Subgroups — C₂×#13128469 #16770798

Order 3328.

14438 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88256	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#13128469	C₂	1	32	yes	maximal, direct product factor
4	C₂×#11719255	C₂	1	4	yes	maximal, complemented
5	C₂×#11719335	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×D₅₂	C₂	1	4	yes	maximal, complemented
7	C₂×#11719314	C₂	1	4	yes	maximal, complemented
8	C₂×#11719230	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11719535	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11719358	C₂	1	4	yes	maximal, complemented
11	C₂×#11719496	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₁₃×#120	C₂	1	4	yes	maximal, complemented
13	C₂×#11719226	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁵×D₁₃	C₂²	1	2	yes	complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	C₂×#88256	—	2	16	no	—
19	C₂×#88256	C₂²	1	16	yes	complemented
20	C₂²×#6131	C₂²	1	2	yes	complemented
21	C₂²×D₄×D₁₃	C₂²	1	2	yes	complemented
22	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
23	C₂²×D₄×D₁₃	C₂²	1	8	yes	complemented
24	C₂²×#6127	C₂²	1	2	yes	complemented
25	C₂²×#6127	C₂²	1	1	yes	characteristic, complemented
26	C₂³×D₅₂	—	2	16	no	—
27	C₂³×D₅₂	C₂²	1	1	yes	characteristic
28	C₂³×D₅₂	C₂²	1	4	yes	complemented
29	C₂³×D₅₂	C₂²	1	4	yes	complemented
30	C₂³×D₅₂	C₂²	1	2	yes	complemented
31	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
32	C₂³×D₅₂	C₂²	1	16	yes	complemented
33	C₂³×D₅₂	C₂²	1	2	yes	complemented
34	C₁₃×#525	C₂²	1	16	yes	complemented
35	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#120	C₂²	1	2	yes	complemented
39	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
40	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂×#88207	C₂²	1	2	yes	complemented
42	#11719535	C₂²	1	16	yes	complemented
43	C₂×#88201	C₂²	1	2	yes	complemented
44	C₂×#88194	C₂²	1	2	yes	complemented
45	C₂×#88191	C₂²	1	8	yes	complemented
46	C₂×#88191	C₂²	1	4	yes	complemented
47	#11719496	C₂²	1	16	yes	complemented
48	C₂×#88184	C₂²	1	4	yes	complemented
49	C₂×#88184	C₂²	1	2	yes	complemented
50	C₂×#88183	C₂²	1	2	yes	complemented
51	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
52	C₂×#88180	C₂²	1	1	yes	characteristic, complemented
53	C₂×#88178	C₂²	1	2	yes	complemented
54	#11719358	C₂²	1	64	yes	complemented
55	#11719335	C₂²	1	64	yes	complemented
56	#11719314	C₂²	1	64	yes	complemented
57	D₁₃×#120	C₂²	1	64	yes	complemented
58	#11719255	C₂²	1	64	yes	complemented
59	D₄×D₅₂	C₂²	1	64	yes	complemented
60	#11719230	C₂²	1	16	yes	complemented
61	#11719226	C₂²	1	16	yes	complemented
62	C₂×#88149	C₂²	1	4	yes	complemented
63	C₂×#88149	C₂²	1	8	yes	complemented
64	C₂×#88148	C₂²	1	8	yes	complemented
65	C₂×#88147	C₂²	1	4	yes	complemented
66	C₂×#88138	C₂²	1	8	yes	complemented
67	C₂×#88136	C₂²	1	8	yes	complemented
68	C₂×#88136	C₂²	1	4	yes	complemented
69	C₂×#88136	C₂²	1	8	yes	complemented
70	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
71	C₂×C₂²⋊C₄×D₁₃	C₂²	1	8	yes	complemented
72	C₂×#88129	C₂²	1	2	yes	complemented
73	C₂×#88128	C₂²	1	2	yes	complemented
74	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
75	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
76	C₂⁴×D₁₃	—	2	16	no	—
77	C₂⁴×D₁₃	—	4	16	no	—
78	C₂⁴×D₁₃	C₂³	1	8	yes	—
79	C₂⁴×D₁₃	C₂³	1	2	yes	—
80	C₂⁴×D₁₃	C₂³	1	2	yes	—
81	C₂⁴×D₁₃	C₂³	1	16	yes	complemented
82	C₂⁴×D₁₃	C₂³	1	4	yes	complemented
83	C₂×C₁₃×#41	—	2	8	no	—
84	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
85	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic, complemented
86	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
87	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
89	C₂³×C₄×C₁₃	—	2	8	no	—
90	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
95	C₂³×C₄×C₁₃	C₂³	1	2	yes	complemented
96	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
97	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
98	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	complemented
99	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
100	#88256	—	2	128	no	—
101	C₂×#6131	—	2	16	no	—
102	C₂×#6131	C₂³	1	16	yes	complemented
