Subgroups — #30615418

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462297	C₂	1	2	yes	maximal
2	#21461756	C₂	1	1	yes	maximal, characteristic, complemented
3	#21461755	C₂	1	1	yes	maximal, characteristic, complemented
4	#21461742	C₂	1	2	yes	maximal, complemented
5	#21461697	C₂	1	2	yes	maximal
6	#21461696	C₂	1	2	yes	maximal
7	#21461633	C₂	1	2	yes	maximal, complemented
8	C₄×#14519846	C₂	1	2	yes	maximal, complemented
9	#405×D₆₁	C₂	1	1	yes	maximal, characteristic
10	C₂×#14519846	C₂²	1	2	yes	—
11	C₂×#14519846	C₂²	1	2	yes	—
12	C₂×#14519846	C₂²	1	2	yes	—
13	C₂×#14519845	C₂²	1	2	yes	—
14	#16840712	—	2	4	no	—
15	#16840711	—	2	4	no	—
16	#16840708	C₂²	1	2	yes	—
17	#16840706	C₂²	1	2	yes	—
18	#16840704	C₂²	1	4	yes	—
19	C₄×C₄⋊#6923	C₂²	1	4	yes	—
20	#16840636	C₂²	1	4	yes	—
21	#16840636	C₂²	1	4	yes	—
22	C₂×M₁₆×D₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₆₁	C₂²	1	1	yes	characteristic
24	#117×D₆₁	C₂²	1	1	yes	characteristic
25	#16839720	C₄	1	1	yes	characteristic, complemented
26	#16839719	C₄	1	1	yes	characteristic, complemented
27	#16839719	C₄	1	1	yes	characteristic, complemented
28	#16839718	C₄	1	1	yes	characteristic, complemented
29	#16839717	C₄	1	1	yes	characteristic, complemented
30	#16839716	C₄	1	1	yes	characteristic, complemented
31	#16839716	C₄	1	1	yes	characteristic, complemented
32	#97×D₆₁	C₂²	1	1	yes	characteristic
33	#97×D₆₁	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#405	C₄	1	1	yes	characteristic, complemented
37	C₂×C₄⋊#6923	—	2	4	no	—
38	C₂×C₄⋊#6923	C₂³	1	4	yes	—
39	C₂×C₄⋊#6923	C₂³	1	4	yes	—
40	C₂×C₂²⋊#6923	—	2	4	no	—
41	C₂×C₄×#6923	—	2	4	no	—
42	#14519846	—	2	4	no	—
43	#14519846	—	2	4	no	—
44	#14519846	—	2	4	no	—
45	#14519845	—	2	4	no	—
46	(C₂×#6923)⋊C₄	—	2	4	no	—
47	(C₂×#6923)⋊C₄	—	2	4	no	—
48	(C₂×#6923)⋊C₄	—	2	4	no	—
49	C₂²×C₄×D₆₁	C₂³	1	1	yes	characteristic
50	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
51	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
52	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
53	M₁₆×D₆₁	—	2	2	no	—
54	M₁₆×D₆₁	—	2	2	no	—
55	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₆₁	—	2	2	no	—
57	C₂×C₈×D₆₁	—	2	2	no	—
58	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
64	#14519736	C₂×C₄	1	1	yes	characteristic
65	#14519735	Q₈	1	2	yes	—
66	#14519734	C₂×C₄	1	1	yes	characteristic
67	#14519734	C₂×C₄	1	1	yes	characteristic
68	#14519733	Q₈	1	2	yes	—
69	C₄⋊C₄×D₆₁	D₄	1	2	yes	—
70	C₂²⋊C₄×D₆₁	D₄	1	2	yes	—
71	C₄²×D₆₁	C₂³	1	1	yes	characteristic
72	C₄²×D₆₁	C₂³	1	1	yes	characteristic
73	#14519688	C₂×C₄	1	1	yes	characteristic
74	#14519688	C₂×C₄	1	1	yes	characteristic
75	#14519687	C₂×C₄	1	1	yes	characteristic
76	#14519687	C₂×C₄	1	1	yes	characteristic
77	#14519687	C₂×C₄	1	1	yes	characteristic
