Subgroups — C₂²×#11719252 #16769574

Order 3328.

14334 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719252	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#88148	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88137	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#88132	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#88138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#88193	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#88136	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#88191	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#88126	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
22	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
23	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
24	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
26	C₂²×#6127	—	2	16	no	—
27	C₂²×#6127	C₂²	1	24	yes	complemented
28	C₂³×D₅₂	C₂²	1	1	yes	characteristic
29	C₂³×D₅₂	C₂²	1	1	yes	characteristic
30	C₂³×C₄×D₁₃	—	2	16	no	—
31	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
32	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
33	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
34	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
35	C₂³×C₄×D₁₃	C₂²	1	24	yes	complemented
36	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
39	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#88193	C₂²	1	24	yes	complemented
46	C₂×#88191	C₂²	1	24	yes	complemented
47	C₂×C₄×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
48	C₂×C₄×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
49	C₂²×#6103	C₂²	1	1	yes	characteristic
50	C₂²×#6103	C₂²	1	1	yes	characteristic
51	C₂²×#6103	C₂²	1	1	yes	characteristic
52	C₂²×#6103	C₂²	1	1	yes	characteristic
53	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
54	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
58	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
59	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
60	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
61	#11719252	C₂²	1	256	yes	direct product factor
62	C₂×#88150	C₂²	1	24	yes	complemented
63	C₂×#88148	C₂²	1	24	yes	complemented
64	C₂×#88138	C₂²	1	24	yes	complemented
65	C₂×#88137	C₂²	1	24	yes	complemented
66	C₂×#88136	C₂²	1	24	yes	complemented
67	C₂×#88132	C₂²	1	24	yes	complemented
68	C₂×C₄×D₅₂	C₂²	1	24	yes	complemented
69	C₂×#88126	C₂²	1	24	yes	complemented
70	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
71	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
72	C₂⁴×D₁₃	—	2	8	no	—
73	C₂⁴×D₁₃	—	2	8	no	—
74	C₂⁴×D₁₃	—	2	8	no	—
75	C₂⁴×D₁₃	C₂³	1	12	yes	—
76	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
77	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
78	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	—	2	8	no	—
80	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
81	C₂³×C₄×C₁₃	—	2	8	no	—
82	C₂³×C₄×C₁₃	—	2	8	no	—
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	12	yes	complemented
90	C₂²×C₂²⋊D₁₃	—	2	8	no	—
91	C₂²×C₂²⋊D₁₃	—	2	8	no	—
92	C₂²×C₂²⋊D₁₃	—	2	8	no	—
93	C₂²×C₂²⋊D₁₃	—	2	8	no	—
94	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
95	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
96	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
97	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	complemented
98	C₂³×Dic₁₃	—	2	8	no	—
99	C₂³×Dic₁₃	C₂³	1	12	yes	—
