Subgroups — C₂²×#11719410 #16769898

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×#11719410	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#88133	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#88139	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88148	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88148	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88137	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#88151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#88150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#88136	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#88147	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#88146	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#88126	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₂²⋊C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
18	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
19	C₂³×D₅₂	C₂²	1	1	yes	characteristic
20	C₂³×D₅₂	C₂²	1	1	yes	characteristic
21	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
22	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
23	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
24	C₂³×C₄×D₁₃	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	C₂×C₁₃×#126	C₂²	1	24	yes	complemented
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
37	C₂²×#6103	C₂²	1	1	yes	characteristic
38	C₂²×#6103	C₂²	1	1	yes	characteristic
39	C₂²×#6103	C₂²	1	1	yes	characteristic
40	C₂²×#6103	C₂²	1	1	yes	characteristic
41	C₂²×#6103	C₂²	1	1	yes	characteristic
42	C₂²×#6103	C₂²	1	1	yes	characteristic
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	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
49	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
50	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
51	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
53	#11719410	C₂²	1	256	yes	direct product factor
54	C₂×#88151	C₂²	1	24	yes	complemented
55	C₂×#88150	C₂²	1	24	yes	complemented
56	C₂×#88148	C₂²	1	24	yes	complemented
57	C₂×#88148	C₂²	1	24	yes	complemented
58	C₂×#88147	C₂²	1	24	yes	complemented
59	C₂×#88146	C₂²	1	24	yes	complemented
60	C₂×#88139	C₂²	1	24	yes	complemented
61	C₂×#88137	C₂²	1	24	yes	complemented
62	C₂×#88136	C₂²	1	24	yes	—
63	C₂×C₂²⋊C₄×D₁₃	C₂²	1	24	yes	complemented
64	C₂×C₂²⋊C₄×D₁₃	C₂²	1	24	yes	complemented
65	C₂×#88133	C₂²	1	24	yes	complemented
66	C₂×C₄×D₅₂	C₂²	1	24	yes	complemented
67	C₂×#88126	C₂²	1	24	yes	complemented
68	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
69	C₂⁴×D₁₃	—	2	8	no	—
70	C₂⁴×D₁₃	—	2	8	no	—
71	C₂⁴×D₁₃	—	4	4	no	—
72	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
73	C₂⁴×D₁₃	C₂³	1	12	yes	—
74	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
75	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	C₂²×C₂²⋊D₁₃	—	4	4	no	—
83	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
84	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
85	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
86	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
87	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
88	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
89	C₂²×D₅₂	—	2	8	no	—
90	C₂²×D₅₂	—	2	8	no	—
91	C₂²×D₅₂	C₂³	1	12	yes	—
92	C₂²×D₅₂	C₂³	1	12	yes	—
93	C₂²×C₄×D₁₃	—	2	8	no	—
94	C₂²×C₄×D₁₃	—	2	8	no	—
95	C₂²×C₄×D₁₃	—	4	4	no	—