78	#14519687	C₂×C₄	1	1	yes	characteristic
79	C₄×#92418	C₂×C₄	1	1	yes	characteristic
80	C₄×#92418	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
85	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
87	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
88	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
89	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
92	C₂³×D₆₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×#6923	—	2	4	no	—
94	C₂²×#6923	—	2	4	no	—
95	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₄×D₆₁	—	2	1	no	—
98	C₂×C₄×D₆₁	—	2	1	no	—
99	C₂×C₄×D₆₁	—	2	1	no	—
100	C₂×C₄×D₆₁	—	2	1	no	—
101	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₆₁	C₂×D₄	1	2	yes	—
104	C₂×C₄×D₆₁	C₂×D₄	1	2	yes	—
105	C₂×C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
107	C₂²⋊#6923	—	8	4	no	—
108	C₄⋊#6923	—	2	4	no	—
109	C₄⋊#6923	—	2	4	no	—
110	C₄⋊#6923	—	2	4	no	—
111	C₄⋊#6923	—	2	4	no	—
112	C₄⋊#6923	—	8	4	no	—
113	C₄×#6923	—	8	4	no	—
114	M₁₆×C₆₁	—	2	2	no	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
120	C₄⋊C₄×C₆₁	C₄⋊C₄	1	2	yes	—
121	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	2	yes	—
122	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²⋊Dic₆₁	C₄⋊C₄	1	2	yes	—
125	#11758198	C₄⋊C₄	1	2	yes	—
126	#11758198	C₄⋊C₄	1	2	yes	—
127	C₄⋊Dic₆₁	C₄⋊C₄	1	2	yes	—
128	#11758196	C₄⋊C₄	1	2	yes	—
129	#11758196	C₄⋊C₄	1	2	yes	—
130	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₆₁	C₂×Q₈	1	2	yes	—
133	C₄×Dic₆₁	C₂×Q₈	1	2	yes	—
134	#11758194	—	2	2	no	—
135	C₂×#92418	—	2	2	no	—
136	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
137	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
138	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
139	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
140	#11758189	—	2	2	no	—
141	#11758189	—	2	2	no	—
142	C₈×D₆₁	—	2	1	no	—
143	C₈×D₆₁	—	2	1	no	—
144	C₈×D₆₁	—	2	1	no	—
145	C₈×D₆₁	—	2	1	no	—
146	C₈×D₆₁	—	2	2	no	—
147	C₈×D₆₁	—	2	2	no	—
148	C₈×D₆₁	#41	1	2	yes	—
149	C₈×D₆₁	#41	1	2	yes	—
150	C₈×D₆₁	#41	1	2	yes	—
151	C₈×D₆₁	#41	1	2	yes	—
152	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂²×D₆₁	—	2	1	no	—
154	C₂²×D₆₁	—	2	1	no	—
155	C₂²×D₆₁	—	2	2	no	—
156	C₂²×D₆₁	—	2	2	no	—
157	C₂²×D₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂²×D₆₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×#6923	—	4	4	no	—
160	C₂×#6923	—	4	4	no	—
161	C₂×#6923	—	4	4	no	—
162	C₂×#6923	—	4	4	no	—
163	C₂×#6923	—	4	4	no	—
164	C₂×#6923	—	4	4	no	—
165	C₂×C₄×C₆₁	—	2	1	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×Dic₆₁	—	2	1	no	—
172	C₂×Dic₆₁	—	2	1	no	—
173	C₂×Dic₆₁	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×Dic₆₁	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×Dic₆₁	C₂²×Q₈	1	1	yes	characteristic
177	C₄×D₆₁	—	2	1	no	—
