—
606	C₄×D₄	—	13	8	no	—
607	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
608	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
609	#117	—	13	16	no	—
610	C₂×C₄⋊C₄	—	13	2	no	—
611	C₂×C₄⋊C₄	—	13	2	no	—
612	C₂×C₄⋊C₄	—	13	2	no	—
613	C₂×C₄⋊C₄	—	13	2	no	—
614	C₂×C₄⋊C₄	—	13	4	no	—
615	C₂×C₄⋊C₄	—	13	1	no	—
616	C₂×C₄⋊C₄	—	13	4	no	—
617	C₂×C₄⋊C₄	—	13	1	no	—
618	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
620	C₂×C₂²⋊C₄	—	13	2	no	—
621	C₂×C₂²⋊C₄	—	13	4	no	—
622	C₂×C₂²⋊C₄	—	13	4	no	—
623	C₂×C₂²⋊C₄	—	13	2	no	—
624	C₂×C₂²⋊C₄	—	13	4	no	—
625	C₂×C₂²⋊C₄	—	13	4	no	—
626	C₂×C₂²⋊C₄	—	13	4	no	—
627	C₂×C₂²⋊C₄	—	13	4	no	—
628	C₂×C₂²⋊C₄	—	13	4	no	—
629	C₂×C₂²⋊C₄	—	13	4	no	—
630	C₂×C₂²⋊C₄	—	13	16	no	—
631	C₂×C₂²⋊C₄	—	13	16	no	—
632	C₂×C₂²⋊C₄	—	13	32	no	—
633	C₂×C₂²⋊C₄	—	13	2	no	—
634	C₂×C₂²⋊C₄	—	13	2	no	—
635	C₂×C₂²⋊C₄	—	13	4	no	—
636	C₂×C₂²⋊C₄	—	13	2	no	—
637	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
638	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
639	C₂×C₄²	—	13	2	no	—
640	C₂×C₄²	—	13	4	no	—
641	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
642	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
644	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
645	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
646	C₂×C₁₃	—	2	4	no	—
647	C₂×C₁₃	—	4	8	no	—
648	C₂×C₁₃	#3558	1	4	yes	complemented
649	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
650	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
651	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
652	D₁₃	—	4	4	no	—
653	D₁₃	—	4	8	no	—
654	C₂⁴	—	13	4	no	—
655	C₂⁴	—	13	2	no	—
656	C₂⁴	—	13	8	no	—
657	C₂⁴	—	13	16	no	—
658	C₂⁴	—	26	8	no	—
659	C₂⁴	—	52	4	no	—
660	C₂⁴	—	52	8	no	—
661	C₂⁴	—	52	8	no	—
662	C₂⁴	—	52	4	no	—
663	C₂⁴	—	52	8	no	—
664	C₂⁴	C₂³×D₁₃	1	4	yes	—
665	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
666	#41	—	4	32	no	—
667	#41	—	52	32	no	—
668	C₂×Q₈	—	4	4	no	—
669	C₂×Q₈	—	13	8	no	—
670	C₂×Q₈	—	13	4	no	—
671	C₂×Q₈	—	13	8	no	—
672	C₂×Q₈	—	26	8	no	—
673	C₂×Q₈	—	52	4	no	—
674	C₂×Q₈	—	52	2	no	—
675	C₂×Q₈	—	52	16	no	—
676	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
677	C₂×D₄	—	2	16	no	—
678	C₂×D₄	—	2	8	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	—	13	8	no	—
682	C₂×D₄	—	13	16	no	—
683	C₂×D₄	—	13	16	no	—
684	C₂×D₄	—	13	16	no	—
685	C₂×D₄	—	13	16	no	—
686	C₂×D₄	—	13	8	no	—
687	C₂×D₄	—	13	4	no	—
688	C₂×D₄	—	13	16	no	—
689	C₂×D₄	—	13	8	no	—
690	C₂×D₄	—	26	8	no	—
691	C₂×D₄	—	26	8	no	—
692	C₂×D₄	—	52	16	no	—
693	C₂×D₄	—	52	8	no	—
694	C₂×D₄	—	52	4	no	—
695	C₂×D₄	—	52	2	no	—
696	C₂×D₄	—	52	32	no	—
