Subgroups — #30586630

Order 15616.

11674 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14519822	C₂	1	1	yes	maximal, characteristic
2	C₄×#14519822	C₂	1	16	yes	maximal, complemented
3	#21459023	C₂	1	16	yes	maximal, complemented
4	#21459020	C₂	1	4	yes	maximal, complemented
5	#21459017	C₂	1	8	yes	maximal, complemented
6	C₂×#16840237	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16840235	C₂	1	8	yes	maximal, complemented
8	#518×D₆₁	C₂	1	8	yes	maximal, complemented
9	C₂×C₆₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14519822	C₄	1	32	yes	complemented
11	C₂×#14519822	C₂²	1	8	yes	—
12	C₂×#14519822	C₂²	1	8	yes	—
13	C₂²×#11758222	C₂²	1	2	yes	—
14	C₂²×#11758224	C₂²	1	4	yes	—
15	C₂³×C₂²⋊D₆₁	C₂²	1	4	yes	—
16	C₂²×D₄×D₆₁	C₂²	1	4	yes	—
17	#16840243	C₂²	1	16	yes	complemented
18	#16840242	C₂²	1	16	yes	complemented
19	#16840241	C₂²	1	64	yes	complemented
20	#16840239	C₂²	1	8	yes	complemented
21	#16840237	C₂²	1	8	yes	complemented
22	#16840237	C₂²	1	8	yes	complemented
23	#16840236	C₂²	1	8	yes	complemented
24	#16840235	C₂²	1	32	yes	complemented
25	#16840235	C₂²	1	16	yes	complemented
26	#16840235	C₂²	1	32	yes	complemented
27	#16840235	C₂²	1	32	yes	complemented
28	#16840234	C₂²	1	64	yes	complemented
29	C₄×#11758222	C₂²	1	16	yes	complemented
30	#16840230	C₂²	1	16	yes	complemented
31	C₄×#11758224	C₂²	1	64	yes	complemented
32	C₂×D₄×Dic₆₁	C₂²	1	8	yes	complemented
33	C₂×C₄×C₂²⋊D₆₁	C₂²	1	32	yes	complemented
34	C₂×#14519737	C₂²	1	32	yes	complemented
35	C₄×D₄×D₆₁	C₂²	1	64	yes	complemented
36	C₂×#14519736	C₂²	1	2	yes	complemented
37	C₂×#14519733	C₂²	1	16	yes	complemented
38	#117×D₆₁	C₂²	1	16	yes	complemented
39	C₂²×C₂²⋊Dic₆₁	C₂²	1	4	yes	complemented
40	C₂×C₂²⋊C₄×D₆₁	C₂²	1	16	yes	complemented
41	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#518	C₂²	1	8	yes	complemented
43	C₆₁×#518	C₂²	1	8	yes	complemented
44	C₂×C₄×D₄×C₆₁	C₂²	1	8	yes	complemented
45	C₂×#117×C₆₁	C₂²	1	2	yes	complemented
46	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	complemented
47	C₂⁴×D₆₁	C₂³	1	4	yes	—
48	#14519822	C₂×C₄	1	128	yes	complemented
49	#14519822	C₂×C₄	1	128	yes	complemented
50	C₂×#11758222	C₂×C₄	1	32	yes	complemented
51	C₂×#11758222	C₂³	1	8	yes	—
52	C₂×#11758222	C₂³	1	8	yes	—
53	C₂×#11758224	C₂×C₄	1	64	yes	complemented
54	C₂×#11758224	C₂³	1	32	yes	—
55	C₂²×Dic₁₂₂	C₂³	1	2	yes	—
56	C₂²×D₂₄₄	C₂³	1	2	yes	—
57	C₂²×C₂²⋊D₆₁	C₂×C₄	1	64	yes	complemented