103	C₂×D₄×D₁₃	—	2	32	no	—
104	C₂×D₄×D₁₃	—	2	16	no	—
105	C₂×D₄×D₁₃	—	4	32	no	—
106	C₂×D₄×D₁₃	C₂³	1	16	yes	complemented
107	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
108	C₂×D₄×D₁₃	C₂³	1	64	yes	complemented
109	C₂×#6127	—	2	8	no	—
110	C₂×#6127	—	2	16	no	—
111	C₂×#6127	C₂³	1	16	yes	complemented
112	C₂×#6127	C₂³	1	8	yes	complemented
113	C₂²×D₅₂	—	2	16	no	—
114	C₂²×D₅₂	—	2	8	no	—
115	C₂²×D₅₂	—	2	32	no	—
116	C₂²×D₅₂	—	2	32	no	—
117	C₂²×D₅₂	—	2	128	no	—
118	C₂²×D₅₂	—	2	16	no	—
119	C₂²×D₅₂	D₄	1	16	yes	complemented
120	C₂²×D₅₂	C₂³	1	2	yes	—
121	C₂²×D₅₂	C₂³	1	8	yes	—
122	C₂²×D₅₂	C₂³	1	2	yes	—
123	C₂²×D₅₂	C₂³	1	2	yes	—
124	C₂²×D₅₂	C₂³	1	2	yes	—
125	C₂²×D₅₂	C₂³	1	8	yes	—
126	C₂²×D₅₂	C₂³	1	8	yes	complemented
127	C₂²×D₅₂	C₂³	1	32	yes	complemented
128	C₂²×D₅₂	C₂³	1	32	yes	complemented
129	C₂²×D₅₂	C₂³	1	16	yes	complemented
130	C₂²×D₅₂	C₂³	1	16	yes	complemented
131	C₂²×D₅₂	C₂³	1	1	yes	characteristic, complemented
132	C₂²×D₅₂	C₂³	1	4	yes	complemented
133	C₂²×D₅₂	C₂³	1	8	yes	complemented
134	C₂²×C₄×D₁₃	C₂³	1	4	yes	complemented
135	C₂²×C₄×D₁₃	C₂³	1	2	yes	complemented
136	C₂²×C₄×D₁₃	C₂³	1	8	yes	complemented
137	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic, complemented
138	C₁₃×#123	C₂³	1	16	yes	complemented
139	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
140	C₁₃×#121	C₂³	1	16	yes	complemented
141	C₁₃×#120	C₂³	1	16	yes	complemented
142	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
143	C₁₃×#117	C₂³	1	8	yes	complemented
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
149	C₂×C₄²×C₁₃	C₂³	1	2	yes	complemented
150	#88207	C₂³	1	16	yes	complemented
151	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
152	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
153	#88201	C₂³	1	16	yes	complemented
154	#88194	C₂³	1	16	yes	complemented
155	#88191	C₂³	1	64	yes	complemented
156	#88191	C₂³	1	32	yes	complemented
157	#88184	C₂³	1	32	yes	complemented
158	#88184	C₂³	1	16	yes	complemented
159	#88183	C₂³	1	16	yes	complemented
160	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
161	C₂×#6103	C₂³	1	8	yes	complemented
162	C₂×#6103	C₂³	1	8	yes	complemented
163	C₂×#6103	C₂³	1	8	yes	complemented
164	C₂×#6103	C₂³	1	4	yes	complemented
165	#88180	C₂³	1	8	yes	complemented
166	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	complemented
167	#88178	C₂³	1	16	yes	complemented
168	C₂×#6101	C₂³	1	4	yes	complemented
169	C₂×C₄×Dic₁₃	C₂³	1	2	yes	complemented
170	#88149	C₂³	1	32	yes	complemented
171	#88149	C₂³	1	64	yes	complemented
172	#88148	C₂³	1	64	yes	complemented
173	#88147	C₂³	1	32	yes	complemented
174	#88138	C₂³	1	64	yes	complemented
175	#88136	C₂³	1	32	yes	complemented
176	#88136	C₂³	1	64	yes	complemented
177	#88136	C₂³	1	64	yes	complemented
178	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
179	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
180	#88129	C₂³	1	16	yes	complemented
181	#88128	C₂³	1	16	yes	complemented
182	C₄×D₅₂	C₂³	1	32	yes	complemented
183	C₂×#3484	—	13	1	no	maximal, Sylow
184	C₂⁴×C₁₃	—	2	4	no	—
185	C₂⁴×C₁₃	—	2	8	no	—
186	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
187	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
188	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
190	C₂³×D₁₃	—	2	8	no	—
191	C₂³×D₁₃	—	2	32	no	—
192	C₂³×D₁₃	—	2	32	no	—
193	C₂³×D₁₃	—	2	64	no	—
194	C₂³×D₁₃	—	2	16	no	—
195	C₂³×D₁₃	—	4	8	no	—
196	C₂³×D₁₃	—	4	16	no	—
197	C₂³×D₁₃	—	4	8	no	—
198	C₂³×D₁₃	—	4	64	no	—
199	C₂³×D₁₃	—	4	16	no	—
200	C₂³×D₁₃	—	4	128	no	—
201	C₂³×D₁₃	C₂×D₄	1	16	yes	complemented
202	C₂³×D₁₃	C₂⁴	1	4	yes	—
203	C₂³×D₁₃	C₂⁴	1	2	yes	—
204	C₂³×D₁₃	C₂⁴	1	32	yes	—
205	C₂³×D₁₃	C₂⁴	1	4	yes	—
206	C₂³×D₁₃	C₂⁴	1	8	yes	—
207	C₂³×D₁₃	C₂⁴	1	8	yes	—
208	C₂³×D₁₃	C₂⁴	1	16	yes	complemented
209	C₁₃×#41	—	2	32	no	—
210	C₂×Q₈×C₁₃	—	2	4	no	—
211	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	complemented
212	C₂×D₄×C₁₃	—	2	8	no	—
213	C₂×D₄×C₁₃	—	2	16	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
216	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
217	C₂×D₄×C₁₃	C₂⁴	1	4	yes	complemented
218	C₂²×C₄×C₁₃	—	2	4	no	—
219	C₂²×C₄×C₁₃	—	2	8	no	—
220	C₂²×C₄×C₁₃	—	2	8	no	—