178	C₄×D₆₁	—	2	1	no	—
179	C₄×D₆₁	—	2	2	no	—
180	C₄×D₆₁	—	2	2	no	—
181	C₄×D₆₁	—	2	2	no	—
182	C₄×D₆₁	—	2	2	no	—
183	C₄×D₆₁	—	2	1	no	—
184	C₄×D₆₁	—	2	1	no	—
185	C₄×D₆₁	—	2	1	no	—
186	C₄×D₆₁	—	2	1	no	—
187	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
188	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
189	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
190	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
191	C₈×C₆₁	—	2	1	no	—
192	C₈×C₆₁	—	2	1	no	—
193	C₈×C₆₁	#117	1	2	yes	—
194	C₈×C₆₁	#117	1	2	yes	—
195	#92418	—	2	1	no	—
196	#92418	—	2	1	no	—
197	#92418	#117	1	2	yes	—
198	#92418	#117	1	2	yes	—
199	#20821	—	61	1	no	maximal, Sylow
200	C₂²×C₆₁	—	2	2	no	—
201	C₂²×C₆₁	—	2	1	no	—
202	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	C₂×D₆₁	—	2	2	no	—
204	C₂×D₆₁	—	2	1	no	—
205	C₂×D₆₁	—	4	2	no	—
206	C₂×D₆₁	—	4	1	no	—
207	C₂×D₆₁	—	4	1	no	—
208	C₂×D₆₁	#532	1	1	yes	characteristic
209	C₂×D₆₁	#532	1	1	yes	characteristic
210	C₂×D₆₁	#576	1	2	yes	—
211	C₂×D₆₁	#578	1	2	yes	—
212	#6923	—	8	4	no	—
213	#6923	—	8	4	no	—
214	C₄×C₆₁	—	2	2	no	—
215	C₄×C₆₁	—	2	2	no	—
216	C₄×C₆₁	—	2	1	no	—
217	C₄×C₆₁	C₂×#117	1	1	yes	characteristic
218	C₄×C₆₁	C₂×#117	1	1	yes	characteristic
219	Dic₆₁	—	2	2	no	—
220	Dic₆₁	—	2	2	no	—
221	Dic₆₁	—	2	1	no	—
222	Dic₆₁	#533	1	1	yes	characteristic
223	Dic₆₁	#533	1	1	yes	characteristic
224	C₂×#405	—	61	1	no	—
225	#2314	—	61	2	no	—
226	#1846	—	61	1	no	—
227	#1845	—	61	1	no	—
228	#1836	—	61	2	no	—
229	#1809	—	61	2	no	—
230	#1808	—	61	2	no	—
231	#1776	—	61	2	no	—
232	C₄×#107	—	61	2	no	—
233	C₂×C₆₁	—	4	1	no	—
234	C₂×C₆₁	#2285	1	1	yes	characteristic
235	C₂×C₆₁	#2913	1	2	yes	—
236	D₆₁	—	4	1	no	—
237	D₆₁	#3175	1	2	yes	—
238	D₆₁	#3176	1	1	yes	characteristic
239	D₆₁	#3177	1	1	yes	characteristic
240	C₂²×M₁₆	—	61	1	no	—
241	C₂³×C₈	—	61	1	no	—
242	C₂×#117	—	61	1	no	—
243	C₂×#107	—	61	2	no	—
244	C₂×#107	—	61	2	no	—
245	C₂×#107	—	61	2	no	—
246	C₂×#106	—	61	2	no	—
247	#405	—	61	1	no	—
248	#405	—	61	1	no	—
249	#405	—	61	1	no	—
250	#405	—	61	1	no	—
251	#405	—	61	1	no	—
252	#405	—	61	1	no	—
253	#405	—	61	1	no	—
254	#405	#6923	1	1	yes	characteristic, complemented
255	C₂×#97	—	61	1	no	—
256	C₂×#97	—	61	1	no	—
257	C₂×C₄×C₈	—	61	1	no	—
258	C₂×C₄×C₈	—	61	1	no	—
259	#388	—	122	4	no	—
260	#387	—	122	4	no	—
261	#384	—	61	2	no	—
262	#382	—	61	2	no	—
263	#380	—	61	4	no	—
264	C₄×C₄⋊C₄	—	61	4	no	—
265	#340	—	61	4	no	—
266	#340	—	61	4	no	—
267	C₆₁	#20821	1	1	yes	characteristic, complemented, Sylow
268	C₂³×C₄	—	61	1	no	—
269	C₂×M₁₆	—	61	1	no	—
270	C₂×M₁₆	—	61	1	no	—
271	C₂×M₁₆	—	61	1	no	—
272	C₂×M₁₆	—	122	2	no	—
273	C₂×M₁₆	—	122	2	no	—
274	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic
275	C₂²×C₈	—	61	1	no	—
276	C₂²×C₈	—	61	1	no	—
277	C₂²×C₈	—	61	1	no	—
