Subgroups — #12107237

Order 1280.

848 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2398	C₂	1	1	yes	maximal, characteristic
2	C₂×#65313	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#65300	C₂	1	1	yes	maximal, characteristic
4	#10602427	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602407	C₂	1	1	yes	maximal, characteristic
6	#10600245	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600245	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600244	C₂	1	1	yes	maximal, characteristic, complemented
9	#10600244	C₂	1	1	yes	maximal, characteristic, complemented
10	#10600241	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600241	C₂	1	1	yes	maximal, characteristic, complemented
12	#10600240	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
14	#10600230	C₂	1	1	yes	maximal, characteristic, complemented
15	#10600227	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×#681	C₂²	1	1	yes	characteristic
19	C₂³×#168	C₂²	1	1	yes	characteristic
20	C₅×#400	C₄	1	1	yes	characteristic
21	C₅×#400	C₄	1	1	yes	characteristic
22	C₅×#397	C₄	1	1	yes	characteristic
23	C₅×#397	C₄	1	1	yes	characteristic
24	C₅×#394	C₄	1	1	yes	characteristic
25	C₅×#394	C₄	1	1	yes	characteristic
26	C₅×#393	C₄	1	1	yes	characteristic
27	C₅×#393	C₄	1	1	yes	characteristic
28	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₅×#376	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
39	#65313	—	2	4	no	—
40	#65300	—	2	4	no	—
41	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
45	C₂×#3935	C₂²	1	1	yes	characteristic
46	C₂×#3935	C₂²	1	1	yes	characteristic
47	C₂×#3935	C₂²	1	1	yes	characteristic
48	C₂×#3935	C₂²	1	1	yes	characteristic
49	C₂×C₄×#168	C₂²	1	1	yes	characteristic
50	C₂×C₄×#168	C₂²	1	1	yes	characteristic
51	C₂×C₄×#168	C₂²	1	1	yes	characteristic
52	C₂×C₄×#168	C₂²	1	1	yes	characteristic
53	#64744	C₂²	1	1	yes	characteristic
54	#64744	C₂²	1	1	yes	characteristic
55	#64744	C₂²	1	1	yes	characteristic
56	#64744	C₂²	1	1	yes	characteristic
57	#64744	C₂²	1	1	yes	characteristic
58	#64744	C₂²	1	1	yes	characteristic
59	#64744	C₂²	1	1	yes	characteristic
60	#64744	C₂²	1	1	yes	characteristic
61	#21637	—	5	1	no	maximal, Sylow
62	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₄×C₅×Q₈	—	2	2	no	—
67	C₄×C₅×Q₈	—	2	2	no	—
68	C₄×C₅×D₄	—	2	2	no	—
69	C₄×C₅×D₄	—	2	2	no	—
70	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₂×#681	—	2	2	no	—
90	C₂×#681	—	2	2	no	—
91	C₂×#681	—	2	2	no	—
92	C₂²×#168	—	2	2	no	—
93	C₂²×#168	—	2	2	no	—
94	C₂²×#168	—	2	2	no	—
95	C₂²×#168	C₂³	1	1	yes	characteristic
96	C₂²×#168	C₂³	1	1	yes	characteristic
97	C₂²×#168	C₂³	1	1	yes	characteristic
98	C₂²×#168	C₂³	1	1	yes	characteristic
99	C₂²×#168	C₂³	1	1	yes	characteristic
100	C₂²×#168	C₂³	1	1	yes	characteristic
101	C₂²×#168	C₂³	1	1	yes	characteristic
102	C₂²×#168	C₂³	1	1	yes	characteristic
103	C₅×#95	C₂×C₄	1	1	yes	characteristic
104	C₅×#95	C₂×C₄	1	1	yes	characteristic
105	C₅×#95	C₂×C₄	1	1	yes	characteristic
106	C₅×#95	C₂×C₄	1	1	yes	characteristic