96	C₂²×C₄×D₁₃	—	4	4	no	—
97	C₂²×C₄×D₁₃	—	4	4	no	—
98	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
99	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
100	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
101	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
102	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
103	C₂²×Dic₂₆	—	4	4	no	—
104	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
105	C₁₃×#126	C₂³	1	64	yes	complemented
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
113	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
114	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
115	C₂×#6103	C₂³	1	12	yes	—
116	C₂×#6103	C₂³	1	12	yes	—
117	C₂×#6103	C₂³	1	12	yes	—
118	C₂×#6103	C₂³	1	12	yes	—
119	C₂×#6103	C₂³	1	12	yes	—
120	C₂×#6103	C₂³	1	12	yes	—
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	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
125	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
126	C₂×#6101	C₂³	1	12	yes	complemented
127	C₂×#6101	C₂³	1	12	yes	complemented
128	C₂×#6101	C₂³	1	12	yes	complemented
129	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
130	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
131	#88151	C₂³	1	64	yes	complemented
132	#88150	C₂³	1	64	yes	complemented
133	#88148	C₂³	1	64	yes	complemented
134	#88148	C₂³	1	64	yes	complemented
135	#88147	C₂³	1	64	yes	complemented
136	#88146	C₂³	1	64	yes	complemented
137	#88139	C₂³	1	64	yes	complemented
138	#88137	C₂³	1	64	yes	complemented
139	#88136	C₂³	1	64	yes	—
140	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
141	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
142	#88133	C₂³	1	64	yes	complemented
143	C₄×D₅₂	C₂³	1	64	yes	complemented
144	#88126	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	C₂⁴	1	6	yes	—
150	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂³×D₁₃	—	2	4	no	—
152	C₂³×D₁₃	—	2	4	no	—
153	C₂³×D₁₃	—	2	4	no	—
154	C₂³×D₁₃	—	2	4	no	—
155	C₂³×D₁₃	—	2	4	no	—
156	C₂³×D₁₃	—	2	4	no	—
157	C₂³×D₁₃	—	2	4	no	—
158	C₂³×D₁₃	—	2	48	no	—
159	C₂³×D₁₃	—	2	48	no	—
160	C₂³×D₁₃	—	4	24	no	—
161	C₂³×D₁₃	—	4	64	no	—
162	C₂³×D₁₃	#41	1	8	yes	—
163	C₂³×D₁₃	#41	1	8	yes	—
164	C₂³×D₁₃	C₂⁴	1	6	yes	—
165	C₂³×D₁₃	C₂⁴	1	16	yes	—
166	C₂³×D₁₃	C₂⁴	1	6	yes	—
167	C₂³×D₁₃	C₂⁴	1	6	yes	—
168	C₂²×C₄×C₁₃	—	2	4	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	—	2	4	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	6	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
180	C₂×C₂²⋊D₁₃	—	4	24	no	—
181	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
182	C₂²×Dic₁₃	—	2	4	no	—
183	C₂²×Dic₁₃	—	2	4	no	—
184	C₂²×Dic₁₃	—	2	4	no	—
185	C₂²×Dic₁₃	—	2	4	no	—
186	C₂²×Dic₁₃	—	2	4	no	—
187	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
188	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
189	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
190	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
191	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
192	C₂×D₅₂	—	2	48	no	—
193	C₂×D₅₂	—	2	48	no	—
194	C₂×D₅₂	C₂⁴	1	16	yes	—
195	C₂×D₅₂	C₂⁴	1	16	yes	—
196	C₂×C₄×D₁₃	—	2	48	no	—
197	C₂×C₄×D₁₃	—	2	48	no	—
198	C₂×C₄×D₁₃	—	4	24	no	—
199	C₂×C₄×D₁₃	—	4	24	no	—
200	C₂×C₄×D₁₃	—	4	24	no	—
201	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
202	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