697	C₂×D₄	—	52	8	no	—
698	C₂×D₄	—	52	8	no	—
699	C₂×D₄	—	52	8	no	—
700	C₂×D₄	—	52	8	no	—
701	C₂×D₄	—	52	64	no	—
702	C₂×D₄	C₂³×D₁₃	1	16	yes	—
703	C₂×D₄	C₂³×D₁₃	1	8	yes	—
704	C₂×D₄	C₂³×D₁₃	1	8	yes	—
705	C₂×D₄	C₂³×D₁₃	1	8	yes	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	4	8	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	13	2	no	—
711	C₂²×C₄	—	13	4	no	—
712	C₂²×C₄	—	13	2	no	—
713	C₂²×C₄	—	13	2	no	—
714	C₂²×C₄	—	13	8	no	—
715	C₂²×C₄	—	13	16	no	—
716	C₂²×C₄	—	13	8	no	—
717	C₂²×C₄	—	13	16	no	—
718	C₂²×C₄	—	26	8	no	—
719	C₂²×C₄	—	52	8	no	—
720	C₂²×C₄	—	52	4	no	—
721	C₂²×C₄	—	52	8	no	—
722	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
723	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
724	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
725	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
727	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
728	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
729	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
730	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
731	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
732	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
733	C₄⋊C₄	—	13	8	no	—
734	C₄⋊C₄	—	13	8	no	—
735	C₄⋊C₄	—	13	8	no	—
736	C₄⋊C₄	—	13	8	no	—
737	C₄⋊C₄	—	13	16	no	—
738	C₄⋊C₄	—	13	4	no	—
739	C₄⋊C₄	—	13	16	no	—
740	C₄⋊C₄	—	13	4	no	—
741	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
742	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
743	C₂²⋊C₄	—	13	8	no	—
744	C₂²⋊C₄	—	13	16	no	—
745	C₂²⋊C₄	—	13	16	no	—
746	C₂²⋊C₄	—	13	8	no	—
747	C₂²⋊C₄	—	13	16	no	—
748	C₂²⋊C₄	—	13	16	no	—
749	C₂²⋊C₄	—	13	16	no	—
750	C₂²⋊C₄	—	13	16	no	—
751	C₂²⋊C₄	—	13	16	no	—
752	C₂²⋊C₄	—	13	16	no	—
753	C₂²⋊C₄	—	13	8	no	—
754	C₂²⋊C₄	—	13	8	no	—
755	C₂²⋊C₄	—	13	16	no	—
756	C₂²⋊C₄	—	13	8	no	—
757	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
758	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
759	C₄²	—	13	8	no	—
760	C₄²	—	13	16	no	—
761	C₄²	C₂³×D₁₃	1	4	yes	—
762	C₄²	C₂³×D₁₃	1	4	yes	—
763	C₄²	C₂³×D₁₃	1	4	yes	—
764	C₄²	C₂³×D₁₃	1	4	yes	—
765	C₁₃	C₂×#3558	1	1	yes	characteristic, complemented, Sylow
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	8	no	—
769	C₂³	—	2	8	no	—
770	C₂³	—	2	8	no	—
771	C₂³	—	13	8	no	—
772	C₂³	—	13	4	no	—
773	C₂³	—	26	8	no	—
774	C₂³	—	26	4	no	—
775	C₂³	—	26	4	no	—
776	C₂³	—	26	8	no	—
777	C₂³	—	26	4	no	—
778	C₂³	—	26	8	no	—
779	C₂³	—	26	16	no	—
780	C₂³	—	52	8	no	—
781	C₂³	—	52	16	no	—
782	C₂³	—	52	16	no	—
783	C₂³	—	52	8	no	—
784	C₂³	—	52	16	no	—
785	C₂³	—	104	16	no	—
