Subgroups — #29701788

Order 15616.

788 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839893	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16839789	C₂	1	1	yes	maximal, characteristic
3	#21446756	C₂	1	1	yes	maximal, characteristic, complemented
4	#21446543	C₂	1	1	yes	maximal, characteristic, complemented
5	#21446543	C₂	1	1	yes	maximal, characteristic, complemented
6	#21446543	C₂	1	1	yes	maximal, characteristic, complemented
7	#21446385	C₂	1	1	yes	maximal, characteristic, complemented
8	#21446378	C₂	1	1	yes	maximal, characteristic, complemented
9	#21446004	C₂	1	1	yes	maximal, characteristic
10	#21445999	C₂	1	1	yes	maximal, characteristic
11	#21445688	C₂	1	1	yes	maximal, characteristic, complemented
12	#21445603	C₂	1	1	yes	maximal, characteristic
13	#21445597	C₂	1	1	yes	maximal, characteristic
14	#21445585	C₂	1	1	yes	maximal, characteristic
15	C₆₁×#2396	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11758194	C₂²	1	1	yes	characteristic
17	C₂³×#92418	C₂²	1	1	yes	characteristic
18	#16839893	—	2	4	no	—
19	#16839789	—	2	4	no	—
20	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊#92418	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊#92418	C₂²	1	1	yes	characteristic
30	C₂×#14519688	C₂²	1	1	yes	characteristic
31	C₂×#14519688	C₂²	1	1	yes	characteristic
32	C₂×#14519688	C₂²	1	1	yes	characteristic
33	C₂×#14519688	C₂²	1	1	yes	characteristic
34	C₂×C₄×#92418	C₂²	1	1	yes	characteristic
35	C₂×C₄×#92418	C₂²	1	1	yes	characteristic
36	#16839517	C₂²	1	1	yes	characteristic
37	#16839517	C₂²	1	1	yes	characteristic
38	#16839517	C₂²	1	1	yes	characteristic
39	#16839517	C₂²	1	1	yes	characteristic
40	#16839517	C₂²	1	1	yes	characteristic
41	#16839517	C₂²	1	1	yes	characteristic
42	#16839517	C₂²	1	1	yes	characteristic
43	#16839517	C₂²	1	1	yes	characteristic
44	#16839517	C₂²	1	1	yes	characteristic
45	#16839517	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#400	C₄	1	1	yes	characteristic
49	C₆₁×#399	C₄	1	1	yes	characteristic
50	C₆₁×#398	C₄	1	1	yes	characteristic
51	C₆₁×#398	C₄	1	1	yes	characteristic
52	C₆₁×#396	C₄	1	1	yes	characteristic
53	C₆₁×#396	C₄	1	1	yes	characteristic
54	C₆₁×#395	C₄	1	1	yes	characteristic
55	C₆₁×#393	C₄	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
61	C₂×#11758194	—	2	2	no	—
62	C₂×#11758194	—	2	2	no	—
63	C₂×#11758194	—	4	1	no	—
64	C₂²×#92418	—	2	2	no	—
65	C₂²×#92418	—	2	2	no	—
66	C₂²×#92418	—	4	1	no	—
67	C₂²×#92418	C₂³	1	1	yes	characteristic
68	C₂²×#92418	C₂³	1	1	yes	characteristic
69	C₂²×#92418	C₂³	1	1	yes	characteristic
70	C₂²×#92418	C₂³	1	1	yes	characteristic
71	C₂²×#92418	C₂³	1	1	yes	characteristic
72	C₂²×#92418	C₂³	1	1	yes	characteristic
73	C₂²×#92418	C₂³	1	1	yes	characteristic
74	C₂²×#92418	C₂³	1	1	yes	characteristic
