Subgroups — #30614718

Order 15616.

870 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁⋊#433	C₂	1	1	yes	maximal, characteristic
2	#21462281	C₂	1	1	yes	maximal, characteristic
3	#21461620	C₂	1	1	yes	maximal, characteristic, complemented
4	#21461620	C₂	1	1	yes	maximal, characteristic, complemented
5	#21461616	C₂	1	1	yes	maximal, characteristic, complemented
6	#21461612	C₂	1	1	yes	maximal, characteristic, complemented
7	#21461608	C₂	1	1	yes	maximal, characteristic, complemented
8	#21461608	C₂	1	1	yes	maximal, characteristic, complemented
9	#21461606	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₈×#6923	C₂	1	1	yes	maximal, characteristic, complemented
11	#21461559	C₂	1	1	yes	maximal, characteristic
12	#21461559	C₂	1	1	yes	maximal, characteristic
13	#21461555	C₂	1	1	yes	maximal, characteristic
14	C₈×C₂²⋊#6923	C₂	1	1	yes	maximal, characteristic
15	#424×D₆₁	C₂	1	1	yes	maximal, characteristic
16	#16840787	C₄	1	2	yes	complemented
17	#16840787	C₄	1	2	yes	complemented
18	#16840786	C₄	1	2	yes	complemented
19	#16840786	C₄	1	2	yes	complemented
20	D₆₁⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
21	D₆₁⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
22	D₆₁⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
23	D₆₁⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
24	#16840721	C₂²	1	1	yes	characteristic
25	C₂×#14519831	C₂²	1	1	yes	characteristic
26	C₂×#14519831	C₂²	1	1	yes	characteristic
27	C₂×#14519831	C₂²	1	1	yes	characteristic
28	C₂×#14519831	C₂²	1	1	yes	characteristic
29	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
31	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
32	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
33	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
34	#16840712	C₄	1	2	yes	—
35	#16840712	C₄	1	2	yes	—
36	#16840711	C₄	1	2	yes	—
37	#16840711	C₄	1	2	yes	—
38	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊#6923	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊#6923	C₂²	1	1	yes	characteristic
42	#16840698	C₂²	1	1	yes	characteristic
43	C₄²×#6923	C₂²	1	1	yes	characteristic
44	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
46	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
50	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
51	(C₂×#6923)⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×M₁₆×D₆₁	C₂²	1	1	yes	characteristic
53	C₂²×C₈×D₆₁	C₂²	1	1	yes	characteristic
54	#117×D₆₁	C₂²	1	1	yes	characteristic
55	#16839790	C₄	1	1	yes	characteristic, complemented
56	#16839789	C₄	1	1	yes	characteristic, complemented
57	#16839788	C₄	1	1	yes	characteristic, complemented
58	#16839787	C₄	1	1	yes	characteristic, complemented
59	#16839787	C₄	1	1	yes	characteristic, complemented
60	#16839787	C₄	1	1	yes	characteristic, complemented
61	#16839787	C₄	1	1	yes	characteristic, complemented