786	C₂³	—	104	32	no	—
787	C₂³	#88251	1	4	yes	—
788	C₂³	C₂⁴×D₁₃	1	8	yes	—
789	C₂³	C₂⁴×D₁₃	1	2	yes	—
790	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
791	Q₈	—	4	8	no	—
792	Q₈	—	26	16	no	—
793	Q₈	—	52	4	no	—
794	Q₈	—	52	8	no	—
795	D₄	—	2	32	no	—
796	D₄	—	2	16	no	—
797	D₄	—	4	8	no	—
798	D₄	—	4	8	no	—
799	D₄	—	26	16	no	—
800	D₄	—	26	16	no	—
801	D₄	—	52	4	no	—
802	D₄	—	52	16	no	—
803	D₄	—	52	8	no	—
804	D₄	—	52	16	no	—
805	D₄	—	52	16	no	—
806	D₄	—	52	16	no	—
807	D₄	—	52	16	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	8	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	8	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	16	no	—
818	C₂×C₄	—	13	4	no	—
819	C₂×C₄	—	13	8	no	—
820	C₂×C₄	—	13	4	no	—
821	C₂×C₄	—	13	4	no	—
822	C₂×C₄	—	26	4	no	—
823	C₂×C₄	—	26	4	no	—
824	C₂×C₄	—	26	8	no	—
825	C₂×C₄	—	26	4	no	—
826	C₂×C₄	—	26	16	no	—
827	C₂×C₄	—	52	16	no	—
828	C₂×C₄	—	52	8	no	—
829	C₂×C₄	—	52	16	no	—
830	C₂×C₄	#88256	1	4	yes	—
831	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
832	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
833	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
834	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
835	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
836	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
837	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
838	C₂²	—	2	8	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	8	no	—
842	C₂²	—	2	8	no	—
843	C₂²	—	2	8	no	—
844	C₂²	—	4	16	no	—
845	C₂²	—	26	8	no	—
846	C₂²	—	26	4	no	—
847	C₂²	—	26	4	no	—
848	C₂²	—	26	8	no	—
849	C₂²	—	26	4	no	—
850	C₂²	—	26	8	no	—
851	C₂²	—	52	16	no	—
852	C₂²	—	52	8	no	—
853	C₂²	—	104	16	no	—
854	C₂²	—	104	32	no	—
855	C₂²	C₂×#88251	1	4	yes	—
856	C₂²	C₂×#88251	1	2	yes	—
857	C₂²	C₂×#88256	1	2	yes	—
858	C₂²	#11719648	1	2	yes	—
859	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	8	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	2	no	—
866	C₄	—	26	4	no	—
867	C₄	—	26	4	no	—
868	C₄	—	26	8	no	—
869	C₄	—	26	4	no	—
870	C₄	C₂×#88256	1	4	yes	—
871	C₂	—	2	4	no	—
872	C₂	—	4	8	no	—
873	C₂	—	52	8	no	—
874	C₂	—	52	4	no	—
875	C₂	#13129359	1	4	yes	direct product factor
876	C₂	C₂²×#88251	1	1	yes	characteristic
877	C₂	C₂²×#88256	1	1	yes	characteristic
878	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×#532	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#532	D₁₃
hypocenter	C₁₃	C₂×#3558
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #13129359	C₂	direct (N × H)
2. C₂×#11719389	C₂	semidirect
3. C₂×#11719388	C₂	semidirect
4. C₂×#11719264	C₂	semidirect