58	C₂²×C₂²⋊D₆₁	C₂³	1	16	yes	—
59	C₂²×C₂²⋊D₆₁	C₂³	1	16	yes	—
60	C₂²×C₂²⋊D₆₁	C₂³	1	8	yes	—
61	C₂²×C₂²⋊D₆₁	C₂³	1	4	yes	—
62	C₂×D₄×D₆₁	C₂×C₄	1	64	yes	complemented
63	C₂×D₄×D₆₁	C₂³	1	32	yes	—
64	C₂³×Dic₆₁	C₂³	1	4	yes	—
65	C₂³×Dic₆₁	C₂³	1	8	yes	complemented
66	C₂²×C₄×D₆₁	C₂³	1	4	yes	—
67	C₂²×C₄×D₆₁	C₂³	1	32	yes	complemented
68	C₄×Dic₁₂₂	C₂³	1	32	yes	complemented
69	#14519742	C₂³	1	32	yes	complemented
70	C₄×D₂₄₄	C₂³	1	32	yes	complemented
71	D₄×Dic₆₁	C₂³	1	64	yes	complemented
72	#14519739	C₂³	1	32	yes	complemented
73	C₄×C₂²⋊D₆₁	C₂³	1	128	yes	complemented
74	C₄×C₂²⋊D₆₁	C₂³	1	64	yes	complemented
75	#14519737	C₂³	1	128	yes	complemented
76	#14519737	C₂³	1	64	yes	complemented
77	#14519736	C₂³	1	8	yes	—
78	#14519736	C₂³	1	8	yes	complemented
79	#14519735	C₂³	1	32	yes	complemented
80	#14519734	C₂³	1	32	yes	complemented
81	#14519733	C₂³	1	32	yes	—
82	#14519733	C₂³	1	64	yes	complemented
83	C₂×C₄⋊Dic₆₁	C₂³	1	4	yes	complemented
84	C₂×#11758196	C₂³	1	32	yes	complemented
85	C₄⋊C₄×D₆₁	C₂³	1	32	yes	complemented
86	C₂×C₂²⋊Dic₆₁	C₂³	1	16	yes	—
87	C₂×C₂²⋊Dic₆₁	C₂³	1	4	yes	—
88	C₂×C₂²⋊Dic₆₁	C₂³	1	16	yes	complemented
89	C₂×C₂²⋊Dic₆₁	C₂³	1	8	yes	complemented
90	C₂×#11758198	C₂³	1	32	yes	complemented
91	C₂²⋊C₄×D₆₁	C₂³	1	32	yes	—
92	C₂²⋊C₄×D₆₁	C₂³	1	64	yes	complemented
93	C₂×C₄×Dic₆₁	C₂³	1	32	yes	complemented
94	C₂×C₄×Dic₆₁	C₂³	1	4	yes	complemented
95	C₄²×D₆₁	C₂³	1	32	yes	complemented
96	C₂⁵×C₆₁	C₂³	1	2	yes	—
97	C₂²×D₄×C₆₁	C₂×C₄	1	16	yes	complemented
98	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
99	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
100	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
101	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₆₁	C₂³	1	8	yes	complemented
103	C₄×D₄×C₆₁	C₂³	1	64	yes	complemented
104	#117×C₆₁	C₂³	1	8	yes	—
105	#117×C₆₁	C₂³	1	8	yes	complemented
106	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	complemented
107	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
108	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	complemented
110	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	complemented
111	C₂×C₄²×C₆₁	C₂³	1	4	yes	complemented
112	C₂⁴×C₆₁	—	8	4	no	—
113	C₂⁴×C₆₁	C₂²×C₄	1	16	yes	complemented
114	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
115	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
116	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