100	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
101	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
102	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
103	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
104	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
105	C₂×#6127	—	2	192	no	—
106	C₂×#6127	C₂³	1	64	yes	complemented
107	C₂²×D₅₂	—	2	8	no	—
108	C₂²×D₅₂	—	2	8	no	—
109	C₂²×D₅₂	C₂³	1	12	yes	—
110	C₂²×D₅₂	C₂³	1	12	yes	—
111	C₂²×C₄×D₁₃	—	2	8	no	—
112	C₂²×C₄×D₁₃	—	2	8	no	—
113	C₂²×C₄×D₁₃	—	2	8	no	—
114	C₂²×C₄×D₁₃	—	2	8	no	—
115	C₂²×C₄×D₁₃	—	2	192	no	—
116	C₂²×C₄×D₁₃	D₄	1	16	yes	complemented
117	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
118	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
119	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
120	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
121	C₂²×C₄×D₁₃	C₂³	1	64	yes	complemented
122	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
123	C₂²×Dic₂₆	—	2	8	no	—
124	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
125	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
129	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
130	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
131	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	complemented
132	#88193	C₂³	1	64	yes	complemented
133	#88191	C₂³	1	64	yes	complemented
134	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
135	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
136	C₂×#6103	C₂³	1	12	yes	—
137	C₂×#6103	C₂³	1	12	yes	—
138	C₂×#6103	C₂³	1	12	yes	—
139	C₂×#6103	C₂³	1	12	yes	—
140	C₂×#6103	C₂³	1	12	yes	complemented
141	C₂×#6103	C₂³	1	12	yes	complemented
142	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
143	C₂×#6101	C₂³	1	12	yes	complemented
144	C₂×#6101	C₂³	1	12	yes	complemented
145	C₂×#6101	C₂³	1	12	yes	complemented
146	C₂×#6101	C₂³	1	12	yes	complemented
147	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
148	#88150	C₂³	1	64	yes	complemented
149	#88148	C₂³	1	64	yes	complemented
150	#88138	C₂³	1	64	yes	complemented
151	#88137	C₂³	1	64	yes	complemented
152	#88136	C₂³	1	64	yes	complemented
153	#88132	C₂³	1	64	yes	complemented
154	C₄×D₅₂	C₂³	1	64	yes	complemented
155	#88126	C₂³	1	64	yes	complemented
156	C₂²×#525	—	13	1	no	maximal, Sylow
157	C₂⁴×C₁₃	—	2	4	no	—
158	C₂⁴×C₁₃	—	2	4	no	—
159	C₂⁴×C₁₃	—	2	4	no	—
160	C₂⁴×C₁₃	—	2	4	no	—
161	C₂⁴×C₁₃	—	2	4	no	—
162	C₂⁴×C₁₃	#41	1	8	yes	complemented
163	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
164	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
165	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂³×D₁₃	—	2	128	no	—
167	C₂³×D₁₃	—	2	4	no	—
168	C₂³×D₁₃	—	2	4	no	—
169	C₂³×D₁₃	—	2	4	no	—
170	C₂³×D₁₃	—	2	4	no	—
171	C₂³×D₁₃	—	2	48	no	—
172	C₂³×D₁₃	—	2	48	no	—
173	C₂³×D₁₃	—	2	48	no	—
174	C₂³×D₁₃	—	2	4	no	—
175	C₂³×D₁₃	—	2	4	no	—
176	C₂³×D₁₃	—	2	4	no	—
177	C₂³×D₁₃	C₂×D₄	1	8	yes	—
178	C₂³×D₁₃	#41	1	8	yes	complemented
179	C₂³×D₁₃	C₂⁴	1	16	yes	—
180	C₂³×D₁₃	C₂⁴	1	6	yes	—
181	C₂³×D₁₃	C₂⁴	1	6	yes	—
182	C₂³×D₁₃	C₂⁴	1	6	yes	—
183	C₂×D₄×C₁₃	—	2	48	no	—
184	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	2	4	no	—
189	C₂²×C₄×C₁₃	—	2	48	no	—
190	C₂²×C₄×C₁₃	—	2	48	no	—
191	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
199	C₂×C₂²⋊D₁₃	—	2	48	no	—
200	C₂×C₂²⋊D₁₃	—	2	48	no	—
201	C₂×C₂²⋊D₁₃	—	2	48	no	—
202	C₂×C₂²⋊D₁₃	—	2	48	no	—
203	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