278	C₂²×C₈	—	61	1	no	—
279	C₂²×C₈	—	61	1	no	—
280	C₂²×C₈	—	61	1	no	—
281	C₂²×C₈	—	61	1	no	—
282	C₂²×C₈	—	122	2	no	—
283	C₂²×C₈	—	122	2	no	—
284	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
285	#117	—	61	1	no	—
286	#117	—	61	2	no	—
287	#117	—	61	2	no	—
288	#117	—	61	1	no	—
289	#117	—	61	1	no	—
290	#117	C₂×#6923	1	1	yes	characteristic
291	C₂×C₄⋊C₄	—	61	2	no	—
292	C₂×C₄⋊C₄	—	61	4	no	—
293	C₂×C₄⋊C₄	—	61	4	no	—
294	C₂×C₄⋊C₄	—	122	4	no	—
295	C₂×C₂²⋊C₄	—	61	2	no	—
296	C₂×C₂²⋊C₄	—	122	4	no	—
297	C₂×C₄²	—	61	1	no	—
298	C₂×C₄²	—	61	1	no	—
299	C₂×C₄²	—	122	4	no	—
300	#107	—	122	4	no	—
301	#107	—	122	4	no	—
302	#107	—	122	4	no	—
303	#106	—	122	4	no	—
304	#97	—	61	1	no	—
305	#97	—	61	1	no	—
306	#97	—	61	1	no	—
307	#97	—	61	1	no	—
308	#97	—	61	1	no	—
309	#97	—	61	1	no	—
310	#97	C₂×#6923	1	1	yes	characteristic
311	#97	C₂×#6923	1	1	yes	characteristic
312	C₄×C₈	—	61	1	no	—
313	C₄×C₈	—	61	1	no	—
314	C₄×C₈	—	61	1	no	—
315	C₄×C₈	—	61	1	no	—
316	C₄×C₈	—	61	1	no	—
317	C₄×C₈	—	61	1	no	—
318	C₄×C₈	C₂×#6923	1	1	yes	characteristic
319	C₄×C₈	C₂×#6923	1	1	yes	characteristic
320	#95	—	122	4	no	—
321	#95	—	122	4	no	—
322	#95	—	122	4	no	—
323	C₂⁴	—	61	1	no	—
324	C₂²×C₄	—	61	1	no	—
325	C₂²×C₄	—	61	1	no	—
326	C₂²×C₄	—	61	1	no	—
327	C₂²×C₄	—	61	2	no	—
328	C₂²×C₄	—	61	2	no	—
329	C₂²×C₄	—	61	1	no	—
330	C₂²×C₄	—	61	1	no	—
331	C₂²×C₄	—	122	1	no	—
332	C₂²×C₄	—	122	1	no	—
333	C₂²×C₄	—	122	1	no	—
334	C₂²×C₄	—	122	1	no	—
335	C₂²×C₄	—	122	4	no	—
336	C₂²×C₄	—	122	4	no	—
337	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
338	M₁₆	—	2	2	no	—
339	M₁₆	—	122	2	no	—
340	M₁₆	—	122	2	no	—
341	M₁₆	—	122	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	61	1	no	—
344	C₂×C₈	—	61	1	no	—
345	C₂×C₈	—	61	2	no	—
346	C₂×C₈	—	61	2	no	—
347	C₂×C₈	—	61	2	no	—
348	C₂×C₈	—	61	2	no	—
349	C₂×C₈	—	61	1	no	—
350	C₂×C₈	—	61	1	no	—
351	C₂×C₈	—	122	2	no	—
352	C₂×C₈	—	122	1	no	—
353	C₂×C₈	—	122	1	no	—
354	C₂×C₈	—	122	1	no	—
355	C₂×C₈	—	122	1	no	—
356	C₂×C₈	—	122	2	no	—
357	C₂×C₈	—	122	2	no	—
358	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
359	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
360	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
361	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
362	C₄⋊C₄	—	61	2	no	—
363	C₄⋊C₄	—	61	2	no	—
364	C₄⋊C₄	—	61	2	no	—
365	C₄⋊C₄	—	122	4	no	—
366	C₄⋊C₄	—	122	4	no	—
367	C₄⋊C₄	—	122	4	no	—
368	C₄⋊C₄	—	122	4	no	—
369	C₄⋊C₄	—	488	4	no	—
370	C₄⋊C₄	C₄⋊#6923	1	2	yes	—
371	C₂²⋊C₄	—	61	2	no	—
372	C₂²⋊C₄	—	61	2	no	—
373	C₂²⋊C₄	—	61	2	no	—
374	C₂²⋊C₄	—	488	4	no	—
375	C₂²⋊C₄	C₄⋊#6923	1	2	yes	—
376	C₄²	—	61	2	no	—
377	C₄²	—	61	2	no	—
378	C₄²	—	61	1	no	—
379	C₄²	—	61	1	no	—
380	C₄²	—	488	4	no	—
381	C₄²	C₂²×#6923	1	1	yes	characteristic
382	C₄²	C₂²×#6923	1	1	yes	characteristic