62	C₄⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
63	C₄⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
64	C₄⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
65	C₄⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
66	C₆₁×#424	C₄	1	1	yes	characteristic, complemented
67	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
68	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊#6923	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊#6923	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊#6923	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊#6923	C₂×C₄	1	2	yes	—
75	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
76	C₂×C₄×#6923	C₂×C₄	1	2	yes	—
77	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
78	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
79	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
80	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
81	#14519844	C₂×C₄	1	2	yes	—
82	#14519844	C₂×C₄	1	2	yes	—
83	C₄⋊#92420	C₂×C₄	1	2	yes	—
84	C₄⋊#92420	C₂×C₄	1	2	yes	—
85	#14519834	C₂×C₄	1	2	yes	—
86	#14519834	C₂×C₄	1	2	yes	—
87	C₂²⋊#92420	C₂×C₄	1	2	yes	—
88	C₂²⋊#92420	C₂×C₄	1	2	yes	—
89	#14519832	C₂×C₄	1	2	yes	—
90	#14519832	C₂×C₄	1	2	yes	—
91	#14519831	—	4	1	no	—
92	#14519831	—	4	1	no	—
93	#14519831	—	4	1	no	—
94	#14519831	—	4	1	no	—
95	C₄×#92420	C₂×C₄	1	2	yes	—
96	C₄×#92420	C₂×C₄	1	2	yes	—
97	C₈×#6923	—	4	1	no	—
98	C₈×#6923	—	4	1	no	—
99	C₈×#6923	—	4	1	no	—
100	C₈×#6923	—	4	1	no	—
101	(C₂×#6923)⋊C₄	C₂×C₄	1	2	yes	—
102	(C₂×#6923)⋊C₄	C₂×C₄	1	2	yes	—
103	(C₂×#6923)⋊C₄	C₂×C₄	1	2	yes	—
104	(C₂×#6923)⋊C₄	C₂×C₄	1	2	yes	—
105	(C₂×#6923)⋊C₄	C₂×C₄	1	2	yes	—
106	(C₂×#6923)⋊C₄	C₂×C₄	1	2	yes	—
107	C₂²×C₄×D₆₁	C₂³	1	1	yes	characteristic
108	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
109	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
110	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
111	M₁₆×D₆₁	—	4	1	no	—
112	M₁₆×D₆₁	—	4	1	no	—
113	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
114	C₂×C₈×D₆₁	—	4	1	no	—
115	C₂×C₈×D₆₁	—	4	1	no	—
116	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
117	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
118	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
119	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
120	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
121	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
122	#14519736	C₂×C₄	1	1	yes	characteristic
123	#14519735	C₂×C₄	1	1	yes	characteristic
124	#14519735	C₂×C₄	1	1	yes	characteristic
125	#14519734	C₂×C₄	1	1	yes	characteristic
126	#14519734	C₂×C₄	1	1	yes	characteristic
127	#14519733	C₂×C₄	1	1	yes	characteristic
128	#14519733	C₂×C₄	1	1	yes	characteristic
129	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
