Subgroups — C₂²×#11719195 #16769841

Order 3328.

14462 conjugacy classes of subgroups.

The subgroup lattice has 780 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×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719195	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#88139	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88183	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88137	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#88132	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#88184	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#88138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#88138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#88136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#88207	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#88135	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₂²⋊D₁₃	—	2	16	no	—
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
25	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
26	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
27	C₂³×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
28	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
31	C₂²×#6127	—	2	16	no	—
32	C₂²×#6127	C₂²	1	24	yes	complemented
33	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
34	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
35	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	24	yes	complemented
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×#88207	C₂²	1	24	yes	complemented
45	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×#88184	C₂²	1	24	yes	complemented
49	C₂×#88183	C₂²	1	24	yes	complemented
50	C₂×C₄×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
51	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
53	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
54	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
55	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
56	C₂²×C₄⋊Dic₁₃	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	C₂×#88139	C₂²	1	24	yes	complemented
62	#11719195	C₂²	1	256	yes	direct product factor
63	C₂×#88138	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×#88135	C₂²	1	24	yes	complemented
68	C₂×C₂²⋊C₄×D₁₃	C₂²	1	24	yes	complemented
69	C₂×#88132	C₂²	1	24	yes	complemented
70	C₂⁵×C₁₃	—	2	8	no	—
71	C₂⁵×C₁₃	—	2	8	no	—
72	C₂⁵×C₁₃	—	4	4	no	—
73	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
74	C₂⁵×C₁₃	C₂³	1	12	yes	—
75	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
76	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
77	C₂⁴×D₁₃	—	2	8	no	—
78	C₂⁴×D₁₃	—	2	8	no	—
79	C₂⁴×D₁₃	—	4	4	no	—
80	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
81	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
82	C₂⁴×D₁₃	C₂³	1	12	yes	—
83	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	—	2	8	no	—
85	C₂³×C₄×C₁₃	—	4	4	no	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	12	yes	complemented
91	C₂³×C₄×C₁₃	C₂³	1	12	yes	complemented
92	C₂²×C₂²⋊D₁₃	—	2	8	no	—
93	C₂²×C₂²⋊D₁₃	—	2	8	no	—
94	C₂²×C₂²⋊D₁₃	—	2	8	no	—
95	C₂²×C₂²⋊D₁₃	—	2	8	no	—
96	C₂²×C₂²⋊D₁₃	—	2	192	no	—
97	C₂²×C₂²⋊D₁₃	—	2	8	no	—
98	C₂²×C₂²⋊D₁₃	—	4	4	no	—
99	C₂²×C₂²⋊D₁₃	D₄	1	16	yes	complemented
100	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
101	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
102	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
103	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
104	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
105	C₂²×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
106	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	complemented