117	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
118	C₂³×D₆₁	—	8	8	no	—
119	C₂³×D₆₁	C₂²×C₄	1	32	yes	complemented
120	C₂³×D₆₁	C₂⁴	1	4	yes	—
121	C₂³×D₆₁	C₂⁴	1	16	yes	—
122	C₂×D₄×C₆₁	C₂²×C₄	1	32	yes	complemented
123	C₂×D₄×C₆₁	C₂²×C₄	1	32	yes	complemented
124	C₂×D₄×C₆₁	C₂²×C₄	1	32	yes	complemented
125	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
126	C₂²×C₄×C₆₁	—	8	8	no	—
127	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	complemented
128	C₂²×C₄×C₆₁	C₂⁴	1	32	yes	—
129	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
130	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
133	C₂×C₂²⋊D₆₁	C₂²×C₄	1	64	yes	complemented
134	C₂×C₂²⋊D₆₁	C₂²×C₄	1	32	yes	complemented
135	C₂×C₂²⋊D₆₁	C₂²×C₄	1	128	yes	complemented
136	C₂×C₂²⋊D₆₁	C₂²×C₄	1	128	yes	complemented
137	C₂×C₂²⋊D₆₁	C₂⁴	1	32	yes	—
138	C₂×C₂²⋊D₆₁	C₂⁴	1	8	yes	—
139	C₂×C₂²⋊D₆₁	C₂⁴	1	8	yes	—
140	C₂²×Dic₆₁	—	8	8	no	—
141	C₂²×Dic₆₁	C₂²×C₄	1	32	yes	complemented
142	C₂²×Dic₆₁	C₂⁴	1	32	yes	—
143	C₂²×Dic₆₁	C₂⁴	1	8	yes	—
144	C₂²×Dic₆₁	C₂⁴	1	4	yes	—
145	C₂²×Dic₆₁	C₂⁴	1	16	yes	—
146	#11758224	C₂²×C₄	1	256	yes	complemented
147	D₄×D₆₁	C₂²×C₄	1	256	yes	complemented
148	#11758222	C₂²×C₄	1	64	yes	complemented
149	#11758222	C₂²×C₄	1	64	yes	complemented
150	C₂×D₂₄₄	C₂²×C₄	1	16	yes	complemented
151	C₂×D₂₄₄	C₂⁴	1	8	yes	—
152	C₂×C₄×D₆₁	—	8	32	no	—
153	C₂×C₄×D₆₁	C₂²×C₄	1	32	yes	complemented
154	C₂×C₄×D₆₁	C₂⁴	1	64	yes	—
155	C₂×C₄×D₆₁	C₂⁴	1	16	yes	—
156	C₂×Dic₁₂₂	C₂²×C₄	1	16	yes	complemented
157	C₂×Dic₁₂₂	C₂⁴	1	8	yes	—
158	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
159	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
160	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
161	C₂²⋊C₄×C₆₁	C₂⁴	1	32	yes	—
162	C₄²×C₆₁	C₂⁴	1	16	yes	—
163	C₂²⋊Dic₆₁	C₂⁴	1	8	yes	—
164	C₂²⋊Dic₆₁	C₂⁴	1	32	yes	—
165	C₂²⋊Dic₆₁	C₂⁴	1	8	yes	—
166	#11758198	C₂⁴	1	64	yes	—
167	C₄⋊Dic₆₁	C₂⁴	1	16	yes	—
168	#11758196	C₂⁴	1	64	yes	—
169	C₄×Dic₆₁	C₂⁴	1	16	yes	—
170	C₄×Dic₆₁	C₂⁴	1	64	yes	—
171	C₂³×C₆₁	—	4	8	no	—
172	C₂³×C₆₁	—	4	8	no	—
173	C₂³×C₆₁	—	4	8	no	—
174	C₂³×C₆₁	—	4	2	no	—
175	C₂³×C₆₁	—	8	16	no	—
176	C₂³×C₆₁	C₂³×C₄	1	16	yes	—
177	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
178	C₂³×C₆₁	C₂³×C₄	1	16	yes	—
179	C₂³×C₆₁	C₂³×C₄	1	16	yes	—
180	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
181	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
182	C₂³×C₆₁	C₂⁵	1	8	yes	—