107	C₅×#95	C₂×C₄	1	1	yes	characteristic
108	C₅×#95	C₂×C₄	1	1	yes	characteristic
109	C₅×#95	C₂×C₄	1	1	yes	characteristic
110	C₅×#95	C₂×C₄	1	1	yes	characteristic
111	C₅×#95	C₂×C₄	1	1	yes	characteristic
112	C₅×#95	C₂×C₄	1	1	yes	characteristic
113	C₅×#95	C₂×C₄	1	1	yes	characteristic
114	C₅×#95	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊#168	—	2	2	no	—
116	C₂²⋊#168	—	2	2	no	—
117	C₂²⋊#168	—	2	2	no	—
118	C₂²⋊#168	—	2	2	no	—
119	C₂²⋊#168	—	2	2	no	—
120	C₂²⋊#168	—	2	2	no	—
121	C₄⋊#168	—	2	2	no	—
122	C₄⋊#168	—	2	2	no	—
123	C₄⋊#168	—	2	2	no	—
124	C₄⋊#168	—	2	2	no	—
125	#3935	—	2	2	no	—
126	#3935	—	2	2	no	—
127	#3935	—	2	2	no	—
128	#3935	D₄	1	4	yes	—
129	C₄×#168	—	2	2	no	—
130	C₄×#168	—	2	2	no	—
131	C₄×#168	—	2	2	no	—
132	C₄×#168	—	2	2	no	—
133	C₂×#446	—	5	1	no	—
134	C₂×#435	—	5	1	no	—
135	#2398	D₅	1	1	yes	characteristic
136	#1984	—	5	1	no	—
137	#1954	—	5	1	no	—
138	#1924	—	5	1	no	—
139	#1924	—	5	1	no	—
140	#1923	—	5	1	no	—
141	#1923	—	5	1	no	—
142	#1832	—	5	1	no	—
143	#1753	—	5	1	no	—
144	#1753	—	5	1	no	—
145	#1752	—	5	1	no	—
146	C₈×C₂²⋊C₄	—	5	1	no	—
147	#1726	—	5	1	no	—
148	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅×Q₈	—	2	2	no	—
151	C₂×C₅×Q₈	—	2	2	no	—
152	C₂×C₅×Q₈	—	4	1	no	—
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	—	2	2	no	—
155	C₂×C₅×D₄	—	4	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
181	C₅×C₄⋊C₄	—	2	2	no	—
182	C₅×C₄⋊C₄	—	2	2	no	—
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	—	2	2	no	—
185	C₅×C₂²⋊C₄	—	2	2	no	—
186	C₅×C₂²⋊C₄	—	2	2	no	—
187	C₅×C₂²⋊C₄	—	2	2	no	—
188	C₅×C₂²⋊C₄	—	2	2	no	—
189	C₅×C₂²⋊C₄	—	2	2	no	—
190	C₅×C₂²⋊C₄	—	2	2	no	—
191	C₅×C₂²⋊C₄	—	4	1	no	—
192	C₅×C₂²⋊C₄	—	4	1	no	—
193	C₅×C₂²⋊C₄	—	4	1	no	—
194	C₅×C₂²⋊C₄	—	4	1	no	—
195	C₄²×C₅	—	2	1	no	—
196	C₄²×C₅	—	2	1	no	—
197	C₄²×C₅	—	2	1	no	—
198	C₄²×C₅	—	2	1	no	—
199	C₄²×C₅	—	2	1	no	—
200	C₄²×C₅	—	2	1	no	—
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	2	1	no	—
203	C₄²×C₅	C₂×D₄	1	2	yes	—
204	C₄²×C₅	#41	1	2	yes	—
205	#681	—	4	4	no	—
206	C₂×#168	—	2	1	no	—
207	C₂×#168	—	2	1	no	—
208	C₂×#168	—	2	1	no	—
209	C₂×#168	—	2	1	no	—
210	C₂×#168	—	2	1	no	—
211	C₂×#168	—	2	1	no	—
212	C₂×#168	—	2	1	no	—
213	C₂×#168	—	2	1	no	—
214	C₂×#168	—	2	1	no	—
215	C₂×#168	—	2	1	no	—
216	C₂×#168	—	2	1	no	—
217	C₂×#168	—	2	1	no	—
218	C₂×#168	—	2	1	no	—
219	C₂×#168	—	2	1	no	—
220	C₂×#168	—	2	1	no	—
221	C₂×#168	—	2	1	no	—
222	C₂×#168	—	2	1	no	—
223	C₂×#168	—	2	1	no	—
224	C₂×#168	—	4	4	no	—
225	C₂×#168	C₂×D₄	1	2	yes	—
226	C₂×#168	C₂×D₄	1	2	yes	—
227	C₂×#168	#41	1	2	yes	—
228	C₂×#168	#41	1	2	yes	—
229	C₂×#168	#41	1	2	yes	—
230	C₂×#168	#41	1	2	yes	—
231	C₂²×M₁₆	—	5	1	no	—
232	C₂³×C₈	—	5	1	no	—
233	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic
235	#446	—	10	4	no	—
236	#435	—	10	4	no	—
237	C₂×C₄⋊C₈	—	5	1	no	—
238	C₂×C₄⋊C₈	—	5	1	no	—
239	C₂×C₄⋊C₈	—	5	1	no	—
240	C₂×C₄⋊C₈	—	5	1	no	—
241	C₂×C₂²⋊C₈	—	5	1	no	—
242	C₂×C₂²⋊C₈	—	5	1	no	—
243	C₂×C₂²⋊C₈	—	5	1	no	—
244	C₂×C₂²⋊C₈	—	5	1	no	—
245	C₂×C₂²⋊C₈	—	5	1	no	—
246	C₂×C₂²⋊C₈	—	5	1	no	—