204	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
205	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
206	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	complemented
207	C₂²×Dic₁₃	—	2	4	no	—
208	C₂²×Dic₁₃	—	2	4	no	—
209	C₂²×Dic₁₃	—	2	4	no	—
210	C₂²×Dic₁₃	—	2	4	no	—
211	C₂²×Dic₁₃	—	2	48	no	—
212	C₂²×Dic₁₃	C₂×D₄	1	8	yes	—
213	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
214	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
215	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
216	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
217	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
218	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
219	#6127	—	2	256	no	—
220	C₂×D₅₂	—	2	48	no	—
221	C₂×D₅₂	—	2	48	no	—
222	C₂×D₅₂	C₂⁴	1	16	yes	—
223	C₂×D₅₂	C₂⁴	1	16	yes	—
224	C₂×C₄×D₁₃	—	2	48	no	—
225	C₂×C₄×D₁₃	—	2	48	no	—
226	C₂×C₄×D₁₃	—	2	48	no	—
227	C₂×C₄×D₁₃	—	2	48	no	—
228	C₂×C₄×D₁₃	—	2	256	no	—
229	C₂×C₄×D₁₃	C₂×D₄	1	96	yes	complemented
230	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
231	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
232	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
233	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
234	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
235	C₂×Dic₂₆	—	2	48	no	—
236	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
237	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
238	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
239	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
240	C₄²×C₁₃	C₂⁴	1	16	yes	complemented
241	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
242	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	complemented
243	#6103	C₂⁴	1	16	yes	—
244	#6103	C₂⁴	1	16	yes	—
245	#6103	C₂⁴	1	16	yes	—
246	#6103	C₂⁴	1	16	yes	—
247	#6103	C₂⁴	1	16	yes	complemented
248	#6103	C₂⁴	1	16	yes	complemented
249	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
250	#6101	C₂⁴	1	16	yes	complemented
251	#6101	C₂⁴	1	16	yes	complemented
252	#6101	C₂⁴	1	16	yes	complemented
253	#6101	C₂⁴	1	16	yes	complemented
254	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
255	C₂³×#41	—	13	1	no	—
256	C₂⁵×C₄	—	13	1	no	—
257	C₂×#525	—	13	48	no	—
258	C₂²×#123	—	13	1	no	—
259	C₂²×#123	—	13	1	no	—
260	C₂²×C₂²⋊Q₈	—	13	1	no	—
261	C₂²×C₂²⋊Q₈	—	13	1	no	—
262	C₂²×#121	—	13	1	no	—
263	C₂²×#121	—	13	1	no	—
264	C₂²×#120	—	13	1	no	—
265	C₂²×#120	—	13	1	no	—
266	C₂²×C₄×D₄	—	13	1	no	—
267	C₂²×C₄×D₄	—	13	1	no	—
268	C₂²×C₄×D₄	—	13	1	no	—
269	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
270	C₂²×#117	—	13	1	no	—
271	C₂³×C₁₃	—	2	32	no	—
272	C₂³×C₁₃	—	2	12	no	—
273	C₂³×C₁₃	—	2	12	no	—
274	C₂³×C₁₃	—	2	12	no	—
275	C₂³×C₁₃	—	2	12	no	—
276	C₂³×C₁₃	—	2	12	no	—
277	C₂³×C₁₃	—	4	16	no	—
278	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
279	C₂³×C₁₃	C₂×#41	1	4	yes	—
280	C₂³×C₁₃	C₂×#41	1	4	yes	—
281	C₂³×C₁₃	C₂×#41	1	24	yes	complemented
282	C₂³×C₁₃	C₂⁵	1	4	yes	—
283	C₂³×C₁₃	C₂⁵	1	4	yes	—
284	C₂³×C₁₃	C₂⁵	1	3	yes	—
285	C₂²×D₁₃	—	2	384	no	—
286	C₂²×D₁₃	—	2	32	no	—
287	C₂²×D₁₃	—	2	32	no	—
288	C₂²×D₁₃	—	2	12	no	—
289	C₂²×D₁₃	—	2	12	no	—
290	C₂²×D₁₃	—	2	12	no	—
291	C₂²×D₁₃	—	2	12	no	—
292	C₂²×D₁₃	—	2	32	no	—
293	C₂²×D₁₃	—	2	32	no	—
294	C₂²×D₁₃	—	2	32	no	—
295	C₂²×D₁₃	—	2	12	no	—
296	C₂²×D₁₃	—	2	12	no	—
297	C₂²×D₁₃	—	2	12	no	—
298	C₂²×D₁₃	—	4	16	no	—
299	C₂²×D₁₃	C₂²×D₄	1	24	yes	—
