Subgroups — #29698923

Order 15616.

740 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839892	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₁₂₂	C₂	1	1	yes	maximal, characteristic
3	#21448296	C₂	1	1	yes	maximal, characteristic
4	#21446539	C₂	1	2	yes	maximal
5	#21446537	C₂	1	1	yes	maximal, characteristic
6	#21446537	C₂	1	1	yes	maximal, characteristic
7	#21446534	C₂	1	2	yes	maximal
8	#21445937	C₂	1	2	yes	maximal
9	#21445936	C₂	1	1	yes	maximal, characteristic
10	#21445675	C₂	1	2	yes	maximal
11	C₄×C₄⋊C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic
13	#16839892	—	2	4	no	—
14	C₈×Dic₁₂₂	—	2	4	no	—
15	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
17	C₂×#14519706	C₂²	1	2	yes	—
18	C₂×#14519706	C₂²	1	2	yes	—
19	C₂×#14519706	C₂²	1	2	yes	—
20	C₂×#14519706	C₂²	1	2	yes	—
21	C₂×#14519687	C₂²	1	2	yes	—
22	C₂×C₈×Dic₆₁	C₂²	1	2	yes	—
23	#16839668	C₄	1	1	yes	characteristic
24	#16839668	C₄	1	1	yes	characteristic
25	#16839660	C₄	1	1	yes	characteristic
26	#16839660	C₄	1	1	yes	characteristic
27	#16839646	C₄	1	2	yes	—
28	#16839646	C₄	1	2	yes	—
29	C₄×#11758196	C₂²	1	2	yes	—
30	C₄×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
31	#16839608	C₂²	1	2	yes	—
32	#16839517	C₂²	1	2	yes	—
33	#16839517	C₂²	1	2	yes	—
34	#16839516	C₂²	1	2	yes	—
35	#16839516	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₄³×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#336	C₂²	1	1	yes	characteristic
42	C₆₁×#336	C₂²	1	1	yes	characteristic
43	C₂²×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
44	C₂²×#92418	C₂³	1	2	yes	—
45	C₂²×#92418	C₂³	1	2	yes	—
46	C₄×Dic₁₂₂	D₄	1	4	yes	—
47	C₄×Dic₁₂₂	Q₈	1	4	yes	—
48	C₂×C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
51	C₂×#11758196	C₂×C₄	1	2	yes	—
52	C₂×#11758196	C₂×C₄	1	2	yes	—
53	C₂×#11758196	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₆₁	C₂³	1	2	yes	—
55	C₂×C₄×Dic₆₁	C₂³	1	2	yes	—
56	C₄⋊#92418	—	2	2	no	—
57	C₄⋊#92418	—	2	2	no	—
58	#14519706	—	2	4	no	—
59	#14519706	—	2	4	no	—
60	#14519706	—	2	4	no	—
61	#14519706	—	2	4	no	—
62	#14519687	—	2	4	no	—
63	C₈×Dic₆₁	—	2	4	no	—
64	#14519684	C₂×C₄	1	2	yes	—
65	#14519684	C₂×C₄	1	2	yes	—
66	#14519684	C₂×C₄	1	2	yes	—
67	#14519684	C₂×C₄	1	2	yes	—
68	#14519684	C₂×C₄	1	2	yes	—
69	#14519684	C₂×C₄	1	2	yes	—
70	#14519684	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₆₁	—	2	2	no	—
83	C₄⋊C₈×C₆₁	—	2	2	no	—
84	C₄×C₈×C₆₁	—	2	2	no	—
85	C₄×C₈×C₆₁	—	2	2	no	—
86	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₆₁	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₆₁	C₂²×C₄	1	2	yes	—
95	C₂²×Dic₆₁	C₂²×C₄	1	2	yes	—
96	C₂²×Dic₆₁	C₂²×C₄	1	2	yes	—
97	C₂×Dic₁₂₂	—	2	2	no	—
98	C₂×Dic₁₂₂	—	2	2	no	—
99	C₂×Dic₁₂₂	C₄⋊C₄	1	4	yes	—
100	C₂×C₈×C₆₁	—	2	1	no	—
101	C₂×C₈×C₆₁	—	2	1	no	—
102	C₂×C₈×C₆₁	—	2	1	no	—
103	C₂×C₈×C₆₁	—	2	1	no	—