221	C₂²×C₄×C₁₃	—	2	8	no	—
222	C₂²×C₄×C₁₃	—	2	32	no	—
223	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	complemented
234	C₂×C₂²⋊D₁₃	—	2	8	no	—
235	C₂×C₂²⋊D₁₃	—	2	16	no	—
236	C₂×C₂²⋊D₁₃	—	2	16	no	—
237	C₂×C₂²⋊D₁₃	—	4	16	no	—
238	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
239	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
240	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	complemented
241	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	complemented
242	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
243	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
244	#6131	—	2	64	no	—
245	D₄×D₁₃	—	2	128	no	—
246	D₄×D₁₃	—	2	64	no	—
247	D₄×D₁₃	—	4	128	no	—
248	#6127	—	2	32	no	—
249	#6127	—	2	64	no	—
250	C₂×D₅₂	—	2	32	no	—
251	C₂×D₅₂	—	2	16	no	—
252	C₂×D₅₂	—	2	64	no	—
253	C₂×D₅₂	—	2	8	no	—
254	C₂×D₅₂	—	2	8	no	—
255	C₂×D₅₂	—	2	4	no	—
256	C₂×D₅₂	—	2	32	no	—
257	C₂×D₅₂	—	2	128	no	—
258	C₂×D₅₂	—	2	128	no	—
259	C₂×D₅₂	—	2	64	no	—
260	C₂×D₅₂	—	4	16	no	—
261	C₂×D₅₂	C₂×D₄	1	16	yes	complemented
262	C₂×D₅₂	C₂×D₄	1	16	yes	complemented
263	C₂×D₅₂	C₂×D₄	1	64	yes	complemented
264	C₂×D₅₂	C₂⁴	1	8	yes	—
265	C₂×D₅₂	C₂⁴	1	32	yes	—
266	C₂×D₅₂	C₂⁴	1	8	yes	—
267	C₂×D₅₂	C₂⁴	1	8	yes	—
268	C₂×D₅₂	C₂⁴	1	8	yes	—
269	C₂×D₅₂	C₂⁴	1	4	yes	complemented
270	C₂×D₅₂	C₂⁴	1	16	yes	complemented
271	C₂×D₅₂	C₂⁴	1	32	yes	complemented
272	C₂×C₄×D₁₃	—	2	16	no	—
273	C₂×C₄×D₁₃	—	2	8	no	—
274	C₂×C₄×D₁₃	—	4	16	no	—
275	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
276	C₂×C₄×D₁₃	C₂⁴	1	8	yes	complemented
277	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
278	C₂×Dic₂₆	—	2	4	no	—
279	C₂×Dic₂₆	C₂⁴	1	4	yes	complemented
280	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	complemented
281	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
282	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
283	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
284	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
285	C₄²×C₁₃	C₂⁴	1	8	yes	complemented
286	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
287	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
288	#6103	C₂⁴	1	32	yes	complemented
289	#6103	C₂⁴	1	32	yes	complemented
290	#6103	C₂⁴	1	32	yes	complemented
291	#6103	C₂⁴	1	16	yes	complemented
292	C₄⋊Dic₁₃	C₂⁴	1	8	yes	complemented
293	#6101	C₂⁴	1	16	yes	complemented
294	C₄×Dic₁₃	C₂⁴	1	8	yes	complemented
295	C₂²×H(5,𝔽₂)	—	13	1	no	—
296	C₂⁴×D₄	—	13	1	no	—
297	#3484	—	13	32	no	—
298	C₂×#546	—	13	4	no	—
299	C₂×#546	—	13	4	no	—
300	C₂×D₄²	—	13	4	no	—
301	C₂×D₄²	—	13	4	no	—
302	C₂×#535	—	13	1	no	—
303	C₂×#535	—	13	1	no	—
304	C₂×#534	—	13	4	no	—
305	C₂×#525	—	13	1	no	—
306	C₂×#525	D₁₃	1	1	yes	characteristic, complemented
307	C₂²×#120	—	13	4	no	—
308	C₂×#518	—	13	1	no	—
309	C₂³×C₁₃	—	2	32	no	—
310	C₂³×C₁₃	—	2	8	no	—
311	C₂³×C₁₃	—	2	4	no	—
312	C₂³×C₁₃	—	2	4	no	—
313	C₂³×C₁₃	—	2	4	no	—
314	C₂³×C₁₃	—	2	16	no	—
315	C₂³×C₁₃	—	2	4	no	—
316	C₂³×C₁₃	—	2	8	no	—
317	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
318	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	complemented
319	C₂³×C₁₃	C₂⁵	1	4	yes	—
320	C₂³×C₁₃	C₂⁵	1	2	yes	—
321	C₂³×C₁₃	C₂⁵	1	4	yes	—
322	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
323	C₂²×D₁₃	—	2	16	no	—
324	C₂²×D₁₃	—	2	4	no	—
325	C₂²×D₁₃	—	2	16	no	—
326	C₂²×D₁₃	—	2	8	no	—
327	C₂²×D₁₃	—	2	8	no	—
328	C₂²×D₁₃	—	2	16	no	—
329	C₂²×D₁₃	—	2	64	no	—
330	C₂²×D₁₃	—	2	64	no	—
331	C₂²×D₁₃	—	2	32	no	—
332	C₂²×D₁₃	—	4	32	no	—
333	C₂²×D₁₃	—	4	16	no	—
334	C₂²×D₁₃	—	4	32	no	—
335	C₂²×D₁₃	—	4	16	no	—
336	C₂²×D₁₃	—	4	32	no	—
337	C₂²×D₁₃	—	4	128	no	—
338	C₂²×D₁₃	—	4	256	no	—
339	C₂²×D₁₃	—	4	32	no	—
340	C₂²×D₁₃	—	8	32	no	—
341	C₂²×D₁₃	C₂²×D₄	1	16	yes	—
342	C₂²×D₁₃	C₂²×D₄	1	32	yes	complemented
343	C₂²×D₁₃	C₂⁵	1	8	yes	—
344	C₂²×D₁₃	C₂⁵	1	4	yes	—
345	C₂²×D₁₃	C₂⁵	1	8	yes	—
346	Q₈×C₁₃	—	2	8	no	—
347	D₄×C₁₃	—	2	16	no	—
348	D₄×C₁₃	—	2	32	no	—
349	D₄×C₁₃	—	2	8	no	—
350	C₂×C₄×C₁₃	—	2	4	no	—
351	C₂×C₄×C₁₃	—	2	8	no	—
352	C₂×C₄×C₁₃	—	2	4	no	—
353	C₂×C₄×C₁₃	—	2	8	no	—
354	C₂×C₄×C₁₃	—	2	16	no	—
355	C₂×C₄×C₁₃	—	2	16	no	—
356	C₂×C₄×C₁₃	—	2	16	no	—
357	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
