Subgroups — #12107547

Order 1280.

712 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#126	C₂	1	1	yes	maximal, characteristic
2	#10600276	C₂	1	1	yes	maximal, characteristic, complemented
3	#10600276	C₂	1	1	yes	maximal, characteristic, complemented
4	#10600275	C₂	1	1	yes	maximal, characteristic, complemented
5	#10600271	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600270	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600245	C₂	1	1	yes	maximal, characteristic
9	#10600245	C₂	1	1	yes	maximal, characteristic
10	#10600244	C₂	1	1	yes	maximal, characteristic
11	#10600241	C₂	1	1	yes	maximal, characteristic
12	#10600241	C₂	1	1	yes	maximal, characteristic
13	#10600241	C₂	1	1	yes	maximal, characteristic
14	#10600186	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#3935	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#126	C₄	1	1	yes	characteristic
17	C₂²×#681	C₂²	1	1	yes	characteristic
18	C₅×#388	C₄	1	1	yes	characteristic
19	C₅×#388	C₄	1	1	yes	characteristic
20	C₅×#388	C₄	1	1	yes	characteristic
21	C₅×#387	C₄	1	1	yes	characteristic
22	C₅×#387	C₄	1	1	yes	characteristic
23	C₅×#387	C₄	1	1	yes	characteristic
24	C₅×#383	C₄	1	1	yes	characteristic
25	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂²	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	C₄³×C₅	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊#168	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×C₄⋊#168	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
38	C₂×#3935	C₂²	1	1	yes	characteristic
39	C₂×#3935	C₂²	1	1	yes	characteristic
40	C₂×#3935	C₂²	1	1	yes	characteristic
41	C₂×#3935	C₂²	1	1	yes	characteristic
42	C₂×#3935	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×C₄×#168	C₂²	1	1	yes	characteristic
46	C₂×C₄×#168	C₂²	1	1	yes	characteristic
47	#64744	C₂²	1	1	yes	characteristic
48	#64744	C₂²	1	1	yes	characteristic
49	#64744	C₂²	1	1	yes	characteristic
50	#64744	C₂²	1	1	yes	characteristic
51	#64744	C₂²	1	1	yes	characteristic
52	#64744	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	#21667	—	5	1	no	maximal, Sylow
60	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₅×#126	—	2	4	no	—
62	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₂×#681	—	2	2	no	—
85	C₂×#681	—	2	2	no	—
86	C₂×#681	—	2	2	no	—
87	C₂²×#168	C₂³	1	1	yes	characteristic
88	C₂²×#168	C₂³	1	1	yes	characteristic
89	C₂²×#168	C₂³	1	1	yes	characteristic
90	C₂²×#168	C₂³	1	1	yes	characteristic
91	C₂²×#168	C₂³	1	1	yes	characteristic
92	C₂²×#168	C₂³	1	1	yes	characteristic
93	C₂²×#168	C₂³	1	1	yes	characteristic
94	C₂²×#168	C₂³	1	1	yes	characteristic
95	C₅×#95	C₂×C₄	1	1	yes	characteristic
96	C₅×#95	C₂×C₄	1	1	yes	characteristic
97	C₅×#95	C₂×C₄	1	1	yes	characteristic
98	C₅×#95	C₂×C₄	1	1	yes	characteristic
99	C₅×#95	C₂×C₄	1	1	yes	characteristic
100	C₅×#95	C₂×C₄	1	1	yes	characteristic
101	C₅×#95	C₂×C₄	1	1	yes	characteristic
102	C₅×#95	C₂×C₄	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	C₂²⋊#168	—	2	2	no	—
108	C₂²⋊#168	—	2	2	no	—
109	C₂²⋊#168	—	2	2	no	—
110	C₄⋊#168	—	2	2	no	—
111	C₄⋊#168	—	2	2	no	—
112	C₄⋊#168	—	2	2	no	—
113	#3935	—	2	2	no	—
114	#3935	—	2	2	no	—
115	#3935	—	2	2	no	—
116	#3935	—	2	2	no	—
117	#3935	—	2	2	no	—
118	C₄×#168	—	2	2	no	—
119	C₄×#168	—	2	2	no	—
120	C₄×#168	—	2	2	no	—
121	C₄×#168	—	2	2	no	—
122	C₄×#126	D₅	1	1	yes	characteristic
123	#1924	—	5	1	no	—
124	#1924	—	5	1	no	—
125	#1923	—	5	1	no	—
126	#1917	—	5	1	no	—
127	#1917	—	5	1	no	—
128	#1916	—	5	1	no	—
129	#1839	—	5	1	no	—
130	#1771	—	5	1	no	—