183	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
184	C₂²×D₆₁	—	4	32	no	—
185	C₂²×D₆₁	—	4	8	no	—
186	C₂²×D₆₁	—	8	32	no	—
187	C₂²×D₆₁	C₂³×C₄	1	16	yes	—
188	C₂²×D₆₁	C₂³×C₄	1	64	yes	—
189	C₂²×D₆₁	C₂⁵	1	8	yes	—
190	D₄×C₆₁	C₂³×C₄	1	64	yes	—
191	C₂×C₄×C₆₁	—	4	32	no	—
192	C₂×C₄×C₆₁	—	4	8	no	—
193	C₂×C₄×C₆₁	C₂³×C₄	1	8	yes	—
194	C₂×C₄×C₆₁	C₂³×C₄	1	8	yes	—
195	C₂×C₄×C₆₁	C₂³×C₄	1	8	yes	—
196	C₂×C₄×C₆₁	C₂⁵	1	16	yes	—
197	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
198	C₂²⋊D₆₁	C₂³×C₄	1	32	yes	—
199	C₂²⋊D₆₁	C₂³×C₄	1	32	yes	—
200	C₂²⋊D₆₁	C₂³×C₄	1	128	yes	—
201	C₂×Dic₆₁	—	4	32	no	—
202	C₂×Dic₆₁	—	4	8	no	—
203	C₂×Dic₆₁	C₂³×C₄	1	16	yes	—
204	C₂×Dic₆₁	C₂³×C₄	1	64	yes	—
205	C₂×Dic₆₁	C₂⁵	1	16	yes	—
206	C₂×Dic₆₁	C₂⁵	1	8	yes	—
207	D₂₄₄	C₂³×C₄	1	32	yes	—
208	C₄×D₆₁	—	4	64	no	—
209	C₄×D₆₁	C₂³×C₄	1	64	yes	—
210	Dic₁₂₂	C₂³×C₄	1	32	yes	—
211	#62652	—	61	1	no	maximal, Sylow
212	C₂²×C₆₁	—	2	2	no	—
213	C₂²×C₆₁	—	2	16	no	—
214	C₂²×C₆₁	—	2	2	no	—
215	C₂²×C₆₁	—	2	2	no	—
216	C₂²×C₆₁	—	4	16	no	—
217	C₂²×C₆₁	—	4	4	no	—
218	C₂²×C₆₁	—	4	16	no	—
219	C₂²×C₆₁	—	4	16	no	—
220	C₂²×C₆₁	C₂⁴×C₄	1	2	yes	—
221	C₂²×C₆₁	C₂⁴×C₄	1	16	yes	—
222	C₂²×C₆₁	C₂⁴×C₄	1	2	yes	—
223	C₂²×C₆₁	C₂⁴×C₄	1	2	yes	—
224	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
225	C₂×D₆₁	—	2	16	no	—
226	C₂×D₆₁	—	4	16	no	—
227	C₂×D₆₁	—	4	64	no	—
228	C₂×D₆₁	C₂⁴×C₄	1	16	yes	—
229	C₄×C₆₁	—	2	16	no	—
230	C₄×C₆₁	C₂⁴×C₄	1	8	yes	—
231	Dic₆₁	—	2	16	no	—
232	Dic₆₁	C₂⁴×C₄	1	16	yes	—
233	C₂²×H(5,𝔽₂)	—	61	1	no	—
234	C₄×H(5,𝔽₂)	—	61	16	no	—
235	C₄×H(5,𝔽₂)	—	61	16	no	—
236	#3428	—	61	8	no	—
237	#3428	—	61	4	no	—
238	C₂×#518	—	61	1	no	—
239	C₂×#518	—	61	8	no	—
240	C₂×#518	—	61	8	no	—
241	C₂×#518	D₆₁	1	1	yes	characteristic, complemented
242	C₂×C₆₁	—	2	2	no	—
243	C₂×C₆₁	—	2	16	no	—
244	C₂×C₆₁	—	2	2	no	—
245	C₂×C₆₁	—	2	2	no	—
246	C₂×C₆₁	C₂⁵×C₄	1	1	yes	characteristic
247	C₂×C₆₁	H(7,𝔽₂)	1	2	yes	—
248	D₆₁	—	2	16	no	—
249	C₂×H(5,𝔽₂)	—	61	32	no	—
250	C₂×H(5,𝔽₂)	—	61	8	no	—
251	C₂×H(5,𝔽₂)	—	61	8	no	—
252	C₂²×#41	—	61	4	no	—
253	C₂²×#41	—	61	2	no	—
254	C₂³×D₄	—	61	4	no	—
255	C₂³×D₄	—	61	4	no	—
256	C₂³×D₄	C₂×D₆₁	1	1	yes	characteristic
257	#520	—	61	64	no	—
258	#520	—	61	16	no	—
259	#520	—	61	16	no	—
260	#519	—	61	8	no	—
261	#518	—	61	8	no	—
262	#518	—	61	8	no	—
263	#518	—	61	64	no	—
264	#518	—	61	8	no	—
265	#518	—	61	32	no	—
266	#518	—	61	16	no	—
267	#518	—	61	32	no	—
268	#518	—	61	32	no	—
269	#518	C₂×D₆₁	1	8	yes	complemented