107	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	complemented
108	C₂³×Dic₁₃	—	2	8	no	—
109	C₂³×Dic₁₃	C₂³	1	12	yes	—
110	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
111	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
112	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
113	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
114	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
115	C₂×#6127	—	2	192	no	—
116	C₂×#6127	C₂³	1	64	yes	complemented
117	C₂²×D₅₂	—	2	8	no	—
118	C₂²×D₅₂	—	4	4	no	—
119	C₂²×D₅₂	C₂³	1	12	yes	complemented
120	C₂²×D₅₂	C₂³	1	12	yes	complemented
121	C₂²×C₄×D₁₃	—	2	8	no	—
122	C₂²×C₄×D₁₃	—	2	8	no	—
123	C₂²×C₄×D₁₃	—	4	4	no	—
124	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
125	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
126	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
127	C₂²×Dic₂₆	—	2	8	no	—
128	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	64	yes	complemented
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
134	#88207	C₂³	1	64	yes	complemented
135	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
136	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	complemented
137	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	complemented
138	#88184	C₂³	1	64	yes	complemented
139	#88183	C₂³	1	64	yes	complemented
140	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
141	C₂×#6103	C₂³	1	12	yes	complemented
142	C₂×#6103	C₂³	1	12	yes	complemented
143	C₂×#6103	C₂³	1	12	yes	complemented
144	C₂×#6103	C₂³	1	12	yes	complemented
145	C₂×#6103	C₂³	1	12	yes	complemented
146	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
147	C₂×#6101	C₂³	1	12	yes	complemented
148	C₂×#6101	C₂³	1	12	yes	complemented
149	C₂×#6101	C₂³	1	12	yes	complemented
150	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
151	#88139	C₂³	1	64	yes	complemented
152	#88138	C₂³	1	64	yes	complemented
153	#88138	C₂³	1	64	yes	complemented
154	#88137	C₂³	1	64	yes	complemented
155	#88136	C₂³	1	64	yes	complemented
156	#88135	C₂³	1	64	yes	complemented
157	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
158	#88132	C₂³	1	64	yes	complemented
159	C₂²×#546	—	13	1	no	maximal, Sylow
160	C₂⁴×C₁₃	—	2	4	no	—
161	C₂⁴×C₁₃	—	2	4	no	—
162	C₂⁴×C₁₃	—	2	4	no	—
163	C₂⁴×C₁₃	—	2	4	no	—
164	C₂⁴×C₁₃	—	2	48	no	—
165	C₂⁴×C₁₃	—	2	4	no	—
166	C₂⁴×C₁₃	—	2	4	no	—
167	C₂⁴×C₁₃	—	2	48	no	—
168	C₂⁴×C₁₃	—	2	4	no	—
169	C₂⁴×C₁₃	—	4	24	no	—
170	C₂⁴×C₁₃	—	4	64	no	—
171	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
172	C₂⁴×C₁₃	#41	1	8	yes	complemented
173	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
174	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
175	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
176	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
177	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂³×D₁₃	—	2	4	no	—
179	C₂³×D₁₃	—	2	4	no	—
180	C₂³×D₁₃	—	2	4	no	—
181	C₂³×D₁₃	—	2	4	no	—
182	C₂³×D₁₃	—	2	4	no	—
183	C₂³×D₁₃	—	2	4	no	—
184	C₂³×D₁₃	—	2	48	no	—
185	C₂³×D₁₃	—	2	4	no	—
186	C₂³×D₁₃	—	2	4	no	—
187	C₂³×D₁₃	—	2	48	no	—
188	C₂³×D₁₃	—	4	24	no	—
189	C₂³×D₁₃	—	4	64	no	—
190	C₂³×D₁₃	C₂×D₄	1	8	yes	—
191	C₂³×D₁₃	C₂⁴	1	6	yes	—
192	C₂³×D₁₃	C₂⁴	1	6	yes	—
193	C₂³×D₁₃	C₂⁴	1	16	yes	—
194	C₂³×D₁₃	C₂⁴	1	6	yes	—
195	C₂²×C₄×C₁₃	—	2	4	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	2	48	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	4	24	no	—
201	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
203	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
206	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
207	C₂×C₂²⋊D₁₃	—	2	48	no	—
208	C₂×C₂²⋊D₁₃	—	2	48	no	—
209	C₂×C₂²⋊D₁₃	—	2	48	no	—
210	C₂×C₂²⋊D₁₃	—	2	48	no	—