358	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
359	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	complemented
360	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
361	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
362	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
363	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
364	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
365	C₂²⋊D₁₃	—	2	16	no	—
366	C₂²⋊D₁₃	—	2	32	no	—
367	C₂²⋊D₁₃	—	2	32	no	—
368	C₂²⋊D₁₃	—	4	32	no	—
369	C₂×Dic₁₃	—	2	4	no	—
370	C₂×Dic₁₃	—	2	8	no	—
371	C₂×Dic₁₃	C₂⁵	1	8	yes	—
372	C₂×Dic₁₃	C₂⁵	1	4	yes	—
373	D₅₂	—	2	64	no	—
374	D₅₂	—	2	32	no	—
375	D₅₂	—	2	16	no	—
376	D₅₂	—	2	16	no	—
377	D₅₂	—	2	8	no	—
378	D₅₂	—	4	32	no	—
379	D₅₂	C₂²×D₄	1	32	yes	complemented
380	D₅₂	C₂²×D₄	1	32	yes	complemented
381	C₄×D₁₃	—	2	32	no	—
382	C₄×D₁₃	—	2	16	no	—
383	C₄×D₁₃	—	4	32	no	—
384	Dic₂₆	—	2	8	no	—
385	C₂⁶	—	13	2	no	—
386	C₂×H(5,𝔽₂)	—	13	16	no	—
387	C₂×H(5,𝔽₂)	—	26	16	no	—
388	C₂²×#41	—	13	2	no	—
389	C₂²×#41	—	13	1	no	—
390	C₂²×#41	—	13	2	no	—
391	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
392	C₂³×D₄	—	13	4	no	—
393	C₂³×D₄	—	13	2	no	—
394	C₂³×D₄	—	13	8	no	—
395	C₂³×D₄	—	13	1	no	—
396	C₂³×D₄	—	13	2	no	—
397	C₂³×D₄	—	13	1	no	—
398	C₂³×D₄	—	13	4	no	—
399	C₂³×D₄	—	13	4	no	—
400	C₂³×D₄	—	13	16	no	—
401	C₂³×D₄	—	13	2	no	—
402	C₂³×D₄	—	26	16	no	—
403	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
404	#546	—	13	64	no	—
405	#546	—	13	64	no	—
406	D₄²	—	13	64	no	—
407	D₄²	—	13	64	no	—
408	#535	—	13	16	no	—
409	#535	—	13	16	no	—
410	#534	—	13	64	no	—
411	C₂×#127	—	13	2	no	—
412	C₂×#127	—	13	2	no	—
413	C₂×#124	—	13	2	no	—
414	C₂×#124	—	13	2	no	—
415	#525	—	13	16	no	—
416	#525	C₂×D₁₃	1	16	yes	complemented
417	C₂×#123	—	13	2	no	—
418	C₂×#123	—	13	8	no	—
419	C₂×#123	C₂×D₁₃	1	2	yes	complemented
420	C₂×C₂²⋊Q₈	—	13	2	no	—
421	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
422	C₂×#121	—	13	2	no	—
423	C₂×#121	—	13	4	no	—
424	C₂×#121	—	13	8	no	—
425	C₂×#121	—	13	4	no	—
426	C₂×#121	—	13	8	no	—
427	C₂×#121	C₂×D₁₃	1	2	yes	complemented
428	C₂×#120	—	13	2	no	—
429	C₂×#120	—	13	4	no	—
430	C₂×#120	—	13	8	no	—
431	C₂×#120	—	13	64	no	—
432	C₂×#120	—	13	4	no	—
433	C₂×#120	—	13	8	no	—
434	C₂×#120	—	13	8	no	—
435	C₂×#120	C₂×D₁₃	1	2	yes	complemented
436	#518	—	13	16	no	—
437	C₂×C₄×D₄	—	13	4	no	—
438	C₂×C₄×D₄	—	13	4	no	—
439	C₂×C₄×D₄	—	13	4	no	—
440	C₂×C₄×D₄	C₂×D₁₃	1	4	yes	complemented
441	C₂×#117	—	13	1	no	—
442	C₂×#117	C₂×D₁₃	1	1	yes	characteristic, complemented
443	C₂²×C₂²⋊C₄	—	13	4	no	—
444	C₂²×C₂²⋊C₄	—	13	8	no	—
445	C₂²×C₁₃	—	2	32	no	—
446	C₂²×C₁₃	—	2	4	no	—
447	C₂²×C₁₃	—	2	4	no	—
448	C₂²×C₁₃	—	2	4	no	—
449	C₂²×C₁₃	—	2	8	no	—
450	C₂²×C₁₃	—	2	16	no	—
451	C₂²×C₁₃	—	2	4	no	—
452	C₂²×C₁₃	—	2	8	no	—
453	C₂²×C₁₃	—	4	8	no	—
454	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
455	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
456	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
457	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	complemented
458	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
459	C₂×D₁₃	—	2	16	no	—
460	C₂×D₁₃	—	2	32	no	—
461	C₂×D₁₃	—	2	4	no	—
462	C₂×D₁₃	—	2	8	no	—
463	C₂×D₁₃	—	2	8	no	—
464	C₂×D₁₃	—	2	16	no	—
465	C₂×D₁₃	—	4	32	no	—
466	C₂×D₁₃	—	4	128	no	—
467	C₂×D₁₃	—	4	32	no	—
468	C₂×D₁₃	—	4	16	no	—
469	C₂×D₁₃	—	4	8	no	—
470	C₂×D₁₃	—	8	32	no	—
471	C₂×D₁₃	C₂³×D₄	1	16	yes	—
472	C₄×C₁₃	—	2	4	no	—
473	C₄×C₁₃	—	2	4	no	—
474	C₄×C₁₃	—	2	8	no	—
475	C₄×C₁₃	C₂³×D₄	1	4	yes	—
476	C₄×C₁₃	C₂³×D₄	1	4	yes	—
477	Dic₁₃	—	2	4	no	—
478	Dic₁₃	—	2	8	no	—
479	C₂⁵	—	13	2	no	—
480	C₂⁵	—	13	8	no	—
481	C₂⁵	—	13	2	no	—
482	C₂⁵	—	13	16	no	—
483	C₂⁵	—	13	4	no	—
484	C₂⁵	—	26	16	no	—
485	C₂⁵	—	52	16	no	—
486	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
487	H(5,𝔽₂)	—	26	128	no	—
488	C₂×#41	—	2	8	no	—
489	C₂×#41	—	13	16	no	—
490	C₂×#41	—	13	8	no	—
491	C₂×#41	—	13	16	no	—
492	C₂×#41	—	26	16	no	—
493	C₂×#41	—	26	16	no	—
494	C₂×#41	—	26	8	no	—
495	C₂×#41	C₂²×D₁₃	1	8	yes	complemented
496	C₂²×Q₈	—	13	1	no	—
497	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic, complemented