270	#518	C₂×D₆₁	1	8	yes	complemented
271	C₄×#41	—	61	64	no	—
272	C₄×#41	—	61	16	no	—
273	C₄×#41	—	61	16	no	—
274	C₂×C₄×D₄	—	61	8	no	—
275	C₂×C₄×D₄	—	61	32	no	—
276	C₂×C₄×D₄	—	61	64	no	—
277	C₂×C₄×D₄	—	61	32	no	—
278	C₂×C₄×D₄	C₂×D₆₁	1	8	yes	complemented
279	C₂×#117	—	61	2	no	—
280	C₂×#117	—	61	16	no	—
281	C₂×#117	—	61	16	no	—
282	C₂×#117	C₂×D₆₁	1	2	yes	complemented
283	C₂²×C₂²⋊C₄	—	61	4	no	—
284	C₂²×C₂²⋊C₄	—	61	16	no	—
285	C₂²×C₂²⋊C₄	C₂×D₆₁	1	4	yes	complemented
286	C₆₁	#62652	1	1	yes	characteristic, complemented, Sylow
287	C₂⁵	—	61	4	no	—
288	C₂⁵	C₂²×D₆₁	1	2	yes	—
289	H(5,𝔽₂)	—	61	128	no	—
290	H(5,𝔽₂)	—	61	128	no	—
291	C₂×#41	—	61	64	no	—
292	C₂×#41	—	61	32	no	—
293	C₂×#41	—	61	32	no	—
294	C₂×#41	—	61	8	no	—
295	C₂×#41	—	61	8	no	—
296	C₂²×Q₈	—	61	2	no	—
297	C₂²×D₄	—	61	64	no	—
298	C₂²×D₄	—	61	16	no	—
299	C₂²×D₄	—	61	16	no	—
300	C₂²×D₄	—	61	8	no	—
301	C₂²×D₄	—	61	4	no	—
302	C₂²×D₄	—	61	64	no	—
303	C₂²×D₄	—	61	32	no	—
304	C₂²×D₄	—	61	2	no	—
305	C₂²×D₄	C₄×D₆₁	1	16	yes	complemented
306	C₂²×D₄	C₂²×D₆₁	1	4	yes	—
307	C₂²×D₄	C₂²×D₆₁	1	4	yes	—
308	C₂²×D₄	C₂²×D₆₁	1	4	yes	—
309	C₂³×C₄	—	61	4	no	—
310	C₂³×C₄	—	61	4	no	—
311	C₂³×C₄	—	61	8	no	—
312	C₂³×C₄	—	61	32	no	—
313	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
314	C₂³×C₄	C₂²×D₆₁	1	8	yes	complemented
315	C₄×Q₈	—	61	32	no	—
316	C₄×Q₈	—	61	32	no	—
317	C₄×D₄	—	61	64	no	—
318	C₄×D₄	—	61	128	no	—
319	C₄×D₄	—	61	64	no	—
320	C₄×D₄	—	61	32	no	—
321	C₄×D₄	—	61	128	no	—
322	C₄×D₄	—	61	64	no	—
323	C₄×D₄	—	61	32	no	—
324	C₄×D₄	C₂²×D₆₁	1	64	yes	complemented
325	#117	—	61	8	no	—
326	#117	—	61	8	no	—
327	#117	—	61	32	no	—
328	#117	—	61	32	no	—
329	#117	—	61	64	no	—
330	#117	—	61	32	no	—
331	#117	C₂²×D₆₁	1	8	yes	—
332	#117	C₂²×D₆₁	1	8	yes	complemented
333	C₂×C₄⋊C₄	—	61	32	no	—
334	C₂×C₄⋊C₄	—	61	4	no	—
335	C₂×C₄⋊C₄	—	61	32	no	—
336	C₂×C₄⋊C₄	C₂²×D₆₁	1	4	yes	complemented
337	C₂×C₂²⋊C₄	—	61	16	no	—
338	C₂×C₂²⋊C₄	—	61	4	no	—
339	C₂×C₂²⋊C₄	—	61	16	no	—
340	C₂×C₂²⋊C₄	—	61	8	no	—
341	C₂×C₂²⋊C₄	—	61	32	no	—
342	C₂×C₂²⋊C₄	—	61	32	no	—
343	C₂×C₂²⋊C₄	—	61	64	no	—
344	C₂×C₂²⋊C₄	C₂²×D₆₁	1	16	yes	—
345	C₂×C₂²⋊C₄	C₂²×D₆₁	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂²×D₆₁	1	16	yes	complemented
347	C₂×C₂²⋊C₄	C₂²×D₆₁	1	8	yes	complemented
348	C₂×C₄²	—	61	32	no	—
349	C₂×C₄²	—	61	4	no	—
350	C₂×C₄²	—	61	32	no	—
351	C₂×C₄²	C₂²×D₆₁	1	4	yes	complemented
352	C₂⁴	—	8	4	no	—
353	C₂⁴	—	61	32	no	—
354	C₂⁴	—	61	4	no	—