203	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
204	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
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×C₄⋊C₄	C₂⁴	1	16	yes	complemented
209	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
210	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
211	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
212	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
213	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
214	C₄²×C₁₃	C₂⁴	1	16	yes	complemented
215	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
216	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
217	#6103	C₂⁴	1	16	yes	—
218	#6103	C₂⁴	1	16	yes	—
219	#6103	C₂⁴	1	16	yes	—
220	#6103	C₂⁴	1	16	yes	—
221	#6103	C₂⁴	1	16	yes	—
222	#6103	C₂⁴	1	16	yes	—
223	#6103	C₂⁴	1	16	yes	complemented
224	#6103	C₂⁴	1	16	yes	complemented
225	#6103	C₂⁴	1	16	yes	complemented
226	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
227	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
228	#6101	C₂⁴	1	16	yes	complemented
229	#6101	C₂⁴	1	16	yes	complemented
230	#6101	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	D₁₃	1	1	yes	characteristic, complemented
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	—	13	1	no	—
249	C₂³×C₁₃	—	2	12	no	—
250	C₂³×C₁₃	—	2	12	no	—
251	C₂³×C₁₃	—	2	12	no	—
252	C₂³×C₁₃	—	4	16	no	—
253	C₂³×C₁₃	C₂×#41	1	4	yes	—
254	C₂³×C₁₃	C₂×#41	1	4	yes	—
255	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
256	C₂³×C₁₃	C₂⁵	1	4	yes	—
257	C₂³×C₁₃	C₂⁵	1	3	yes	—
258	C₂²×D₁₃	—	2	32	no	—
259	C₂²×D₁₃	—	2	32	no	—
260	C₂²×D₁₃	—	2	12	no	—
261	C₂²×D₁₃	—	2	12	no	—
262	C₂²×D₁₃	—	2	12	no	—
263	C₂²×D₁₃	—	2	12	no	—
264	C₂²×D₁₃	—	2	12	no	—
265	C₂²×D₁₃	—	2	12	no	—
266	C₂²×D₁₃	—	2	12	no	—
267	C₂²×D₁₃	—	2	32	no	—
268	C₂²×D₁₃	—	2	32	no	—
269	C₂²×D₁₃	—	4	16	no	—
270	C₂²×D₁₃	—	4	192	no	—
271	C₂²×D₁₃	—	4	16	no	—
272	C₂²×D₁₃	C₂×#41	1	24	yes	—
273	C₂²×D₁₃	C₂×#41	1	24	yes	—
274	C₂²×D₁₃	C₂⁵	1	4	yes	—
275	C₂²×D₁₃	C₂⁵	1	4	yes	—
276	C₂²×D₁₃	C₂⁵	1	4	yes	—
277	C₂×C₄×C₁₃	—	2	12	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	—	2	12	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	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
288	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
289	C₂²⋊D₁₃	—	4	16	no	—
290	C₂×Dic₁₃	—	2	12	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	C₂⁵	1	4	yes	—
296	C₂×Dic₁₃	C₂⁵	1	4	yes	—
297	C₂×Dic₁₃	C₂⁵	1	4	yes	—
298	C₂×Dic₁₃	C₂⁵	1	4	yes	—
299	C₂×Dic₁₃	C₂⁵	1	4	yes	—
300	D₅₂	—	2	32	no	—
301	D₅₂	—	2	32	no	—
302	C₄×D₁₃	—	2	32	no	—
303	C₄×D₁₃	—	2	32	no	—
304	C₄×D₁₃	—	4	16	no	—
305	C₄×D₁₃	—	4	16	no	—
306	C₄×D₁₃	—	4	16	no	—
307	Dic₂₆	—	4	16	no	—
308	C₂⁶	—	13	1	no	—
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	—	13	1	no	—
317	C₂⁴×C₄	—	13	1	no	—
318	#551	—	13	256	no	—
319	C₂×#126	—	13	24	no	—
320	C₂×#126	C₂×D₁₃	1	24	yes	complemented
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	C₂×D₁₃	1	1	yes	characteristic, complemented
338	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
339	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
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	1	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	—	13	24	no	—
352	C₂²×C₂²⋊C₄	—	13	24	no	—
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	1	yes	characteristic
356	C₂²×C₄²	—	13	1	no	—