383	C₂³	—	61	1	no	—
384	C₂³	—	61	1	no	—
385	C₂³	—	122	2	no	—
386	C₂³	—	122	1	no	—
387	C₂³	—	122	1	no	—
388	C₂³	—	122	2	no	—
389	C₂³	C₂×C₄⋊#6923	1	1	yes	characteristic
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	61	1	no	—
393	C₂×C₄	—	61	1	no	—
394	C₂×C₄	—	61	1	no	—
395	C₂×C₄	—	61	1	no	—
396	C₂×C₄	—	61	1	no	—
397	C₂×C₄	—	61	2	no	—
398	C₂×C₄	—	61	2	no	—
399	C₂×C₄	—	61	1	no	—
400	C₂×C₄	—	122	1	no	—
401	C₂×C₄	—	122	1	no	—
402	C₂×C₄	—	122	2	no	—
403	C₂×C₄	—	122	2	no	—
404	C₂×C₄	—	122	2	no	—
405	C₂×C₄	—	122	2	no	—
406	C₂×C₄	—	122	1	no	—
407	C₂×C₄	—	122	1	no	—
408	C₂×C₄	—	122	1	no	—
409	C₂×C₄	—	122	1	no	—
410	C₂×C₄	—	122	1	no	—
411	C₂×C₄	—	122	1	no	—
412	C₂×C₄	—	244	4	no	—
413	C₂×C₄	—	244	4	no	—
414	C₂×C₄	—	244	4	no	—
415	C₂×C₄	—	244	4	no	—
416	C₂×C₄	—	244	4	no	—
417	C₂×C₄	—	244	4	no	—
418	C₂×C₄	C₂×C₄⋊#6923	1	2	yes	—
419	C₂×C₄	C₂×C₄⋊#6923	1	2	yes	—
420	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
421	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
422	C₈	—	2	1	no	—
423	C₈	—	2	1	no	—
424	C₈	—	61	2	no	—
425	C₈	—	61	2	no	—
426	C₈	—	122	1	no	—
427	C₈	—	122	1	no	—
428	C₈	#14519856	1	2	yes	—
429	C₈	#14519856	1	2	yes	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	61	2	no	—
433	C₂²	—	61	2	no	—
434	C₂²	—	61	1	no	—
435	C₂²	—	61	1	no	—
436	C₂²	—	122	2	no	—
437	C₂²	—	122	1	no	—
438	C₂²	—	244	1	no	—
439	C₂²	—	244	2	no	—
440	C₂²	—	244	1	no	—
441	C₂²	C₂²×C₄⋊#6923	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	61	1	no	—
446	C₄	—	61	1	no	—
447	C₄	—	122	2	no	—
448	C₄	—	122	2	no	—
449	C₄	—	122	1	no	—
450	C₄	—	488	4	no	—
451	C₄	—	488	4	no	—
452	C₄	C₂×#14519856	1	1	yes	characteristic
453	C₄	C₂×#14519856	1	1	yes	characteristic
454	C₂	—	4	1	no	—
455	C₂	—	61	1	no	—
456	C₂	—	61	2	no	—
457	C₂	—	61	1	no	—
458	C₂	—	244	1	no	—
459	C₂	#21462268	1	1	yes	characteristic
460	C₂	#21462474	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₆₁×#405	C₄
socle	C₂²×C₆₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₆₁	C₂×D₄
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	#405	#6923
hypocenter	C₆₁	#20821
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #21461756	C₂	semidirect
3. #21461755	C₂	semidirect
4. #21461742	C₂	semidirect
7. #21461633	C₂	semidirect
8. C₄×#14519846	C₂	semidirect
25. #16839720	C₄	semidirect
26. #16839719	C₄	semidirect
27. #16839719	C₄	semidirect
28. #16839718	C₄	semidirect
29. #16839717	C₄	semidirect
30. #16839716	C₄	semidirect
31. #16839716	C₄	semidirect
36. C₆₁×#405	C₄	semidirect
254. #405	#6923	semidirect
267. C₆₁	#20821	semidirect

Maximal subgroups

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

subgroup	index
#21462297	2
#21461756	2
#21461755	2
#21461742	2
#21461697	2
#21461696	2
#21461633	2
C₄×#14519846	2
#405×D₆₁	2
#20821	61