355	C₂⁴	—	61	16	no	—
356	C₂⁴	—	488	8	no	—
357	C₂⁴	C₂×C₄×D₆₁	1	16	yes	complemented
358	C₂⁴	C₂³×D₆₁	1	4	yes	—
359	C₂⁴	C₂³×D₆₁	1	1	yes	characteristic
360	C₂⁴	C₂³×D₆₁	1	4	yes	—
361	C₂⁴	C₂³×D₆₁	1	4	yes	—
362	#41	—	61	256	no	—
363	#41	—	61	64	no	—
364	#41	—	61	64	no	—
365	C₂×Q₈	—	61	16	no	—
366	C₂×Q₈	—	61	8	no	—
367	C₂×D₄	—	61	64	no	—
368	C₂×D₄	—	61	32	no	—
369	C₂×D₄	—	61	128	no	—
370	C₂×D₄	—	61	128	no	—
371	C₂×D₄	—	61	8	no	—
372	C₂×D₄	—	61	32	no	—
373	C₂×D₄	—	61	8	no	—
374	C₂×D₄	—	61	256	no	—
375	C₂×D₄	—	61	16	no	—
376	C₂×D₄	—	61	8	no	—
377	C₂×D₄	C₂×C₄×D₆₁	1	32	yes	complemented
378	C₂×D₄	C₂×C₄×D₆₁	1	32	yes	complemented
379	C₂×D₄	C₂×C₄×D₆₁	1	32	yes	complemented
380	C₂×D₄	C₂³×D₆₁	1	16	yes	—
381	C₂²×C₄	—	8	8	no	—
382	C₂²×C₄	—	61	32	no	—
383	C₂²×C₄	—	61	16	no	—
384	C₂²×C₄	—	61	4	no	—
385	C₂²×C₄	—	61	32	no	—
386	C₂²×C₄	—	61	16	no	—
387	C₂²×C₄	—	61	32	no	—
388	C₂²×C₄	—	61	8	no	—
389	C₂²×C₄	—	61	64	no	—
390	C₂²×C₄	—	488	32	no	—
391	C₂²×C₄	—	488	8	no	—
392	C₂²×C₄	C₂×C₄×D₆₁	1	8	yes	complemented
393	C₂²×C₄	C₂³×D₆₁	1	32	yes	—
394	C₂²×C₄	C₂³×D₆₁	1	8	yes	—
395	C₂²×C₄	C₂³×D₆₁	1	2	yes	—
396	C₂²×C₄	C₂³×D₆₁	1	2	yes	—
397	C₂²×C₄	C₂³×D₆₁	1	2	yes	—
398	C₄⋊C₄	—	61	64	no	—
399	C₄⋊C₄	—	61	16	no	—
400	C₄⋊C₄	C₂³×D₆₁	1	16	yes	—
401	C₂²⋊C₄	—	61	8	no	—
402	C₂²⋊C₄	—	61	8	no	—
403	C₂²⋊C₄	—	61	32	no	—
404	C₂²⋊C₄	—	61	64	no	—
405	C₂²⋊C₄	C₂³×D₆₁	1	8	yes	—
406	C₂²⋊C₄	C₂³×D₆₁	1	32	yes	—
407	C₂²⋊C₄	C₂³×D₆₁	1	8	yes	—
408	C₄²	—	61	64	no	—
409	C₄²	—	61	16	no	—
410	C₄²	C₂³×D₆₁	1	16	yes	—
411	C₂³	—	4	8	no	—
412	C₂³	—	4	8	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	8	no	—
415	C₂³	—	8	16	no	—
416	C₂³	—	61	8	no	—
417	C₂³	—	61	16	no	—
418	C₂³	—	61	64	no	—
419	C₂³	—	488	32	no	—
420	C₂³	—	244	32	no	—
421	C₂³	—	244	8	no	—
422	C₂³	C₂²×C₄×D₆₁	1	16	yes	—
423	C₂³	C₂²×C₄×D₆₁	1	4	yes	—
424	C₂³	C₂²×C₄×D₆₁	1	16	yes	—
425	C₂³	C₂²×C₄×D₆₁	1	16	yes	—
426	C₂³	C₂⁴×D₆₁	1	1	yes	characteristic
427	C₂³	C₂⁴×D₆₁	1	1	yes	characteristic
428	C₂³	C₂⁴×D₆₁	1	8	yes	—
429	C₂³	C₂⁴×D₆₁	1	1	yes	characteristic
430	Q₈	—	61	32	no	—
431	D₄	—	61	128	no	—
432	D₄	—	61	32	no	—
433	D₄	—	61	32	no	—
434	D₄	—	61	32	no	—
435	D₄	C₂²×C₄×D₆₁	1	64	yes	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	32	no	—
438	C₂×C₄	—	61	16	no	—
439	C₂×C₄	—	61	64	no	—
440	C₂×C₄	—	61	8	no	—
441	C₂×C₄	—	61	64	no	—
442	C₂×C₄	—	61	16	no	—
443	C₂×C₄	—	244	64	no	—
444	C₂×C₄	—	244	32	no	—
445	C₂×C₄	—	244	8	no	—
446	C₂×C₄	C₂²×C₄×D₆₁	1	8	yes	—