498	C₂²×D₄	—	13	4	no	—
499	C₂²×D₄	—	13	2	no	—
500	C₂²×D₄	—	13	4	no	—
501	C₂²×D₄	—	13	8	no	—
502	C₂²×D₄	—	13	32	no	—
503	C₂²×D₄	—	13	16	no	—
504	C₂²×D₄	—	13	64	no	—
505	C₂²×D₄	—	13	16	no	—
506	C₂²×D₄	—	13	2	no	—
507	C₂²×D₄	—	13	2	no	—
508	C₂²×D₄	—	13	8	no	—
509	C₂²×D₄	—	13	4	no	—
510	C₂²×D₄	—	13	8	no	—
511	C₂²×D₄	—	13	2	no	—
512	C₂²×D₄	—	13	2	no	—
513	C₂²×D₄	—	13	1	no	—
514	C₂²×D₄	—	13	16	no	—
515	C₂²×D₄	—	13	8	no	—
516	C₂²×D₄	—	13	32	no	—
517	C₂²×D₄	—	13	32	no	—
518	C₂²×D₄	—	13	8	no	—
519	C₂²×D₄	—	13	16	no	—
520	C₂²×D₄	—	26	32	no	—
521	C₂²×D₄	—	26	32	no	—
522	C₂²×D₄	—	26	128	no	—
523	C₂²×D₄	—	26	16	no	—
524	C₂²×D₄	—	26	16	no	—
525	C₂²×D₄	—	26	16	no	—
526	C₂²×D₄	—	26	32	no	—
527	C₂²×D₄	—	26	8	no	—
528	C₂²×D₄	—	52	32	no	—
529	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
530	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
531	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic, complemented
532	C₂³×C₄	—	2	8	no	—
533	C₂³×C₄	—	13	4	no	—
534	C₂³×C₄	—	13	2	no	—
535	C₂³×C₄	—	13	8	no	—
536	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
537	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
538	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
539	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
540	C₂³×C₄	C₂²×D₁₃	1	8	yes	complemented
541	C₂³×C₄	C₂²×D₁₃	1	2	yes	complemented
542	#127	—	13	16	no	—
543	#127	—	13	16	no	—
544	#124	—	13	16	no	—
545	#124	—	13	16	no	—
546	#123	—	13	16	no	—
547	#123	—	13	64	no	—
548	#123	C₂²×D₁₃	1	16	yes	complemented
549	C₂²⋊Q₈	—	13	16	no	—
550	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
551	#121	—	13	16	no	—
552	#121	—	13	32	no	—
553	#121	—	13	64	no	—
554	#121	—	13	32	no	—
555	#121	—	13	64	no	—
556	#121	C₂²×D₁₃	1	16	yes	complemented
557	#120	—	13	16	no	—
558	#120	—	13	32	no	—
559	#120	—	13	64	no	—
560	#120	—	13	32	no	—
561	#120	—	13	64	no	—
562	#120	—	13	64	no	—
563	#120	C₂²×D₁₃	1	16	yes	complemented
564	C₄×D₄	—	13	32	no	—
565	C₄×D₄	—	13	32	no	—
566	C₄×D₄	—	13	32	no	—
567	C₄×D₄	C₂²×D₁₃	1	32	yes	complemented
568	#117	—	13	8	no	—
569	#117	C₂²×D₁₃	1	8	yes	complemented
570	C₂×C₄⋊C₄	—	13	2	no	—
571	C₂×C₄⋊C₄	—	13	4	no	—
572	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	complemented
573	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	complemented
574	C₂×C₂²⋊C₄	—	13	2	no	—
575	C₂×C₂²⋊C₄	—	13	4	no	—
576	C₂×C₂²⋊C₄	—	13	8	no	—
577	C₂×C₂²⋊C₄	—	13	8	no	—
578	C₂×C₂²⋊C₄	—	13	8	no	—
579	C₂×C₂²⋊C₄	—	13	4	no	—
580	C₂×C₂²⋊C₄	—	13	32	no	—
581	C₂×C₂²⋊C₄	—	13	64	no	—
582	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
584	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	complemented
585	C₂×C₄²	—	13	2	no	—
586	C₂×C₄²	C₂²×D₁₃	1	2	yes	complemented
587	C₂×C₁₃	—	2	4	no	—
588	C₂×C₁₃	—	2	8	no	—
589	C₂×C₁₃	—	4	4	no	—
590	C₂×C₁₃	#3484	1	4	yes	complemented
591	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
592	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
593	D₁₃	—	2	16	no	—
594	D₁₃	—	4	8	no	—
595	D₁₃	—	4	4	no	—
596	C₂⁴	—	2	4	no	—
597	C₂⁴	—	2	8	no	—
598	C₂⁴	—	13	4	no	—
599	C₂⁴	—	13	16	no	—
600	C₂⁴	—	13	8	no	—
601	C₂⁴	—	13	4	no	—
602	C₂⁴	—	13	2	no	—
603	C₂⁴	—	13	32	no	—
604	C₂⁴	—	13	8	no	—
605	C₂⁴	—	13	16	no	—
606	C₂⁴	—	26	32	no	—
607	C₂⁴	—	26	64	no	—
608	C₂⁴	—	26	16	no	—
609	C₂⁴	—	26	8	no	—
610	C₂⁴	—	26	32	no	—
611	C₂⁴	—	52	8	no	—
612	C₂⁴	—	52	16	no	—
613	C₂⁴	—	52	8	no	—
614	C₂⁴	—	52	64	no	—
615	C₂⁴	—	52	16	no	—
616	C₂⁴	—	52	128	no	—
617	C₂⁴	C₂³×D₁₃	1	4	yes	—
618	C₂⁴	C₂³×D₁₃	1	2	yes	—
619	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
620	C₂⁴	C₂³×D₁₃	1	2	yes	—
621	#41	—	2	32	no	—
622	#41	—	26	64	no	—
623	#41	—	26	64	no	—
624	#41	—	26	32	no	—
625	C₂×Q₈	—	2	4	no	—
626	C₂×Q₈	—	13	4	no	—
627	C₂×Q₈	—	26	4	no	—
628	C₂×Q₈	C₂³×D₁₃	1	4	yes	complemented
629	C₂×D₄	—	2	8	no	—
630	C₂×D₄	—	2	16	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	13	16	no	—
633	C₂×D₄	—	13	8	no	—
634	C₂×D₄	—	13	16	no	—
635	C₂×D₄	—	13	32	no	—
636	C₂×D₄	—	13	16	no	—
637	C₂×D₄	—	13	16	no	—
638	C₂×D₄	—	13	64	no	—
639	C₂×D₄	—	13	8	no	—
640	C₂×D₄	—	13	8	no	—
641	C₂×D₄	—	13	16	no	—
642	C₂×D₄	—	13	32	no	—
643	C₂×D₄	—	13	8	no	—