211	C₂×C₂²⋊D₁₃	—	2	256	no	—
212	C₂×C₂²⋊D₁₃	—	2	48	no	—
213	C₂×C₂²⋊D₁₃	—	4	24	no	—
214	C₂×C₂²⋊D₁₃	C₂×D₄	1	96	yes	complemented
215	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
216	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
217	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
218	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
219	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
220	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	complemented
221	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	complemented
222	C₂²×Dic₁₃	—	2	4	no	—
223	C₂²×Dic₁₃	—	2	4	no	—
224	C₂²×Dic₁₃	—	2	4	no	—
225	C₂²×Dic₁₃	—	2	4	no	—
226	C₂²×Dic₁₃	—	2	48	no	—
227	C₂²×Dic₁₃	C₂×D₄	1	8	yes	—
228	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
229	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
230	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
231	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
232	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
233	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
234	#6127	—	2	256	no	—
235	C₂×D₅₂	—	2	48	no	—
236	C₂×D₅₂	—	4	24	no	—
237	C₂×D₅₂	C₂⁴	1	16	yes	complemented
238	C₂×D₅₂	C₂⁴	1	16	yes	complemented
239	C₂×C₄×D₁₃	—	2	48	no	—
240	C₂×C₄×D₁₃	—	2	48	no	—
241	C₂×C₄×D₁₃	—	4	24	no	—
242	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
243	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
244	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
245	C₂×Dic₂₆	—	2	48	no	—
246	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
247	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
248	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
249	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
250	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
251	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
252	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	complemented
253	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	complemented
254	#6103	C₂⁴	1	16	yes	complemented
255	#6103	C₂⁴	1	16	yes	complemented
256	#6103	C₂⁴	1	16	yes	complemented
257	#6103	C₂⁴	1	16	yes	complemented
258	#6103	C₂⁴	1	16	yes	complemented
259	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
260	#6101	C₂⁴	1	16	yes	complemented
261	#6101	C₂⁴	1	16	yes	complemented
262	#6101	C₂⁴	1	16	yes	complemented
263	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
264	C₂³×#41	—	13	1	no	—
265	C₂⁴×D₄	—	13	1	no	—
266	C₂×#546	—	13	48	no	—
267	C₂²×#124	—	13	1	no	—
268	C₂²×#123	—	13	1	no	—
269	C₂²×#123	—	13	1	no	—
270	C₂²×C₂²⋊Q₈	—	13	1	no	—
271	C₂²×#121	—	13	1	no	—
272	C₂²×#121	—	13	1	no	—
273	C₂²×#121	—	13	1	no	—
274	C₂²×#120	—	13	1	no	—
275	C₂²×#120	—	13	1	no	—
276	C₂²×C₄×D₄	—	13	1	no	—
277	C₂²×C₄×D₄	—	13	1	no	—
278	C₂³×C₂²⋊C₄	—	13	1	no	—
279	C₂³×C₂²⋊C₄	D₁₃	1	1	yes	characteristic, complemented
280	C₂³×C₁₃	—	2	32	no	—
281	C₂³×C₁₃	—	2	32	no	—
282	C₂³×C₁₃	—	2	12	no	—
283	C₂³×C₁₃	—	2	12	no	—
284	C₂³×C₁₃	—	2	12	no	—
285	C₂³×C₁₃	—	2	12	no	—
286	C₂³×C₁₃	—	2	32	no	—
287	C₂³×C₁₃	—	2	12	no	—
288	C₂³×C₁₃	—	2	12	no	—
289	C₂³×C₁₃	—	2	32	no	—
290	C₂³×C₁₃	—	2	12	no	—
291	C₂³×C₁₃	—	4	16	no	—
292	C₂³×C₁₃	—	4	192	no	—
293	C₂³×C₁₃	—	4	16	no	—
294	C₂³×C₁₃	C₂²×D₄	1	24	yes	—
295	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
296	C₂³×C₁₃	C₂×#41	1	4	yes	—
297	C₂³×C₁₃	C₂×#41	1	24	yes	complemented
298	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
299	C₂³×C₁₃	C₂⁵	1	4	yes	—
300	C₂³×C₁₃	C₂⁵	1	4	yes	—
301	C₂³×C₁₃	C₂⁵	1	4	yes	—
302	C₂³×C₁₃	C₂⁵	1	3	yes	—
303	C₂²×D₁₃	—	2	32	no	—
304	C₂²×D₁₃	—	2	12	no	—
305	C₂²×D₁₃	—	2	12	no	—
306	C₂²×D₁₃	—	2	12	no	—
307	C₂²×D₁₃	—	2	12	no	—
308	C₂²×D₁₃	—	2	12	no	—
309	C₂²×D₁₃	—	2	12	no	—