357	C₂²×C₄²	—	13	1	no	—
358	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
359	C₂²×C₁₃	—	2	4	no	—
360	C₂²×C₁₃	—	2	4	no	—
361	C₂²×C₁₃	—	2	4	no	—
362	C₂²×C₁₃	—	4	24	no	—
363	C₂²×C₁₃	#551	1	16	yes	complemented
364	C₂²×C₁₃	C₂²×#41	1	6	yes	—
365	C₂²×C₁₃	C₂²×#41	1	6	yes	—
366	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
367	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
368	C₂×D₁₃	—	2	4	no	—
369	C₂×D₁₃	—	2	4	no	—
370	C₂×D₁₃	—	2	4	no	—
371	C₂×D₁₃	—	2	4	no	—
372	C₂×D₁₃	—	2	48	no	—
373	C₂×D₁₃	—	2	48	no	—
374	C₂×D₁₃	—	2	4	no	—
375	C₂×D₁₃	—	2	4	no	—
376	C₂×D₁₃	—	2	4	no	—
377	C₂×D₁₃	—	4	64	no	—
378	C₂×D₁₃	—	4	24	no	—
379	C₂×D₁₃	C₂²×#41	1	8	yes	—
380	C₂×D₁₃	C₂²×#41	1	8	yes	—
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	C₄×C₁₃	—	2	4	no	—
386	C₄×C₁₃	—	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	—	13	1	no	—
393	C₂⁵	—	13	1	no	—
394	C₂⁵	—	13	1	no	—
395	C₂⁵	—	13	12	no	—
396	C₂⁵	—	26	8	no	—
397	C₂⁵	—	26	8	no	—
398	C₂⁵	—	52	4	no	—
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	—	13	1	no	—
409	C₂³×C₄	—	13	1	no	—
410	C₂³×C₄	—	13	1	no	—
411	C₂³×C₄	—	13	1	no	—
412	C₂³×C₄	—	13	1	no	—
413	C₂³×C₄	—	13	12	no	—
414	C₂³×C₄	—	13	12	no	—
415	C₂³×C₄	—	13	12	no	—
416	C₂³×C₄	—	13	12	no	—
417	C₂³×C₄	—	13	12	no	—
418	C₂³×C₄	—	26	8	no	—
419	C₂³×C₄	—	26	8	no	—
420	C₂³×C₄	—	52	4	no	—
421	C₂³×C₄	—	52	4	no	—
422	C₂³×C₄	—	52	4	no	—
423	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	yes	characteristic
429	#126	—	13	64	no	—
430	#126	C₂²×D₁₃	1	64	yes	complemented
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	C₂²×D₁₃	1	12	yes	complemented
448	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
449	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
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	12	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	—	13	64	no	—
462	C₂×C₂²⋊C₄	—	13	64	no	—
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	12	yes	—
466	C₂×C₄²	—	13	12	no	—
467	C₂×C₄²	—	13	12	no	—
468	C₂×C₄²	C₂²×D₁₃	1	12	yes	complemented
469	C₂×C₁₃	—	4	4	no	—
470	C₂×C₁₃	C₂×#551	1	12	yes	complemented
471	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
472	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
473	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
474	D₁₃	—	2	8	no	—
475	D₁₃	—	2	8	no	—
476	D₁₃	—	4	4	no	—
477	C₂⁴	—	2	4	no	—
478	C₂⁴	—	2	4	no	—
479	C₂⁴	—	2	4	no	—
480	C₂⁴	—	13	8	no	—
481	C₂⁴	—	13	8	no	—
482	C₂⁴	—	13	6	no	—
483	C₂⁴	—	13	6	no	—
484	C₂⁴	—	13	6	no	—
485	C₂⁴	—	13	16	no	—
486	C₂⁴	—	26	48	no	—
487	C₂⁴	—	26	48	no	—
488	C₂⁴	—	26	4	no	—
489	C₂⁴	—	26	4	no	—
490	C₂⁴	—	26	4	no	—
491	C₂⁴	—	26	4	no	—
492	C₂⁴	—	26	4	no	—
493	C₂⁴	—	26	4	no	—
494	C₂⁴	—	26	4	no	—
495	C₂⁴	—	52	24	no	—
496	C₂⁴	—	52	64	no	—
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	4	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	—	2	4	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	16	no	—
519	C₂²×C₄	—	13	16	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	48	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	—	52	24	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	6	yes	—
538	C₂²×C₄	C₂³×D₁₃	1	6	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	C₂³×D₁₃	1	16	yes	complemented
545	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
546	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
