Subgroups — C₂²×#11719200 #16769895

Order 3328.

9526 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719200	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#88133	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#88133	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88139	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88140	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88183	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#88137	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#88178	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#88132	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#88207	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#88135	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#88180	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#88131	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×C₂²⋊Dic₁₃	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	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
21	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
22	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
23	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
24	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
25	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	24	yes	complemented
32	C₂×#88207	C₂²	1	24	yes	—
33	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊Dic₁₃	C₂²	1	24	yes	complemented
41	C₂×#88183	C₂²	1	24	yes	complemented
42	C₂×C₄×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
43	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
44	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
46	C₂×#88180	C₂²	1	24	yes	complemented
47	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×#88178	C₂²	1	24	yes	complemented
51	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
53	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
54	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
55	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
56	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
59	#11719200	C₂²	1	256	yes	direct product factor
60	C₂×#88140	C₂²	1	24	yes	complemented
61	C₂×#88139	C₂²	1	24	yes	complemented
62	C₂×#88137	C₂²	1	24	yes	complemented
63	C₂×#88135	C₂²	1	24	yes	complemented
64	C₂×#88133	C₂²	1	24	yes	complemented
65	C₂×#88133	C₂²	1	24	yes	complemented
66	C₂×#88132	C₂²	1	24	yes	complemented
67	C₂×#88131	C₂²	1	24	yes	complemented
68	C₂⁵×C₁₃	—	2	8	no	—
69	C₂⁵×C₁₃	—	2	8	no	—
70	C₂⁵×C₁₃	—	4	4	no	—
71	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
72	C₂⁵×C₁₃	C₂³	1	12	yes	—
73	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
74	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
75	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	—	2	8	no	—
77	C₂³×C₄×C₁₃	—	4	4	no	—
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
84	C₂²×C₂²⋊D₁₃	—	2	8	no	—
85	C₂²×C₂²⋊D₁₃	—	2	8	no	—
86	C₂²×C₂²⋊D₁₃	—	4	4	no	—
87	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
88	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