644	C₂×D₄	—	13	8	no	—
645	C₂×D₄	—	13	4	no	—
646	C₂×D₄	—	13	32	no	—
647	C₂×D₄	—	26	128	no	—
648	C₂×D₄	—	26	128	no	—
649	C₂×D₄	—	26	64	no	—
650	C₂×D₄	—	26	32	no	—
651	C₂×D₄	—	26	64	no	—
652	C₂×D₄	—	26	16	no	—
653	C₂×D₄	—	26	64	no	—
654	C₂×D₄	—	26	128	no	—
655	C₂×D₄	—	26	16	no	—
656	C₂×D₄	—	26	8	no	—
657	C₂×D₄	—	26	16	no	—
658	C₂×D₄	—	26	8	no	—
659	C₂×D₄	—	26	8	no	—
660	C₂×D₄	—	26	4	no	—
661	C₂×D₄	—	26	32	no	—
662	C₂×D₄	—	52	16	no	—
663	C₂×D₄	—	52	16	no	—
664	C₂×D₄	—	52	128	no	—
665	C₂×D₄	C₂³×D₁₃	1	16	yes	—
666	C₂×D₄	C₂³×D₁₃	1	8	yes	—
667	C₂×D₄	C₂³×D₁₃	1	4	yes	complemented
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	8	no	—
670	C₂²×C₄	—	2	8	no	—
671	C₂²×C₄	—	2	8	no	—
672	C₂²×C₄	—	2	32	no	—
673	C₂²×C₄	—	13	4	no	—
674	C₂²×C₄	—	13	2	no	—
675	C₂²×C₄	—	13	16	no	—
676	C₂²×C₄	—	13	8	no	—
677	C₂²×C₄	—	13	32	no	—
678	C₂²×C₄	—	26	16	no	—
679	C₂²×C₄	—	26	8	no	—
680	C₂²×C₄	—	52	16	no	—
681	C₂²×C₄	D₄×D₁₃	1	8	yes	complemented
682	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
683	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
684	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
685	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
686	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
687	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
688	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
689	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
690	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
691	C₂²×C₄	C₂³×D₁₃	1	8	yes	complemented
692	C₄⋊C₄	—	13	8	no	—
693	C₄⋊C₄	—	13	16	no	—
694	C₄⋊C₄	C₂³×D₁₃	1	8	yes	complemented
695	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
696	C₂²⋊C₄	—	13	8	no	—
697	C₂²⋊C₄	—	13	16	no	—
698	C₂²⋊C₄	—	13	32	no	—
699	C₂²⋊C₄	—	13	32	no	—
700	C₂²⋊C₄	—	13	32	no	—
701	C₂²⋊C₄	—	13	16	no	—
702	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
703	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
704	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	complemented
705	C₄²	—	13	8	no	—
706	C₄²	C₂³×D₁₃	1	8	yes	complemented
707	C₁₃	C₂×#3484	1	1	yes	characteristic, complemented, Sylow
708	C₂³	—	2	32	no	—
709	C₂³	—	2	8	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	4	no	—
713	C₂³	—	2	16	no	—
714	C₂³	—	2	4	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	13	16	no	—
717	C₂³	—	13	8	no	—
718	C₂³	—	13	32	no	—
719	C₂³	—	13	8	no	—
720	C₂³	—	13	4	no	—
721	C₂³	—	26	64	no	—
722	C₂³	—	26	32	no	—
723	C₂³	—	26	16	no	—
724	C₂³	—	26	4	no	—
725	C₂³	—	26	16	no	—
726	C₂³	—	26	8	no	—
727	C₂³	—	26	8	no	—
728	C₂³	—	26	16	no	—
729	C₂³	—	26	64	no	—
730	C₂³	—	52	32	no	—
731	C₂³	—	52	16	no	—
732	C₂³	—	52	32	no	—
733	C₂³	—	52	16	no	—
734	C₂³	—	52	32	no	—
735	C₂³	—	52	128	no	—
736	C₂³	—	52	256	no	—
737	C₂³	—	52	32	no	—
738	C₂³	—	104	32	no	—
739	C₂³	C₂×D₄×D₁₃	1	4	yes	—
740	C₂³	#88256	1	8	yes	complemented
741	C₂³	C₂⁴×D₁₃	1	4	yes	—
742	C₂³	C₂⁴×D₁₃	1	2	yes	—
743	C₂³	C₂⁴×D₁₃	1	4	yes	—
744	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
745	Q₈	—	2	8	no	—
746	Q₈	—	26	8	no	—
747	D₄	—	2	16	no	—
748	D₄	—	2	32	no	—
749	D₄	—	2	8	no	—
750	D₄	—	13	32	no	—
751	D₄	—	13	32	no	—
752	D₄	—	26	64	no	—
753	D₄	—	26	32	no	—
754	D₄	—	26	32	no	—
755	D₄	—	26	16	no	—
756	D₄	—	26	32	no	—
757	D₄	—	26	16	no	—
758	D₄	—	26	16	no	—
759	D₄	—	26	8	no	—
760	D₄	—	52	32	no	—
761	D₄	—	52	32	no	—
762	C₂×C₄	—	2	8	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	8	no	—
766	C₂×C₄	—	2	16	no	—
767	C₂×C₄	—	2	16	no	—
768	C₂×C₄	—	2	16	no	—
769	C₂×C₄	—	13	8	no	—
770	C₂×C₄	—	13	4	no	—
771	C₂×C₄	—	26	32	no	—
772	C₂×C₄	—	26	4	no	—
773	C₂×C₄	—	26	8	no	—
774	C₂×C₄	—	26	16	no	—
775	C₂×C₄	—	52	32	no	—
776	C₂×C₄	C₂×D₄×D₁₃	1	4	yes	—
777	C₂×C₄	C₂×D₄×D₁₃	1	4	yes	—
778	C₂×C₄	C₂×D₄×D₁₃	1	16	yes	complemented
779	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
780	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
781	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
782	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
783	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
784	C₂²	—	2	32	no	—
785	C₂²	—	2	8	no	—