247	C₂×#97	—	5	1	no	—
248	C₂×#97	—	5	1	no	—
249	C₂×#97	—	5	1	no	—
250	C₂×#97	—	5	1	no	—
251	C₂×C₄×C₈	—	5	1	no	—
252	C₂×C₄×C₈	—	5	1	no	—
253	C₂×C₄×C₈	—	5	1	no	—
254	C₂×C₄×C₈	—	5	1	no	—
255	#400	Dic₅	1	1	yes	characteristic
256	#400	Dic₅	1	1	yes	characteristic
257	#397	Dic₅	1	1	yes	characteristic
258	#397	Dic₅	1	1	yes	characteristic
259	#394	Dic₅	1	1	yes	characteristic
260	#394	Dic₅	1	1	yes	characteristic
261	#393	Dic₅	1	1	yes	characteristic
262	#393	Dic₅	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
264	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
266	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
267	#376	C₂×D₅	1	1	yes	characteristic
268	#336	—	5	1	no	—
269	#336	—	5	1	no	—
270	#336	—	5	1	no	—
271	#336	—	5	1	no	—
272	#336	—	5	1	no	—
273	#336	—	5	1	no	—
274	#336	—	5	1	no	—
275	#336	—	5	1	no	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	—	2	1	no	—
279	C₂³×C₅	—	2	1	no	—
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	—	2	1	no	—
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	—	2	1	no	—
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	—	2	1	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	#131	1	2	yes	—
290	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
291	C₅×Q₈	—	4	4	no	—
292	C₅×D₄	—	4	4	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	1	no	—
334	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
335	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
336	C₂×C₄×C₅	#131	1	2	yes	—
337	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
343	#168	—	2	2	no	—
344	#168	—	2	2	no	—
345	#168	—	2	2	no	—
346	#168	—	4	1	no	—
347	#168	—	4	1	no	—
348	#168	—	4	1	no	—
349	#168	—	4	1	no	—
350	#168	#124	1	4	yes	—
351	C₂²×Q₈	C₂×Dic₅	1	1	yes	characteristic
352	C₂²×D₄	C₂×Dic₅	1	1	yes	characteristic
353	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
354	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
355	C₂×M₁₆	—	10	2	no	—
356	C₂×M₁₆	—	10	2	no	—
357	C₂×M₁₆	—	10	2	no	—
358	C₂²×C₈	—	5	1	no	—
359	C₂²×C₈	—	5	1	no	—
360	C₂²×C₈	—	5	1	no	—
361	C₂²×C₈	—	5	1	no	—
362	C₂²×C₈	—	5	1	no	—
363	C₂²×C₈	—	5	1	no	—
364	C₂²×C₈	—	5	1	no	—
365	C₂²×C₈	—	5	1	no	—
366	C₂²×C₈	—	10	2	no	—
367	C₂²×C₈	—	10	2	no	—
368	C₂²×C₈	—	10	2	no	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×Q₈	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
387	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
388	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
389	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
390	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
391	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
392	C₄⋊C₈	—	10	2	no	—
393	C₄⋊C₈	—	10	2	no	—
394	C₄⋊C₈	—	10	2	no	—
395	C₄⋊C₈	—	10	2	no	—
396	C₂²⋊C₈	—	10	2	no	—
397	C₂²⋊C₈	—	10	2	no	—
398	C₂²⋊C₈	—	10	2	no	—
399	C₂²⋊C₈	—	10	2	no	—
400	C₂²⋊C₈	—	10	2	no	—
401	C₂²⋊C₈	—	10	2	no	—
402	#97	—	5	4	no	—
403	#97	—	10	2	no	—
404	#97	—	10	2	no	—
405	#97	—	10	2	no	—
406	C₄×C₈	—	10	2	no	—
407	C₄×C₈	—	10	2	no	—