89	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
90	C₂³×Dic₁₃	—	2	8	no	—
91	C₂³×Dic₁₃	—	4	4	no	—
92	C₂³×Dic₁₃	C₂³	1	12	yes	—
93	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
94	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
95	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
96	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
97	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
98	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
99	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
100	C₂³×Dic₁₃	C₂³	1	12	yes	—
101	C₂²×C₄×D₁₃	—	4	4	no	—
102	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
103	C₂²×Dic₂₆	—	4	4	no	—
104	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	64	yes	complemented
110	#88207	C₂³	1	64	yes	—
111	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
112	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
113	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
114	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
115	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
116	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
117	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
118	C₂×C₂²⋊Dic₁₃	C₂³	1	64	yes	complemented
119	#88183	C₂³	1	64	yes	complemented
120	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
121	C₂×#6103	C₂³	1	12	yes	complemented
122	C₂×#6103	C₂³	1	12	yes	complemented
123	C₂×#6103	C₂³	1	12	yes	complemented
124	#88180	C₂³	1	64	yes	complemented
125	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
126	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
127	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
128	#88178	C₂³	1	64	yes	complemented
129	C₂×#6101	C₂³	1	12	yes	complemented
130	C₂×#6101	C₂³	1	12	yes	complemented
131	C₂×#6101	C₂³	1	12	yes	complemented
132	C₂×#6101	C₂³	1	12	yes	complemented
133	C₂×#6101	C₂³	1	12	yes	complemented
134	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
135	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
136	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
137	#88140	C₂³	1	64	yes	complemented
138	#88139	C₂³	1	64	yes	complemented
139	#88137	C₂³	1	64	yes	complemented
140	#88135	C₂³	1	64	yes	complemented
141	#88133	C₂³	1	64	yes	complemented
142	#88133	C₂³	1	64	yes	complemented
143	#88132	C₂³	1	64	yes	complemented
144	#88131	C₂³	1	64	yes	complemented
145	C₂²×#551	—	13	1	no	maximal, Sylow
146	C₂⁴×C₁₃	—	2	4	no	—
147	C₂⁴×C₁₃	—	2	4	no	—
148	C₂⁴×C₁₃	—	2	4	no	—
149	C₂⁴×C₁₃	—	2	4	no	—
150	C₂⁴×C₁₃	—	2	48	no	—
151	C₂⁴×C₁₃	—	2	4	no	—
152	C₂⁴×C₁₃	—	2	48	no	—
153	C₂⁴×C₁₃	—	2	4	no	—
154	C₂⁴×C₁₃	—	2	4	no	—
155	C₂⁴×C₁₃	—	4	24	no	—
156	C₂⁴×C₁₃	—	4	64	no	—
157	C₂⁴×C₁₃	#41	1	8	yes	—
158	C₂⁴×C₁₃	#41	1	8	yes	—
159	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
160	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
161	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
162	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
163	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂³×D₁₃	—	2	4	no	—
165	C₂³×D₁₃	—	2	4	no	—
166	C₂³×D₁₃	—	2	4	no	—
167	C₂³×D₁₃	C₂⁴	1	6	yes	—