300	C₂²×D₁₃	C₂×#41	1	24	yes	complemented
301	C₂²×D₁₃	C₂⁵	1	4	yes	—
302	C₂²×D₁₃	C₂⁵	1	4	yes	—
303	C₂²×D₁₃	C₂⁵	1	4	yes	—
304	D₄×C₁₃	—	2	32	no	—
305	C₂×C₄×C₁₃	—	2	12	no	—
306	C₂×C₄×C₁₃	—	2	12	no	—
307	C₂×C₄×C₁₃	—	2	12	no	—
308	C₂×C₄×C₁₃	—	2	12	no	—
309	C₂×C₄×C₁₃	—	2	32	no	—
310	C₂×C₄×C₁₃	—	2	32	no	—
311	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
312	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
313	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
314	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
315	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
316	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
317	C₂²⋊D₁₃	—	2	32	no	—
318	C₂²⋊D₁₃	—	2	32	no	—
319	C₂²⋊D₁₃	—	2	32	no	—
320	C₂²⋊D₁₃	—	2	32	no	—
321	C₂×Dic₁₃	—	2	12	no	—
322	C₂×Dic₁₃	—	2	12	no	—
323	C₂×Dic₁₃	—	2	12	no	—
324	C₂×Dic₁₃	—	2	12	no	—
325	C₂×Dic₁₃	—	2	32	no	—
326	C₂×Dic₁₃	C₂²×D₄	1	24	yes	—
327	C₂×Dic₁₃	C₂⁵	1	4	yes	—
328	C₂×Dic₁₃	C₂⁵	1	4	yes	—
329	C₂×Dic₁₃	C₂⁵	1	4	yes	—
330	C₂×Dic₁₃	C₂⁵	1	4	yes	—
331	C₂×Dic₁₃	C₂⁵	1	4	yes	—
332	D₅₂	—	2	32	no	—
333	D₅₂	—	2	32	no	—
334	C₄×D₁₃	—	2	32	no	—
335	C₄×D₁₃	—	2	32	no	—
336	C₄×D₁₃	—	2	32	no	—
337	C₄×D₁₃	—	2	32	no	—
338	C₄×D₁₃	C₂²×D₄	1	64	yes	complemented
339	Dic₂₆	—	2	32	no	—
340	C₂⁶	—	13	1	no	—
341	C₂²×#41	—	13	24	no	—
342	C₂²×#41	—	26	16	no	—
343	C₂³×Q₈	—	13	1	no	—
344	C₂³×D₄	—	13	1	no	—
345	C₂³×D₄	—	13	1	no	—
346	C₂³×D₄	—	13	1	no	—
347	C₂³×D₄	—	13	1	no	—
348	C₂³×D₄	—	13	1	no	—
349	C₂³×D₄	—	13	1	no	—
350	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
351	C₂⁴×C₄	—	13	1	no	—
352	C₂⁴×C₄	—	13	1	no	—
353	C₂⁴×C₄	—	13	1	no	—
354	C₂⁴×C₄	—	13	1	no	—
355	C₂⁴×C₄	—	13	24	no	—
356	C₂⁴×C₄	—	13	1	no	—
357	C₂⁴×C₄	—	13	1	no	—
358	C₂⁴×C₄	—	26	16	no	—
359	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
360	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
361	#525	—	13	256	no	—
362	C₂×#123	—	13	24	no	—
363	C₂×#123	—	13	24	no	—
364	C₂×C₂²⋊Q₈	—	13	24	no	—
365	C₂×C₂²⋊Q₈	—	13	24	no	—
366	C₂×#121	—	13	24	no	—
367	C₂×#121	—	13	24	no	—
368	C₂×#120	—	13	24	no	—
369	C₂×#120	—	13	24	no	—
370	C₂×C₄×D₄	—	13	24	no	—
371	C₂×C₄×D₄	—	13	24	no	—
372	C₂×C₄×D₄	—	13	24	no	—
373	C₂×C₄×D₄	C₂×D₁₃	1	24	yes	complemented
374	C₂×#117	—	13	24	no	—
375	C₂²×C₄⋊C₄	—	13	1	no	—
376	C₂²×C₄⋊C₄	—	13	1	no	—
377	C₂²×C₄⋊C₄	—	13	1	no	—
378	C₂²×C₄⋊C₄	—	13	1	no	—
379	C₂²×C₄⋊C₄	—	13	1	no	—
380	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
381	C₂²×C₂²⋊C₄	—	13	1	no	—
382	C₂²×C₂²⋊C₄	—	13	1	no	—
383	C₂²×C₂²⋊C₄	—	13	1	no	—
384	C₂²×C₂²⋊C₄	—	13	1	no	—
385	C₂²×C₂²⋊C₄	—	13	1	no	—
386	C₂²×C₂²⋊C₄	—	13	1	no	—
387	C₂²×C₂²⋊C₄	—	13	1	no	—
388	C₂²×C₂²⋊C₄	—	13	1	no	—
389	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
390	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
391	C₂²×C₄²	—	13	1	no	—
392	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
393	C₂²×C₁₃	—	2	4	no	—
394	C₂²×C₁₃	—	2	4	no	—
395	C₂²×C₁₃	—	2	48	no	—
396	C₂²×C₁₃	—	2	4	no	—
397	C₂²×C₁₃	—	2	4	no	—
398	C₂²×C₁₃	—	2	4	no	—
399	C₂²×C₁₃	—	4	24	no	—
400	C₂²×C₁₃	#525	1	16	yes	complemented
401	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
402	C₂²×C₁₃	C₂²×#41	1	6	yes	—
403	C₂²×C₁₃	C₂²×#41	1	6	yes	—
404	C₂²×C₁₃	C₂²×#41	1	8	yes	complemented
405	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
406	C₂×D₁₃	—	2	128	no	—
407	C₂×D₁₃	—	2	4	no	—
408	C₂×D₁₃	—	2	4	no	—
409	C₂×D₁₃	—	2	4	no	—
410	C₂×D₁₃	—	2	4	no	—
411	C₂×D₁₃	—	2	48	no	—