5. C₂×#11719303	C₂	semidirect
6. C₂×#11719259	C₂	semidirect
7. C₂×#11719534	C₂	semidirect
8. C₂×#11719314	C₂	semidirect
9. C₂×#11719438	C₂	semidirect
10. C₂×#11719322	C₂	semidirect
11. C₂×#11719265	C₂	semidirect
12. C₂×#11719420	C₂	semidirect
13. C₂×#11719310	C₂	semidirect
14. C₂×#11719184	C₂	semidirect
15. C₂²×#88129	C₂	semidirect
16. C₂×C₁₃×#532	C₂	semidirect
17. C₂²×C₁₃×#41	C₂²	semidirect
18. C₂²×#6129	C₂²	semidirect
19. C₂²×D₄×D₁₃	C₂²	semidirect
20. C₂²×D₄×D₁₃	C₂²	semidirect
22. C₂³×Dic₂₆	C₂²	semidirect
23. C₁₃×#532	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×#127	C₂²	semidirect
26. C₂×C₁₃×#124	C₂²	semidirect
27. C₂×C₁₃×#121	C₂²	semidirect
28. C₂×C₁₃×#121	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂²×C₄²×C₁₃	C₂²	semidirect
32. #11719534	C₂²	semidirect
33. C₂×#88201	C₂²	semidirect
34. C₂×#88200	C₂²	semidirect
36. C₂×#88193	C₂²	semidirect
37. C₂×#88193	C₂²	semidirect
38. C₂×#88193	C₂²	semidirect
39. C₂×#88191	C₂²	semidirect
40. C₂×#88191	C₂²	semidirect
41. C₂×#88191	C₂²	semidirect
42. C₂×#88190	C₂²	semidirect
43. C₂×D₄×Dic₁₃	C₂²	semidirect
45. C₂×#88184	C₂²	semidirect
46. C₂×#88183	C₂²	semidirect
47. C₂×#88183	C₂²	semidirect
48. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
49. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
50. C₂²×#6103	C₂²	semidirect
51. C₂²×#6103	C₂²	semidirect
52. C₂²×#6103	C₂²	semidirect
53. C₂×#88178	C₂²	semidirect
54. #11719438	C₂²	semidirect
55. #11719420	C₂²	semidirect
56. #11719389	C₂²	semidirect
57. #11719388	C₂²	semidirect
58. #11719322	C₂²	semidirect
59. #11719314	C₂²	semidirect
60. #11719310	C₂²	semidirect
61. #11719303	C₂²	semidirect
62. #11719265	C₂²	semidirect
63. #11719264	C₂²	semidirect
64. #11719259	C₂²	semidirect
65. C₂×#88152	C₂²	semidirect
66. C₂×#88151	C₂²	semidirect
68. C₂×#88148	C₂²	semidirect
69. C₂×#88147	C₂²	semidirect
70. C₂×#88141	C₂²	semidirect
71. C₂×#88140	C₂²	semidirect
72. C₂×#88139	C₂²	semidirect
73. C₂×#88139	C₂²	semidirect
74. C₂×#88138	C₂²	semidirect
75. C₂×#88137	C₂²	semidirect
76. C₂×#88136	C₂²	semidirect
77. C₂×#88136	C₂²	semidirect
78. C₂×#88132	C₂²	semidirect
79. #11719184	C₂²	semidirect
80. C₂×#88130	C₂²	semidirect
81. C₂×#88129	C₂²	semidirect
82. C₂×#88129	C₂²	semidirect
83. C₂×#88129	C₂²	semidirect
84. C₂×#88129	C₂²	semidirect
85. C₂×#88129	C₂²	semidirect
86. C₂×#88129	C₂²	semidirect
87. C₂×C₄×D₅₂	C₂²	semidirect
88. C₂×#88126	C₂²	semidirect
89. C₂×#88124	C₂²	semidirect
90. C₂×C₄×Dic₂₆	C₂²	semidirect
94. C₂×C₁₃×#41	C₂³	semidirect
112. C₂×#6129	C₂³	semidirect
115. C₂×D₄×D₁₃	C₂³	semidirect