168	C₂²×C₄×C₁₃	—	2	48	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	4	24	no	—
174	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
180	C₂×C₂²⋊D₁₃	—	2	48	no	—
181	C₂×C₂²⋊D₁₃	—	2	48	no	—
182	C₂×C₂²⋊D₁₃	—	4	24	no	—
183	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
184	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
185	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
186	C₂²×Dic₁₃	—	2	48	no	—
187	C₂²×Dic₁₃	—	2	4	no	—
188	C₂²×Dic₁₃	—	2	4	no	—
189	C₂²×Dic₁₃	—	2	4	no	—
190	C₂²×Dic₁₃	—	2	4	no	—
191	C₂²×Dic₁₃	—	2	4	no	—
192	C₂²×Dic₁₃	—	2	4	no	—
193	C₂²×Dic₁₃	—	2	4	no	—
194	C₂²×Dic₁₃	—	4	24	no	—
195	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
196	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
197	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
198	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
199	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
200	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
201	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
202	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
203	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
204	C₂×C₄×D₁₃	—	4	24	no	—
205	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
206	C₂×Dic₂₆	—	4	24	no	—
207	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
208	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
209	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
210	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
211	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
212	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
213	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
214	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
215	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
216	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
217	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
218	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
219	#6103	C₂⁴	1	16	yes	complemented
220	#6103	C₂⁴	1	16	yes	complemented
221	#6103	C₂⁴	1	16	yes	complemented
222	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
223	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
224	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
225	#6101	C₂⁴	1	16	yes	complemented
226	#6101	C₂⁴	1	16	yes	complemented
227	#6101	C₂⁴	1	16	yes	complemented
228	#6101	C₂⁴	1	16	yes	complemented
229	#6101	C₂⁴	1	16	yes	complemented
230	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
231	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
232	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
233	C₂×#551	—	13	48	no	—
234	C₂²×#126	—	13	1	no	—
235	C₂²×#126	—	13	1	no	—
236	C₂²×#124	—	13	1	no	—
237	C₂²×#123	—	13	1	no	—
238	C₂²×#123	—	13	1	no	—
239	C₂²×#123	—	13	1	no	—
240	C₂²×C₂²⋊Q₈	—	13	1	no	—
241	C₂²×C₂²⋊Q₈	—	13	1	no	—
242	C₂²×#120	—	13	1	no	—
243	C₂²×C₄×D₄	—	13	1	no	—
244	C₂²×C₄×D₄	—	13	1	no	—
245	C₂²×#117	—	13	1	no	—
246	C₂²×#117	—	13	1	no	—
247	C₂³×C₂²⋊C₄	—	13	1	no	—
248	C₂³×C₂²⋊C₄	D₁₃	1	1	yes	characteristic, complemented
