Subgroups — #30612407

Order 15616.

688 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462628	C₂	1	1	yes	maximal, characteristic, complemented
2	#41×#92420	C₂	1	1	yes	maximal, characteristic, complemented
3	#21461448	C₂	1	2	yes	maximal, complemented
4	#21461444	C₂	1	2	yes	maximal, complemented
5	#21461440	C₂	1	2	yes	maximal, complemented
6	#21461436	C₂	1	2	yes	maximal, complemented
7	#21461368	C₂	1	1	yes	maximal, characteristic, complemented
8	#21461110	C₂	1	1	yes	maximal, characteristic, complemented
9	#21461110	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#92420⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#135×Dic₆₁	C₂	1	1	yes	maximal, characteristic
12	#16840813	C₂²	1	2	yes	—
13	Q₈×#92420	C₂²	1	2	yes	—
14	#16840797	C₂²	1	2	yes	—
15	#16840793	—	2	2	no	—
16	D₄×#92420	—	2	2	no	—
17	D₄×#92420	C₂²	1	2	yes	—
18	#16840779	—	2	1	no	—
19	#16840778	—	2	1	no	—
20	#16840778	C₂²	1	1	yes	characteristic
21	#16840778	C₂²	1	1	yes	characteristic
22	C₄×#11758217	—	2	1	no	—
23	C₂×C₄×#92420	—	2	1	no	—
24	C₂×C₄×#92420	C₂²	1	1	yes	characteristic
25	C₂×C₄×#92420	C₂²	1	1	yes	characteristic
26	#16840626	C₂²	1	2	yes	—
27	#16840624	C₂²	1	2	yes	—
28	Q₈⋊#92420	C₂²	1	2	yes	—
29	Q₈⋊#92420	C₂²	1	2	yes	—
30	D₄⋊#92420	C₂²	1	2	yes	—
31	D₄⋊#92420	C₂²	1	2	yes	—
32	#92420⋊C₈	C₂²	1	2	yes	—
33	#92420⋊C₈	C₂²	1	2	yes	—
34	#41×Dic₆₁	C₂²	1	1	yes	characteristic
35	#41×Dic₆₁	C₂²	1	1	yes	characteristic
36	Q₁₆×Dic₆₁	C₄	1	1	yes	characteristic
37	Q₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
38	SD₁₆×Dic₆₁	C₄	1	1	yes	characteristic
39	SD₁₆×Dic₆₁	C₄	1	1	yes	characteristic
40	SD₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
41	SD₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
42	D₈×Dic₆₁	C₄	1	1	yes	characteristic
43	D₈×Dic₆₁	C₂²	1	1	yes	characteristic
44	#16839800	C₄	1	1	yes	characteristic
45	#16839758	C₄	1	1	yes	characteristic
46	#16839758	C₄	1	1	yes	characteristic
47	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
48	C₂×#135×C₆₁	C₄	1	1	yes	characteristic
49	C₂×#11758217	—	2	2	no	—
50	C₂²×#92420	—	2	1	no	—
51	C₂²×#92420	—	2	2	no	—
52	C₂²×#92420	D₄	1	2	yes	—
53	#14519844	—	2	2	no	—
54	C₄⋊#92420	—	2	2	no	—
55	C₄⋊#92420	C₂³	1	2	yes	—
56	C₄⋊#92420	C₂³	1	2	yes	—
57	C₂²⋊#92420	—	2	1	no	—
58	C₂²⋊#92420	—	2	1	no	—
59	C₂²⋊#92420	—	2	2	no	—
60	C₂²⋊#92420	—	2	2	no	—
61	#14519832	—	2	2	no	—
62	C₄×#92420	—	2	2	no	—
63	C₄×#92420	—	2	1	no	—
64	C₄×#92420	—	2	1	no	—
65	C₄×#92420	—	2	1	no	—
66	C₄×#92420	D₄	1	1	yes	characteristic
67	C₄×#92420	D₄	1	1	yes	characteristic
68	C₄×#92420	C₂³	1	2	yes	—