104	C₂×C₈×C₆₁	—	2	1	no	—
105	C₂×C₈×C₆₁	—	2	1	no	—
106	C₂×C₈×C₆₁	—	2	1	no	—
107	C₂×C₈×C₆₁	—	2	1	no	—
108	C₂×C₈×C₆₁	—	2	1	no	—
109	C₂×C₈×C₆₁	—	2	1	no	—
110	C₂×C₈×C₆₁	#41	1	2	yes	—
111	C₂×C₈×C₆₁	#41	1	2	yes	—
112	C₄²×C₆₁	—	2	2	no	—
113	C₄²×C₆₁	—	2	2	no	—
114	C₄²×C₆₁	—	2	2	no	—
115	C₄²×C₆₁	—	2	1	no	—
116	C₄²×C₆₁	—	2	1	no	—
117	C₄²×C₆₁	—	2	1	no	—
118	C₄²×C₆₁	—	2	1	no	—
119	C₄²×C₆₁	—	4	1	no	—
120	C₄²×C₆₁	C₂×D₄	1	2	yes	—
121	C₄²×C₆₁	C₂×Q₈	1	2	yes	—
122	C₄⋊Dic₆₁	—	2	2	no	—
123	C₄⋊Dic₆₁	—	2	2	no	—
124	C₄⋊Dic₆₁	C₄⋊C₄	1	4	yes	—
125	#11758196	—	2	4	no	—
126	#11758196	—	4	2	no	—
127	#11758196	C₄⋊C₄	1	8	yes	—
128	C₄×Dic₆₁	—	2	2	no	—
129	C₄×Dic₆₁	—	2	2	no	—
130	C₄×Dic₆₁	C₂×D₄	1	4	yes	—
131	C₄×Dic₆₁	C₂×Q₈	1	4	yes	—
132	C₂×#92418	—	2	2	no	—
133	C₂×#92418	—	2	2	no	—
134	C₂×#92418	—	2	2	no	—
135	C₂×#92418	—	2	2	no	—
136	C₂×#92418	—	2	2	no	—
137	C₂×#92418	—	2	2	no	—
138	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₆₁	—	2	1	no	—
140	C₂×C₄×C₆₁	—	2	1	no	—
141	C₂×C₄×C₆₁	—	2	1	no	—
142	C₂×C₄×C₆₁	—	2	1	no	—
143	C₂×C₄×C₆₁	—	2	1	no	—
144	C₂×C₄×C₆₁	—	2	1	no	—
145	C₂×C₄×C₆₁	—	2	1	no	—
146	C₂×C₄×C₆₁	—	2	1	no	—
147	C₂×C₄×C₆₁	—	2	1	no	—
148	C₂×C₄×C₆₁	—	2	1	no	—
149	C₂×C₄×C₆₁	—	2	1	no	—
150	C₂×C₄×C₆₁	—	2	1	no	—
151	C₂×C₄×C₆₁	—	2	1	no	—
152	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
153	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₆₁	#131	1	2	yes	—
155	C₂×C₄×C₆₁	#131	1	2	yes	—
156	C₂×C₄×C₆₁	#131	1	2	yes	—
157	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂×Dic₆₁	—	2	2	no	—
164	C₂×Dic₆₁	—	2	2	no	—
165	C₂×Dic₆₁	—	2	2	no	—
166	C₂×Dic₆₁	—	2	2	no	—
167	C₂×Dic₆₁	—	2	2	no	—
168	C₂×Dic₆₁	—	2	2	no	—
169	C₂×Dic₆₁	—	2	2	no	—
170	C₂×Dic₆₁	—	2	2	no	—
171	C₂×Dic₆₁	—	2	2	no	—
172	C₂×Dic₆₁	—	2	2	no	—
173	C₂×Dic₆₁	C₂×C₄⋊C₄	1	4	yes	—
174	C₂×Dic₆₁	C₂×C₄⋊C₄	1	4	yes	—
175	Dic₁₂₂	—	2	8	no	—
176	C₈×C₆₁	—	2	2	no	—
177	C₈×C₆₁	—	2	2	no	—
178	C₈×C₆₁	—	4	1	no	—
179	C₈×C₆₁	—	4	1	no	—
180	#92418	—	4	2	no	—
181	#92418	—	4	2	no	—
182	#22735	—	61	1	no	maximal, Sylow
183	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
185	C₂²×C₆₁	#519	1	1	yes	characteristic
186	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
187	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
188	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
189	C₂²×C₆₁	#568	1	1	yes	characteristic
190	C₄×C₆₁	—	2	2	no	—
191	C₄×C₆₁	—	2	2	no	—
192	C₄×C₆₁	—	4	1	no	—
193	C₄×C₆₁	—	4	1	no	—
194	C₄×C₆₁	—	4	1	no	—
195	C₄×C₆₁	#424	1	4	yes	—
196	C₄×C₆₁	#548	1	1	yes	characteristic
197	C₄×C₆₁	#548	1	1	yes	characteristic
198	C₄×C₆₁	#557	1	1	yes	characteristic
199	C₄×C₆₁	#557	1	1	yes	characteristic
200	Dic₆₁	—	2	4	no	—
201	Dic₆₁	—	2	4	no	—
202	Dic₆₁	—	4	2	no	—
203	Dic₆₁	—	4	2	no	—
204	C₂×#446	—	61	1	no	—
205	C₂×C₈×Q₈	—	61	1	no	—
206	#2295	—	61	1	no	—
207	#1940	—	61	2	no	—