447	C₂×C₄	C₂²×C₄×D₆₁	1	8	yes	—
448	C₂×C₄	C₂²×C₄×D₆₁	1	8	yes	—
449	C₂×C₄	C₂⁴×D₆₁	1	16	yes	—
450	C₂×C₄	C₂⁴×D₆₁	1	4	yes	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	16	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	16	no	—
457	C₂²	—	4	16	no	—
458	C₂²	—	4	16	no	—
459	C₂²	—	61	16	no	—
460	C₂²	—	122	16	no	—
461	C₂²	—	244	16	no	—
462	C₂²	—	244	64	no	—
463	C₂²	C₂³×C₄×D₆₁	1	2	yes	—
464	C₂²	C₂³×C₄×D₆₁	1	16	yes	—
465	C₂²	C₂³×C₄×D₆₁	1	2	yes	—
466	C₂²	C₂³×C₄×D₆₁	1	2	yes	—
467	C₂²	C₂⁵×D₆₁	1	1	yes	characteristic
468	C₄	—	2	16	no	—
469	C₄	—	61	16	no	—
470	C₄	—	122	16	no	—
471	C₄	C₂³×C₄×D₆₁	1	8	yes	—
472	C₂	—	2	2	no	—
473	C₂	—	2	2	no	—
474	C₂	—	2	2	no	—
475	C₂	—	2	16	no	—
476	C₂	—	122	16	no	—
477	C₂	C₂⁴×C₄×D₆₁	1	1	yes	characteristic
478	C₂	#21460629	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₆₁
commutator	C₂×C₆₁	C₂⁵×C₄
Fitting	C₂×C₆₁×#518	C₂
socle, cosocle	C₂²×C₆₁	C₂⁶
prime radical	C₂²×#14519822	C₂
hypercenter	C₂×#518	D₆₁
hypocenter	C₆₁	#62652
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
2. C₄×#14519822	C₂	semidirect
3. #21459023	C₂	semidirect
4. #21459020	C₂	semidirect
5. #21459017	C₂	semidirect
6. C₂×#16840237	C₂	semidirect
7. C₂×#16840235	C₂	semidirect
8. #518×D₆₁	C₂	semidirect
9. C₂×C₆₁×#518	C₂	semidirect
10. C₂×#14519822	C₄	semidirect
17. #16840243	C₂²	semidirect
18. #16840242	C₂²	semidirect
19. #16840241	C₂²	semidirect
20. #16840239	C₂²	semidirect
21. #16840237	C₂²	semidirect
22. #16840237	C₂²	semidirect
23. #16840236	C₂²	semidirect
24. #16840235	C₂²	semidirect
25. #16840235	C₂²	semidirect
26. #16840235	C₂²	semidirect
27. #16840235	C₂²	semidirect
28. #16840234	C₂²	semidirect
29. C₄×#11758222	C₂²	semidirect
30. #16840230	C₂²	semidirect
31. C₄×#11758224	C₂²	semidirect
32. C₂×D₄×Dic₆₁	C₂²	semidirect
33. C₂×C₄×C₂²⋊D₆₁	C₂²	semidirect
34. C₂×#14519737	C₂²	semidirect
35. C₄×D₄×D₆₁	C₂²	semidirect
36. C₂×#14519736	C₂²	semidirect
37. C₂×#14519733	C₂²	semidirect
38. #117×D₆₁	C₂²	semidirect
39. C₂²×C₂²⋊Dic₆₁	C₂²	semidirect
40. C₂×C₂²⋊C₄×D₆₁	C₂²	semidirect
42. C₆₁×#518	C₂²	semidirect
43. C₆₁×#518	C₂²	semidirect
44. C₂×C₄×D₄×C₆₁	C₂²	semidirect
45. C₂×#117×C₆₁	C₂²	semidirect
46. C₂²×C₂²⋊C₄×C₆₁	C₂²	semidirect
48. #14519822	C₂×C₄	semidirect
49. #14519822	C₂×C₄	semidirect
50. C₂×#11758222	C₂×C₄	semidirect
53. C₂×#11758224	C₂×C₄	semidirect
57. C₂²×C₂²⋊D₆₁	C₂×C₄	semidirect
62. C₂×D₄×D₆₁	C₂×C₄	semidirect