310	C₂²×D₁₃	—	2	32	no	—
311	C₂²×D₁₃	—	2	12	no	—
312	C₂²×D₁₃	—	2	12	no	—
313	C₂²×D₁₃	—	2	32	no	—
314	C₂²×D₁₃	—	4	16	no	—
315	C₂²×D₁₃	—	4	192	no	—
316	C₂²×D₁₃	—	4	16	no	—
317	C₂²×D₁₃	—	4	16	no	—
318	C₂²×D₁₃	C₂²×D₄	1	24	yes	—
319	C₂²×D₁₃	C₂⁵	1	4	yes	—
320	C₂²×D₁₃	C₂⁵	1	4	yes	—
321	C₂²×D₁₃	C₂⁵	1	4	yes	—
322	C₂×C₄×C₁₃	—	2	12	no	—
323	C₂×C₄×C₁₃	—	2	12	no	—
324	C₂×C₄×C₁₃	—	2	32	no	—
325	C₂×C₄×C₁₃	—	2	12	no	—
326	C₂×C₄×C₁₃	—	2	12	no	—
327	C₂×C₄×C₁₃	—	4	16	no	—
328	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
329	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
330	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
331	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
332	C₂²⋊D₁₃	—	2	32	no	—
333	C₂²⋊D₁₃	—	2	32	no	—
334	C₂²⋊D₁₃	—	2	32	no	—
335	C₂²⋊D₁₃	—	2	32	no	—
336	C₂²⋊D₁₃	—	2	32	no	—
337	C₂²⋊D₁₃	—	4	16	no	—
338	C₂²⋊D₁₃	C₂²×D₄	1	64	yes	complemented
339	C₂×Dic₁₃	—	2	12	no	—
340	C₂×Dic₁₃	—	2	12	no	—
341	C₂×Dic₁₃	—	2	12	no	—
342	C₂×Dic₁₃	—	2	12	no	—
343	C₂×Dic₁₃	—	2	32	no	—
344	C₂×Dic₁₃	C₂²×D₄	1	24	yes	—
345	C₂×Dic₁₃	C₂⁵	1	4	yes	—
346	C₂×Dic₁₃	C₂⁵	1	4	yes	—
347	C₂×Dic₁₃	C₂⁵	1	4	yes	—
348	C₂×Dic₁₃	C₂⁵	1	4	yes	—
349	C₂×Dic₁₃	C₂⁵	1	4	yes	—
350	D₅₂	—	2	32	no	—
351	D₅₂	—	4	16	no	—
352	C₄×D₁₃	—	2	32	no	—
353	C₄×D₁₃	—	2	32	no	—
354	C₄×D₁₃	—	4	16	no	—
355	Dic₂₆	—	2	32	no	—
356	C₂⁶	—	13	1	no	—
357	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
358	C₂²×#41	—	13	24	no	—
359	C₂²×#41	—	26	16	no	—
360	C₂³×Q₈	—	13	1	no	—
361	C₂³×D₄	—	13	1	no	—
362	C₂³×D₄	—	13	1	no	—
363	C₂³×D₄	—	13	1	no	—
364	C₂³×D₄	—	13	1	no	—
365	C₂³×D₄	—	13	24	no	—
366	C₂³×D₄	—	13	1	no	—
367	C₂³×D₄	—	13	1	no	—
368	C₂³×D₄	—	13	1	no	—
369	C₂³×D₄	—	13	1	no	—
370	C₂³×D₄	—	13	1	no	—
371	C₂³×D₄	—	26	16	no	—
372	C₂⁴×C₄	—	13	1	no	—
373	C₂⁴×C₄	—	13	1	no	—
374	C₂⁴×C₄	—	13	1	no	—
375	C₂⁴×C₄	—	13	1	no	—
376	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
377	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
378	#546	—	13	256	no	—
379	C₂×#124	—	13	24	no	—
380	C₂×#123	—	13	24	no	—
381	C₂×#123	—	13	24	no	—
382	C₂×C₂²⋊Q₈	—	13	24	no	—
383	C₂×#121	—	13	24	no	—
384	C₂×#121	—	13	24	no	—
385	C₂×#121	—	13	24	no	—
386	C₂×#120	—	13	24	no	—
387	C₂×#120	—	13	24	no	—
388	C₂×C₄×D₄	—	13	24	no	—
389	C₂×C₄×D₄	—	13	24	no	—
390	C₂²×C₄⋊C₄	—	13	1	no	—
391	C₂²×C₄⋊C₄	—	13	1	no	—
392	C₂²×C₄⋊C₄	—	13	1	no	—
393	C₂²×C₄⋊C₄	—	13	1	no	—
394	C₂²×C₂²⋊C₄	—	13	1	no	—
395	C₂²×C₂²⋊C₄	—	13	1	no	—
396	C₂²×C₂²⋊C₄	—	13	1	no	—
397	C₂²×C₂²⋊C₄	—	13	1	no	—
398	C₂²×C₂²⋊C₄	—	13	1	no	—
399	C₂²×C₂²⋊C₄	—	13	1	no	—
400	C₂²×C₂²⋊C₄	—	13	1	no	—
401	C₂²×C₂²⋊C₄	—	13	1	no	—
402	C₂²×C₂²⋊C₄	—	13	24	no	—
403	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
405	C₂²×C₂²⋊C₄	C₂×D₁₃	1	24	yes	complemented
406	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
407	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
408	C₂²×C₄²	—	13	1	no	—
409	C₂²×C₁₃	—	2	4	no	—
410	C₂²×C₁₃	—	2	4	no	—
411	C₂²×C₁₃	—	2	4	no	—
412	C₂²×C₁₃	—	2	4	no	—
413	C₂²×C₁₃	—	2	48	no	—
414	C₂²×C₁₃	—	2	48	no	—
415	C₂²×C₁₃	—	2	4	no	—
416	C₂²×C₁₃	—	2	4	no	—
417	C₂²×C₁₃	—	2	4	no	—
418	C₂²×C₁₃	—	4	64	no	—
419	C₂²×C₁₃	—	4	24	no	—
420	C₂²×C₁₃	#546	1	16	yes	complemented
421	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
422	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
423	C₂²×C₁₃	C₂²×#41	1	6	yes	—
424	C₂²×C₁₃	C₂²×#41	1	8	yes	complemented
425	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
426	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
427	C₂×D₁₃	—	2	4	no	—
428	C₂×D₁₃	—	2	4	no	—
429	C₂×D₁₃	—	2	48	no	—
430	C₂×D₁₃	—	2	4	no	—
431	C₂×D₁₃	—	2	4	no	—
432	C₂×D₁₃	—	2	4	no	—
433	C₂×D₁₃	—	2	4	no	—
434	C₂×D₁₃	—	2	4	no	—
435	C₂×D₁₃	—	2	4	no	—
436	C₂×D₁₃	—	4	64	no	—
437	C₂×D₁₃	—	4	24	no	—