208	#1939	—	61	2	no	—
209	#1939	—	61	1	no	—
210	#1939	—	61	1	no	—
211	#1832	—	61	2	no	—
212	#1831	—	61	1	no	—
213	#1768	—	61	2	no	—
214	C₄×C₄⋊C₈	D₆₁	1	1	yes	characteristic
215	C₂×C₆₁	#2351	1	1	yes	characteristic
216	C₂×C₆₁	C₂×#424	1	1	yes	characteristic
217	C₂×C₆₁	#2906	1	1	yes	characteristic
218	C₂×C₆₁	#2966	1	1	yes	characteristic
219	C₂×C₆₁	#2969	1	1	yes	characteristic
220	C₂×C₆₁	#2985	1	1	yes	characteristic
221	C₂×C₆₁	#2986	1	1	yes	characteristic
222	C₂×C₄×Q₈	—	61	1	no	—
223	#446	—	122	4	no	—
224	C₈×Q₈	—	122	4	no	—
225	C₂×C₄⋊C₈	—	61	2	no	—
226	C₂×C₄⋊C₈	—	61	2	no	—
227	C₂×C₄⋊C₈	—	61	2	no	—
228	C₂×C₄⋊C₈	—	61	2	no	—
229	C₂×C₄⋊C₈	—	61	1	no	—
230	C₂×C₄⋊C₈	—	61	1	no	—
231	C₂×C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
233	C₂×#97	—	61	2	no	—
234	C₂×C₄×C₈	—	61	2	no	—
235	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
237	#391	—	61	1	no	—
238	#391	—	61	1	no	—
239	#389	—	61	1	no	—
240	#389	—	61	1	no	—
241	#387	—	61	2	no	—
242	#387	—	61	2	no	—
243	C₄×C₄⋊C₄	—	61	1	no	—
244	C₄×C₄⋊C₄	—	61	2	no	—
245	#376	—	61	2	no	—
246	C₄³	C₂×D₆₁	1	1	yes	characteristic
247	#336	—	61	2	no	—
248	#336	—	61	2	no	—
249	#336	—	61	2	no	—
250	#336	—	61	2	no	—
251	#336	C₂×D₆₁	1	1	yes	characteristic
252	#336	C₂×D₆₁	1	1	yes	characteristic
253	C₆₁	#22735	1	1	yes	characteristic, complemented, Sylow
254	C₂²×Q₈	—	61	1	no	—
255	C₂²×C₈	—	61	2	no	—
256	C₂²×C₈	—	61	2	no	—
257	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
258	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
259	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
261	C₄×Q₈	—	61	4	no	—
262	C₄×Q₈	—	61	4	no	—
263	C₂×C₄⋊C₄	—	61	2	no	—
264	C₂×C₄⋊C₄	—	61	1	no	—
265	C₂×C₄⋊C₄	—	61	2	no	—
266	C₂×C₄⋊C₄	—	61	1	no	—
267	C₂×C₄⋊C₄	—	61	1	no	—
268	C₂×C₄⋊C₄	—	61	2	no	—
269	C₂×C₄²	—	61	2	no	—
270	C₂×C₄²	—	61	2	no	—
271	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
272	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
273	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
274	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
275	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
276	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
277	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	122	4	no	—
281	C₄⋊C₈	—	122	4	no	—
282	C₄⋊C₈	—	122	4	no	—
283	C₄⋊C₈	—	122	4	no	—
284	C₄⋊C₈	—	122	2	no	—
285	C₄⋊C₈	—	122	2	no	—
286	#97	—	122	4	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	C₄×C₈	—	122	4	no	—
290	#95	—	61	2	no	—
291	#95	—	61	2	no	—
292	#95	—	61	2	no	—
293	#95	—	61	2	no	—
294	#95	—	61	2	no	—
295	#95	—	61	2	no	—
296	#95	—	61	2	no	—
297	C₂×Q₈	—	61	4	no	—
298	C₂×Q₈	—	122	2	no	—
299	C₂×Q₈	—	122	2	no	—
300	C₂²×C₄	—	61	2	no	—
301	C₂²×C₄	—	61	2	no	—
302	C₂²×C₄	—	61	2	no	—
303	C₂²×C₄	—	61	2	no	—
304	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