786	C₂²	—	2	16	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	2	4	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	2	8	no	—
792	C₂²	—	4	8	no	—
793	C₂²	—	13	16	no	—
794	C₂²	—	26	32	no	—
795	C₂²	—	26	16	no	—
796	C₂²	—	26	4	no	—
797	C₂²	—	26	8	no	—
798	C₂²	—	26	8	no	—
799	C₂²	—	26	16	no	—
800	C₂²	—	52	32	no	—
801	C₂²	—	52	128	no	—
802	C₂²	—	52	32	no	—
803	C₂²	—	52	16	no	—
804	C₂²	—	52	8	no	—
805	C₂²	—	104	32	no	—
806	C₂²	C₂²×D₄×D₁₃	1	4	yes	—
807	C₂²	C₂²×D₄×D₁₃	1	2	yes	—
808	C₂²	C₂×#88256	1	4	yes	—
809	C₂²	C₂×#88256	1	8	yes	complemented
810	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
811	C₄	—	2	4	no	—
812	C₄	—	2	4	no	—
813	C₄	—	2	8	no	—
814	C₄	—	26	4	no	—
815	C₄	—	26	8	no	—
816	C₄	C₂²×D₄×D₁₃	1	4	yes	—
817	C₄	C₂²×D₄×D₁₃	1	4	yes	—
818	C₂	—	2	4	no	—
819	C₂	—	2	8	no	—
820	C₂	—	4	4	no	—
821	C₂	—	26	16	no	—
822	C₂	—	52	8	no	—
823	C₂	—	52	4	no	—
824	C₂	#13128469	1	4	yes	direct product factor
825	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
826	C₂	C₂²×#88256	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#525	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#525	D₁₃
hypocenter	C₁₃	C₂×#3484
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. C₂²×#88256	C₂	semidirect
2. C₂⁴×D₅₂	C₂	semidirect
3. #13128469	C₂	direct (N × H)
4. C₂×#11719255	C₂	semidirect
5. C₂×#11719335	C₂	semidirect
6. C₂×D₄×D₅₂	C₂	semidirect
7. C₂×#11719314	C₂	semidirect
8. C₂×#11719230	C₂	semidirect
9. C₂×#11719535	C₂	semidirect
10. C₂×#11719358	C₂	semidirect
11. C₂×#11719496	C₂	semidirect
12. C₂×D₁₃×#120	C₂	semidirect
13. C₂×#11719226	C₂	semidirect
14. C₂×C₁₃×#525	C₂	semidirect
15. C₂⁵×D₁₃	C₂²	semidirect
16. C₂²×C₁₃×#41	C₂²	semidirect
17. C₂⁴×C₄×C₁₃	C₂²	semidirect
19. C₂×#88256	C₂²	semidirect
20. C₂²×#6131	C₂²	semidirect
21. C₂²×D₄×D₁₃	C₂²	semidirect
22. C₂²×D₄×D₁₃	C₂²	semidirect
23. C₂²×D₄×D₁₃	C₂²	semidirect
24. C₂²×#6127	C₂²	semidirect
25. C₂²×#6127	C₂²	semidirect
28. C₂³×D₅₂	C₂²	semidirect
29. C₂³×D₅₂	C₂²	semidirect
30. C₂³×D₅₂	C₂²	semidirect
31. C₂³×D₅₂	C₂²	semidirect
32. C₂³×D₅₂	C₂²	semidirect
33. C₂³×D₅₂	C₂²	semidirect
34. C₁₃×#525	C₂²	semidirect
35. C₂×C₁₃×#123	C₂²	semidirect
36. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₁₃×#121	C₂²	semidirect
38. C₂×C₁₃×#120	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃	C₂²	semidirect
40. C₂×C₁₃×#117	C₂²	semidirect
41. C₂×#88207	C₂²	semidirect
42. #11719535	C₂²	semidirect
43. C₂×#88201	C₂²	semidirect
44. C₂×#88194	C₂²	semidirect
45. C₂×#88191	C₂²	semidirect
46. C₂×#88191	C₂²	semidirect
47. #11719496	C₂²	semidirect
48. C₂×#88184	C₂²	semidirect
49. C₂×#88184	C₂²	semidirect
50. C₂×#88183	C₂²	semidirect
51. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
52. C₂×#88180	C₂²	semidirect
53. C₂×#88178	C₂²	semidirect
54. #11719358	C₂²	semidirect
55. #11719335	C₂²	semidirect
56. #11719314	C₂²	semidirect
57. D₁₃×#120	C₂²	semidirect
58. #11719255	C₂²	semidirect
59. D₄×D₅₂	C₂²	semidirect
60. #11719230	C₂²	semidirect
61. #11719226	C₂²	semidirect
62. C₂×#88149	C₂²	semidirect
63. C₂×#88149	C₂²	semidirect
64. C₂×#88148	C₂²	semidirect
65. C₂×#88147	C₂²	semidirect
66. C₂×#88138	C₂²	semidirect
67. C₂×#88136	C₂²	semidirect
68. C₂×#88136	C₂²	semidirect
69. C₂×#88136	C₂²	semidirect
70. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
71. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
72. C₂×#88129	C₂²	semidirect
73. C₂×#88128	C₂²	semidirect
74. C₂×C₄×D₅₂	C₂²	semidirect
81. C₂⁴×D₁₃	C₂³	semidirect
82. C₂⁴×D₁₃	C₂³	semidirect
84. C₂×C₁₃×#41	C₂³	semidirect
85. C₂²×Q₈×C₁₃	C₂³	semidirect
88. C₂²×D₄×C₁₃	C₂³	semidirect
94. C₂³×C₄×C₁₃	C₂³	semidirect
95. C₂³×C₄×C₁₃	C₂³	semidirect
98. C₂²×C₂²⋊D₁₃	C₂³	semidirect
99. C₂²×C₂²⋊D₁₃	C₂³	semidirect
102. C₂×#6131	C₂³	semidirect
106. C₂×D₄×D₁₃	C₂³	semidirect
107. C₂×D₄×D₁₃	C₂³	semidirect
108. C₂×D₄×D₁₃	C₂³	semidirect
111. C₂×#6127	C₂³	semidirect
112. C₂×#6127	C₂³	semidirect
119. C₂²×D₅₂	D₄	semidirect
126. C₂²×D₅₂	C₂³	semidirect
127. C₂²×D₅₂	C₂³	semidirect
128. C₂²×D₅₂	C₂³	semidirect
129. C₂²×D₅₂	C₂³	semidirect
130. C₂²×D₅₂	C₂³	semidirect
131. C₂²×D₅₂	C₂³	semidirect
132. C₂²×D₅₂	C₂³	semidirect
133. C₂²×D₅₂	C₂³	semidirect
134. C₂²×C₄×D₁₃	C₂³	semidirect
135. C₂²×C₄×D₁₃	C₂³	semidirect