438	C₂×D₁₃	—	4	24	no	—
439	C₂×D₁₃	C₂³×D₄	1	8	yes	—
440	C₄×C₁₃	—	2	4	no	—
441	C₄×C₁₃	—	2	4	no	—
442	C₄×C₁₃	—	2	4	no	—
443	C₄×C₁₃	—	2	4	no	—
444	Dic₁₃	—	2	4	no	—
445	Dic₁₃	—	2	4	no	—
446	Dic₁₃	—	2	4	no	—
447	Dic₁₃	—	2	4	no	—
448	Dic₁₃	C₂³×D₄	1	8	yes	—
449	C₂⁵	—	2	8	no	—
450	C₂⁵	—	2	8	no	—
451	C₂⁵	—	4	4	no	—
452	C₂⁵	—	13	1	no	—
453	C₂⁵	—	13	1	no	—
454	C₂⁵	—	13	1	no	—
455	C₂⁵	—	13	12	no	—
456	C₂⁵	—	26	8	no	—
457	C₂⁵	—	26	8	no	—
458	C₂⁵	—	52	4	no	—
459	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
460	C₂⁵	C₂²×D₁₃	1	12	yes	—
461	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
462	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
463	C₂×#41	—	13	64	no	—
464	C₂×#41	—	26	192	no	—
465	C₂²×Q₈	—	13	12	no	—
466	C₂²×Q₈	—	26	8	no	—
467	C₂²×D₄	—	13	16	no	—
468	C₂²×D₄	—	13	12	no	—
469	C₂²×D₄	—	13	12	no	—
470	C₂²×D₄	—	13	12	no	—
471	C₂²×D₄	—	13	12	no	—
472	C₂²×D₄	—	13	12	no	—
473	C₂²×D₄	—	13	12	no	—
474	C₂²×D₄	—	13	64	no	—
475	C₂²×D₄	—	13	12	no	—
476	C₂²×D₄	—	13	12	no	—
477	C₂²×D₄	—	13	12	no	—
478	C₂²×D₄	—	26	8	no	—
479	C₂²×D₄	—	26	8	no	—
480	C₂²×D₄	—	26	192	no	—
481	C₂²×D₄	—	26	8	no	—
482	C₂²×D₄	—	26	8	no	—
483	C₂²×D₄	—	26	8	no	—
484	C₂²×D₄	—	26	8	no	—
485	C₂²×D₄	—	52	4	no	—
486	C₂²×D₄	—	52	4	no	—
487	C₂³×C₄	—	2	8	no	—
488	C₂³×C₄	—	4	4	no	—
489	C₂³×C₄	—	13	1	no	—
490	C₂³×C₄	—	13	12	no	—
491	C₂³×C₄	—	13	1	no	—
492	C₂³×C₄	—	13	1	no	—
493	C₂³×C₄	—	13	1	no	—
494	C₂³×C₄	—	13	1	no	—
495	C₂³×C₄	—	13	12	no	—
496	C₂³×C₄	—	13	12	no	—
497	C₂³×C₄	—	13	12	no	—
498	C₂³×C₄	—	26	8	no	—
499	C₂³×C₄	—	26	8	no	—
500	C₂³×C₄	—	26	8	no	—
501	C₂³×C₄	—	52	4	no	—
502	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
503	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
504	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
505	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
506	C₂³×C₄	C₂²×D₁₃	1	12	yes	complemented
507	C₂³×C₄	C₂²×D₁₃	1	12	yes	complemented
508	#124	—	13	64	no	—
509	#123	—	13	64	no	—
510	#123	—	13	64	no	—
511	C₂²⋊Q₈	—	13	64	no	—
512	#121	—	13	64	no	—
513	#121	—	13	64	no	—
514	#121	—	13	64	no	—
515	#120	—	13	64	no	—
516	#120	—	13	64	no	—
517	C₄×D₄	—	13	64	no	—
518	C₄×D₄	—	13	64	no	—
519	C₂×C₄⋊C₄	—	13	12	no	—
520	C₂×C₄⋊C₄	—	13	12	no	—
521	C₂×C₄⋊C₄	—	13	12	no	—
522	C₂×C₄⋊C₄	—	13	12	no	—
523	C₂×C₂²⋊C₄	—	13	12	no	—
524	C₂×C₂²⋊C₄	—	13	12	no	—
525	C₂×C₂²⋊C₄	—	13	12	no	—
526	C₂×C₂²⋊C₄	—	13	12	no	—
527	C₂×C₂²⋊C₄	—	13	12	no	—
528	C₂×C₂²⋊C₄	—	13	12	no	—
529	C₂×C₂²⋊C₄	—	13	12	no	—
530	C₂×C₂²⋊C₄	—	13	12	no	—
531	C₂×C₂²⋊C₄	—	13	64	no	—
532	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	—
533	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	—
534	C₂×C₂²⋊C₄	C₂²×D₁₃	1	64	yes	complemented
535	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	complemented
536	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	complemented
537	C₂×C₄²	—	13	12	no	—
538	C₂×C₁₃	—	2	8	no	—
539	C₂×C₁₃	—	2	8	no	—
540	C₂×C₁₃	—	4	4	no	—
541	C₂×C₁₃	C₂×#546	1	12	yes	complemented
542	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
543	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
544	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
545	D₁₃	—	2	8	no	—
546	D₁₃	—	4	4	no	—
547	D₁₃	—	4	4	no	—
548	C₂⁴	—	2	4	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	2	48	no	—
554	C₂⁴	—	2	48	no	—
555	C₂⁴	—	2	4	no	—
556	C₂⁴	—	2	4	no	—
557	C₂⁴	—	4	24	no	—
558	C₂⁴	—	4	64	no	—
559	C₂⁴	—	13	8	no	—
560	C₂⁴	—	13	6	no	—
561	C₂⁴	—	13	6	no	—
562	C₂⁴	—	13	6	no	—
563	C₂⁴	—	13	16	no	—
564	C₂⁴	—	26	48	no	—
565	C₂⁴	—	26	4	no	—
566	C₂⁴	—	26	4	no	—
567	C₂⁴	—	26	4	no	—
568	C₂⁴	—	26	4	no	—
569	C₂⁴	—	26	48	no	—
570	C₂⁴	—	26	4	no	—
571	C₂⁴	—	26	4	no	—
572	C₂⁴	—	26	4	no	—
573	C₂⁴	—	26	4	no	—