75	C₄⋊#92418	—	2	2	no	—
76	C₄⋊#92418	—	2	2	no	—
77	C₄⋊#92418	—	2	2	no	—
78	C₄⋊#92418	—	2	2	no	—
79	C₄⋊#92418	—	2	2	no	—
80	C₄⋊#92418	—	4	1	no	—
81	C₄⋊#92418	—	4	1	no	—
82	C₄⋊#92418	D₄	1	4	yes	—
83	C₂²⋊#92418	—	2	2	no	—
84	C₂²⋊#92418	Q₈	1	4	yes	complemented
85	#14519688	—	2	2	no	—
86	#14519688	—	2	2	no	—
87	#14519688	—	4	1	no	—
88	#14519688	—	4	1	no	—
89	C₄×#92418	—	2	2	no	—
90	C₄×#92418	—	2	2	no	—
91	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
92	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
93	C₄×Q₈×C₆₁	—	2	2	no	—
94	C₄×Q₈×C₆₁	—	2	2	no	—
95	#117×C₆₁	—	2	2	no	—
96	#117×C₆₁	—	2	2	no	—
97	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
120	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
121	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
122	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
123	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
124	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
125	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
126	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
127	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
128	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
129	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
130	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×Q₈×C₆₁	—	2	2	no	—
132	C₂×Q₈×C₆₁	—	2	2	no	—
133	C₂×Q₈×C₆₁	—	4	1	no	—
134	C₂²×C₄×C₆₁	—	2	1	no	—
135	C₂²×C₄×C₆₁	—	2	1	no	—
136	C₂²×C₄×C₆₁	—	2	1	no	—
137	C₂²×C₄×C₆₁	—	2	1	no	—
138	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
152	C₂²×C₄×C₆₁	#41	1	2	yes	—
153	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
154	C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₄⋊C₄×C₆₁	—	2	2	no	—
156	C₄⋊C₄×C₆₁	—	2	2	no	—
157	C₄⋊C₄×C₆₁	—	2	2	no	—
158	C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	—	4	1	no	—
161	C₄⋊C₄×C₆₁	—	4	1	no	—
162	C₄⋊C₄×C₆₁	—	4	1	no	—
163	C₄⋊C₄×C₆₁	—	4	1	no	—
164	C₄⋊C₄×C₆₁	—	4	1	no	—
165	C₂²⋊C₄×C₆₁	—	2	2	no	—
166	C₂²⋊C₄×C₆₁	—	2	2	no	—
167	C₂²⋊C₄×C₆₁	—	2	2	no	—
168	C₂²⋊C₄×C₆₁	—	4	1	no	—
169	C₂²⋊C₄×C₆₁	—	4	1	no	—
170	C₂²⋊C₄×C₆₁	—	4	1	no	—
171	C₄²×C₆₁	—	2	1	no	—
172	C₄²×C₆₁	—	2	1	no	—
173	C₄²×C₆₁	—	2	1	no	—
174	C₄²×C₆₁	—	2	1	no	—
175	C₄²×C₆₁	—	2	1	no	—
176	C₄²×C₆₁	—	2	1	no	—
177	C₄²×C₆₁	—	2	1	no	—
178	C₄²×C₆₁	—	2	1	no	—
179	C₄²×C₆₁	—	2	1	no	—
180	C₄²×C₆₁	—	2	1	no	—
181	C₄²×C₆₁	C₂×D₄	1	2	yes	—
182	C₄²×C₆₁	#41	1	2	yes	—
183	#11758194	—	4	4	no	—
184	C₂×#92418	—	2	1	no	—
185	C₂×#92418	—	2	1	no	—
186	C₂×#92418	—	2	1	no	—
187	C₂×#92418	—	2	1	no	—
188	C₂×#92418	—	2	1	no	—
189	C₂×#92418	—	2	1	no	—
190	C₂×#92418	—	2	1	no	—
191	C₂×#92418	—	2	1	no	—
192	C₂×#92418	—	2	1	no	—
193	C₂×#92418	—	2	1	no	—
194	C₂×#92418	—	2	1	no	—
195	C₂×#92418	—	2	1	no	—