131	C₂²⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
132	C₂²⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
133	C₄²×D₆₁	C₂³	1	1	yes	characteristic
134	C₄²×D₆₁	C₂³	1	1	yes	characteristic
135	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
136	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
137	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
138	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
139	#14519706	C₂×C₄	1	1	yes	characteristic
140	#14519706	C₂×C₄	1	1	yes	characteristic
141	#14519706	C₂×C₄	1	1	yes	characteristic
142	#14519706	C₂×C₄	1	1	yes	characteristic
143	#14519706	C₂×C₄	1	1	yes	characteristic
144	#14519706	C₂×C₄	1	1	yes	characteristic
145	#14519706	C₂×C₄	1	1	yes	characteristic
146	#14519706	C₂×C₄	1	1	yes	characteristic
147	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
148	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
149	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
150	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
151	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
152	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
153	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
154	C₂³×D₆₁	C₂²×C₄	1	1	yes	characteristic
155	C₂²×#6923	C₂²×C₄	1	2	yes	—
156	C₂²×#6923	C₂²×C₄	1	2	yes	—
157	C₂²×#6923	C₂²×C₄	1	2	yes	—
158	C₂²×#6923	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
160	C₂²×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₆₁	—	2	1	no	—
162	C₂×C₄×D₆₁	—	2	1	no	—
163	C₂×C₄×D₆₁	—	2	1	no	—
164	C₂×C₄×D₆₁	—	2	1	no	—
165	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
173	C₂²⋊#6923	—	2	4	no	—
174	C₂²⋊#6923	—	4	2	no	—
175	C₂×#92420	C₂²×C₄	1	2	yes	—
176	C₂×#92420	C₂²×C₄	1	2	yes	—
177	C₂×#92420	C₂²×C₄	1	2	yes	—
178	C₂×#92420	C₂²×C₄	1	2	yes	—
179	C₄⋊#6923	—	2	4	no	—
180	C₄⋊#6923	—	4	2	no	—
181	C₄×#6923	—	2	4	no	—
182	C₄×#6923	—	2	1	no	—
183	C₄×#6923	—	2	1	no	—
184	C₄×#6923	—	2	1	no	—
185	C₄×#6923	—	2	1	no	—
186	C₄×#6923	—	2	1	no	—
187	C₄×#6923	—	2	1	no	—
188	C₄×#6923	—	2	1	no	—
189	C₄×#6923	—	2	1	no	—
190	C₄×#6923	—	4	2	no	—
191	D₆₁⋊C₈	—	2	1	no	—
192	D₆₁⋊C₈	—	2	1	no	—
193	D₆₁⋊C₈	—	2	1	no	—
194	D₆₁⋊C₈	—	2	1	no	—
195	D₆₁⋊C₈	—	2	1	no	—
196	D₆₁⋊C₈	—	2	1	no	—
197	D₆₁⋊C₈	—	2	1	no	—
198	D₆₁⋊C₈	—	2	1	no	—
199	M₁₆×C₆₁	—	4	1	no	—
200	C₂×C₈×C₆₁	—	4	1	no	—
201	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
206	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
207	C₂²⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
208	C₂²⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
209	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
211	C₂²⋊Dic₆₁	C₄²	1	1	yes	characteristic
212	C₂²⋊Dic₆₁	C₄²	1	1	yes	characteristic
213	#11758198	C₄²	1	1	yes	characteristic
214	#11758198	C₄²	1	1	yes	characteristic
215	#11758198	C₄²	1	1	yes	characteristic