412	C₂×D₁₃	—	2	48	no	—
413	C₂×D₁₃	—	2	4	no	—
414	C₂×D₁₃	—	2	4	no	—
415	C₂×D₁₃	—	2	4	no	—
416	C₂×D₁₃	—	4	24	no	—
417	C₂×D₁₃	C₂³×D₄	1	8	yes	—
418	C₂×D₁₃	C₂²×#41	1	8	yes	complemented
419	C₄×C₁₃	—	2	4	no	—
420	C₄×C₁₃	—	2	4	no	—
421	C₄×C₁₃	—	2	4	no	—
422	C₄×C₁₃	—	2	4	no	—
423	C₄×C₁₃	C₂³×D₄	1	8	yes	—
424	Dic₁₃	—	2	4	no	—
425	Dic₁₃	—	2	4	no	—
426	Dic₁₃	—	2	4	no	—
427	Dic₁₃	—	2	4	no	—
428	Dic₁₃	C₂³×D₄	1	8	yes	—
429	C₂⁵	—	13	1	no	—
430	C₂⁵	—	13	1	no	—
431	C₂⁵	—	13	1	no	—
432	C₂⁵	—	13	12	no	—
433	C₂⁵	—	26	8	no	—
434	C₂⁵	—	26	8	no	—
435	C₂⁵	—	26	8	no	—
436	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
437	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
438	C₂×#41	—	13	64	no	—
439	C₂×#41	—	26	192	no	—
440	C₂²×Q₈	—	13	12	no	—
441	C₂²×Q₈	—	26	8	no	—
442	C₂²×D₄	—	2	8	no	—
443	C₂²×D₄	—	13	12	no	—
444	C₂²×D₄	—	13	12	no	—
445	C₂²×D₄	—	13	12	no	—
446	C₂²×D₄	—	13	12	no	—
447	C₂²×D₄	—	13	12	no	—
448	C₂²×D₄	—	13	12	no	—
449	C₂²×D₄	—	26	8	no	—
450	C₂²×D₄	—	26	8	no	—
451	C₂²×D₄	—	26	8	no	—
452	C₂²×D₄	—	26	8	no	—
453	C₂²×D₄	—	26	8	no	—
454	C₂²×D₄	—	26	8	no	—
455	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
456	C₂³×C₄	—	2	8	no	—
457	C₂³×C₄	—	2	8	no	—
458	C₂³×C₄	—	13	1	no	—
459	C₂³×C₄	—	13	16	no	—
460	C₂³×C₄	—	13	12	no	—
461	C₂³×C₄	—	13	1	no	—
462	C₂³×C₄	—	13	1	no	—
463	C₂³×C₄	—	13	1	no	—
464	C₂³×C₄	—	13	1	no	—
465	C₂³×C₄	—	13	12	no	—
466	C₂³×C₄	—	13	12	no	—
467	C₂³×C₄	—	13	12	no	—
468	C₂³×C₄	—	13	12	no	—
469	C₂³×C₄	—	13	12	no	—
470	C₂³×C₄	—	13	64	no	—
471	C₂³×C₄	—	26	8	no	—
472	C₂³×C₄	—	26	192	no	—
473	C₂³×C₄	—	26	8	no	—
474	C₂³×C₄	—	26	8	no	—
475	C₂³×C₄	—	26	8	no	—
476	C₂³×C₄	—	26	8	no	—
477	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
478	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
479	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
480	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
481	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
482	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
483	C₂³×C₄	C₂²×D₁₃	1	12	yes	complemented
484	#123	—	13	64	no	—
485	#123	—	13	64	no	—
486	C₂²⋊Q₈	—	13	64	no	—
487	C₂²⋊Q₈	—	13	64	no	—
488	#121	—	13	64	no	—
489	#121	—	13	64	no	—
490	#120	—	13	64	no	—
491	#120	—	13	64	no	—
492	C₄×D₄	—	13	64	no	—
493	C₄×D₄	—	13	64	no	—
494	C₄×D₄	—	13	64	no	—
495	C₄×D₄	C₂²×D₁₃	1	64	yes	complemented
496	#117	—	13	64	no	—
497	C₂×C₄⋊C₄	—	13	12	no	—
498	C₂×C₄⋊C₄	—	13	12	no	—
499	C₂×C₄⋊C₄	—	13	12	no	—
500	C₂×C₄⋊C₄	—	13	12	no	—
501	C₂×C₄⋊C₄	—	13	12	no	—
502	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
503	C₂×C₂²⋊C₄	—	13	12	no	—
504	C₂×C₂²⋊C₄	—	13	12	no	—
505	C₂×C₂²⋊C₄	—	13	12	no	—
506	C₂×C₂²⋊C₄	—	13	12	no	—
507	C₂×C₂²⋊C₄	—	13	12	no	—
508	C₂×C₂²⋊C₄	—	13	12	no	—
509	C₂×C₂²⋊C₄	—	13	12	no	—
510	C₂×C₂²⋊C₄	—	13	12	no	—
511	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	—
512	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	complemented
513	C₂×C₄²	—	13	12	no	—
514	C₂×C₄²	C₂²×D₁₃	1	12	yes	complemented
515	C₂×C₁₃	—	2	8	no	—
516	C₂×C₁₃	—	4	4	no	—
517	C₂×C₁₃	C₂×#525	1	12	yes	complemented
518	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
519	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
520	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
521	D₁₃	—	2	8	no	—
522	D₁₃	—	2	8	no	—
523	D₁₃	—	4	4	no	—
524	C₂⁴	—	2	4	no	—
525	C₂⁴	—	2	4	no	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	2	4	no	—
528	C₂⁴	—	2	4	no	—
529	C₂⁴	—	13	8	no	—