249	C₂³×C₁₃	—	2	32	no	—
250	C₂³×C₁₃	—	2	32	no	—
251	C₂³×C₁₃	—	2	12	no	—
252	C₂³×C₁₃	—	2	12	no	—
253	C₂³×C₁₃	—	2	12	no	—
254	C₂³×C₁₃	—	2	12	no	—
255	C₂³×C₁₃	—	2	32	no	—
256	C₂³×C₁₃	—	2	32	no	—
257	C₂³×C₁₃	—	2	12	no	—
258	C₂³×C₁₃	—	2	12	no	—
259	C₂³×C₁₃	—	2	12	no	—
260	C₂³×C₁₃	—	4	16	no	—
261	C₂³×C₁₃	—	4	192	no	—
262	C₂³×C₁₃	—	4	16	no	—
263	C₂³×C₁₃	C₂×#41	1	24	yes	—
264	C₂³×C₁₃	C₂×#41	1	24	yes	—
265	C₂³×C₁₃	C₂×#41	1	4	yes	—
266	C₂³×C₁₃	C₂×#41	1	4	yes	—
267	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
268	C₂³×C₁₃	C₂⁵	1	4	yes	—
269	C₂³×C₁₃	C₂⁵	1	4	yes	—
270	C₂³×C₁₃	C₂⁵	1	4	yes	—
271	C₂³×C₁₃	C₂⁵	1	3	yes	—
272	C₂²×D₁₃	—	2	12	no	—
273	C₂²×D₁₃	—	2	12	no	—
274	C₂²×D₁₃	—	2	12	no	—
275	C₂²×D₁₃	—	4	16	no	—
276	C₂²×D₁₃	C₂⁵	1	4	yes	—
277	C₂×C₄×C₁₃	—	2	32	no	—
278	C₂×C₄×C₁₃	—	2	12	no	—
279	C₂×C₄×C₁₃	—	2	12	no	—
280	C₂×C₄×C₁₃	—	2	12	no	—
281	C₂×C₄×C₁₃	—	2	12	no	—
282	C₂×C₄×C₁₃	—	4	16	no	—
283	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
284	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
285	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
286	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
287	C₂²⋊D₁₃	—	2	32	no	—
288	C₂²⋊D₁₃	—	2	32	no	—
289	C₂²⋊D₁₃	—	4	16	no	—
290	C₂×Dic₁₃	—	2	32	no	—
291	C₂×Dic₁₃	—	2	12	no	—
292	C₂×Dic₁₃	—	2	12	no	—
293	C₂×Dic₁₃	—	2	12	no	—
294	C₂×Dic₁₃	—	2	12	no	—
295	C₂×Dic₁₃	—	2	12	no	—
296	C₂×Dic₁₃	—	2	12	no	—
297	C₂×Dic₁₃	—	2	12	no	—
298	C₂×Dic₁₃	—	4	16	no	—
299	C₂×Dic₁₃	C₂⁵	1	4	yes	—
300	C₂×Dic₁₃	C₂⁵	1	4	yes	—
301	C₂×Dic₁₃	C₂⁵	1	4	yes	—
302	C₂×Dic₁₃	C₂⁵	1	4	yes	—
303	C₂×Dic₁₃	C₂⁵	1	4	yes	—
304	C₂×Dic₁₃	C₂⁵	1	4	yes	—
305	C₂×Dic₁₃	C₂⁵	1	4	yes	—
306	C₄×D₁₃	—	4	16	no	—
307	Dic₂₆	—	4	16	no	—
308	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
309	C₂³×Q₈	—	13	1	no	—
310	C₂³×D₄	—	13	1	no	—
311	C₂³×D₄	—	13	1	no	—
312	C₂³×D₄	—	13	1	no	—
313	C₂⁴×C₄	—	13	1	no	—
314	C₂⁴×C₄	—	13	1	no	—
315	C₂⁴×C₄	—	13	1	no	—
316	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
317	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
318	#551	—	13	256	no	—
319	C₂×#126	—	13	24	no	—
320	C₂×#126	—	13	24	no	—
321	C₂×#124	—	13	24	no	—
322	C₂×#123	—	13	24	no	—
323	C₂×#123	—	13	24	no	—
324	C₂×#123	—	13	24	no	—
325	C₂×C₂²⋊Q₈	—	13	24	no	—
326	C₂×C₂²⋊Q₈	—	13	24	no	—
327	C₂×#120	—	13	24	no	—
328	C₂×C₄×D₄	—	13	24	no	—
329	C₂×C₄×D₄	—	13	24	no	—
330	C₂×#117	—	13	24	no	—
331	C₂×#117	—	13	24	no	—
332	C₂²×C₄⋊C₄	—	13	1	no	—
333	C₂²×C₄⋊C₄	—	13	1	no	—
334	C₂²×C₄⋊C₄	—	13	1	no	—
335	C₂²×C₄⋊C₄	—	13	1	no	—
336	C₂²×C₄⋊C₄	—	13	1	no	—
337	C₂²×C₄⋊C₄	—	13	1	no	—
338	C₂²×C₄⋊C₄	—	13	1	no	—
339	C₂²×C₄⋊C₄	—	13	1	no	—
340	C₂²×C₂²⋊C₄	—	13	1	no	—
341	C₂²×C₂²⋊C₄	—	13	1	no	—
342	C₂²×C₂²⋊C₄	—	13	1	no	—
343	C₂²×C₂²⋊C₄	—	13	1	no	—
344	C₂²×C₂²⋊C₄	—	13	24	no	—
345	C₂²×C₂²⋊C₄	—	13	1	no	—
346	C₂²×C₂²⋊C₄	—	13	1	no	—
347	C₂²×C₂²⋊C₄	—	13	1	no	—
348	C₂²×C₂²⋊C₄	—	13	1	no	—
349	C₂²×C₂²⋊C₄	—	13	1	no	—
350	C₂²×C₂²⋊C₄	—	13	1	no	—
351	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
352	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
353	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