574	C₂⁴	—	52	24	no	—
575	C₂⁴	—	52	64	no	—
576	C₂⁴	#6127	1	8	yes	complemented
577	C₂⁴	D₄×D₁₃	1	8	yes	—
578	C₂⁴	C₂³×D₁₃	1	6	yes	—
579	C₂⁴	C₂³×D₁₃	1	16	yes	—
580	C₂⁴	C₂³×D₁₃	1	6	yes	—
581	C₂⁴	C₂³×D₁₃	1	6	yes	—
582	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
583	#41	—	26	256	no	—
584	C₂×Q₈	—	13	16	no	—
585	C₂×Q₈	—	26	48	no	—
586	C₂×D₄	—	13	96	no	—
587	C₂×D₄	—	13	16	no	—
588	C₂×D₄	—	13	16	no	—
589	C₂×D₄	—	13	16	no	—
590	C₂×D₄	—	13	16	no	—
591	C₂×D₄	—	13	16	no	—
592	C₂×D₄	—	13	16	no	—
593	C₂×D₄	—	13	16	no	—
594	C₂×D₄	—	13	16	no	—
595	C₂×D₄	—	13	16	no	—
596	C₂×D₄	—	26	48	no	—
597	C₂×D₄	—	26	48	no	—
598	C₂×D₄	—	26	256	no	—
599	C₂×D₄	—	26	48	no	—
600	C₂×D₄	—	26	48	no	—
601	C₂×D₄	—	26	48	no	—
602	C₂×D₄	—	26	48	no	—
603	C₂×D₄	—	52	24	no	—
604	C₂×D₄	—	52	24	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	48	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	4	24	no	—
611	C₂²×C₄	—	13	8	no	—
612	C₂²×C₄	—	13	6	no	—
613	C₂²×C₄	—	13	6	no	—
614	C₂²×C₄	—	13	6	no	—
615	C₂²×C₄	—	13	6	no	—
616	C₂²×C₄	—	13	6	no	—
617	C₂²×C₄	—	13	16	no	—
618	C₂²×C₄	—	13	16	no	—
619	C₂²×C₄	—	13	16	no	—
620	C₂²×C₄	—	13	16	no	—
621	C₂²×C₄	—	26	48	no	—
622	C₂²×C₄	—	26	48	no	—
623	C₂²×C₄	—	26	48	no	—
624	C₂²×C₄	—	26	4	no	—
625	C₂²×C₄	—	26	4	no	—
626	C₂²×C₄	—	26	4	no	—
627	C₂²×C₄	—	26	4	no	—
628	C₂²×C₄	—	52	24	no	—
629	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
630	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
631	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
632	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
633	C₂²×C₄	C₂³×D₁₃	1	16	yes	complemented
634	C₂²×C₄	C₂³×D₁₃	1	16	yes	complemented
635	C₄⋊C₄	—	13	16	no	—
636	C₄⋊C₄	—	13	16	no	—
637	C₄⋊C₄	—	13	16	no	—
638	C₄⋊C₄	—	13	16	no	—
639	C₂²⋊C₄	—	13	16	no	—
640	C₂²⋊C₄	—	13	16	no	—
641	C₂²⋊C₄	—	13	16	no	—
642	C₂²⋊C₄	—	13	16	no	—
643	C₂²⋊C₄	—	13	16	no	—
644	C₂²⋊C₄	—	13	16	no	—
645	C₂²⋊C₄	—	13	16	no	—
646	C₂²⋊C₄	—	13	16	no	—
647	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
648	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
649	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	complemented
650	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	complemented
651	C₄²	—	13	16	no	—
652	C₁₃	C₂²×#546	1	1	yes	characteristic, complemented, Sylow
653	C₂³	—	2	32	no	—
654	C₂³	—	2	32	no	—
655	C₂³	—	2	12	no	—
656	C₂³	—	2	12	no	—
657	C₂³	—	2	12	no	—
658	C₂³	—	2	12	no	—
659	C₂³	—	2	12	no	—
660	C₂³	—	2	32	no	—
661	C₂³	—	2	32	no	—
662	C₂³	—	2	12	no	—
663	C₂³	—	2	12	no	—
664	C₂³	—	4	16	no	—
665	C₂³	—	4	192	no	—
666	C₂³	—	4	16	no	—
667	C₂³	—	13	24	no	—
668	C₂³	—	13	4	no	—
669	C₂³	—	13	4	no	—
670	C₂³	—	13	4	no	—
671	C₂³	—	26	32	no	—
672	C₂³	—	26	32	no	—
673	C₂³	—	26	12	no	—
674	C₂³	—	26	12	no	—
675	C₂³	—	26	12	no	—
676	C₂³	—	26	12	no	—
677	C₂³	—	26	32	no	—
678	C₂³	—	26	12	no	—
679	C₂³	—	26	12	no	—
680	C₂³	—	26	12	no	—
681	C₂³	—	26	12	no	—
682	C₂³	—	52	16	no	—
683	C₂³	—	52	192	no	—
684	C₂³	—	52	16	no	—
685	C₂³	—	52	16	no	—
686	C₂³	C₂×#6127	1	4	yes	—
687	C₂³	C₂×#6127	1	24	yes	complemented
688	C₂³	C₂×D₄×D₁₃	1	24	yes	—
689	C₂³	C₂×D₄×D₁₃	1	4	yes	—
690	C₂³	#88251	1	4	yes	—
691	C₂³	C₂⁴×D₁₃	1	4	yes	—
692	C₂³	C₂⁴×D₁₃	1	4	yes	—
693	C₂³	C₂⁴×D₁₃	1	4	yes	—
694	C₂³	C₂⁴×D₁₃	1	3	yes	—
695	Q₈	—	26	32	no	—
696	D₄	—	13	64	no	—
697	D₄	—	26	32	no	—
698	D₄	—	26	32	no	—
699	D₄	—	26	32	no	—
700	D₄	—	26	32	no	—
701	D₄	—	26	32	no	—
702	D₄	—	26	32	no	—
703	D₄	—	52	16	no	—
704	D₄	—	52	16	no	—
705	C₂×C₄	—	2	12	no	—
706	C₂×C₄	—	2	12	no	—
707	C₂×C₄	—	2	32	no	—
708	C₂×C₄	—	2	12	no	—
709	C₂×C₄	—	2	12	no	—
710	C₂×C₄	—	4	16	no	—
711	C₂×C₄	—	13	24	no	—
712	C₂×C₄	—	13	4	no	—
713	C₂×C₄	—	13	4	no	—
714	C₂×C₄	—	13	4	no	—
715	C₂×C₄	—	13	4	no	—