530	C₂⁴	—	13	8	no	—
531	C₂⁴	—	13	6	no	—
532	C₂⁴	—	13	6	no	—
533	C₂⁴	—	13	6	no	—
534	C₂⁴	—	13	16	no	—
535	C₂⁴	—	26	48	no	—
536	C₂⁴	—	26	48	no	—
537	C₂⁴	—	26	128	no	—
538	C₂⁴	—	26	4	no	—
539	C₂⁴	—	26	4	no	—
540	C₂⁴	—	26	48	no	—
541	C₂⁴	—	26	4	no	—
542	C₂⁴	—	26	4	no	—
543	C₂⁴	—	26	4	no	—
544	C₂⁴	—	26	4	no	—
545	C₂⁴	—	26	4	no	—
546	C₂⁴	#6127	1	8	yes	complemented
547	C₂⁴	C₂³×D₁₃	1	6	yes	—
548	C₂⁴	C₂³×D₁₃	1	6	yes	—
549	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
550	#41	—	26	256	no	—
551	C₂×Q₈	—	13	16	no	—
552	C₂×Q₈	—	26	48	no	—
553	C₂×D₄	—	2	48	no	—
554	C₂×D₄	—	13	16	no	—
555	C₂×D₄	—	13	16	no	—
556	C₂×D₄	—	13	16	no	—
557	C₂×D₄	—	13	16	no	—
558	C₂×D₄	—	13	16	no	—
559	C₂×D₄	—	13	16	no	—
560	C₂×D₄	—	26	48	no	—
561	C₂×D₄	—	26	48	no	—
562	C₂×D₄	—	26	48	no	—
563	C₂×D₄	—	26	48	no	—
564	C₂×D₄	—	26	48	no	—
565	C₂×D₄	—	26	48	no	—
566	C₂×D₄	C₂³×D₁₃	1	16	yes	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	48	no	—
572	C₂²×C₄	—	2	48	no	—
573	C₂²×C₄	—	13	8	no	—
574	C₂²×C₄	—	13	6	no	—
575	C₂²×C₄	—	13	96	no	—
576	C₂²×C₄	—	13	16	no	—
577	C₂²×C₄	—	13	6	no	—
578	C₂²×C₄	—	13	6	no	—
579	C₂²×C₄	—	13	6	no	—
580	C₂²×C₄	—	13	6	no	—
581	C₂²×C₄	—	13	16	no	—
582	C₂²×C₄	—	13	16	no	—
583	C₂²×C₄	—	13	16	no	—
584	C₂²×C₄	—	13	16	no	—
585	C₂²×C₄	—	13	16	no	—
586	C₂²×C₄	—	26	48	no	—
587	C₂²×C₄	—	26	256	no	—
588	C₂²×C₄	—	26	48	no	—
589	C₂²×C₄	—	26	48	no	—
590	C₂²×C₄	—	26	4	no	—
591	C₂²×C₄	—	26	4	no	—
592	C₂²×C₄	—	26	4	no	—
593	C₂²×C₄	—	26	4	no	—
594	C₂²×C₄	—	26	48	no	—
595	C₂²×C₄	—	26	48	no	—
596	C₂²×C₄	D₄×D₁₃	1	8	yes	—
597	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
598	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
599	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
600	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
601	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
602	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
603	C₂²×C₄	C₂³×D₁₃	1	16	yes	complemented
604	C₄⋊C₄	—	13	16	no	—
605	C₄⋊C₄	—	13	16	no	—
606	C₄⋊C₄	—	13	16	no	—
607	C₄⋊C₄	—	13	16	no	—
608	C₄⋊C₄	—	13	16	no	—
609	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
610	C₂²⋊C₄	—	13	16	no	—
611	C₂²⋊C₄	—	13	16	no	—
612	C₂²⋊C₄	—	13	16	no	—
613	C₂²⋊C₄	—	13	16	no	—
614	C₂²⋊C₄	—	13	16	no	—
615	C₂²⋊C₄	—	13	16	no	—
616	C₂²⋊C₄	—	13	16	no	—
617	C₂²⋊C₄	—	13	16	no	—
618	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
619	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	complemented
620	C₄²	—	13	16	no	—
621	C₄²	C₂³×D₁₃	1	16	yes	complemented
622	C₁₃	C₂²×#525	1	1	yes	characteristic, complemented, Sylow
623	C₂³	—	2	32	no	—
624	C₂³	—	2	12	no	—
625	C₂³	—	2	12	no	—
626	C₂³	—	2	12	no	—
627	C₂³	—	2	12	no	—
628	C₂³	—	2	12	no	—
629	C₂³	—	4	16	no	—
630	C₂³	—	13	24	no	—
631	C₂³	—	13	24	no	—
632	C₂³	—	13	4	no	—
633	C₂³	—	13	4	no	—
634	C₂³	—	13	4	no	—
635	C₂³	—	26	32	no	—
636	C₂³	—	26	32	no	—
637	C₂³	—	26	384	no	—
638	C₂³	—	26	32	no	—
639	C₂³	—	26	32	no	—
640	C₂³	—	26	12	no	—
641	C₂³	—	26	12	no	—
642	C₂³	—	26	32	no	—
643	C₂³	—	26	12	no	—
644	C₂³	—	26	12	no	—
645	C₂³	—	26	12	no	—
646	C₂³	—	26	12	no	—
647	C₂³	—	26	12	no	—
648	C₂³	—	52	16	no	—
649	C₂³	C₂×#6127	1	4	yes	—
650	C₂³	C₂×#6127	1	24	yes	complemented
651	C₂³	C₂×D₄×D₁₃	1	4	yes	—
652	C₂³	#41×D₁₃	1	4	yes	—
653	C₂³	C₂⁴×D₁₃	1	4	yes	—
654	C₂³	C₂⁴×D₁₃	1	4	yes	—
655	C₂³	C₂⁴×D₁₃	1	3	yes	—
656	Q₈	—	26	32	no	—
657	D₄	—	2	32	no	—
658	D₄	—	26	32	no	—
659	D₄	—	26	32	no	—