65. C₂³×Dic₆₁	C₂³	semidirect
67. C₂²×C₄×D₆₁	C₂³	semidirect
68. C₄×Dic₁₂₂	C₂³	semidirect
69. #14519742	C₂³	semidirect
70. C₄×D₂₄₄	C₂³	semidirect
71. D₄×Dic₆₁	C₂³	semidirect
72. #14519739	C₂³	semidirect
73. C₄×C₂²⋊D₆₁	C₂³	semidirect
74. C₄×C₂²⋊D₆₁	C₂³	semidirect
75. #14519737	C₂³	semidirect
76. #14519737	C₂³	semidirect
78. #14519736	C₂³	semidirect
79. #14519735	C₂³	semidirect
80. #14519734	C₂³	semidirect
82. #14519733	C₂³	semidirect
83. C₂×C₄⋊Dic₆₁	C₂³	semidirect
84. C₂×#11758196	C₂³	semidirect
85. C₄⋊C₄×D₆₁	C₂³	semidirect
88. C₂×C₂²⋊Dic₆₁	C₂³	semidirect
89. C₂×C₂²⋊Dic₆₁	C₂³	semidirect
90. C₂×#11758198	C₂³	semidirect
92. C₂²⋊C₄×D₆₁	C₂³	semidirect
93. C₂×C₄×Dic₆₁	C₂³	semidirect
94. C₂×C₄×Dic₆₁	C₂³	semidirect
95. C₄²×D₆₁	C₂³	semidirect
97. C₂²×D₄×C₆₁	C₂×C₄	semidirect
102. C₂³×C₄×C₆₁	C₂³	semidirect
103. C₄×D₄×C₆₁	C₂³	semidirect
105. #117×C₆₁	C₂³	semidirect
106. C₂×C₄⋊C₄×C₆₁	C₂³	semidirect
109. C₂×C₂²⋊C₄×C₆₁	C₂³	semidirect
110. C₂×C₂²⋊C₄×C₆₁	C₂³	semidirect
111. C₂×C₄²×C₆₁	C₂³	semidirect
113. C₂⁴×C₆₁	C₂²×C₄	semidirect
119. C₂³×D₆₁	C₂²×C₄	semidirect
122. C₂×D₄×C₆₁	C₂²×C₄	semidirect
123. C₂×D₄×C₆₁	C₂²×C₄	semidirect
124. C₂×D₄×C₆₁	C₂²×C₄	semidirect
127. C₂²×C₄×C₆₁	C₂²×C₄	semidirect
133. C₂×C₂²⋊D₆₁	C₂²×C₄	semidirect
134. C₂×C₂²⋊D₆₁	C₂²×C₄	semidirect
135. C₂×C₂²⋊D₆₁	C₂²×C₄	semidirect
136. C₂×C₂²⋊D₆₁	C₂²×C₄	semidirect
141. C₂²×Dic₆₁	C₂²×C₄	semidirect
146. #11758224	C₂²×C₄	semidirect
147. D₄×D₆₁	C₂²×C₄	semidirect
148. #11758222	C₂²×C₄	semidirect
149. #11758222	C₂²×C₄	semidirect
150. C₂×D₂₄₄	C₂²×C₄	semidirect
153. C₂×C₄×D₆₁	C₂²×C₄	semidirect
156. C₂×Dic₁₂₂	C₂²×C₄	semidirect
241. C₂×#518	D₆₁	semidirect
269. #518	C₂×D₆₁	semidirect
270. #518	C₂×D₆₁	semidirect
278. C₂×C₄×D₄	C₂×D₆₁	semidirect
282. C₂×#117	C₂×D₆₁	semidirect
285. C₂²×C₂²⋊C₄	C₂×D₆₁	semidirect
286. C₆₁	#62652	semidirect
305. C₂²×D₄	C₄×D₆₁	semidirect
314. C₂³×C₄	C₂²×D₆₁	semidirect
324. C₄×D₄	C₂²×D₆₁	semidirect
332. #117	C₂²×D₆₁	semidirect
336. C₂×C₄⋊C₄	C₂²×D₆₁	semidirect
346. C₂×C₂²⋊C₄	C₂²×D₆₁	semidirect
347. C₂×C₂²⋊C₄	C₂²×D₆₁	semidirect
351. C₂×C₄²	C₂²×D₆₁	semidirect
357. C₂⁴	C₂×C₄×D₆₁	semidirect
377. C₂×D₄	C₂×C₄×D₆₁	semidirect
378. C₂×D₄	C₂×C₄×D₆₁	semidirect
379. C₂×D₄	C₂×C₄×D₆₁	semidirect
392. C₂²×C₄	C₂×C₄×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14519822	2
C₄×#14519822	2
#21459023	2
#21459020	2
#21459017	2
C₂×#16840237	2
C₂×#16840235	2
#518×D₆₁	2
C₂×C₆₁×#518	2
#62652	61