69	C₄×#92420	C₂³	1	2	yes	—
70	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
71	Q₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
72	Q₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
73	Q₈×Dic₆₁	C₂³	1	1	yes	characteristic
74	Q₈×Dic₆₁	C₂³	1	1	yes	characteristic
75	D₄×Dic₆₁	—	2	1	no	—
76	D₄×Dic₆₁	—	2	1	no	—
77	D₄×Dic₆₁	—	2	1	no	—
78	D₄×Dic₆₁	—	2	1	no	—
79	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
80	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
81	D₄×Dic₆₁	C₂³	1	1	yes	characteristic
82	D₄×Dic₆₁	C₂³	1	1	yes	characteristic
83	#14519736	—	2	1	no	—
84	#14519736	—	2	1	no	—
85	#14519736	C₂×C₄	1	1	yes	characteristic
86	#14519736	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×Dic₆₁	—	2	1	no	—
88	C₂×C₄×Dic₆₁	—	2	1	no	—
89	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
90	#14519711	C₂×C₄	1	1	yes	characteristic
91	#14519711	C₂×C₄	1	1	yes	characteristic
92	#14519709	C₂×C₄	1	1	yes	characteristic
93	#14519709	C₂×C₄	1	1	yes	characteristic
94	#14519701	C₂×C₄	1	1	yes	characteristic
95	#14519701	C₂×C₄	1	1	yes	characteristic
96	#14519701	C₂×C₄	1	1	yes	characteristic
97	#14519701	C₂×C₄	1	1	yes	characteristic
98	#14519698	C₂×C₄	1	1	yes	characteristic
99	#14519698	C₂×C₄	1	1	yes	characteristic
100	#14519698	C₂×C₄	1	1	yes	characteristic
101	#14519698	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
104	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
105	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
106	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
107	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
108	#135×C₆₁	—	2	4	no	—
109	C₂×Q₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
110	C₂×SD₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
111	C₂×SD₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
112	C₂×D₈×C₆₁	C₂×C₄	1	1	yes	characteristic
113	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
114	#41×C₆₁	—	2	2	no	—
115	#41×C₆₁	—	2	2	no	—
116	#41×C₆₁	—	2	2	no	—
117	#41×C₆₁	M₁₆	1	4	yes	complemented
118	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₄×C₆₁	—	2	1	no	—
121	C₂×D₄×C₆₁	—	2	1	no	—
122	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	—	2	1	no	—
125	C₂²×C₄×C₆₁	—	2	1	no	—
126	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₆₁	—	2	1	no	—
128	C₂²×Dic₆₁	—	2	1	no	—
129	C₂²×Dic₆₁	—	2	1	no	—
130	C₂²×Dic₆₁	—	2	1	no	—
131	C₂²×Dic₆₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×Dic₆₁	#41	1	1	yes	characteristic
133	#11758217	—	4	4	no	—
134	C₂×#92420	—	2	4	no	—
135	C₂×#92420	—	2	2	no	—
136	C₂×#92420	—	2	2	no	—