216	#11758198	C₄²	1	1	yes	characteristic
217	C₄⋊Dic₆₁	C₄²	1	1	yes	characteristic
218	C₄⋊Dic₆₁	C₄²	1	1	yes	characteristic
219	#11758196	C₄²	1	1	yes	characteristic
220	#11758196	C₄²	1	1	yes	characteristic
221	#11758196	C₄²	1	1	yes	characteristic
222	#11758196	C₄²	1	1	yes	characteristic
223	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
224	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
225	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
226	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
227	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
228	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
229	#11758194	—	4	1	no	—
230	C₂×#92418	—	4	1	no	—
231	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
232	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
233	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
234	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
235	#11758189	—	4	1	no	—
236	#11758189	—	4	1	no	—
237	C₈×D₆₁	—	2	1	no	—
238	C₈×D₆₁	—	2	1	no	—
239	C₈×D₆₁	—	2	1	no	—
240	C₈×D₆₁	—	2	1	no	—
241	C₈×D₆₁	—	2	1	no	—
242	C₈×D₆₁	—	2	1	no	—
243	C₈×D₆₁	—	2	1	no	—
244	C₈×D₆₁	—	2	1	no	—
245	C₈×D₆₁	—	4	1	no	—
246	C₈×D₆₁	—	4	1	no	—
247	C₂³×C₆₁	C₂×C₄²	1	1	yes	characteristic
248	C₂²×D₆₁	—	2	1	no	—
249	C₂²×D₆₁	—	2	1	no	—
250	C₂²×D₆₁	—	2	2	no	—
251	C₂²×D₆₁	—	2	2	no	—
252	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
253	C₂²×D₆₁	C₂³×C₄	1	1	yes	characteristic
254	C₂×#6923	—	2	2	no	—
255	C₂×#6923	—	2	2	no	—
256	C₂×#6923	—	2	2	no	—
257	C₂×#6923	—	2	2	no	—
258	C₂×#6923	—	2	2	no	—
259	C₂×#6923	—	2	2	no	—
260	C₂×#6923	—	2	2	no	—
261	C₂×#6923	—	2	2	no	—
262	C₂×#6923	—	2	2	no	—
263	C₂×#6923	—	2	2	no	—
264	C₂×#6923	—	2	2	no	—
265	C₂×#6923	#131	1	4	yes	—
266	C₂×C₄×C₆₁	—	2	1	no	—
267	C₂×C₄×C₆₁	—	2	1	no	—
268	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
269	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
270	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
271	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
272	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
273	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
274	C₂×Dic₆₁	—	2	1	no	—
275	C₂×Dic₆₁	—	2	1	no	—
276	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
277	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
278	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
279	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
280	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
281	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
282	C₄×D₆₁	—	2	1	no	—
283	C₄×D₆₁	—	2	1	no	—
284	C₄×D₆₁	—	2	2	no	—
285	C₄×D₆₁	—	2	2	no	—
286	C₄×D₆₁	—	2	2	no	—
287	C₄×D₆₁	—	2	2	no	—
288	C₄×D₆₁	—	2	1	no	—
289	C₄×D₆₁	—	2	1	no	—
290	C₄×D₆₁	—	2	1	no	—
291	C₄×D₆₁	—	2	1	no	—
292	C₄×D₆₁	H(5,𝔽₂)	1	1	yes	characteristic