408	C₄×C₈	—	10	2	no	—
409	C₄×C₈	—	10	2	no	—
410	#95	C₂×Dic₅	1	1	yes	characteristic
411	#95	C₂×Dic₅	1	1	yes	characteristic
412	#95	C₂×Dic₅	1	1	yes	characteristic
413	#95	C₂×Dic₅	1	1	yes	characteristic
414	#95	C₂×Dic₅	1	1	yes	characteristic
415	#95	C₂×Dic₅	1	1	yes	characteristic
416	#95	C₂×Dic₅	1	1	yes	characteristic
417	#95	C₂×Dic₅	1	1	yes	characteristic
418	#95	C₂×Dic₅	1	1	yes	characteristic
419	#95	C₂×Dic₅	1	1	yes	characteristic
420	#95	C₂×Dic₅	1	1	yes	characteristic
421	#95	C₂×Dic₅	1	1	yes	characteristic
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	2	2	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	—	4	1	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	—	4	1	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	—	4	1	no	—
436	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
437	C₂²×C₅	C₄×#41	1	1	yes	characteristic
438	C₂²×C₅	C₄×#41	1	1	yes	characteristic
439	C₂²×C₅	C₂×#131	1	1	yes	characteristic
440	C₂²×C₅	C₂×#131	1	1	yes	characteristic
441	C₂²×C₅	#568	1	1	yes	characteristic
442	C₂²×C₅	#568	1	1	yes	characteristic
443	C₄×C₅	—	2	2	no	—
444	C₄×C₅	—	2	2	no	—
445	C₄×C₅	—	2	2	no	—
446	C₄×C₅	—	4	1	no	—
447	C₄×C₅	—	4	1	no	—
448	C₄×C₅	—	4	1	no	—
449	C₄×C₅	—	4	1	no	—
450	C₄×C₅	—	4	1	no	—
451	C₄×C₅	—	4	1	no	—
452	C₄×C₅	—	4	1	no	—
453	C₄×C₅	—	4	1	no	—
454	C₄×C₅	—	4	1	no	—
455	C₄×C₅	C₂×#124	1	1	yes	characteristic
456	C₄×C₅	#529	1	1	yes	characteristic
457	C₄×C₅	#529	1	1	yes	characteristic
458	C₄×C₅	#532	1	1	yes	characteristic
459	C₂⁴	C₂²×Dic₅	1	1	yes	characteristic
460	C₂⁴	C₂²×Dic₅	1	1	yes	characteristic
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	4	1	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	4	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
480	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
481	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
482	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
483	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
484	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
485	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
486	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
487	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
489	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
490	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
491	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
492	M₁₆	—	20	4	no	—
493	C₂×C₈	—	5	2	no	—
494	C₂×C₈	—	5	2	no	—
495	C₂×C₈	—	5	2	no	—
496	C₂×C₈	—	5	2	no	—
497	C₂×C₈	—	5	2	no	—
498	C₂×C₈	—	5	2	no	—
499	C₂×C₈	—	10	1	no	—
500	C₂×C₈	—	10	1	no	—
501	C₂×C₈	—	10	1	no	—
502	C₂×C₈	—	10	1	no	—
503	C₂×C₈	—	10	1	no	—
504	C₂×C₈	—	10	1	no	—
505	C₂×C₈	—	10	1	no	—
506	C₂×C₈	—	10	1	no	—
507	C₂×C₈	—	10	1	no	—
508	C₂×C₈	—	10	1	no	—
509	C₂×C₈	—	10	1	no	—
510	C₂×C₈	—	10	1	no	—
511	C₂×C₈	—	10	1	no	—
512	C₂×C₈	—	10	1	no	—
513	C₂×C₈	—	10	1	no	—
514	C₂×C₈	—	10	1	no	—
515	C₂×C₈	—	10	1	no	—
516	C₂×C₈	—	10	1	no	—
517	C₂×C₈	—	20	4	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₂²⋊C₄	—	4	1	no	—