716	C₂×C₄	—	13	4	no	—
717	C₂×C₄	—	26	32	no	—
718	C₂×C₄	—	26	32	no	—
719	C₂×C₄	—	26	32	no	—
720	C₂×C₄	—	26	12	no	—
721	C₂×C₄	—	26	12	no	—
722	C₂×C₄	—	26	12	no	—
723	C₂×C₄	—	26	12	no	—
724	C₂×C₄	—	52	16	no	—
725	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
726	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
727	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
728	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
729	C₂²	—	2	48	no	—
730	C₂²	—	2	48	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	4	64	no	—
739	C₂²	—	4	24	no	—
740	C₂²	—	13	8	no	—
741	C₂²	—	26	48	no	—
742	C₂²	—	26	4	no	—
743	C₂²	—	26	4	no	—
744	C₂²	—	26	4	no	—
745	C₂²	—	26	4	no	—
746	C₂²	—	26	4	no	—
747	C₂²	—	26	4	no	—
748	C₂²	—	26	4	no	—
749	C₂²	—	26	4	no	—
750	C₂²	—	52	64	no	—
751	C₂²	—	52	24	no	—
752	C₂²	—	52	24	no	—
753	C₂²	#11719195	1	16	yes	direct product factor
754	C₂²	C₂²×#6127	1	6	yes	—
755	C₂²	C₂²×#6127	1	8	yes	complemented
756	C₂²	C₂²×D₄×D₁₃	1	8	yes	—
757	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
758	C₂²	C₂×#88251	1	6	yes	—
759	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
760	C₄	—	2	4	no	—
761	C₄	—	2	4	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	4	no	—
764	C₄	—	13	8	no	—
765	C₄	—	26	4	no	—
766	C₄	—	26	4	no	—
767	C₄	—	26	4	no	—
768	C₄	—	26	4	no	—
769	C₂	—	2	8	no	—
770	C₂	—	2	8	no	—
771	C₂	—	4	4	no	—
772	C₂	—	26	8	no	—
773	C₂	—	52	4	no	—
774	C₂	—	52	4	no	—
775	C₂	C₂×#11719195	1	12	yes	direct product factor
776	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
777	C₂	C₂³×#6127	1	1	yes	characteristic
778	C₂	C₂²×#88251	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂³×C₁₃×C₂²⋊C₄	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂³×C₂²⋊C₄	D₁₃
hypocenter	C₁₃	C₂²×#546
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#6127	C₂	semidirect
2. C₂⁴×C₂²⋊D₁₃	C₂	semidirect
3. C₂×#11719195	C₂	direct (N × H)
4. C₂²×#88139	C₂	semidirect
5. C₂²×#88183	C₂	semidirect
6. C₂²×#88137	C₂	semidirect
7. C₂²×#88132	C₂	semidirect
8. C₂²×#88184	C₂	semidirect
9. C₂²×#88138	C₂	semidirect
10. C₂²×#88138	C₂	semidirect
11. C₂²×#88136	C₂	semidirect
12. C₂²×#88207	C₂	semidirect
13. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
14. C₂²×#88135	C₂	semidirect
15. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
16. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
19. C₂⁴×C₄×C₁₃	C₂²	semidirect
20. C₂⁴×C₄×C₁₃	C₂²	semidirect
27. C₂³×C₂²⋊D₁₃	C₂²	semidirect
28. C₂³×C₂²⋊D₁₃	C₂²	semidirect
29. C₂³×C₂²⋊D₁₃	C₂²	semidirect
32. C₂²×#6127	C₂²	semidirect
33. C₂³×D₅₂	C₂²	semidirect
34. C₂³×D₅₂	C₂²	semidirect
35. C₂³×C₄×D₁₃	C₂²	semidirect
36. C₂³×C₄×D₁₃	C₂²	semidirect
37. C₂³×C₄×D₁₃	C₂²	semidirect
38. C₂³×Dic₂₆	C₂²	semidirect
41. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
42. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
43. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
44. C₂×#88207	C₂²	semidirect
46. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
47. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
48. C₂×#88184	C₂²	semidirect
49. C₂×#88183	C₂²	semidirect
50. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
51. C₂²×#6103	C₂²	semidirect
52. C₂²×#6103	C₂²	semidirect
53. C₂²×#6103	C₂²	semidirect
54. C₂²×#6103	C₂²	semidirect
55. C₂²×#6103	C₂²	semidirect
56. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
57. C₂²×#6101	C₂²	semidirect
58. C₂²×#6101	C₂²	semidirect
59. C₂²×#6101	C₂²	semidirect
60. C₂²×C₄×Dic₁₃	C₂²	semidirect
61. C₂×#88139	C₂²	semidirect
62. #11719195	C₂²	direct (N × H)
63. C₂×#88138	C₂²	semidirect
64. C₂×#88138	C₂²	semidirect
65. C₂×#88137	C₂²	semidirect
66. C₂×#88136	C₂²	semidirect
67. C₂×#88135	C₂²	semidirect
68. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
69. C₂×#88132	C₂²	semidirect
90. C₂³×C₄×C₁₃	C₂³	semidirect
91. C₂³×C₄×C₁₃	C₂³	semidirect
99. C₂²×C₂²⋊D₁₃	D₄	semidirect
105. C₂²×C₂²⋊D₁₃	C₂³	semidirect
106. C₂²×C₂²⋊D₁₃	C₂³	semidirect
107. C₂²×C₂²⋊D₁₃	C₂³	semidirect
116. C₂×#6127	C₂³	semidirect
119. C₂²×D₅₂	C₂³	semidirect
120. C₂²×D₅₂	C₂³	semidirect
124. C₂²×C₄×D₁₃	C₂³	semidirect
125. C₂²×C₄×D₁₃	C₂³	semidirect
126. C₂²×C₄×D₁₃	C₂³	semidirect
128. C₂²×Dic₂₆	C₂³	semidirect
131. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
132. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
133. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
134. #88207	C₂³	semidirect
136. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
137. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
138. #88184	C₂³	semidirect
139. #88183	C₂³	semidirect
140. C₄×C₂²⋊D₁₃	C₂³	semidirect
141. C₂×#6103	C₂³	semidirect
142. C₂×#6103	C₂³	semidirect
143. C₂×#6103	C₂³	semidirect
144. C₂×#6103	C₂³	semidirect
145. C₂×#6103	C₂³	semidirect
146. C₂×C₄⋊Dic₁₃	C₂³	semidirect
147. C₂×#6101	C₂³	semidirect
148. C₂×#6101	C₂³	semidirect
149. C₂×#6101	C₂³	semidirect
150. C₂×C₄×Dic₁₃	C₂³	semidirect
151. #88139	C₂³	semidirect
152. #88138	C₂³	semidirect
153. #88138	C₂³	semidirect
154. #88137	C₂³	semidirect
155. #88136	C₂³	semidirect
156. #88135	C₂³	semidirect
157. C₂²⋊C₄×D₁₃	C₂³	semidirect
158. #88132	C₂³	semidirect
172. C₂⁴×C₁₃	#41	semidirect
205. C₂²×C₄×C₁₃	C₂⁴	semidirect
206. C₂²×C₄×C₁₃	C₂⁴	semidirect
214. C₂×C₂²⋊D₁₃	C₂×D₄	semidirect
220. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
221. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
237. C₂×D₅₂	C₂⁴	semidirect
238. C₂×D₅₂	C₂⁴	semidirect
242. C₂×C₄×D₁₃	C₂⁴	semidirect
243. C₂×C₄×D₁₃	C₂⁴	semidirect
244. C₂×C₄×D₁₃	C₂⁴	semidirect
246. C₂×Dic₂₆	C₂⁴	semidirect
249. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
250. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
252. C₂²⋊Dic₁₃	C₂⁴	semidirect
253. C₂²⋊Dic₁₃	C₂⁴	semidirect
254. #6103	C₂⁴	semidirect
255. #6103	C₂⁴	semidirect
256. #6103	C₂⁴	semidirect
257. #6103	C₂⁴	semidirect
258. #6103	C₂⁴	semidirect
259. C₄⋊Dic₁₃	C₂⁴	semidirect
260. #6101	C₂⁴	semidirect
261. #6101	C₂⁴	semidirect
262. #6101	C₂⁴	semidirect
263. C₄×Dic₁₃	C₂⁴	semidirect
279. C₂³×C₂²⋊C₄	D₁₃	semidirect
297. C₂³×C₁₃	C₂×#41	semidirect
338. C₂²⋊D₁₃	C₂²×D₄	semidirect
376. C₂⁴×C₄	C₂×D₁₃	semidirect
377. C₂⁴×C₄	C₂×D₁₃	semidirect
405. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
406. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
407. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
420. C₂²×C₁₃	#546	semidirect
424. C₂²×C₁₃	C₂²×#41	semidirect
506. C₂³×C₄	C₂²×D₁₃	semidirect
507. C₂³×C₄	C₂²×D₁₃	semidirect
534. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
535. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
536. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
541. C₂×C₁₃	C₂×#546	semidirect
576. C₂⁴	#6127	semidirect
633. C₂²×C₄	C₂³×D₁₃	semidirect
634. C₂²×C₄	C₂³×D₁₃	semidirect
649. C₂²⋊C₄	C₂³×D₁₃	semidirect
650. C₂²⋊C₄	C₂³×D₁₃	semidirect
652. C₁₃	C₂²×#546	semidirect
687. C₂³	C₂×#6127	semidirect
753. C₂²	#11719195	direct (N × H)
755. C₂²	C₂²×#6127	semidirect
775. C₂	C₂×#11719195	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×C₂²⋊D₁₃	2
C₂×#11719195	2
C₂²×#88139	2
C₂²×#88183	2
C₂²×#88137	2
C₂²×#88132	2
C₂²×#88184	2
C₂²×#88138	2
C₂²×#88136	2
C₂²×#88207	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂²×#88135	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂³×C₁₃×C₂²⋊C₄	2
C₂²×#546	13

Subgroups — C22×#11719195 #16769841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719195 #16769841