196	C₂×#92418	—	2	1	no	—
197	C₂×#92418	—	2	1	no	—
198	C₂×#92418	—	2	1	no	—
199	C₂×#92418	—	2	1	no	—
200	C₂×#92418	—	2	1	no	—
201	C₂×#92418	—	2	1	no	—
202	C₂×#92418	—	2	1	no	—
203	C₂×#92418	—	2	1	no	—
204	C₂×#92418	—	4	4	no	—
205	C₂×#92418	C₂×D₄	1	2	yes	—
206	C₂×#92418	C₂×D₄	1	2	yes	—
207	C₂×#92418	C₂×Q₈	1	2	yes	—
208	C₂×#92418	C₂×Q₈	1	2	yes	—
209	C₂³×C₆₁	—	2	1	no	—
210	C₂³×C₆₁	—	2	1	no	—
211	C₂³×C₆₁	—	2	1	no	—
212	C₂³×C₆₁	—	2	1	no	—
213	C₂³×C₆₁	—	2	1	no	—
214	C₂³×C₆₁	—	2	1	no	—
215	C₂³×C₆₁	C₄×Q₈	1	2	yes	—
216	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
217	Q₈×C₆₁	—	4	4	no	—
218	C₂×C₄×C₆₁	—	2	1	no	—
219	C₂×C₄×C₆₁	—	2	1	no	—
220	C₂×C₄×C₆₁	—	2	1	no	—
221	C₂×C₄×C₆₁	—	2	1	no	—
222	C₂×C₄×C₆₁	—	2	1	no	—
223	C₂×C₄×C₆₁	—	2	1	no	—
224	C₂×C₄×C₆₁	—	2	1	no	—
225	C₂×C₄×C₆₁	—	2	1	no	—
226	C₂×C₄×C₆₁	—	2	2	no	—
227	C₂×C₄×C₆₁	—	2	2	no	—
228	C₂×C₄×C₆₁	—	2	2	no	—
229	C₂×C₄×C₆₁	—	2	2	no	—
230	C₂×C₄×C₆₁	—	2	1	no	—
231	C₂×C₄×C₆₁	—	2	1	no	—
232	C₂×C₄×C₆₁	—	2	1	no	—
233	C₂×C₄×C₆₁	—	2	1	no	—
234	C₂×C₄×C₆₁	—	2	1	no	—
235	C₂×C₄×C₆₁	—	2	1	no	—
236	C₂×C₄×C₆₁	—	2	1	no	—
237	C₂×C₄×C₆₁	—	2	1	no	—
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	2	1	no	—
240	C₂×C₄×C₆₁	—	2	1	no	—
241	C₂×C₄×C₆₁	—	2	1	no	—
242	C₂×C₄×C₆₁	—	2	1	no	—
243	C₂×C₄×C₆₁	—	2	1	no	—
244	C₂×C₄×C₆₁	—	2	1	no	—
245	C₂×C₄×C₆₁	—	2	1	no	—
246	C₂×C₄×C₆₁	—	2	1	no	—
247	C₂×C₄×C₆₁	—	2	1	no	—
248	C₂×C₄×C₆₁	—	2	1	no	—
249	C₂×C₄×C₆₁	—	2	1	no	—
250	C₂×C₄×C₆₁	—	2	1	no	—
251	C₂×C₄×C₆₁	—	2	1	no	—
252	C₂×C₄×C₆₁	—	2	1	no	—
253	C₂×C₄×C₆₁	—	2	1	no	—
254	C₂×C₄×C₆₁	—	2	1	no	—
255	C₂×C₄×C₆₁	—	2	1	no	—
256	C₂×C₄×C₆₁	—	2	1	no	—
257	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
258	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
259	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
260	C₂×C₄×C₆₁	#131	1	2	yes	—
261	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
263	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
267	#92418	—	2	2	no	—
268	#92418	—	2	2	no	—
269	#92418	—	2	2	no	—
270	#92418	—	2	2	no	—
271	#92418	—	4	1	no	—
272	#92418	—	4	1	no	—
273	#92418	—	4	1	no	—
274	#92418	—	4	1	no	—
275	#22960	—	61	1	no	maximal, Sylow
276	C₂²×C₆₁	—	2	2	no	—
277	C₂²×C₆₁	—	2	2	no	—
278	C₂²×C₆₁	—	2	2	no	—
279	C₂²×C₆₁	—	4	1	no	—
280	C₂²×C₆₁	—	4	1	no	—
281	C₂²×C₆₁	—	4	1	no	—
282	C₂²×C₆₁	—	4	1	no	—
283	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
284	C₂²×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
285	C₂²×C₆₁	#520	1	1	yes	characteristic
286	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
287	C₂²×C₆₁	#568	1	1	yes	characteristic
288	C₂²×C₆₁	#568	1	1	yes	characteristic
289	C₂²×C₆₁	#568	1	1	yes	characteristic
290	C₄×C₆₁	—	2	2	no	—
291	C₄×C₆₁	—	2	2	no	—
292	C₄×C₆₁	—	2	2	no	—
293	C₄×C₆₁	—	2	2	no	—