137	C₂×#92420	—	2	2	no	—
138	C₂×#92420	—	4	2	no	—
139	C₂×#92420	—	4	4	no	—
140	C₂×#92420	C₂×D₄	1	2	yes	—
141	C₂×#92420	C₂×D₄	1	2	yes	—
142	Q₁₆×C₆₁	—	2	2	no	—
143	SD₁₆×C₆₁	—	2	2	no	—
144	SD₁₆×C₆₁	—	2	2	no	—
145	D₈×C₆₁	—	2	2	no	—
146	C₂×C₈×C₆₁	—	2	2	no	—
147	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
149	C₂²⋊Dic₆₁	—	2	1	no	—
150	C₂²⋊Dic₆₁	—	2	1	no	—
151	C₂²⋊Dic₆₁	—	2	1	no	—
152	C₂²⋊Dic₆₁	—	2	1	no	—
153	C₂²⋊Dic₆₁	—	2	1	no	—
154	C₂²⋊Dic₆₁	—	2	1	no	—
155	C₄⋊Dic₆₁	—	2	1	no	—
156	C₄⋊Dic₆₁	—	2	1	no	—
157	C₄⋊Dic₆₁	—	2	1	no	—
158	C₄⋊Dic₆₁	—	2	1	no	—
159	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
160	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
161	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
162	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₆₁	—	2	1	no	—
164	C₄×Dic₆₁	—	2	1	no	—
165	C₄×Dic₆₁	—	2	1	no	—
166	C₄×Dic₆₁	—	2	1	no	—
167	C₄×Dic₆₁	—	2	1	no	—
168	C₄×Dic₆₁	—	2	1	no	—
169	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
170	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
171	C₄×Dic₆₁	#41	1	1	yes	characteristic
172	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
173	C₂×#92418	—	2	2	no	—
174	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
175	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
176	C₂³×C₆₁	—	2	1	no	—
177	C₂³×C₆₁	—	2	1	no	—
178	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
179	Q₈×C₆₁	—	2	1	no	—
180	Q₈×C₆₁	—	2	1	no	—
181	Q₈×C₆₁	—	2	1	no	—
182	Q₈×C₆₁	C₂×M₁₆	1	2	yes	—
183	D₄×C₆₁	—	2	4	no	—
184	D₄×C₆₁	—	2	1	no	—
185	D₄×C₆₁	—	2	1	no	—
186	D₄×C₆₁	—	2	1	no	—
187	D₄×C₆₁	—	4	2	no	—
188	D₄×C₆₁	C₂×M₁₆	1	2	yes	—
189	C₂×C₄×C₆₁	—	2	1	no	—
190	C₂×C₄×C₆₁	—	2	4	no	—
191	C₂×C₄×C₆₁	—	2	1	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₆₁	#131	1	2	yes	—
196	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
197	C₂×Dic₆₁	—	2	2	no	—
198	C₂×Dic₆₁	—	2	2	no	—
199	C₂×Dic₆₁	—	2	1	no	—
200	C₂×Dic₆₁	—	2	1	no	—
201	C₂×Dic₆₁	—	2	1	no	—
202	C₂×Dic₆₁	—	2	1	no	—
203	C₂×Dic₆₁	—	4	2	no	—
204	C₂×Dic₆₁	—	4	2	no	—
205	C₂×Dic₆₁	—	4	2	no	—
206	C₂×Dic₆₁	—	4	2	no	—
207	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
208	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
209	C₂×Dic₆₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×Dic₆₁	C₂×#41	1	1	yes	characteristic
211	#92420	—	2	4	no	—
212	#92420	—	2	2	no	—
213	#92420	—	2	2	no	—
214	#92420	—	4	2	no	—
215	#92420	—	4	2	no	—
216	C₈×C₆₁	—	2	1	no	—
217	C₈×C₆₁	—	2	1	no	—
218	#92418	—	2	1	no	—
219	#92418	—	2	1	no	—
220	#17868	—	61	1	no	maximal, Sylow
221	C₂²×C₆₁	—	2	1	no	—