131	#1770	—	5	1	no	—
132	C₈×C₄⋊C₄	—	5	1	no	—
133	#1753	—	5	1	no	—
134	#1753	—	5	1	no	—
135	#1753	—	5	1	no	—
136	C₄×#97	—	5	1	no	—
137	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	4	1	no	—
162	C₅×C₄⋊C₄	—	4	1	no	—
163	C₅×C₄⋊C₄	M₁₆	1	4	yes	complemented
164	C₅×C₂²⋊C₄	—	2	2	no	—
165	C₅×C₂²⋊C₄	—	2	2	no	—
166	C₅×C₂²⋊C₄	—	2	2	no	—
167	C₅×C₂²⋊C₄	—	2	2	no	—
168	C₅×C₂²⋊C₄	—	4	1	no	—
169	C₅×C₂²⋊C₄	—	4	1	no	—
170	C₄²×C₅	—	2	2	no	—
171	C₄²×C₅	—	2	2	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	—	2	1	no	—
176	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	—	2	1	no	—
179	C₄²×C₅	—	2	1	no	—
180	C₄²×C₅	—	2	1	no	—
181	C₄²×C₅	—	2	1	no	—
182	C₄²×C₅	—	2	1	no	—
183	C₄²×C₅	—	2	1	no	—
184	C₄²×C₅	—	4	1	no	—
185	C₄²×C₅	—	4	1	no	—
186	#681	—	4	4	no	—
187	C₂×#168	—	2	1	no	—
188	C₂×#168	—	2	1	no	—
189	C₂×#168	—	2	1	no	—
190	C₂×#168	—	2	1	no	—
191	C₂×#168	—	2	1	no	—
192	C₂×#168	—	2	1	no	—
193	C₂×#168	—	2	1	no	—
194	C₂×#168	—	2	1	no	—
195	C₂×#168	—	2	1	no	—
196	C₂×#168	—	2	1	no	—
197	C₂×#168	—	2	1	no	—
198	C₂×#168	—	2	1	no	—
199	C₂×#168	—	2	1	no	—
200	C₂×#168	—	2	1	no	—
201	C₂×#168	—	2	1	no	—
202	C₂×#168	—	2	1	no	—
203	C₂×#168	—	2	1	no	—
204	C₂×#168	—	2	1	no	—
205	C₂×#168	#41	1	2	yes	—
206	C₂×#168	#41	1	2	yes	—
207	C₂×#168	#41	1	2	yes	—
208	C₂×#168	#41	1	2	yes	—
209	C₂×#168	#41	1	2	yes	—
210	C₂×#168	#41	1	2	yes	—
211	C₂²×M₁₆	—	5	1	no	—
212	C₂×#126	Dic₅	1	1	yes	characteristic
213	C₂×C₄⋊C₈	—	5	1	no	—
214	C₂×C₄⋊C₈	—	5	1	no	—
215	C₂×C₄⋊C₈	—	5	1	no	—
216	C₂×C₂²⋊C₈	—	5	1	no	—
217	C₂×C₂²⋊C₈	—	5	1	no	—
218	C₂×C₂²⋊C₈	—	5	1	no	—
219	C₂×#97	—	5	1	no	—
220	C₂×#97	—	5	1	no	—
221	C₂×#97	—	5	1	no	—
222	C₂×#97	—	5	1	no	—
223	C₂×#97	—	5	1	no	—
224	C₂×C₄×C₈	—	5	1	no	—
225	C₂×C₄×C₈	—	5	1	no	—
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂×C₄×C₈	—	5	1	no	—
228	#388	Dic₅	1	1	yes	characteristic
229	#388	Dic₅	1	1	yes	characteristic
230	#388	Dic₅	1	1	yes	characteristic
231	#387	Dic₅	1	1	yes	characteristic
232	#387	Dic₅	1	1	yes	characteristic
233	#387	Dic₅	1	1	yes	characteristic
234	#383	Dic₅	1	1	yes	characteristic
235	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
236	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
238	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
239	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
240	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
241	C₄³	C₂×D₅	1	1	yes	characteristic
242	#336	—	5	1	no	—
243	#336	—	5	1	no	—
244	#336	—	5	1	no	—
245	#336	—	5	1	no	—
246	#336	—	5	1	no	—
247	#336	—	5	1	no	—
248	#336	—	5	1	no	—
249	#336	—	5	1	no	—
250	#336	—	5	1	no	—
251	#336	—	5	1	no	—
252	#336	—	5	1	no	—
253	#336	—	5	1	no	—
254	C₂³×C₅	—	2	1	no	—
255	C₂³×C₅	—	2	1	no	—
256	C₂³×C₅	—	2	1	no	—
257	C₂³×C₅	—	2	1	no	—
258	C₂³×C₅	—	2	1	no	—
259	C₂³×C₅	—	2	1	no	—
260	C₂³×C₅	—	2	1	no	—
261	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	1	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	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	—	4	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
302	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
303	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
304	C₂×C₄×C₅	#131	1	2	yes	—
305	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
311	#168	—	2	2	no	—
312	#168	—	2	2	no	—
313	#168	—	2	2	no	—
314	#168	—	4	1	no	—
315	#168	—	4	1	no	—
316	#168	—	4	1	no	—
317	#168	—	4	1	no	—
318	#168	#126	1	4	yes	complemented
319	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