294	C₄×C₆₁	—	4	1	no	—
295	C₄×C₆₁	—	4	1	no	—
296	C₄×C₆₁	—	4	1	no	—
297	C₄×C₆₁	—	4	1	no	—
298	C₄×C₆₁	—	4	1	no	—
299	C₄×C₆₁	—	4	1	no	—
300	C₄×C₆₁	—	4	1	no	—
301	C₄×C₆₁	—	4	1	no	—
302	C₄×C₆₁	—	4	1	no	—
303	C₄×C₆₁	#546	1	1	yes	characteristic
304	C₄×C₆₁	D₄×Q₈	1	1	yes	characteristic
305	C₄×C₆₁	#552	1	1	yes	characteristic
306	C₄×C₆₁	#554	1	1	yes	characteristic
307	C₂×#446	—	61	1	no	—
308	C₂×#424	—	61	1	no	—
309	#2396	D₆₁	1	1	yes	characteristic
310	#1984	—	61	1	no	—
311	#1940	—	61	1	no	—
312	#1940	—	61	1	no	—
313	#1940	—	61	1	no	—
314	#1917	—	61	1	no	—
315	#1916	—	61	1	no	—
316	#1851	—	61	1	no	—
317	#1850	—	61	1	no	—
318	#1770	—	61	1	no	—
319	#1753	—	61	1	no	—
320	#1752	—	61	1	no	—
321	#1750	—	61	1	no	—
322	C₂×C₆₁	—	4	2	no	—
323	C₂×C₆₁	#2360	1	1	yes	characteristic
324	C₂×C₆₁	#2932	1	1	yes	characteristic
325	C₂×C₆₁	#2933	1	1	yes	characteristic
326	C₂×C₆₁	#2961	1	1	yes	characteristic
327	C₂×C₆₁	#2962	1	1	yes	characteristic
328	C₂×C₆₁	#2993	1	1	yes	characteristic
329	C₂×C₆₁	#2995	1	1	yes	characteristic
330	C₂²×M₁₆	—	61	1	no	—
331	C₂³×C₈	—	61	1	no	—
332	C₂×C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic
333	C₂×#117	C₂×D₆₁	1	1	yes	characteristic
334	#446	—	122	4	no	—
335	#424	—	122	4	no	—
336	C₂×C₄⋊C₈	—	61	1	no	—
337	C₂×C₄⋊C₈	—	61	1	no	—
338	C₂×C₄⋊C₈	—	61	1	no	—
339	C₂×C₄⋊C₈	—	61	1	no	—
340	C₂×C₄⋊C₈	—	61	1	no	—
341	C₂×C₄⋊C₈	—	61	1	no	—
342	C₂×C₄⋊C₈	—	61	1	no	—
343	C₂×C₄⋊C₈	—	61	1	no	—
344	C₂×C₂²⋊C₈	—	61	1	no	—
345	C₂×C₂²⋊C₈	—	61	1	no	—
346	C₂×#97	—	61	1	no	—
347	C₂×#97	—	61	1	no	—
348	C₂×#97	—	61	1	no	—
349	C₂×#97	—	61	1	no	—
350	C₂×C₄×C₈	—	61	1	no	—
351	C₂×C₄×C₈	—	61	1	no	—
352	#400	Dic₆₁	1	1	yes	characteristic
353	#399	Dic₆₁	1	1	yes	characteristic
354	#398	Dic₆₁	1	1	yes	characteristic
355	#398	Dic₆₁	1	1	yes	characteristic
356	#396	Dic₆₁	1	1	yes	characteristic
357	#396	Dic₆₁	1	1	yes	characteristic
358	#395	Dic₆₁	1	1	yes	characteristic
359	#393	Dic₆₁	1	1	yes	characteristic
360	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
361	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
362	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
363	C₄×C₂²⋊C₄	C₂×D₆₁	1	1	yes	characteristic
364	C₄×C₂²⋊C₄	C₂×D₆₁	1	1	yes	characteristic
365	#336	—	61	1	no	—
366	#336	—	61	1	no	—
367	#336	—	61	1	no	—
368	#336	—	61	1	no	—
369	#336	—	61	1	no	—
370	#336	—	61	1	no	—
371	#336	—	61	1	no	—
372	#336	—	61	1	no	—
373	#336	—	61	1	no	—
374	#336	—	61	1	no	—
375	C₆₁	#22960	1	1	yes	characteristic, complemented, Sylow
376	C₂²×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
377	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
378	C₂×M₁₆	—	122	2	no	—
379	C₂×M₁₆	—	122	2	no	—
380	C₂×M₁₆	—	244	1	no	—
381	C₂²×C₈	—	61	1	no	—
382	C₂²×C₈	—	61	1	no	—
383	C₂²×C₈	—	61	1	no	—