293	C₄×D₆₁	H(5,𝔽₂)	1	1	yes	characteristic
294	C₄×D₆₁	2₋¹⁺⁴	1	1	yes	characteristic
295	C₄×D₆₁	2₋¹⁺⁴	1	1	yes	characteristic
296	#92420	—	2	2	no	—
297	#92420	—	2	2	no	—
298	#92420	—	2	2	no	—
299	#92420	—	2	2	no	—
300	C₈×C₆₁	—	2	1	no	—
301	C₈×C₆₁	—	2	1	no	—
302	C₈×C₆₁	—	2	1	no	—
303	C₈×C₆₁	—	2	1	no	—
304	#92418	—	2	1	no	—
305	#92418	—	2	1	no	—
306	#92418	—	2	1	no	—
307	#92418	—	2	1	no	—
308	#20553	—	61	1	no	maximal, Sylow
309	C₂²×C₆₁	—	2	1	no	—
310	C₂²×C₆₁	—	2	1	no	—
311	C₂²×C₆₁	—	2	1	no	—
312	C₂²×C₆₁	C₂²×C₄²	1	1	yes	characteristic
313	C₂×D₆₁	—	2	1	no	—
314	C₂×D₆₁	—	2	1	no	—
315	C₂×D₆₁	—	2	1	no	—
316	C₂×D₆₁	—	4	2	no	—
317	C₂×D₆₁	—	4	2	no	—
318	C₂×D₆₁	#520	1	1	yes	characteristic
319	C₂×D₆₁	#520	1	1	yes	characteristic
320	C₂×D₆₁	C₂×#131	1	2	yes	—
321	C₂×D₆₁	#568	1	2	yes	—
322	#6923	—	2	4	no	—
323	#6923	—	4	2	no	—
324	#6923	—	4	2	no	—
325	#6923	—	4	2	no	—
326	C₄×C₆₁	—	2	1	no	—
327	C₄×C₆₁	—	2	1	no	—
328	C₄×C₆₁	—	2	1	no	—
329	C₄×C₆₁	—	2	1	no	—
330	C₄×C₆₁	—	2	1	no	—
331	C₄×C₆₁	#518	1	1	yes	characteristic
332	C₄×C₆₁	#519	1	1	yes	characteristic
333	Dic₆₁	—	2	1	no	—
334	Dic₆₁	—	2	1	no	—
335	Dic₆₁	—	2	1	no	—
336	Dic₆₁	—	2	1	no	—
337	Dic₆₁	—	2	1	no	—
338	Dic₆₁	#520	1	1	yes	characteristic
339	Dic₆₁	#520	1	1	yes	characteristic
340	C₂×#433	—	61	1	no	—
341	C₂×#424	—	61	1	no	—
342	#2298	—	61	1	no	—
343	#1771	—	61	1	no	—
344	#1771	—	61	1	no	—
345	#1770	—	61	1	no	—
346	C₈×C₄⋊C₄	—	61	1	no	—
347	#1768	—	61	1	no	—
348	#1768	—	61	1	no	—
349	#1767	—	61	1	no	—
350	C₄×C₄⋊C₈	—	61	1	no	—
351	#1753	—	61	1	no	—
352	#1753	—	61	1	no	—
353	#1752	—	61	1	no	—
354	C₈×C₂²⋊C₄	—	61	1	no	—
355	C₂×C₆₁	—	4	1	no	—
356	C₂×C₆₁	#2274	1	1	yes	characteristic
357	C₂×C₆₁	C₄×#131	1	1	yes	characteristic
358	C₂×C₆₁	#2875	1	1	yes	characteristic
359	D₆₁	—	4	1	no	—
360	D₆₁	#2992	1	2	yes	—
361	D₆₁	#2993	1	2	yes	—
362	C₂²×M₁₆	—	61	1	no	—
363	C₂³×C₈	—	61	1	no	—
364	C₂×#117	—	61	1	no	—
365	#433	—	61	2	no	—
366	#433	—	61	2	no	—
367	#433	—	61	2	no	—
368	#433	—	61	2	no	—
369	#424	—	61	1	no	—
370	#424	—	61	1	no	—
371	#424	—	61	1	no	—
372	#424	—	61	1	no	—
373	#424	—	61	1	no	—
374	#424	—	61	1	no	—
375	#424	—	61	1	no	—
376	#424	#6923	1	1	yes	characteristic, complemented
377	C₂×C₄⋊C₈	—	61	1	no	—
378	C₂×C₄⋊C₈	—	61	1	no	—
379	C₂×C₄⋊C₈	—	61	1	no	—
380	C₂×C₄⋊C₈	—	61	1	no	—
381	C₂×C₄⋊C₈	—	61	1	no	—
382	C₂×C₄⋊C₈	—	61	1	no	—
383	C₂×C₂²⋊C₈	—	61	1	no	—
384	C₂×C₂²⋊C₈	—	61	1	no	—
385	C₂×#97	—	61	1	no	—
386	C₂×#97	—	61	1	no	—
387	C₂×#97	—	61	1	no	—
388	C₂×#97	—	61	1	no	—
389	C₂×#97	—	61	1	no	—
390	C₂×C₄×C₈	—	61	1	no	—
391	C₂×C₄×C₈	—	61	1	no	—
392	C₂×C₄×C₈	—	61	1	no	—
393	C₂×C₄×C₈	—	61	1	no	—
394	C₂×C₄×C₈	—	61	1	no	—
395	#388	—	61	2	no	—
396	#388	—	61	2	no	—
397	#387	—	61	2	no	—
398	#387	—	61	2	no	—
399	C₄×C₄⋊C₄	—	61	1	no	—
400	C₄×C₄⋊C₄	—	61	1	no	—
401	C₄×C₂²⋊C₄	—	61	1	no	—
402	C₄×C₂²⋊C₄	—	61	1	no	—
403	#376	—	61	1	no	—