116. C₂×D₄×D₁₃	C₂³	semidirect
129. C₂²×Dic₂₆	C₂³	semidirect
130. C₁₃×C₄⋊Q₈	C₂³	semidirect
131. C₁₃×#127	C₂³	semidirect
132. C₁₃×#124	C₂³	semidirect
133. C₁₃×#121	C₂³	semidirect
134. C₁₃×#121	C₂³	semidirect
135. C₄×D₄×C₁₃	C₂³	semidirect
136. C₄×D₄×C₁₃	C₂³	semidirect
145. C₂×C₄²×C₁₃	C₂³	semidirect
149. #88201	C₂³	semidirect
150. #88200	C₂³	semidirect
152. #88193	C₂³	semidirect
153. #88193	C₂³	semidirect
154. #88193	C₂³	semidirect
155. #88191	C₂³	semidirect
156. #88191	C₂³	semidirect
157. #88191	C₂³	semidirect
158. #88190	C₂³	semidirect
159. D₄×Dic₁₃	C₂³	semidirect
161. #88184	C₂³	semidirect
162. #88183	C₂³	semidirect
163. #88183	C₂³	semidirect
164. C₄×C₂²⋊D₁₃	C₂³	semidirect
165. C₄×C₂²⋊D₁₃	C₂³	semidirect
177. C₂×#6103	C₂³	semidirect
178. C₂×#6103	C₂³	semidirect
179. C₂×#6103	C₂³	semidirect
183. #88178	C₂³	semidirect
191. #88152	C₂³	semidirect
192. #88151	C₂³	semidirect
194. #88148	C₂³	semidirect
195. #88147	C₂³	semidirect
196. #88141	C₂³	semidirect
197. #88140	C₂³	semidirect
198. #88139	C₂³	semidirect
199. #88139	C₂³	semidirect
200. #88138	C₂³	semidirect
201. #88137	C₂³	semidirect
202. #88136	C₂³	semidirect
203. #88136	C₂³	semidirect
204. #88132	C₂³	semidirect
205. #88130	C₂³	semidirect
206. #88129	C₂³	semidirect
207. #88129	C₂³	semidirect
208. #88129	C₂³	semidirect
209. #88129	C₂³	semidirect
210. #88129	C₂³	semidirect
211. C₄×D₅₂	C₂³	semidirect
212. #88126	C₂³	semidirect
213. #88124	C₂³	semidirect
214. C₄×Dic₂₆	C₂³	semidirect
340. C₂×#532	D₁₃	semidirect
416. C₂²×#41	C₂×D₁₃	semidirect
433. #532	C₂×D₁₃	semidirect
434. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
436. C₂×#127	C₂×D₁₃	semidirect
451. C₂×#124	C₂×D₁₃	semidirect
468. C₂×#121	C₂×D₁₃	semidirect
469. C₂×#121	C₂×D₁₃	semidirect
482. C₂×C₄×D₄	C₂×D₁₃	semidirect
483. C₂×C₄×D₄	C₂×D₁₃	semidirect
488. C₂²×C₄²	C₂×D₁₃	semidirect
527. C₂×#41	C₂²×D₁₃	semidirect
561. C₄⋊Q₈	C₂²×D₁₃	semidirect
563. #127	C₂²×D₁₃	semidirect
576. #124	C₂²×D₁₃	semidirect
593. #121	C₂²×D₁₃	semidirect
594. #121	C₂²×D₁₃	semidirect
607. C₄×D₄	C₂²×D₁₃	semidirect
608. C₄×D₄	C₂²×D₁₃	semidirect
645. C₂×C₄²	C₂²×D₁₃	semidirect
648. C₂×C₁₃	#3558	semidirect
765. C₁₃	C₂×#3558	semidirect
875. C₂	#13129359	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129359	2
C₂×#11719389	2
C₂×#11719388	2
C₂×#11719264	2
C₂×#11719303	2
C₂×#11719259	2
C₂×#11719534	2
C₂×#11719314	2
C₂×#11719438	2
C₂×#11719322	2
C₂×#11719265	2
C₂×#11719420	2
C₂×#11719310	2
C₂×#11719184	2
C₂²×#88129	2
C₂×C₁₃×#532	2
C₂×#3558	13

Subgroups — C2×#13129359 #16770249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129359 #16770249