354	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂×D₁₃	1	24	yes	complemented
356	C₂²×C₄²	—	13	1	no	—
357	C₂²×C₄²	—	13	1	no	—
358	C₂²×C₄²	—	13	1	no	—
359	C₂²×C₁₃	—	2	4	no	—
360	C₂²×C₁₃	—	2	4	no	—
361	C₂²×C₁₃	—	2	4	no	—
362	C₂²×C₁₃	—	2	4	no	—
363	C₂²×C₁₃	—	2	48	no	—
364	C₂²×C₁₃	—	2	48	no	—
365	C₂²×C₁₃	—	2	4	no	—
366	C₂²×C₁₃	—	2	4	no	—
367	C₂²×C₁₃	—	2	4	no	—
368	C₂²×C₁₃	—	4	64	no	—
369	C₂²×C₁₃	—	4	24	no	—
370	C₂²×C₁₃	#551	1	16	yes	complemented
371	C₂²×C₁₃	C₂²×#41	1	8	yes	—
372	C₂²×C₁₃	C₂²×#41	1	6	yes	—
373	C₂²×C₁₃	C₂²×#41	1	8	yes	—
374	C₂²×C₁₃	C₂²×#41	1	6	yes	—
375	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
376	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
377	C₂×D₁₃	—	2	4	no	—
378	C₂×D₁₃	—	2	4	no	—
379	C₂×D₁₃	—	2	4	no	—
380	C₂×D₁₃	—	4	24	no	—
381	C₄×C₁₃	—	2	4	no	—
382	C₄×C₁₃	—	2	4	no	—
383	C₄×C₁₃	—	2	4	no	—
384	C₄×C₁₃	—	2	4	no	—
385	Dic₁₃	—	2	4	no	—
386	Dic₁₃	—	2	4	no	—
387	Dic₁₃	—	2	4	no	—
388	Dic₁₃	—	2	4	no	—
389	Dic₁₃	—	2	4	no	—
390	Dic₁₃	—	2	4	no	—
391	Dic₁₃	—	2	4	no	—
392	C₂⁵	—	2	8	no	—
393	C₂⁵	—	2	8	no	—
394	C₂⁵	—	4	4	no	—
395	C₂⁵	—	13	1	no	—
396	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
397	C₂⁵	C₂²×D₁₃	1	12	yes	—
398	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
399	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
400	C₂²×Q₈	—	13	12	no	—
401	C₂²×Q₈	—	52	4	no	—
402	C₂²×D₄	—	13	12	no	—
403	C₂²×D₄	—	13	12	no	—
404	C₂²×D₄	—	13	12	no	—
405	C₂²×D₄	—	26	8	no	—
406	C₂²×D₄	—	26	8	no	—
407	C₂²×D₄	—	52	4	no	—
408	C₂³×C₄	—	2	8	no	—
409	C₂³×C₄	—	4	4	no	—
410	C₂³×C₄	—	13	12	no	—
411	C₂³×C₄	—	13	1	no	—
412	C₂³×C₄	—	13	1	no	—
413	C₂³×C₄	—	13	1	no	—
414	C₂³×C₄	—	13	1	no	—
415	C₂³×C₄	—	13	1	no	—
416	C₂³×C₄	—	13	1	no	—
417	C₂³×C₄	—	13	1	no	—
418	C₂³×C₄	—	13	12	no	—
419	C₂³×C₄	—	13	12	no	—
420	C₂³×C₄	—	26	8	no	—
421	C₂³×C₄	—	52	4	no	—
422	C₂³×C₄	—	52	4	no	—
423	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
424	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
425	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
426	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
427	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
428	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
429	#126	—	13	64	no	—
430	#126	—	13	64	no	—
431	#124	—	13	64	no	—
432	#123	—	13	64	no	—
433	#123	—	13	64	no	—
434	#123	—	13	64	no	—
435	C₂²⋊Q₈	—	13	64	no	—
436	C₂²⋊Q₈	—	13	64	no	—
437	#120	—	13	64	no	—
438	C₄×D₄	—	13	64	no	—
439	C₄×D₄	—	13	64	no	—
440	#117	—	13	64	no	—
441	#117	—	13	64	no	—
442	C₂×C₄⋊C₄	—	13	12	no	—
443	C₂×C₄⋊C₄	—	13	12	no	—
444	C₂×C₄⋊C₄	—	13	12	no	—
445	C₂×C₄⋊C₄	—	13	12	no	—
446	C₂×C₄⋊C₄	—	13	12	no	—
447	C₂×C₄⋊C₄	—	13	12	no	—
448	C₂×C₄⋊C₄	—	13	12	no	—
449	C₂×C₄⋊C₄	—	13	12	no	—
450	C₂×C₂²⋊C₄	—	13	12	no	—
451	C₂×C₂²⋊C₄	—	13	12	no	—
452	C₂×C₂²⋊C₄	—	13	12	no	—
453	C₂×C₂²⋊C₄	—	13	12	no	—
454	C₂×C₂²⋊C₄	—	13	64	no	—
455	C₂×C₂²⋊C₄	—	13	12	no	—
456	C₂×C₂²⋊C₄	—	13	12	no	—
457	C₂×C₂²⋊C₄	—	13	12	no	—
458	C₂×C₂²⋊C₄	—	13	12	no	—
459	C₂×C₂²⋊C₄	—	13	12	no	—
460	C₂×C₂²⋊C₄	—	13	12	no	—
461	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	—
462	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	—