222	C₂²×C₆₁	—	2	1	no	—
223	C₂²×C₆₁	—	2	2	no	—
224	C₂²×C₆₁	—	4	1	no	—
225	C₂²×C₆₁	—	4	1	no	—
226	C₂²×C₆₁	—	4	1	no	—
227	C₂²×C₆₁	—	4	1	no	—
228	C₂²×C₆₁	—	4	1	no	—
229	C₂²×C₆₁	#435	1	2	yes	—
230	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
231	C₄×C₆₁	—	2	2	no	—
232	C₄×C₆₁	—	4	1	no	—
233	C₄×C₆₁	#435	1	2	yes	—
234	C₄×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
235	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
236	Dic₆₁	—	2	1	no	—
237	Dic₆₁	—	2	1	no	—
238	Dic₆₁	—	4	1	no	—
239	Dic₆₁	—	4	1	no	—
240	Dic₆₁	—	4	1	no	—
241	Dic₆₁	—	4	1	no	—
242	Dic₆₁	#443	1	2	yes	—
243	Dic₆₁	#575	1	2	yes	—
244	#2965	—	61	1	no	—
245	C₈×#41	—	61	1	no	—
246	C₄×#135	—	61	1	no	—
247	#1588	—	61	2	no	—
248	#1587	—	61	2	no	—
249	#1586	—	61	2	no	—
250	#1585	—	61	2	no	—
251	#1564	—	61	1	no	—
252	#1476	—	61	1	no	—
253	#1476	—	61	1	no	—
254	C₂×#322	—	61	1	no	—
255	C₂×C₆₁	—	2	2	no	—
256	C₂×C₆₁	—	4	2	no	—
257	C₂×C₆₁	—	8	1	no	—
258	C₂×C₆₁	C₂×#435	1	1	yes	characteristic
259	C₂×C₆₁	#2943	1	1	yes	characteristic
260	C₂×C₆₁	C₂×#443	1	1	yes	characteristic
261	C₂×#135	#6923	1	1	yes	characteristic
262	C₄×#41	—	61	1	no	—
263	C₄×#41	—	61	1	no	—
264	#446	—	61	2	no	—
265	C₈×Q₈	—	61	2	no	—
266	C₄×Q₁₆	—	61	1	no	—
267	C₄×Q₁₆	—	61	1	no	—
268	C₄×SD₁₆	—	61	1	no	—
269	C₄×SD₁₆	—	61	1	no	—
270	C₄×SD₁₆	—	61	1	no	—
271	C₄×SD₁₆	—	61	1	no	—
272	C₄×D₈	—	61	1	no	—
273	C₄×D₈	—	61	1	no	—
274	#436	—	61	2	no	—
275	#435	—	122	2	no	—
276	C₈×D₄	—	61	2	no	—
277	C₈×D₄	—	122	2	no	—
278	#431	—	61	1	no	—
279	#431	—	61	1	no	—
280	#431	—	122	1	no	—
281	#431	—	122	1	no	—
282	#427	—	61	1	no	—
283	#416	—	61	1	no	—
284	#416	—	61	1	no	—
285	C₄×M₁₆	—	122	1	no	—
286	C₂×C₄×C₈	—	61	1	no	—
287	C₂×C₄×C₈	—	61	1	no	—
288	C₂×C₄×C₈	—	61	1	no	—
289	C₂×C₄×C₈	—	122	1	no	—
290	#335	—	61	2	no	—
291	#334	—	61	2	no	—
292	Q₈⋊C₈	—	61	2	no	—
293	Q₈⋊C₈	—	61	2	no	—
294	D₄⋊C₈	—	61	2	no	—
295	D₄⋊C₈	—	61	2	no	—
296	#322	—	61	2	no	—
297	#322	—	61	2	no	—
298	C₆₁	#17868	1	1	yes	characteristic, complemented, Sylow
299	C₂×#41	C₂×#6923	1	1	yes	characteristic
300	C₂×#41	C₂×#6923	1	1	yes	characteristic
301	#135	—	2	4	no	—
302	C₂×Q₁₆	C₂×#6923	1	1	yes	characteristic
303	C₂×SD₁₆	C₂×#6923	1	1	yes	characteristic
304	C₂×SD₁₆	C₂×#6923	1	1	yes	characteristic
305	C₂×D₈	C₂×#6923	1	1	yes	characteristic
306	C₂×M₁₆	—	122	2	no	—
307	C₂²×C₈	—	61	1	no	—
308	C₂²×C₈	—	61	2	no	—
309	C₂²×C₈	—	122	2	no	—
310	C₂²×C₈	—	122	1	no	—
311	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
312	C₄×Q₈	—	61	1	no	—
313	C₄×Q₈	—	61	1	no	—
314	C₄×Q₈	—	61	1	no	—
315	C₄×Q₈	—	61	1	no	—
316	C₄×D₄	—	61	1	no	—