384	C₂²×C₈	—	61	1	no	—
385	C₂²×C₈	—	61	1	no	—
386	C₂²×C₈	—	61	1	no	—
387	C₂²×C₈	—	61	1	no	—
388	C₂²×C₈	—	61	1	no	—
389	C₂²×C₈	—	122	2	no	—
390	C₂²×C₈	—	122	2	no	—
391	C₂²×C₈	—	244	1	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	#117	—	2	2	no	—
395	#117	—	2	2	no	—
396	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
413	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
414	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
415	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
416	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
417	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
418	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
419	C₄⋊C₈	—	61	4	no	—
420	C₄⋊C₈	—	122	2	no	—
421	C₄⋊C₈	—	122	2	no	—
422	C₄⋊C₈	—	122	2	no	—
423	C₄⋊C₈	—	122	2	no	—
424	C₄⋊C₈	—	122	2	no	—
425	C₄⋊C₈	—	244	1	no	—
426	C₄⋊C₈	—	244	1	no	—
427	C₂²⋊C₈	—	61	4	no	—
428	C₂²⋊C₈	—	122	2	no	—
429	#97	—	122	2	no	—
430	#97	—	122	2	no	—
431	#97	—	244	1	no	—
432	#97	—	244	1	no	—
433	C₄×C₈	—	122	2	no	—
434	C₄×C₈	—	122	2	no	—
435	#95	C₂×Dic₆₁	1	1	yes	characteristic
436	#95	C₂×Dic₆₁	1	1	yes	characteristic
437	#95	C₂×Dic₆₁	1	1	yes	characteristic
438	#95	C₂×Dic₆₁	1	1	yes	characteristic
439	#95	C₂×Dic₆₁	1	1	yes	characteristic
440	#95	C₂×Dic₆₁	1	1	yes	characteristic
441	#95	C₂×Dic₆₁	1	1	yes	characteristic
442	#95	C₂×Dic₆₁	1	1	yes	characteristic
443	#95	C₂×Dic₆₁	1	1	yes	characteristic
444	#95	C₂×Dic₆₁	1	1	yes	characteristic
445	C₂⁴	C₂²×Dic₆₁	1	1	yes	characteristic
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	4	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	Q₈×D₆₁	1	2	yes	—
454	C₂²×C₄	#11758226	1	2	yes	—
455	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
456	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
457	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
459	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
461	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
462	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
463	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
464	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
465	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
466	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
467	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
468	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
469	M₁₆	—	244	4	no	—
470	C₂×C₈	—	61	2	no	—
471	C₂×C₈	—	61	2	no	—
472	C₂×C₈	—	61	2	no	—
473	C₂×C₈	—	61	2	no	—
474	C₂×C₈	—	122	1	no	—
475	C₂×C₈	—	122	1	no	—
476	C₂×C₈	—	122	1	no	—
477	C₂×C₈	—	122	1	no	—
478	C₂×C₈	—	122	1	no	—
479	C₂×C₈	—	122	1	no	—
480	C₂×C₈	—	122	1	no	—
481	C₂×C₈	—	122	1	no	—
482	C₂×C₈	—	122	1	no	—
483	C₂×C₈	—	122	1	no	—
484	C₂×C₈	—	122	1	no	—