136. C₂²×C₄×D₁₃	C₂³	semidirect
137. C₂²×Dic₂₆	C₂³	semidirect
138. C₁₃×#123	C₂³	semidirect
139. C₁₃×C₂²⋊Q₈	C₂³	semidirect
140. C₁₃×#121	C₂³	semidirect
141. C₁₃×#120	C₂³	semidirect
142. C₄×D₄×C₁₃	C₂³	semidirect
143. C₁₃×#117	C₂³	semidirect
144. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
145. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
148. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
149. C₂×C₄²×C₁₃	C₂³	semidirect
150. #88207	C₂³	semidirect
153. #88201	C₂³	semidirect
154. #88194	C₂³	semidirect
155. #88191	C₂³	semidirect
156. #88191	C₂³	semidirect
157. #88184	C₂³	semidirect
158. #88184	C₂³	semidirect
159. #88183	C₂³	semidirect
160. C₄×C₂²⋊D₁₃	C₂³	semidirect
161. C₂×#6103	C₂³	semidirect
162. C₂×#6103	C₂³	semidirect
163. C₂×#6103	C₂³	semidirect
164. C₂×#6103	C₂³	semidirect
165. #88180	C₂³	semidirect
166. C₂×C₄⋊Dic₁₃	C₂³	semidirect
167. #88178	C₂³	semidirect
168. C₂×#6101	C₂³	semidirect
169. C₂×C₄×Dic₁₃	C₂³	semidirect
170. #88149	C₂³	semidirect
171. #88149	C₂³	semidirect
172. #88148	C₂³	semidirect
173. #88147	C₂³	semidirect
174. #88138	C₂³	semidirect
175. #88136	C₂³	semidirect
176. #88136	C₂³	semidirect
177. #88136	C₂³	semidirect
178. C₂²⋊C₄×D₁₃	C₂³	semidirect
179. C₂²⋊C₄×D₁₃	C₂³	semidirect
180. #88129	C₂³	semidirect
181. #88128	C₂³	semidirect
182. C₄×D₅₂	C₂³	semidirect
201. C₂³×D₁₃	C₂×D₄	semidirect
208. C₂³×D₁₃	C₂⁴	semidirect
211. C₂×Q₈×C₁₃	C₂⁴	semidirect
217. C₂×D₄×C₁₃	C₂⁴	semidirect
223. C₂²×C₄×C₁₃	C₂×D₄	semidirect
233. C₂²×C₄×C₁₃	C₂⁴	semidirect
240. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
241. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
261. C₂×D₅₂	C₂×D₄	semidirect
262. C₂×D₅₂	C₂×D₄	semidirect
263. C₂×D₅₂	C₂×D₄	semidirect
269. C₂×D₅₂	C₂⁴	semidirect
270. C₂×D₅₂	C₂⁴	semidirect
271. C₂×D₅₂	C₂⁴	semidirect
275. C₂×C₄×D₁₃	C₂⁴	semidirect
276. C₂×C₄×D₁₃	C₂⁴	semidirect
277. C₂×C₄×D₁₃	C₂⁴	semidirect
279. C₂×Dic₂₆	C₂⁴	semidirect
280. C₁₃×C₄⋊C₄	C₂⁴	semidirect
281. C₁₃×C₄⋊C₄	C₂⁴	semidirect
284. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
285. C₄²×C₁₃	C₂⁴	semidirect
288. #6103	C₂⁴	semidirect
289. #6103	C₂⁴	semidirect
290. #6103	C₂⁴	semidirect
291. #6103	C₂⁴	semidirect
292. C₄⋊Dic₁₃	C₂⁴	semidirect
293. #6101	C₂⁴	semidirect
294. C₄×Dic₁₃	C₂⁴	semidirect
306. C₂×#525	D₁₃	semidirect
318. C₂³×C₁₃	H(5,𝔽₂)	semidirect
342. C₂²×D₁₃	C₂²×D₄	semidirect
359. C₂×C₄×C₁₃	C₂²×D₄	semidirect
379. D₅₂	C₂²×D₄	semidirect
380. D₅₂	C₂²×D₄	semidirect
391. C₂²×#41	C₂×D₁₃	semidirect
403. C₂⁴×C₄	C₂×D₁₃	semidirect
416. #525	C₂×D₁₃	semidirect
419. C₂×#123	C₂×D₁₃	semidirect
421. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
427. C₂×#121	C₂×D₁₃	semidirect
435. C₂×#120	C₂×D₁₃	semidirect
440. C₂×C₄×D₄	C₂×D₁₃	semidirect
442. C₂×#117	C₂×D₁₃	semidirect
457. C₂²×C₁₃	C₂×H(5,𝔽₂)	semidirect
495. C₂×#41	C₂²×D₁₃	semidirect
497. C₂²×Q₈	C₂²×D₁₃	semidirect
531. C₂²×D₄	C₂²×D₁₃	semidirect
540. C₂³×C₄	C₂²×D₁₃	semidirect
541. C₂³×C₄	C₂²×D₁₃	semidirect
548. #123	C₂²×D₁₃	semidirect
550. C₂²⋊Q₈	C₂²×D₁₃	semidirect
556. #121	C₂²×D₁₃	semidirect
563. #120	C₂²×D₁₃	semidirect
567. C₄×D₄	C₂²×D₁₃	semidirect
569. #117	C₂²×D₁₃	semidirect
572. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
573. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
584. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
586. C₂×C₄²	C₂²×D₁₃	semidirect
590. C₂×C₁₃	#3484	semidirect
628. C₂×Q₈	C₂³×D₁₃	semidirect
667. C₂×D₄	C₂³×D₁₃	semidirect
681. C₂²×C₄	D₄×D₁₃	semidirect
691. C₂²×C₄	C₂³×D₁₃	semidirect
694. C₄⋊C₄	C₂³×D₁₃	semidirect
695. C₄⋊C₄	C₂³×D₁₃	semidirect
704. C₂²⋊C₄	C₂³×D₁₃	semidirect
706. C₄²	C₂³×D₁₃	semidirect
707. C₁₃	C₂×#3484	semidirect
740. C₂³	#88256	semidirect
778. C₂×C₄	C₂×D₄×D₁₃	semidirect
809. C₂²	C₂×#88256	semidirect
824. C₂	#13128469	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88256	2
C₂⁴×D₅₂	2
#13128469	2
C₂×#11719255	2
C₂×#11719335	2
C₂×D₄×D₅₂	2
C₂×#11719314	2
C₂×#11719230	2
C₂×#11719535	2
C₂×#11719358	2
C₂×#11719496	2
C₂×D₁₃×#120	2
C₂×#11719226	2
C₂×C₁₃×#525	2
C₂×#3484	13

Subgroups — C2×#13128469 #16770798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128469 #16770798