404	C₄³	—	61	1	no	—
405	#336	—	61	1	no	—
406	#336	—	61	1	no	—
407	#336	—	61	1	no	—
408	#336	—	61	1	no	—
409	#336	—	61	1	no	—
410	#336	—	61	1	no	—
411	#336	—	61	1	no	—
412	#336	—	61	1	no	—
413	C₆₁	#20553	1	1	yes	characteristic, complemented, Sylow
414	C₂³×C₄	—	61	1	no	—
415	C₂×M₁₆	—	61	1	no	—
416	C₂×M₁₆	—	61	1	no	—
417	C₂×M₁₆	—	61	1	no	—
418	C₂×M₁₆	—	244	1	no	—
419	C₂×M₁₆	—	244	1	no	—
420	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic
421	C₂²×C₈	—	61	1	no	—
422	C₂²×C₈	—	61	1	no	—
423	C₂²×C₈	—	61	1	no	—
424	C₂²×C₈	—	61	1	no	—
425	C₂²×C₈	—	61	1	no	—
426	C₂²×C₈	—	61	1	no	—
427	C₂²×C₈	—	61	1	no	—
428	C₂²×C₈	—	61	1	no	—
429	C₂²×C₈	—	61	1	no	—
430	C₂²×C₈	—	61	1	no	—
431	C₂²×C₈	—	61	1	no	—
432	C₂²×C₈	—	244	1	no	—
433	C₂²×C₈	—	244	1	no	—
434	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
435	#117	—	61	1	no	—
436	#117	—	61	1	no	—
437	#117	—	61	1	no	—
438	#117	—	61	1	no	—
439	#117	—	61	1	no	—
440	#117	—	61	1	no	—
441	#117	—	61	1	no	—
442	#117	C₂×#6923	1	1	yes	characteristic
443	C₂×C₄⋊C₄	—	61	1	no	—
444	C₂×C₄⋊C₄	—	61	1	no	—
445	C₂×C₄⋊C₄	—	61	2	no	—
446	C₂×C₄⋊C₄	—	61	2	no	—
447	C₂×C₂²⋊C₄	—	61	1	no	—
448	C₂×C₂²⋊C₄	—	61	1	no	—
449	C₂×C₂²⋊C₄	—	61	2	no	—
450	C₂×C₂²⋊C₄	—	61	2	no	—
451	C₂×C₄²	—	61	1	no	—
452	C₂×C₄²	—	61	1	no	—
453	C₂×C₄²	—	61	2	no	—
454	C₂×C₄²	—	61	1	no	—
455	C₂×C₄²	—	61	1	no	—
456	C₂×C₄²	—	61	1	no	—
457	C₂×C₄²	—	61	1	no	—
458	C₂×C₄²	—	61	2	no	—
459	C₄⋊C₈	—	61	2	no	—
460	C₄⋊C₈	—	61	2	no	—
461	C₄⋊C₈	—	61	2	no	—
462	C₄⋊C₈	—	61	2	no	—
463	C₄⋊C₈	—	61	1	no	—
464	C₄⋊C₈	—	61	1	no	—
465	C₄⋊C₈	—	61	1	no	—
466	C₄⋊C₈	—	61	1	no	—
467	C₄⋊C₈	—	61	1	no	—
468	C₄⋊C₈	—	61	1	no	—
469	C₄⋊C₈	—	61	1	no	—
470	C₄⋊C₈	—	61	1	no	—
471	C₄⋊C₈	—	61	1	no	—
472	C₄⋊C₈	—	61	1	no	—
473	C₄⋊C₈	—	61	1	no	—
474	C₄⋊C₈	—	61	1	no	—
475	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic
476	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic
477	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic
478	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic
479	C₂²⋊C₈	—	61	2	no	—
480	C₂²⋊C₈	—	61	2	no	—
481	C₂²⋊C₈	—	61	2	no	—
482	C₂²⋊C₈	—	61	2	no	—
483	#97	—	61	2	no	—
484	#97	—	61	2	no	—
485	#97	—	244	1	no	—
486	#97	—	244	1	no	—
487	#97	—	244	1	no	—
488	#97	—	244	1	no	—
489	C₄×C₈	—	61	2	no	—
490	C₄×C₈	—	61	2	no	—
491	C₄×C₈	—	244	1	no	—
492	C₄×C₈	—	244	1	no	—
493	C₄×C₈	—	244	1	no	—
494	C₄×C₈	—	244	1	no	—
495	#95	—	61	2	no	—
496	#95	—	61	2	no	—
497	#95	—	61	2	no	—
498	#95	—	61	2	no	—
499	#95	—	61	2	no	—
500	#95	—	61	2	no	—
501	C₂⁴	—	61	1	no	—
502	C₂²×C₄	—	61	1	no	—
503	C₂²×C₄	—	61	2	no	—
504	C₂²×C₄	—	61	1	no	—
505	C₂²×C₄	—	61	1	no	—
506	C₂²×C₄	—	61	1	no	—
507	C₂²×C₄	—	61	1	no	—
508	C₂²×C₄	—	61	1	no	—
509	C₂²×C₄	—	61	1	no	—
510	C₂²×C₄	—	61	1	no	—
511	C₂²×C₄	—	61	1	no	—
512	C₂²×C₄	—	61	2	no	—
513	C₂²×C₄	—	61	2	no	—
514	C₂²×C₄	—	61	2	no	—
515	C₂²×C₄	—	122	1	no	—