660	D₄	—	26	32	no	—
661	D₄	—	26	32	no	—
662	D₄	—	26	32	no	—
663	D₄	—	26	32	no	—
664	C₂×C₄	—	2	12	no	—
665	C₂×C₄	—	2	12	no	—
666	C₂×C₄	—	2	12	no	—
667	C₂×C₄	—	2	12	no	—
668	C₂×C₄	—	2	32	no	—
669	C₂×C₄	—	2	32	no	—
670	C₂×C₄	—	13	24	no	—
671	C₂×C₄	—	13	4	no	—
672	C₂×C₄	—	13	64	no	—
673	C₂×C₄	—	13	4	no	—
674	C₂×C₄	—	13	4	no	—
675	C₂×C₄	—	13	4	no	—
676	C₂×C₄	—	13	4	no	—
677	C₂×C₄	—	26	32	no	—
678	C₂×C₄	—	26	32	no	—
679	C₂×C₄	—	26	32	no	—
680	C₂×C₄	—	26	12	no	—
681	C₂×C₄	—	26	12	no	—
682	C₂×C₄	—	26	12	no	—
683	C₂×C₄	—	26	12	no	—
684	C₂×C₄	—	26	32	no	—
685	C₂×C₄	—	26	32	no	—
686	C₂×C₄	C₂×D₄×D₁₃	1	24	yes	—
687	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
688	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
689	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
690	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
691	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
692	C₂²	—	2	48	no	—
693	C₂²	—	2	4	no	—
694	C₂²	—	2	4	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	4	24	no	—
699	C₂²	—	13	8	no	—
700	C₂²	—	13	8	no	—
701	C₂²	—	26	128	no	—
702	C₂²	—	26	48	no	—
703	C₂²	—	26	48	no	—
704	C₂²	—	26	4	no	—
705	C₂²	—	26	4	no	—
706	C₂²	—	26	4	no	—
707	C₂²	—	26	4	no	—
708	C₂²	—	26	4	no	—
709	C₂²	—	26	4	no	—
710	C₂²	—	26	4	no	—
711	C₂²	—	52	24	no	—
712	C₂²	#11719252	1	16	yes	direct product factor
713	C₂²	C₂²×#6127	1	6	yes	—
714	C₂²	C₂²×#6127	1	8	yes	complemented
715	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
716	C₂²	C₂×#41×D₁₃	1	6	yes	—
717	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
718	C₄	—	2	4	no	—
719	C₄	—	2	4	no	—
720	C₄	—	2	4	no	—
721	C₄	—	2	4	no	—
722	C₄	—	13	8	no	—
723	C₄	—	26	4	no	—
724	C₄	—	26	4	no	—
725	C₄	—	26	4	no	—
726	C₄	—	26	4	no	—
727	C₄	C₂²×D₄×D₁₃	1	8	yes	—
728	C₂	—	2	8	no	—
729	C₂	—	4	4	no	—
730	C₂	—	26	8	no	—
731	C₂	—	26	8	no	—
732	C₂	—	52	4	no	—
733	C₂	C₂×#11719252	1	12	yes	direct product factor
734	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
735	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic
736	C₂	C₂³×#6127	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂²×#525
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#6127	C₂	semidirect
2. C₂⁴×C₄×D₁₃	C₂	semidirect
3. C₂×#11719252	C₂	direct (N × H)
4. C₂²×#88148	C₂	semidirect
5. C₂²×#88137	C₂	semidirect
6. C₂²×#88150	C₂	semidirect
7. C₂²×#88132	C₂	semidirect
8. C₂²×#88138	C₂	semidirect
9. C₂²×#88193	C₂	semidirect
10. C₂²×#88136	C₂	semidirect
11. C₂²×#88191	C₂	semidirect
12. C₂²×C₄×D₅₂	C₂	semidirect
13. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
14. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
15. C₂²×#88126	C₂	semidirect
16. C₂²×C₄×D₄×C₁₃	C₂	semidirect
20. C₂⁴×C₄×C₁₃	C₂²	semidirect
24. C₂³×C₂²⋊D₁₃	C₂²	semidirect
27. C₂²×#6127	C₂²	semidirect
35. C₂³×C₄×D₁₃	C₂²	semidirect
36. C₂³×C₄×D₁₃	C₂²	semidirect
37. C₂³×Dic₂₆	C₂²	semidirect
38. C₂×C₄×D₄×C₁₃	C₂²	semidirect
39. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
41. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
42. C₂²×C₄²×C₁₃	C₂²	semidirect
44. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
45. C₂×#88193	C₂²	semidirect
46. C₂×#88191	C₂²	semidirect
47. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
48. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
53. C₂²×#6103	C₂²	semidirect
54. C₂²×#6103	C₂²	semidirect
55. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
56. C₂²×#6101	C₂²	semidirect