317	C₄×D₄	—	61	1	no	—
318	C₄×D₄	—	61	1	no	—
319	C₄×D₄	—	61	1	no	—
320	C₄×D₄	—	122	1	no	—
321	C₄×D₄	—	122	1	no	—
322	C₄×D₄	—	122	1	no	—
323	C₄×D₄	—	122	1	no	—
324	#117	—	61	1	no	—
325	#117	—	61	1	no	—
326	#117	—	122	1	no	—
327	#117	—	122	1	no	—
328	C₂×C₄²	—	61	1	no	—
329	C₂×C₄²	—	122	1	no	—
330	C₂×C₄²	—	122	1	no	—
331	#107	—	61	1	no	—
332	#107	—	61	1	no	—
333	#106	—	61	1	no	—
334	#106	—	61	1	no	—
335	C₄⋊C₈	—	61	2	no	—
336	C₄⋊C₈	—	61	2	no	—
337	C₄⋊C₈	—	122	2	no	—
338	C₄⋊C₈	—	122	2	no	—
339	#103	—	61	1	no	—
340	#103	—	61	1	no	—
341	#103	—	61	1	no	—
342	#103	—	61	1	no	—
343	#102	—	61	1	no	—
344	#102	—	61	1	no	—
345	#102	—	61	1	no	—
346	#102	—	61	1	no	—
347	C₂²⋊C₈	—	122	2	no	—
348	C₂²⋊C₈	—	122	2	no	—
349	C₂²⋊C₈	—	122	1	no	—
350	C₂²⋊C₈	—	122	1	no	—
351	#97	—	122	2	no	—
352	C₄×C₈	—	61	1	no	—
353	C₄×C₈	—	61	1	no	—
354	C₄×C₈	—	61	2	no	—
355	C₄×C₈	—	61	1	no	—
356	C₄×C₈	—	61	1	no	—
357	C₄×C₈	—	61	1	no	—
358	C₄×C₈	—	61	1	no	—
359	C₄×C₈	—	61	2	no	—
360	C₄×C₈	—	122	1	no	—
361	C₄×C₈	—	122	1	no	—
362	C₄×C₈	—	122	1	no	—
363	C₄×C₈	—	122	2	no	—
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	#41	—	2	2	no	—
367	#41	#11758217	1	4	yes	complemented
368	C₂×Q₈	C₂²×#6923	1	1	yes	characteristic
369	C₂×Q₈	C₂²×#6923	1	1	yes	characteristic
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	C₂²×#6923	1	1	yes	characteristic
373	C₂×D₄	C₂²×#6923	1	1	yes	characteristic
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	61	1	no	—
377	C₂²×C₄	—	61	1	no	—
378	C₂²×C₄	—	122	1	no	—
379	C₂²×C₄	—	122	1	no	—
380	C₂²×C₄	—	122	1	no	—
381	C₂²×C₄	—	122	1	no	—
382	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
383	Q₁₆	—	2	2	no	—
384	SD₁₆	—	2	2	no	—
385	SD₁₆	—	2	2	no	—
386	D₈	—	2	2	no	—
387	M₁₆	—	244	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	61	2	no	—
390	C₂×C₈	—	61	2	no	—
391	C₂×C₈	—	61	1	no	—
392	C₂×C₈	—	61	1	no	—
393	C₂×C₈	—	122	2	no	—
394	C₂×C₈	—	122	4	no	—
395	C₂×C₈	—	122	2	no	—
396	C₂×C₈	—	122	2	no	—
397	C₂×C₈	—	122	2	no	—
398	C₂×C₈	—	244	2	no	—
399	C₂×C₈	—	244	4	no	—
400	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
401	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
402	C₄⋊C₄	—	61	1	no	—
403	C₄⋊C₄	—	61	1	no	—
404	C₄⋊C₄	—	61	1	no	—
405	C₄⋊C₄	—	61	1	no	—
406	C₄⋊C₄	—	122	1	no	—
407	C₄⋊C₄	—	122	1	no	—
408	C₄⋊C₄	—	122	1	no	—
409	C₄⋊C₄	—	122	1	no	—
410	C₂²⋊C₄	—	122	1	no	—
411	C₂²⋊C₄	—	122	1	no	—
412	C₂²⋊C₄	—	122	1	no	—
413	C₂²⋊C₄	—	122	1	no	—
414	C₂²⋊C₄	—	122	1	no	—
415	C₂²⋊C₄	—	122	1	no	—
416	C₄²	—	61	1	no	—
417	C₄²	—	61	1	no	—
418	C₄²	—	61	1	no	—
419	C₄²	—	61	1	no	—
420	C₄²	—	122	1	no	—