485	C₂×C₈	—	122	1	no	—
486	C₂×C₈	—	122	1	no	—
487	C₂×C₈	—	122	1	no	—
488	C₂×C₈	—	122	1	no	—
489	C₂×C₈	—	122	1	no	—
490	C₂×C₈	—	122	1	no	—
491	C₂×C₈	—	122	1	no	—
492	C₂×C₈	—	122	1	no	—
493	C₂×C₈	—	122	1	no	—
494	C₂×C₈	—	244	4	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	D₄×D₆₁	1	2	yes	—
523	C₄²	#11758224	1	2	yes	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	Q₈×Dic₆₁	1	2	yes	—
531	C₂³	C₂³×Dic₆₁	1	1	yes	characteristic
532	Q₈	—	4	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
573	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
574	C₂×C₄	Q₈×Dic₆₁	1	2	yes	—
575	C₂×C₄	#14519784	1	2	yes	—
576	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
577	C₂×C₄	C₂×Q₈×D₆₁	1	1	yes	characteristic
578	C₂×C₄	C₂×#11758224	1	1	yes	characteristic
579	C₂×C₄	C₂×#11758226	1	1	yes	characteristic
580	C₂×C₄	#14519823	1	1	yes	characteristic
581	C₂×C₄	#14519824	1	1	yes	characteristic
582	C₈	—	122	2	no	—
583	C₈	—	122	2	no	—
584	C₈	—	122	2	no	—
585	C₈	—	122	2	no	—
586	C₈	—	244	1	no	—
587	C₈	—	244	1	no	—
588	C₈	—	244	1	no	—
589	C₈	—	244	1	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	C₂×D₄×Dic₆₁	1	1	yes	characteristic
598	C₂²	C₂×Q₈×Dic₆₁	1	1	yes	characteristic
599	C₂²	#16840245	1	1	yes	characteristic
600	C₂²	C₂×#14519784	1	1	yes	characteristic
601	C₂²	#16840529	1	1	yes	characteristic
602	C₂²	#16840529	1	1	yes	characteristic
603	C₂²	#16840529	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	#16840403	1	1	yes	characteristic
618	C₄	#16840425	1	1	yes	characteristic
619	C₄	#16840454	1	1	yes	characteristic
620	C₄	#16840470	1	1	yes	characteristic
621	C₂	—	4	2	no	—
622	C₂	#21448828	1	1	yes	characteristic
623	C₂	#21454537	1	1	yes	characteristic
624	C₂	#21454546	1	1	yes	characteristic
625	C₂	#21454760	1	1	yes	characteristic
626	C₂	#21454768	1	1	yes	characteristic
627	C₂	#21454968	1	1	yes	characteristic
628	C₂	#21454989	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₁
commutator, socle	C₂³×C₆₁	C₂³×C₄
Fitting	C₆₁×#2396	C₂
prime radical	C₂⁴×C₆₁	C₂²×C₄
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	#2396	D₆₁
hypocenter	C₆₁	#22960
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ #2396

Complements

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

N	H ≅ G/N	type
1. C₂×#16839893	C₂	semidirect
3. #21446756	C₂	semidirect
4. #21446543	C₂	semidirect
5. #21446543	C₂	semidirect
6. #21446543	C₂	semidirect
7. #21446385	C₂	semidirect
8. #21446378	C₂	semidirect
11. #21445688	C₂	semidirect
84. C₂²⋊#92418	Q₈	semidirect
375. C₆₁	#22960	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16839893	2
C₂×#16839789	2
#21446756	2
#21446543	2
#21446385	2
#21446378	2
#21446004	2
#21445999	2
#21445688	2
#21445603	2
#21445597	2
#21445585	2
C₆₁×#2396	2
#22960	61