57. C₂²×#6101	C₂²	semidirect
58. C₂²×#6101	C₂²	semidirect
59. C₂²×#6101	C₂²	semidirect
60. C₂²×C₄×Dic₁₃	C₂²	semidirect
61. #11719252	C₂²	direct (N × H)
62. C₂×#88150	C₂²	semidirect
63. C₂×#88148	C₂²	semidirect
64. C₂×#88138	C₂²	semidirect
65. C₂×#88137	C₂²	semidirect
66. C₂×#88136	C₂²	semidirect
67. C₂×#88132	C₂²	semidirect
68. C₂×C₄×D₅₂	C₂²	semidirect
69. C₂×#88126	C₂²	semidirect
89. C₂³×C₄×C₁₃	C₂³	semidirect
97. C₂²×C₂²⋊D₁₃	C₂³	semidirect
106. C₂×#6127	C₂³	semidirect
116. C₂²×C₄×D₁₃	D₄	semidirect
121. C₂²×C₄×D₁₃	C₂³	semidirect
122. C₂²×C₄×D₁₃	C₂³	semidirect
124. C₂²×Dic₂₆	C₂³	semidirect
125. C₄×D₄×C₁₃	C₂³	semidirect
126. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
128. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
129. C₂×C₄²×C₁₃	C₂³	semidirect
131. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
132. #88193	C₂³	semidirect
133. #88191	C₂³	semidirect
134. C₄×C₂²⋊D₁₃	C₂³	semidirect
135. C₄×C₂²⋊D₁₃	C₂³	semidirect
140. C₂×#6103	C₂³	semidirect
141. C₂×#6103	C₂³	semidirect
142. C₂×C₄⋊Dic₁₃	C₂³	semidirect
143. C₂×#6101	C₂³	semidirect
144. C₂×#6101	C₂³	semidirect
145. C₂×#6101	C₂³	semidirect
146. C₂×#6101	C₂³	semidirect
147. C₂×C₄×Dic₁₃	C₂³	semidirect
148. #88150	C₂³	semidirect
149. #88148	C₂³	semidirect
150. #88138	C₂³	semidirect
151. #88137	C₂³	semidirect
152. #88136	C₂³	semidirect
153. #88132	C₂³	semidirect
154. C₄×D₅₂	C₂³	semidirect
155. #88126	C₂³	semidirect
162. C₂⁴×C₁₃	#41	semidirect
178. C₂³×D₁₃	#41	semidirect
198. C₂²×C₄×C₁₃	C₂⁴	semidirect
206. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
229. C₂×C₄×D₁₃	C₂×D₄	semidirect
234. C₂×C₄×D₁₃	C₂⁴	semidirect
236. C₂×Dic₂₆	C₂⁴	semidirect
237. C₁₃×C₄⋊C₄	C₂⁴	semidirect
239. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
240. C₄²×C₁₃	C₂⁴	semidirect
242. C₂²⋊Dic₁₃	C₂⁴	semidirect
247. #6103	C₂⁴	semidirect
248. #6103	C₂⁴	semidirect
249. C₄⋊Dic₁₃	C₂⁴	semidirect
250. #6101	C₂⁴	semidirect
251. #6101	C₂⁴	semidirect
252. #6101	C₂⁴	semidirect
253. #6101	C₂⁴	semidirect
254. C₄×Dic₁₃	C₂⁴	semidirect
269. C₂²×C₄×D₄	D₁₃	semidirect
281. C₂³×C₁₃	C₂×#41	semidirect
300. C₂²×D₁₃	C₂×#41	semidirect
338. C₄×D₁₃	C₂²×D₄	semidirect
360. C₂⁴×C₄	C₂×D₁₃	semidirect
373. C₂×C₄×D₄	C₂×D₁₃	semidirect
380. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
390. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
392. C₂²×C₄²	C₂×D₁₃	semidirect
400. C₂²×C₁₃	#525	semidirect
404. C₂²×C₁₃	C₂²×#41	semidirect
418. C₂×D₁₃	C₂²×#41	semidirect
483. C₂³×C₄	C₂²×D₁₃	semidirect
495. C₄×D₄	C₂²×D₁₃	semidirect
502. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
512. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
514. C₂×C₄²	C₂²×D₁₃	semidirect
517. C₂×C₁₃	C₂×#525	semidirect
546. C₂⁴	#6127	semidirect
603. C₂²×C₄	C₂³×D₁₃	semidirect
609. C₄⋊C₄	C₂³×D₁₃	semidirect
619. C₂²⋊C₄	C₂³×D₁₃	semidirect
621. C₄²	C₂³×D₁₃	semidirect
622. C₁₃	C₂²×#525	semidirect
650. C₂³	C₂×#6127	semidirect
712. C₂²	#11719252	direct (N × H)
714. C₂²	C₂²×#6127	semidirect
733. C₂	C₂×#11719252	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#6127	2
C₂⁴×C₄×D₁₃	2
C₂×#11719252	2
C₂²×#88148	2
C₂²×#88137	2
C₂²×#88150	2
C₂²×#88132	2
C₂²×#88138	2
C₂²×#88193	2
C₂²×#88136	2
C₂²×#88191	2
C₂²×C₄×D₅₂	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂²×#88126	2
C₂²×C₄×D₄×C₁₃	2
C₂²×#525	13

Subgroups — C22×#11719252 #16769574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719252 #16769574