516	C₂²×C₄	—	122	1	no	—
517	C₂²×C₄	—	122	1	no	—
518	C₂²×C₄	—	122	1	no	—
519	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
520	M₁₆	—	4	1	no	—
521	M₁₆	—	244	1	no	—
522	M₁₆	—	244	1	no	—
523	M₁₆	—	244	1	no	—
524	C₂×C₈	—	4	1	no	—
525	C₂×C₈	—	61	2	no	—
526	C₂×C₈	—	61	2	no	—
527	C₂×C₈	—	61	2	no	—
528	C₂×C₈	—	61	2	no	—
529	C₂×C₈	—	61	1	no	—
530	C₂×C₈	—	61	1	no	—
531	C₂×C₈	—	61	1	no	—
532	C₂×C₈	—	61	1	no	—
533	C₂×C₈	—	122	1	no	—
534	C₂×C₈	—	122	1	no	—
535	C₂×C₈	—	122	1	no	—
536	C₂×C₈	—	122	1	no	—
537	C₂×C₈	—	122	1	no	—
538	C₂×C₈	—	122	1	no	—
539	C₂×C₈	—	122	1	no	—
540	C₂×C₈	—	122	1	no	—
541	C₂×C₈	—	122	1	no	—
542	C₂×C₈	—	122	1	no	—
543	C₂×C₈	—	122	1	no	—
544	C₂×C₈	—	122	1	no	—
545	C₂×C₈	—	122	1	no	—
546	C₂×C₈	—	122	1	no	—
547	C₂×C₈	—	122	1	no	—
548	C₂×C₈	—	122	1	no	—
549	C₂×C₈	—	244	1	no	—
550	C₂×C₈	—	244	1	no	—
551	C₂×C₈	—	244	1	no	—
552	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
553	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
554	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
555	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
556	C₄⋊C₄	—	61	1	no	—
557	C₄⋊C₄	—	61	1	no	—
558	C₄⋊C₄	—	61	1	no	—
559	C₄⋊C₄	—	61	1	no	—
560	C₄⋊C₄	—	61	1	no	—
561	C₄⋊C₄	—	61	1	no	—
562	C₄⋊C₄	—	122	4	no	—
563	C₄⋊C₄	—	244	2	no	—
564	C₄⋊C₄	C₄×#6923	1	1	yes	characteristic
565	C₄⋊C₄	C₄×#6923	1	1	yes	characteristic
566	C₂²⋊C₄	—	61	1	no	—
567	C₂²⋊C₄	—	61	1	no	—
568	C₂²⋊C₄	—	61	1	no	—
569	C₂²⋊C₄	—	61	1	no	—
570	C₂²⋊C₄	—	61	1	no	—
571	C₂²⋊C₄	—	61	1	no	—
572	C₂²⋊C₄	—	122	4	no	—
573	C₂²⋊C₄	—	244	2	no	—
574	C₂²⋊C₄	C₄×#6923	1	1	yes	characteristic
575	C₂²⋊C₄	C₄×#6923	1	1	yes	characteristic
576	C₄²	—	61	1	no	—
577	C₄²	—	61	1	no	—
578	C₄²	—	61	1	no	—
579	C₄²	—	61	1	no	—
580	C₄²	—	61	1	no	—
581	C₄²	—	61	1	no	—
582	C₄²	—	122	1	no	—
583	C₄²	—	122	1	no	—
584	C₄²	—	122	1	no	—
585	C₄²	—	122	1	no	—
586	C₄²	—	122	1	no	—
587	C₄²	—	122	1	no	—
588	C₄²	—	122	1	no	—
589	C₄²	—	122	1	no	—
590	C₄²	—	122	4	no	—
591	C₄²	—	244	2	no	—
592	C₄²	C₂²×#6923	1	1	yes	characteristic
593	C₄²	C₂²×#6923	1	1	yes	characteristic
594	C₂³	—	61	1	no	—
595	C₂³	—	61	1	no	—
596	C₂³	—	122	2	no	—
597	C₂³	—	122	2	no	—
598	C₂³	—	122	1	no	—
599	C₂³	—	122	1	no	—
600	C₂³	C₂×C₄×#6923	1	1	yes	characteristic
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	61	1	no	—
604	C₂×C₄	—	61	1	no	—
605	C₂×C₄	—	61	1	no	—
606	C₂×C₄	—	61	1	no	—
607	C₂×C₄	—	61	1	no	—
608	C₂×C₄	—	61	4	no	—
609	C₂×C₄	—	61	1	no	—
610	C₂×C₄	—	61	1	no	—
611	C₂×C₄	—	61	1	no	—
612	C₂×C₄	—	61	1	no	—
613	C₂×C₄	—	61	1	no	—
614	C₂×C₄	—	122	1	no	—
615	C₂×C₄	—	122	1	no	—
616	C₂×C₄	—	122	2	no	—
617	C₂×C₄	—	122	2	no	—
618	C₂×C₄	—	122	2	no	—
619	C₂×C₄	—	122	2	no	—
620	C₂×C₄	—	122	1	no	—
621	C₂×C₄	—	122	1	no	—
622	C₂×C₄	—	122	1	no	—
623	C₂×C₄	—	122	1	no	—
624	C₂×C₄	—	122	2	no	—
625	C₂×C₄	—	122	2	no	—
626	C₂×C₄	—	122	1	no	—