320	C₂×M₁₆	—	10	2	no	—
321	C₂×M₁₆	—	10	2	no	—
322	C₂×M₁₆	—	10	2	no	—
323	C₂²×C₈	—	5	1	no	—
324	C₂²×C₈	—	5	1	no	—
325	C₂²×C₈	—	5	1	no	—
326	C₂²×C₈	—	5	1	no	—
327	C₂²×C₈	—	5	1	no	—
328	C₂²×C₈	—	5	1	no	—
329	C₂²×C₈	—	5	1	no	—
330	C₂²×C₈	—	5	1	no	—
331	#126	—	2	4	no	—
332	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
344	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
345	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
346	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
347	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
348	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
349	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
350	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
351	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
352	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
353	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
354	C₄⋊C₈	—	10	2	no	—
355	C₄⋊C₈	—	10	2	no	—
356	C₄⋊C₈	—	10	2	no	—
357	C₂²⋊C₈	—	10	2	no	—
358	C₂²⋊C₈	—	10	2	no	—
359	C₂²⋊C₈	—	10	2	no	—
360	#97	—	10	2	no	—
361	#97	—	10	2	no	—
362	#97	—	10	2	no	—
363	#97	—	10	2	no	—
364	#97	—	10	2	no	—
365	C₄×C₈	—	10	2	no	—
366	C₄×C₈	—	10	2	no	—
367	C₄×C₈	—	10	2	no	—
368	C₄×C₈	—	10	2	no	—
369	#95	C₂×Dic₅	1	1	yes	characteristic
370	#95	C₂×Dic₅	1	1	yes	characteristic
371	#95	C₂×Dic₅	1	1	yes	characteristic
372	#95	C₂×Dic₅	1	1	yes	characteristic
373	#95	C₂×Dic₅	1	1	yes	characteristic
374	#95	C₂×Dic₅	1	1	yes	characteristic
375	#95	C₂×Dic₅	1	1	yes	characteristic
376	#95	C₂×Dic₅	1	1	yes	characteristic
377	#95	C₂×Dic₅	1	1	yes	characteristic
378	#95	C₂×Dic₅	1	1	yes	characteristic
379	#95	C₂×Dic₅	1	1	yes	characteristic
380	#95	C₂×Dic₅	1	1	yes	characteristic
381	C₂²×C₅	—	4	1	no	—
382	C₂²×C₅	—	4	1	no	—
383	C₂²×C₅	—	4	1	no	—
384	C₂²×C₅	—	4	1	no	—
385	C₂²×C₅	—	4	1	no	—
386	C₂²×C₅	—	4	1	no	—
387	C₂²×C₅	—	4	1	no	—
388	C₂²×C₅	C₄×#41	1	1	yes	characteristic
389	C₂²×C₅	C₄×#41	1	1	yes	characteristic
390	C₂²×C₅	C₄×#41	1	1	yes	characteristic
391	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
392	C₂²×C₅	C₂×#131	1	1	yes	characteristic
393	C₂²×C₅	#568	1	1	yes	characteristic
394	C₂²×C₅	#568	1	1	yes	characteristic
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	—	2	2	no	—
397	C₄×C₅	—	2	2	no	—
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	4	1	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	—	4	1	no	—
402	C₄×C₅	—	4	1	no	—
403	C₄×C₅	—	4	1	no	—
404	C₄×C₅	—	4	1	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	1	no	—
408	C₄×C₅	C₂×#126	1	1	yes	characteristic
409	C₄×C₅	#529	1	1	yes	characteristic
410	C₄×C₅	#529	1	1	yes	characteristic
411	C₄×C₅	#529	1	1	yes	characteristic
412	C₂⁴	C₂²×Dic₅	1	1	yes	characteristic
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
420	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
421	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
422	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
423	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
424	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
425	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
426	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
427	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
428	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
429	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
430	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
431	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