421	C₄²	—	122	1	no	—
422	C₄²	—	122	1	no	—
423	C₄²	—	122	1	no	—
424	C₄²	—	122	1	no	—
425	C₄²	—	122	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	D₄×#6923	1	1	yes	characteristic
429	Q₈	—	2	1	no	—
430	Q₈	—	2	1	no	—
431	Q₈	—	2	1	no	—
432	Q₈	C₂×#11758217	1	2	yes	—
433	D₄	—	2	4	no	—
434	D₄	—	2	1	no	—
435	D₄	—	2	1	no	—
436	D₄	—	2	1	no	—
437	D₄	—	4	2	no	—
438	D₄	C₂×#11758217	1	2	yes	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	61	1	no	—
444	C₂×C₄	—	61	1	no	—
445	C₂×C₄	—	61	1	no	—
446	C₂×C₄	—	61	1	no	—
447	C₂×C₄	—	122	2	no	—
448	C₂×C₄	—	122	2	no	—
449	C₂×C₄	—	122	1	no	—
450	C₂×C₄	—	122	1	no	—
451	C₂×C₄	—	122	1	no	—
452	C₂×C₄	—	122	1	no	—
453	C₂×C₄	—	244	2	no	—
454	C₂×C₄	—	244	2	no	—
455	C₂×C₄	—	244	2	no	—
456	C₂×C₄	—	244	2	no	—
457	C₂×C₄	D₄×#6923	1	1	yes	characteristic
458	C₂×C₄	C₂×#11758217	1	2	yes	—
459	C₂×C₄	#14519864	1	2	yes	—
460	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	122	2	no	—
464	C₈	—	122	2	no	—
465	C₈	—	122	4	no	—
466	C₈	—	122	1	no	—
467	C₈	—	122	1	no	—
468	C₈	—	244	2	no	—
469	C₈	—	244	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	#16840793	1	2	yes	—
479	C₂²	C₂×D₄×#6923	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	4	1	no	—
482	C₄	—	61	2	no	—
483	C₄	—	61	2	no	—
484	C₄	—	122	1	no	—
485	C₄	—	122	1	no	—
486	C₄	—	244	1	no	—
487	C₄	—	244	1	no	—
488	C₄	—	244	1	no	—
489	C₄	—	244	1	no	—
490	C₄	#16840793	1	2	yes	—
491	C₄	C₂²×#11758217	1	1	yes	characteristic
492	C₄	C₂×#14519864	1	1	yes	characteristic
493	C₂	—	2	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	8	1	no	—
496	C₂	C₂×#16840793	1	1	yes	characteristic
497	C₂	#21462573	1	1	yes	characteristic
498	C₂	D₆₁⋊#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#6923
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6923
Fitting, prime radical	C₂×#135×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄×D₄
cosocle	C₄×Dic₆₁	C₂⁴
hypercenter	C₂×#135	#6923
hypocenter	C₆₁	#17868
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. #21462628	C₂	semidirect
2. #41×#92420	C₂	semidirect
3. #21461448	C₂	semidirect
4. #21461444	C₂	semidirect
5. #21461440	C₂	semidirect
6. #21461436	C₂	semidirect
7. #21461368	C₂	semidirect
8. #21461110	C₂	semidirect
9. #21461110	C₂	semidirect
10. C₂×#92420⋊C₈	C₂	semidirect
117. #41×C₆₁	M₁₆	semidirect
298. C₆₁	#17868	semidirect
367. #41	#11758217	semidirect

Maximal subgroups

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

subgroup	index
#21462628	2
#41×#92420	2
#21461448	2
#21461444	2
#21461440	2
#21461436	2
#21461368	2
#21461110	2
C₂×#92420⋊C₈	2
#135×Dic₆₁	2
#17868	61