627	C₂×C₄	—	122	1	no	—
628	C₂×C₄	—	122	2	no	—
629	C₂×C₄	—	122	2	no	—
630	C₂×C₄	—	122	2	no	—
631	C₂×C₄	—	122	2	no	—
632	C₂×C₄	—	122	2	no	—
633	C₂×C₄	—	122	2	no	—
634	C₂×C₄	—	122	2	no	—
635	C₂×C₄	—	122	2	no	—
636	C₂×C₄	—	122	2	no	—
637	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
638	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
639	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
640	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
641	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
642	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
643	C₈	—	2	1	no	—
644	C₈	—	2	1	no	—
645	C₈	—	2	1	no	—
646	C₈	—	2	1	no	—
647	C₈	—	122	2	no	—
648	C₈	—	122	2	no	—
649	C₈	—	122	2	no	—
650	C₈	—	122	2	no	—
651	C₈	—	122	1	no	—
652	C₈	—	122	1	no	—
653	C₈	—	122	1	no	—
654	C₈	—	122	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	61	2	no	—
659	C₂²	—	61	2	no	—
660	C₂²	—	61	1	no	—
661	C₂²	—	61	1	no	—
662	C₂²	—	122	1	no	—
663	C₂²	—	122	1	no	—
664	C₂²	—	122	1	no	—
665	C₂²	—	244	2	no	—
666	C₂²	—	244	2	no	—
667	C₂²	C₂²×C₄×#6923	1	1	yes	characteristic
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	61	1	no	—
674	C₄	—	61	1	no	—
675	C₄	—	122	4	no	—
676	C₄	—	122	1	no	—
677	C₄	—	122	1	no	—
678	C₄	—	122	1	no	—
679	C₄	—	122	1	no	—
680	C₄	—	122	1	no	—
681	C₄	—	244	2	no	—
682	C₄	—	244	2	no	—
683	C₄	—	244	2	no	—
684	C₄	#16840829	1	1	yes	characteristic
685	C₄	#16840830	1	1	yes	characteristic
686	C₂	—	4	1	no	—
687	C₂	—	61	2	no	—
688	C₂	—	61	2	no	—
689	C₂	—	244	1	no	—
690	C₂	#21462257	1	1	yes	characteristic
691	C₂	#131×#6923	1	1	yes	characteristic
692	C₂	#21462389	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₄²
Fitting	C₆₁×#424	C₄
prime radical	C₂³×D₆₁	C₂²×C₄
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	#424	#6923
hypocenter	C₆₁	#20553
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #424

Complements

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

N	H ≅ G/N	type
3. #21461620	C₂	semidirect
4. #21461620	C₂	semidirect
5. #21461616	C₂	semidirect
6. #21461612	C₂	semidirect
7. #21461608	C₂	semidirect
8. #21461608	C₂	semidirect
9. #21461606	C₂	semidirect
10. C₄⋊C₈×#6923	C₂	semidirect
16. #16840787	C₄	semidirect
17. #16840787	C₄	semidirect
18. #16840786	C₄	semidirect
19. #16840786	C₄	semidirect
55. #16839790	C₄	semidirect
56. #16839789	C₄	semidirect
57. #16839788	C₄	semidirect
58. #16839787	C₄	semidirect
59. #16839787	C₄	semidirect
60. #16839787	C₄	semidirect
61. #16839787	C₄	semidirect
66. C₆₁×#424	C₄	semidirect
376. #424	#6923	semidirect
413. C₆₁	#20553	semidirect

Maximal subgroups

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

subgroup	index
D₆₁⋊#433	2
#21462281	2
#21461620	2
#21461616	2
#21461612	2
#21461608	2
#21461606	2
C₄⋊C₈×#6923	2
#21461559	2
#21461555	2
C₈×C₂²⋊#6923	2
#424×D₆₁	2
#20553	61