463	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	—
464	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	—
465	C₂×C₂²⋊C₄	C₂²×D₁₃	1	64	yes	complemented
466	C₂×C₄²	—	13	12	no	—
467	C₂×C₄²	—	13	12	no	—
468	C₂×C₄²	—	13	12	no	—
469	C₂×C₁₃	—	2	8	no	—
470	C₂×C₁₃	—	2	8	no	—
471	C₂×C₁₃	—	4	4	no	—
472	C₂×C₁₃	C₂×#551	1	12	yes	complemented
473	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
474	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
475	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
476	D₁₃	—	4	4	no	—
477	C₂⁴	—	2	4	no	—
478	C₂⁴	—	2	4	no	—
479	C₂⁴	—	2	4	no	—
480	C₂⁴	—	2	4	no	—
481	C₂⁴	—	2	48	no	—
482	C₂⁴	—	2	4	no	—
483	C₂⁴	—	2	48	no	—
484	C₂⁴	—	2	4	no	—
485	C₂⁴	—	2	4	no	—
486	C₂⁴	—	4	24	no	—
487	C₂⁴	—	4	64	no	—
488	C₂⁴	—	13	6	no	—
489	C₂⁴	—	26	4	no	—
490	C₂⁴	—	26	4	no	—
491	C₂⁴	—	26	4	no	—
492	C₂⁴	#6127	1	8	yes	—
493	C₂⁴	#6129	1	8	yes	—
494	C₂⁴	C₂³×D₁₃	1	6	yes	—
495	C₂⁴	C₂³×D₁₃	1	16	yes	—
496	C₂⁴	C₂³×D₁₃	1	6	yes	—
497	C₂⁴	C₂³×D₁₃	1	6	yes	—
498	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
499	C₂×Q₈	—	13	16	no	—
500	C₂×Q₈	—	52	24	no	—
501	C₂×D₄	—	13	16	no	—
502	C₂×D₄	—	13	16	no	—
503	C₂×D₄	—	13	16	no	—
504	C₂×D₄	—	26	48	no	—
505	C₂×D₄	—	26	48	no	—
506	C₂×D₄	—	52	24	no	—
507	C₂²×C₄	—	2	48	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	4	24	no	—
513	C₂²×C₄	—	13	6	no	—
514	C₂²×C₄	—	13	6	no	—
515	C₂²×C₄	—	13	6	no	—
516	C₂²×C₄	—	13	6	no	—
517	C₂²×C₄	—	13	6	no	—
518	C₂²×C₄	—	13	6	no	—
519	C₂²×C₄	—	13	6	no	—
520	C₂²×C₄	—	13	16	no	—
521	C₂²×C₄	—	13	16	no	—
522	C₂²×C₄	—	13	16	no	—
523	C₂²×C₄	—	26	48	no	—
524	C₂²×C₄	—	26	4	no	—
525	C₂²×C₄	—	26	4	no	—
526	C₂²×C₄	—	26	4	no	—
527	C₂²×C₄	—	26	4	no	—
528	C₂²×C₄	—	26	4	no	—
529	C₂²×C₄	—	26	4	no	—
530	C₂²×C₄	—	26	4	no	—
531	C₂²×C₄	—	52	24	no	—
532	C₂²×C₄	—	52	24	no	—
533	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
534	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
535	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
536	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
537	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
538	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
539	C₄⋊C₄	—	13	16	no	—
540	C₄⋊C₄	—	13	16	no	—
541	C₄⋊C₄	—	13	16	no	—
542	C₄⋊C₄	—	13	16	no	—
543	C₄⋊C₄	—	13	16	no	—
544	C₄⋊C₄	—	13	16	no	—
545	C₄⋊C₄	—	13	16	no	—
546	C₄⋊C₄	—	13	16	no	—
547	C₂²⋊C₄	—	13	16	no	—
548	C₂²⋊C₄	—	13	16	no	—
549	C₂²⋊C₄	—	13	16	no	—
550	C₂²⋊C₄	—	13	16	no	—
551	C₂²⋊C₄	—	13	16	no	—
552	C₂²⋊C₄	—	13	16	no	—
553	C₂²⋊C₄	—	13	16	no	—
554	C₂²⋊C₄	—	13	16	no	—
555	C₂²⋊C₄	—	13	16	no	—
556	C₂²⋊C₄	—	13	16	no	—
557	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
558	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
559	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
560	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
561	C₄²	—	13	16	no	—
562	C₄²	—	13	16	no	—
563	C₄²	—	13	16	no	—
564	C₁₃	C₂²×#551	1	1	yes	characteristic, complemented, Sylow
565	C₂³	—	2	32	no	—
566	C₂³	—	2	32	no	—
567	C₂³	—	2	12	no	—
568	C₂³	—	2	12	no	—
569	C₂³	—	2	12	no	—
570	C₂³	—	2	12	no	—