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	—	13	16	no	—
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	C₂³×D₁₃	1	16	yes	complemented
564	C₁₃	C₂²×#551	1	1	yes	characteristic, complemented, Sylow
565	C₂³	—	2	12	no	—
566	C₂³	—	2	12	no	—
567	C₂³	—	2	12	no	—
568	C₂³	—	4	16	no	—
569	C₂³	—	13	24	no	—
570	C₂³	—	13	24	no	—
571	C₂³	—	13	4	no	—
572	C₂³	—	13	4	no	—
573	C₂³	—	13	4	no	—
574	C₂³	—	26	32	no	—
575	C₂³	—	26	32	no	—
576	C₂³	—	26	12	no	—
577	C₂³	—	26	12	no	—
578	C₂³	—	26	12	no	—
579	C₂³	—	26	12	no	—
580	C₂³	—	26	32	no	—
581	C₂³	—	26	32	no	—
582	C₂³	—	26	12	no	—
583	C₂³	—	26	12	no	—
584	C₂³	—	26	12	no	—
585	C₂³	—	52	16	no	—
586	C₂³	—	52	192	no	—
587	C₂³	—	52	16	no	—
588	C₂³	#41×D₁₃	1	4	yes	—
589	C₂³	#41×D₁₃	1	4	yes	—
590	C₂³	#88256	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	12	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	—	2	12	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	—	26	32	no	—
609	C₂×C₄	—	26	32	no	—
610	C₂×C₄	—	26	12	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	—	52	16	no	—
616	C₂×C₄	—	52	16	no	—
617	C₂×C₄	—	52	16	no	—
618	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
619	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
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	4	no	—
625	C₂²	—	2	4	no	—
626	C₂²	—	2	4	no	—
627	C₂²	—	4	24	no	—
628	C₂²	—	13	8	no	—
629	C₂²	—	13	8	no	—
630	C₂²	—	26	48	no	—
631	C₂²	—	26	48	no	—
632	C₂²	—	26	4	no	—
633	C₂²	—	26	4	no	—
634	C₂²	—	26	4	no	—
635	C₂²	—	26	4	no	—
636	C₂²	—	26	4	no	—
637	C₂²	—	26	4	no	—
638	C₂²	—	26	4	no	—
639	C₂²	—	52	64	no	—
640	C₂²	—	52	24	no	—
641	C₂²	#11719410	1	16	yes	direct product factor
642	C₂²	C₂×#41×D₁₃	1	6	yes	—
643	C₂²	C₂×#41×D₁₃	1	6	yes	—
644	C₂²	C₂×#88256	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	—	2	4	no	—
651	C₄	—	2	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	—	4	4	no	—
658	C₂	—	26	8	no	—
659	C₂	—	26	8	no	—
660	C₂	—	52	4	no	—
661	C₂	C₂×#11719410	1	12	yes	direct product factor
662	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic
663	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic
664	C₂	C₂²×#88256	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#126	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂²×#88136	C₂
hypercenter	C₂²×#126	D₁₃
hypocenter	C₁₃	C₂²×#551
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#126

Complements

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

N	H ≅ G/N	type
1. C₂×#11719410	C₂	direct (N × H)
2. C₂²×#88133	C₂	semidirect
3. C₂²×#88139	C₂	semidirect
4. C₂²×#88148	C₂	semidirect
5. C₂²×#88148	C₂	semidirect
6. C₂²×#88137	C₂	semidirect
7. C₂²×#88151	C₂	semidirect
8. C₂²×#88150	C₂	semidirect
10. C₂²×C₄×D₅₂	C₂	semidirect
11. C₂²×#88147	C₂	semidirect
12. C₂²×#88146	C₂	semidirect
13. C₂²×#88126	C₂	semidirect
14. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
15. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
16. C₂²×C₁₃×#126	C₂	semidirect
25. C₂³×C₄×D₁₃	C₂²	semidirect
26. C₂³×Dic₂₆	C₂²	semidirect
27. C₂×C₁₃×#126	C₂²	semidirect
28. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
29. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
30. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
34. C₂²×C₄²×C₁₃	C₂²	semidirect
43. C₂²×#6103	C₂²	semidirect
44. C₂²×#6103	C₂²	semidirect
45. C₂²×#6103	C₂²	semidirect
46. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
47. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
48. C₂²×#6101	C₂²	semidirect
49. C₂²×#6101	C₂²	semidirect
50. C₂²×#6101	C₂²	semidirect
51. C₂²×C₄×Dic₁₃	C₂²	semidirect
52. C₂²×C₄×Dic₁₃	C₂²	semidirect
53. #11719410	C₂²	direct (N × H)
54. C₂×#88151	C₂²	semidirect
55. C₂×#88150	C₂²	semidirect
56. C₂×#88148	C₂²	semidirect
57. C₂×#88148	C₂²	semidirect
58. C₂×#88147	C₂²	semidirect
59. C₂×#88146	C₂²	semidirect
60. C₂×#88139	C₂²	semidirect
61. C₂×#88137	C₂²	semidirect
63. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
64. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
65. C₂×#88133	C₂²	semidirect
66. C₂×C₄×D₅₂	C₂²	semidirect
67. C₂×#88126	C₂²	semidirect
102. C₂²×C₄×D₁₃	C₂³	semidirect
104. C₂²×Dic₂₆	C₂³	semidirect
105. C₁₃×#126	C₂³	semidirect
106. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
107. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
108. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
112. C₂×C₄²×C₁₃	C₂³	semidirect
121. C₂×#6103	C₂³	semidirect
122. C₂×#6103	C₂³	semidirect
123. C₂×#6103	C₂³	semidirect
124. C₂×C₄⋊Dic₁₃	C₂³	semidirect
125. C₂×C₄⋊Dic₁₃	C₂³	semidirect
126. C₂×#6101	C₂³	semidirect
127. C₂×#6101	C₂³	semidirect
128. C₂×#6101	C₂³	semidirect
129. C₂×C₄×Dic₁₃	C₂³	semidirect
130. C₂×C₄×Dic₁₃	C₂³	semidirect
131. #88151	C₂³	semidirect
132. #88150	C₂³	semidirect
133. #88148	C₂³	semidirect
134. #88148	C₂³	semidirect
135. #88147	C₂³	semidirect
136. #88146	C₂³	semidirect
137. #88139	C₂³	semidirect
138. #88137	C₂³	semidirect
140. C₂²⋊C₄×D₁₃	C₂³	semidirect
141. C₂²⋊C₄×D₁₃	C₂³	semidirect
142. #88133	C₂³	semidirect
143. C₄×D₅₂	C₂³	semidirect
144. #88126	C₂³	semidirect
205. C₂×C₄×D₁₃	C₂⁴	semidirect
207. C₂×Dic₂₆	C₂⁴	semidirect
208. C₁₃×C₄⋊C₄	C₂⁴	semidirect
209. C₁₃×C₄⋊C₄	C₂⁴	semidirect
210. C₁₃×C₄⋊C₄	C₂⁴	semidirect
214. C₄²×C₁₃	C₂⁴	semidirect
223. #6103	C₂⁴	semidirect
224. #6103	C₂⁴	semidirect
225. #6103	C₂⁴	semidirect
226. C₄⋊Dic₁₃	C₂⁴	semidirect
227. C₄⋊Dic₁₃	C₂⁴	semidirect
228. #6101	C₂⁴	semidirect
229. #6101	C₂⁴	semidirect
230. #6101	C₂⁴	semidirect
231. C₄×Dic₁₃	C₂⁴	semidirect
232. C₄×Dic₁₃	C₂⁴	semidirect
235. C₂²×#126	D₁₃	semidirect
320. C₂×#126	C₂×D₁₃	semidirect
337. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
338. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
339. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
358. C₂²×C₄²	C₂×D₁₃	semidirect
363. C₂²×C₁₃	#551	semidirect
430. #126	C₂²×D₁₃	semidirect
447. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
448. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
449. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
468. C₂×C₄²	C₂²×D₁₃	semidirect
470. C₂×C₁₃	C₂×#551	semidirect
544. C₄⋊C₄	C₂³×D₁₃	semidirect
545. C₄⋊C₄	C₂³×D₁₃	semidirect
546. C₄⋊C₄	C₂³×D₁₃	semidirect
563. C₄²	C₂³×D₁₃	semidirect
564. C₁₃	C₂²×#551	semidirect
641. C₂²	#11719410	direct (N × H)
661. C₂	C₂×#11719410	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×#11719410	2
C₂²×#88133	2
C₂²×#88139	2
C₂²×#88148	2
C₂²×#88137	2
C₂²×#88151	2
C₂²×#88150	2
C₂²×#88136	2
C₂²×C₄×D₅₂	2
C₂²×#88147	2
C₂²×#88146	2
C₂²×#88126	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂²×C₁₃×#126	2
C₂²×#551	13

Subgroups — C22×#11719410 #16769898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719410 #16769898