310	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	122	2	no	—
322	C₂×C₈	—	122	2	no	—
323	C₂×C₈	—	122	2	no	—
324	C₂×C₈	—	122	2	no	—
325	C₂×C₈	—	122	2	no	—
326	C₂×C₈	—	122	2	no	—
327	C₂×C₈	#11758222	1	2	yes	—
328	C₂×C₈	#11758222	1	2	yes	—
329	C₄⋊C₄	—	61	8	no	—
330	C₄⋊C₄	—	61	4	no	—
331	C₄⋊C₄	—	122	4	no	—
332	C₄⋊C₄	—	122	2	no	—
333	C₄⋊C₄	—	122	2	no	—
334	C₄⋊C₄	—	244	2	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	61	4	no	—
344	C₄²	—	61	4	no	—
345	C₄²	—	122	2	no	—
346	C₄²	—	122	2	no	—
347	C₄²	D₄×D₆₁	1	2	yes	—
348	C₄²	Q₈×D₆₁	1	2	yes	—
349	C₂³	C₂²×C₄×D₆₁	1	1	yes	characteristic
350	Q₈	—	122	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	61	4	no	—
365	C₂×C₄	—	61	4	no	—
366	C₂×C₄	—	122	2	no	—
367	C₂×C₄	—	122	2	no	—
368	C₂×C₄	—	122	2	no	—
369	C₂×C₄	—	122	2	no	—
370	C₂×C₄	—	122	2	no	—
371	C₂×C₄	—	122	2	no	—
372	C₂×C₄	—	122	2	no	—
373	C₂×C₄	—	122	2	no	—
374	C₂×C₄	—	122	2	no	—
375	C₂×C₄	—	122	2	no	—
376	C₂×C₄	C₄⋊C₄×D₆₁	1	2	yes	—
377	C₂×C₄	C₄⋊C₄×D₆₁	1	2	yes	—
378	C₂×C₄	#14519783	1	2	yes	—
379	C₂×C₄	#14519783	1	2	yes	—
380	C₂×C₄	#14519785	1	2	yes	—
381	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₈×D₆₁	1	1	yes	characteristic
383	C₂×C₄	C₂×#11758222	1	1	yes	characteristic
384	C₂×C₄	C₂×#11758222	1	1	yes	characteristic
385	C₂×C₄	#14519824	1	1	yes	characteristic
386	C₂×C₄	#14519824	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	1	no	—
391	C₈	—	244	2	no	—
392	C₈	—	244	2	no	—
393	C₂²	C₂×C₄⋊C₄×D₆₁	1	1	yes	characteristic
394	C₂²	C₄×#11758222	1	1	yes	characteristic
395	C₂²	#16840239	1	1	yes	characteristic
396	C₂²	C₂×#14519783	1	1	yes	characteristic
397	C₂²	C₂×#14519783	1	1	yes	characteristic
398	C₂²	C₂×#14519785	1	1	yes	characteristic
399	C₂²	#16840528	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	122	4	no	—
406	C₄	—	122	4	no	—
407	C₄	—	244	2	no	—
408	C₄	—	244	2	no	—
409	C₄	#16839787	1	4	yes	—
410	C₄	#16840421	1	1	yes	characteristic
411	C₄	#16840421	1	1	yes	characteristic
412	C₄	#16840490	1	1	yes	characteristic
413	C₄	#16840490	1	1	yes	characteristic
414	C₂	#21448739	1	1	yes	characteristic
415	C₂	C₂×#16839787	1	1	yes	characteristic
416	C₂	#21454384	1	1	yes	characteristic
417	C₂	#21454794	1	1	yes	characteristic
418	C₂	#21454823	1	1	yes	characteristic
419	C₂	#21454913	1	1	yes	characteristic
420	C₂	#21454920	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₁
commutator, socle, prime radical	C₂³×C₆₁	C₂³×C₄
Fitting	C₄×C₄⋊C₈×C₆₁	C₂
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	C₄×C₄⋊C₈	D₆₁
hypocenter	C₆₁	#22735
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
253. C₆₁	#22735	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16839892	2
C₂×C₈×Dic₁₂₂	2
#21448296	2
#21446539	2
#21446537	2
#21446534	2
#21445937	2
#21445936	2
#21445675	2
C₄×C₄⋊C₈×C₆₁	2
#22735	61