531	C₂²⋊C₄	—	4	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	D₄×D₅	1	2	yes	—
541	C₄²	#711	1	2	yes	—
542	C₂×C₅	—	4	2	no	—
543	C₂×C₅	—	8	1	no	—
544	C₂×C₅	C₄×#124	1	1	yes	characteristic
545	C₂×C₅	#2933	1	1	yes	characteristic
546	C₂×C₅	#2933	1	1	yes	characteristic
547	C₂×C₅	#2966	1	1	yes	characteristic
548	C₂×C₅	#2967	1	1	yes	characteristic
549	C₂×C₅	#2968	1	1	yes	characteristic
550	C₂×C₅	#2969	1	1	yes	characteristic
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	#4094	1	2	yes	—
565	C₂³	C₂³×Dic₅	1	1	yes	characteristic
566	Q₈	—	4	4	no	—
567	D₄	—	4	4	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	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	D₄×Dic₅	1	2	yes	—
610	C₂×C₄	D₄×Dic₅	1	2	yes	—
611	C₂×C₄	#4094	1	2	yes	—
612	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
613	C₂×C₄	C₂×#711	1	1	yes	characteristic
614	C₂×C₄	D₅×#41	1	1	yes	characteristic
615	C₂×C₄	D₅×#41	1	1	yes	characteristic
616	C₂×C₄	D₅×#41	1	1	yes	characteristic
617	C₂×C₄	D₅×#41	1	1	yes	characteristic
618	C₈	—	5	4	no	—
619	C₈	—	10	2	no	—
620	C₈	—	10	2	no	—
621	C₈	—	10	2	no	—
622	C₈	—	20	1	no	—
623	C₈	—	20	1	no	—
624	C₈	—	20	1	no	—
625	C₈	—	20	1	no	—
626	C₅	#21637	1	1	yes	characteristic, complemented, Sylow
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	C₂×D₄×Dic₅	1	1	yes	characteristic
642	C₂²	C₂×#4094	1	1	yes	characteristic
643	C₂²	C₂×#4094	1	1	yes	characteristic
644	C₂²	#66153	1	1	yes	characteristic
645	C₂²	#66153	1	1	yes	characteristic
646	C₂²	#41×Dic₅	1	1	yes	characteristic
647	C₂²	#41×Dic₅	1	1	yes	characteristic
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	#66002	1	1	yes	characteristic
661	C₄	D₅×#124	1	1	yes	characteristic
662	C₄	#66014	1	1	yes	characteristic
663	C₄	#66014	1	1	yes	characteristic
664	C₂	—	4	2	no	—
665	C₂	—	8	1	no	—
666	C₂	#10614649	1	1	yes	characteristic
667	C₂	#10614649	1	1	yes	characteristic
668	C₂	Dic₅×#124	1	1	yes	characteristic
669	C₂	#10614857	1	1	yes	characteristic
670	C₂	#10614858	1	1	yes	characteristic
671	C₂	#10614859	1	1	yes	characteristic
672	C₂	#10614860	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator, socle	C₂³×C₅	C₂³×C₄
Fitting	C₅×#2398	C₂
prime radical	C₂²×C₅×D₄	C₂×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#2398	D₅
hypocenter	C₅	#21637
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ #2398

Complements

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

N	H ≅ G/N	type
2. C₂×#65313	C₂	semidirect
4. #10602427	C₂	semidirect
6. #10600245	C₂	semidirect
7. #10600245	C₂	semidirect
8. #10600244	C₂	semidirect
9. #10600244	C₂	semidirect
10. #10600241	C₂	semidirect
11. #10600241	C₂	semidirect
12. #10600240	C₂	semidirect
13. C₂²⋊C₄×#168	C₂	semidirect
14. #10600230	C₂	semidirect
15. #10600227	C₂	semidirect
626. C₅	#21637	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2398	2
C₂×#65313	2
C₂×#65300	2
#10602427	2
#10602407	2
#10600245	2
#10600244	2
#10600241	2
#10600240	2
C₂²⋊C₄×#168	2
#10600230	2
#10600227	2
#21637	5