432	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
433	M₁₆	—	20	4	no	—
434	C₂×C₈	—	5	2	no	—
435	C₂×C₈	—	5	2	no	—
436	C₂×C₈	—	5	2	no	—
437	C₂×C₈	—	5	2	no	—
438	C₂×C₈	—	5	2	no	—
439	C₂×C₈	—	5	2	no	—
440	C₂×C₈	—	10	1	no	—
441	C₂×C₈	—	10	1	no	—
442	C₂×C₈	—	10	1	no	—
443	C₂×C₈	—	10	1	no	—
444	C₂×C₈	—	10	1	no	—
445	C₂×C₈	—	10	1	no	—
446	C₂×C₈	—	10	1	no	—
447	C₂×C₈	—	10	1	no	—
448	C₂×C₈	—	10	1	no	—
449	C₂×C₈	—	10	1	no	—
450	C₂×C₈	—	10	1	no	—
451	C₂×C₈	—	10	1	no	—
452	C₂×C₈	—	10	1	no	—
453	C₂×C₈	—	10	1	no	—
454	C₂×C₈	—	10	1	no	—
455	C₂×C₈	—	10	1	no	—
456	C₂×C₈	—	10	1	no	—
457	C₂×C₈	—	10	1	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	#681	1	4	yes	complemented
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	4	1	no	—
485	C₄²	—	4	1	no	—
486	C₂×C₅	—	8	1	no	—
487	C₂×C₅	C₄×#126	1	1	yes	characteristic
488	C₂×C₅	#2965	1	1	yes	characteristic
489	C₂×C₅	#2967	1	1	yes	characteristic
490	C₂×C₅	#2968	1	1	yes	characteristic
491	C₂×C₅	#2969	1	1	yes	characteristic
492	C₂×C₅	#2970	1	1	yes	characteristic
493	C₂×C₅	#2971	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	C₂³×Dic₅	1	1	yes	characteristic
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	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	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	C₂×#681	1	2	yes	—
542	C₂×C₄	C₂×#681	1	2	yes	—
543	C₂×C₄	C₂×#681	1	2	yes	—
544	C₂×C₄	#4094	1	2	yes	—
545	C₂×C₄	D₅×#41	1	1	yes	characteristic
546	C₂×C₄	D₅×#41	1	1	yes	characteristic
547	C₂×C₄	D₅×#41	1	1	yes	characteristic
548	C₂×C₄	D₅×#41	1	1	yes	characteristic
549	C₂×C₄	D₅×#41	1	1	yes	characteristic
550	C₂×C₄	D₅×#41	1	1	yes	characteristic
551	C₈	—	5	4	no	—
552	C₈	—	10	2	no	—
553	C₈	—	10	2	no	—
554	C₈	—	10	2	no	—
555	C₈	—	20	1	no	—
556	C₈	—	20	1	no	—
557	C₈	—	20	1	no	—
558	C₈	—	20	1	no	—
559	C₅	#21667	1	1	yes	characteristic, complemented, Sylow
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	C₂²×#681	1	1	yes	characteristic
568	C₂²	C₂×#4094	1	1	yes	characteristic
569	C₂²	#66153	1	1	yes	characteristic
570	C₂²	#66153	1	1	yes	characteristic
571	C₂²	#41×Dic₅	1	1	yes	characteristic
572	C₂²	#41×Dic₅	1	1	yes	characteristic
573	C₂²	#41×Dic₅	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	D₅×#126	1	1	yes	characteristic
588	C₄	#66040	1	1	yes	characteristic
589	C₄	#66040	1	1	yes	characteristic
590	C₄	#66040	1	1	yes	characteristic
591	C₂	—	8	1	no	—
592	C₂	#10614248	1	1	yes	characteristic
593	C₂	#10614249	1	1	yes	characteristic
594	C₂	#10614250	1	1	yes	characteristic
595	C₂	Dic₅×#126	1	1	yes	characteristic
596	C₂	#10614858	1	1	yes	characteristic
597	C₂	#10614859	1	1	yes	characteristic
598	C₂	#10614860	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator, socle	C₂³×C₅	C₂³×C₄
Fitting	C₄×C₅×#126	C₂
prime radical	C₂⁴×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	C₄×#126	D₅
hypocenter	C₅	#21667
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#126

Complements

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

N	H ≅ G/N	type
2. #10600276	C₂	semidirect
3. #10600276	C₂	semidirect
4. #10600275	C₂	semidirect
5. #10600271	C₂	semidirect
6. #10600270	C₂	semidirect
7. C₄⋊C₄×#168	C₂	semidirect
14. #10600186	C₂	semidirect
15. C₄×#3935	C₂	semidirect
163. C₅×C₄⋊C₄	M₁₆	semidirect
318. #168	#126	semidirect
463. C₄⋊C₄	#681	semidirect
559. C₅	#21667	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#126	2
#10600276	2
#10600275	2
#10600271	2
#10600270	2
C₄⋊C₄×#168	2
#10600245	2
#10600244	2
#10600241	2
#10600186	2
C₄×#3935	2
#21667	5