571	C₂³	—	2	32	no	—
572	C₂³	—	2	12	no	—
573	C₂³	—	2	32	no	—
574	C₂³	—	2	12	no	—
575	C₂³	—	2	12	no	—
576	C₂³	—	4	16	no	—
577	C₂³	—	4	192	no	—
578	C₂³	—	4	16	no	—
579	C₂³	—	13	4	no	—
580	C₂³	—	26	12	no	—
581	C₂³	—	26	12	no	—
582	C₂³	—	26	12	no	—
583	C₂³	—	52	16	no	—
584	C₂³	C₂×#6127	1	24	yes	—
585	C₂³	C₂×#6127	1	4	yes	—
586	C₂³	C₂×#6129	1	24	yes	—
587	C₂³	C₂×#6129	1	4	yes	—
588	C₂³	#88251	1	4	yes	—
589	C₂³	C₂⁴×D₁₃	1	4	yes	—
590	C₂³	C₂⁴×D₁₃	1	4	yes	—
591	C₂³	C₂⁴×D₁₃	1	4	yes	—
592	C₂³	C₂⁴×D₁₃	1	3	yes	—
593	Q₈	—	52	16	no	—
594	D₄	—	26	32	no	—
595	D₄	—	26	32	no	—
596	D₄	—	52	16	no	—
597	C₂×C₄	—	2	32	no	—
598	C₂×C₄	—	2	12	no	—
599	C₂×C₄	—	2	12	no	—
600	C₂×C₄	—	2	12	no	—
601	C₂×C₄	—	2	12	no	—
602	C₂×C₄	—	4	16	no	—
603	C₂×C₄	—	13	4	no	—
604	C₂×C₄	—	13	4	no	—
605	C₂×C₄	—	13	4	no	—
606	C₂×C₄	—	13	4	no	—
607	C₂×C₄	—	13	4	no	—
608	C₂×C₄	—	13	4	no	—
609	C₂×C₄	—	13	4	no	—
610	C₂×C₄	—	26	32	no	—
611	C₂×C₄	—	26	12	no	—
612	C₂×C₄	—	26	12	no	—
613	C₂×C₄	—	26	12	no	—
614	C₂×C₄	—	26	12	no	—
615	C₂×C₄	—	26	12	no	—
616	C₂×C₄	—	26	12	no	—
617	C₂×C₄	—	26	12	no	—
618	C₂×C₄	—	52	16	no	—
619	C₂×C₄	—	52	16	no	—
620	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
621	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
622	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
623	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
624	C₂²	—	2	48	no	—
625	C₂²	—	2	48	no	—
626	C₂²	—	2	4	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	2	4	no	—
632	C₂²	—	2	4	no	—
633	C₂²	—	4	64	no	—
634	C₂²	—	4	24	no	—
635	C₂²	—	26	4	no	—
636	C₂²	—	26	4	no	—
637	C₂²	—	26	4	no	—
638	C₂²	—	52	24	no	—
639	C₂²	#11719200	1	16	yes	direct product factor
640	C₂²	C₂²×#6127	1	8	yes	—
641	C₂²	C₂²×#6127	1	6	yes	—
642	C₂²	C₂²×#6129	1	8	yes	—
643	C₂²	C₂²×#6129	1	6	yes	—
644	C₂²	C₂×#88251	1	6	yes	—
645	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
646	C₄	—	2	4	no	—
647	C₄	—	2	4	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	4	no	—
650	C₄	—	26	4	no	—
651	C₄	—	26	4	no	—
652	C₄	—	26	4	no	—
653	C₄	—	26	4	no	—
654	C₄	—	26	4	no	—
655	C₄	—	26	4	no	—
656	C₄	—	26	4	no	—
657	C₂	—	2	8	no	—
658	C₂	—	2	8	no	—
659	C₂	—	4	4	no	—
660	C₂	—	52	4	no	—
661	C₂	C₂×#11719200	1	12	yes	direct product factor
662	C₂	C₂³×#6129	1	1	yes	characteristic
663	C₂	C₂³×#6127	1	1	yes	characteristic
664	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
prime radical	C₂²×#88207	C₂
hypercenter	C₂³×C₂²⋊C₄	D₁₃
hypocenter	C₁₃	C₂²×#551
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. C₂×#11719200	C₂	direct (N × H)
2. C₂²×#88133	C₂	semidirect
3. C₂²×#88133	C₂	semidirect
4. C₂²×#88139	C₂	semidirect
5. C₂²×#88140	C₂	semidirect
6. C₂²×#88183	C₂	semidirect
7. C₂²×#88137	C₂	semidirect
8. C₂²×#88178	C₂	semidirect
9. C₂²×#88132	C₂	semidirect
11. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
12. C₂²×#88135	C₂	semidirect
13. C₂²×#88180	C₂	semidirect
14. C₂²×#88131	C₂	semidirect
15. C₂³×C₂²⋊Dic₁₃	C₂	semidirect
16. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
25. C₂³×C₄×D₁₃	C₂²	semidirect
26. C₂³×Dic₂₆	C₂²	semidirect
31. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
40. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
41. C₂×#88183	C₂²	semidirect
42. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
43. C₂²×#6103	C₂²	semidirect
44. C₂²×#6103	C₂²	semidirect
45. C₂²×#6103	C₂²	semidirect
46. C₂×#88180	C₂²	semidirect
47. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
48. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
49. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
50. C₂×#88178	C₂²	semidirect
51. C₂²×#6101	C₂²	semidirect
52. C₂²×#6101	C₂²	semidirect
53. C₂²×#6101	C₂²	semidirect
54. C₂²×#6101	C₂²	semidirect
55. C₂²×#6101	C₂²	semidirect
56. C₂²×C₄×Dic₁₃	C₂²	semidirect
57. C₂²×C₄×Dic₁₃	C₂²	semidirect
58. C₂²×C₄×Dic₁₃	C₂²	semidirect
59. #11719200	C₂²	direct (N × H)
60. C₂×#88140	C₂²	semidirect
61. C₂×#88139	C₂²	semidirect
62. C₂×#88137	C₂²	semidirect
63. C₂×#88135	C₂²	semidirect
64. C₂×#88133	C₂²	semidirect
65. C₂×#88133	C₂²	semidirect
66. C₂×#88132	C₂²	semidirect
67. C₂×#88131	C₂²	semidirect
102. C₂²×C₄×D₁₃	C₂³	semidirect
104. C₂²×Dic₂₆	C₂³	semidirect
109. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
118. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
119. #88183	C₂³	semidirect
120. C₄×C₂²⋊D₁₃	C₂³	semidirect
121. C₂×#6103	C₂³	semidirect
122. C₂×#6103	C₂³	semidirect
123. C₂×#6103	C₂³	semidirect
124. #88180	C₂³	semidirect
125. C₂×C₄⋊Dic₁₃	C₂³	semidirect
126. C₂×C₄⋊Dic₁₃	C₂³	semidirect
127. C₂×C₄⋊Dic₁₃	C₂³	semidirect
128. #88178	C₂³	semidirect
129. C₂×#6101	C₂³	semidirect
130. C₂×#6101	C₂³	semidirect
131. C₂×#6101	C₂³	semidirect
132. C₂×#6101	C₂³	semidirect
133. C₂×#6101	C₂³	semidirect
134. C₂×C₄×Dic₁₃	C₂³	semidirect
135. C₂×C₄×Dic₁₃	C₂³	semidirect
136. C₂×C₄×Dic₁₃	C₂³	semidirect
137. #88140	C₂³	semidirect
138. #88139	C₂³	semidirect
139. #88137	C₂³	semidirect
140. #88135	C₂³	semidirect
141. #88133	C₂³	semidirect
142. #88133	C₂³	semidirect
143. #88132	C₂³	semidirect
144. #88131	C₂³	semidirect
205. C₂×C₄×D₁₃	C₂⁴	semidirect
207. C₂×Dic₂₆	C₂⁴	semidirect
219. #6103	C₂⁴	semidirect
220. #6103	C₂⁴	semidirect
221. #6103	C₂⁴	semidirect
222. C₄⋊Dic₁₃	C₂⁴	semidirect
223. C₄⋊Dic₁₃	C₂⁴	semidirect
224. C₄⋊Dic₁₃	C₂⁴	semidirect
225. #6101	C₂⁴	semidirect
226. #6101	C₂⁴	semidirect
227. #6101	C₂⁴	semidirect
228. #6101	C₂⁴	semidirect
229. #6101	C₂⁴	semidirect
230. C₄×Dic₁₃	C₂⁴	semidirect
231. C₄×Dic₁₃	C₂⁴	semidirect
232. C₄×Dic₁₃	C₂⁴	semidirect
248. C₂³×C₂²⋊C₄	D₁₃	semidirect
355. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
370. C₂²×C₁₃	#551	semidirect
465. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
472. C₂×C₁₃	C₂×#551	semidirect
564. C₁₃	C₂²×#551	semidirect
639. C₂²	#11719200	direct (N × H)
661. C₂	C₂×#11719200	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11719200	2
C₂²×#88133	2
C₂²×#88139	2
C₂²×#88140	2
C₂²×#88183	2
C₂²×#88137	2
C₂²×#88178	2
C₂²×#88132	2
C₂²×#88207	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂²×#88135	2
C₂²×#88180	2
C₂²×#88131	2
C₂³×C₂²⋊Dic₁₃	2
C₂³×C₁₃×C₂²⋊C₄	2
C₂²×#551	13

Subgroups — C22×#11719200 #16769895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719200 #16769895