Subgroups — C₅×#23704 #11946424

Order 1280.

820 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#433	C₂	1	1	yes	maximal, characteristic
3	C₅×#2323	C₂	1	2	yes	maximal
4	C₅×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2076	C₂	1	1	yes	maximal, characteristic
6	C₅×#2066	C₂	1	2	yes	maximal, complemented
7	C₅×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2035	C₂	1	2	yes	maximal
9	C₅×#2001	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
15	C₂×C₅×#117	C₂²	1	1	yes	characteristic
16	C₄×C₅×Q₁₆	—	2	4	no	—
17	C₅×#433	—	2	4	no	—
18	C₂×C₅×#107	C₂²	1	1	yes	characteristic
19	C₂×C₅×#106	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×#103	C₂²	1	2	yes	—
23	C₂×C₅×#103	C₂²	1	2	yes	—
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×#97	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₅×#391	C₂²	1	2	yes	—
30	C₅×#389	—	2	2	no	—
31	C₅×#389	C₂²	1	2	yes	—
32	C₅×#388	—	2	2	no	—
33	C₅×#388	—	2	2	no	—
34	C₅×#387	—	2	2	no	—
35	C₅×#380	C₂²	1	2	yes	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	1	yes	characteristic
41	#23704	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	C₂³	1	2	yes	—
43	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₅×Q₁₆	—	2	4	no	—
45	C₂×C₅×Q₁₆	—	2	2	no	—
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₅×C₂²⋊Q₈	—	2	4	no	—
51	C₅×C₂²⋊Q₈	—	2	4	no	—
52	C₄×C₅×Q₈	—	2	4	no	—
53	C₄×C₅×Q₈	—	2	4	no	—
54	C₅×#117	—	2	2	no	—
55	C₅×#117	—	2	2	no	—
56	C₂×C₅×C₄⋊C₄	—	2	2	no	—
57	C₂×C₅×C₄⋊C₄	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	—	2	2	no	—
59	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₅	—	2	2	no	—
69	C₂×C₄²×C₅	—	2	2	no	—
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#107	—	2	2	no	—
73	C₅×#106	—	2	4	no	—
74	C₅×C₄⋊C₈	—	2	2	no	—
75	C₅×C₄⋊C₈	—	2	2	no	—
76	C₅×#103	—	2	4	no	—
77	C₅×#103	—	2	4	no	—
78	C₅×#103	—	2	4	no	—
79	C₅×C₂²⋊C₈	—	2	2	no	—
80	C₅×C₂²⋊C₈	—	2	2	no	—
81	C₅×#97	—	2	2	no	—
82	C₄×C₅×C₈	D₄	1	4	yes	—
83	C₅×#95	—	2	2	no	—
84	C₅×#95	—	2	2	no	—
85	C₅×#95	—	2	2	no	—
86	C₅×#95	—	2	2	no	—
87	C₅×#95	—	2	2	no	—
88	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×#433	C₂×C₅	1	1	yes	characteristic
90	#2323	C₂×C₅	1	2	yes	—
91	#2087	C₂×C₅	1	1	yes	characteristic, complemented
92	#2076	C₂×C₅	1	1	yes	characteristic
93	#2066	C₂×C₅	1	2	yes	complemented
94	#2056	C₂×C₅	1	1	yes	characteristic, complemented
95	#2035	C₂×C₅	1	2	yes	—
96	#2001	C₂×C₅	1	1	yes	characteristic
97	C₄×#106	C₂×C₅	1	1	yes	characteristic, complemented
98	#1763	C₂×C₅	1	2	yes	complemented
99	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₅×Q₈	—	2	2	no	—
101	C₂×C₅×Q₈	—	2	2	no	—
102	C₂×C₅×Q₈	—	2	2	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	#41	1	4	yes	—
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₅×Q₁₆	—	2	8	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
128	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
129	C₅×C₄⋊C₄	—	2	8	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	4	4	no	—
138	C₅×C₄⋊C₄	—	8	2	no	—
139	C₅×C₄⋊C₄	#41	1	4	yes	—
140	C₅×C₂²⋊C₄	—	2	8	no	—
141	C₅×C₂²⋊C₄	—	2	2	no	—
142	C₅×C₂²⋊C₄	—	2	2	no	—
143	C₅×C₂²⋊C₄	—	8	2	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₄²×C₅	—	2	1	no	—
146	C₄²×C₅	—	4	4	no	—
147	C₄²×C₅	—	8	2	no	—
148	C₄²×C₅	C₂×D₄	1	2	yes	—
149	C₄²×C₅	#41	1	2	yes	—
150	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
152	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
153	C₂×#117	C₂²×C₅	1	1	yes	characteristic
154	C₄×Q₁₆	—	2	4	no	—
155	#433	—	2	4	no	—
156	C₂×#107	C₂²×C₅	1	1	yes	characteristic
157	C₂×#106	C₂²×C₅	1	2	yes	—
158	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
160	C₂×#103	C₂²×C₅	1	2	yes	—
161	C₂×#103	C₂²×C₅	1	2	yes	—
162	C₂×#103	C₂²×C₅	1	2	yes	—
163	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
165	C₂×#97	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
167	#391	C₂²×C₅	1	2	yes	—
168	#389	—	2	2	no	—
169	#389	C₂²×C₅	1	2	yes	—
170	#388	—	2	2	no	—
171	#388	—	2	2	no	—
172	#387	—	2	2	no	—
173	#380	C₂²×C₅	1	2	yes	—
174	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
175	#340	C₂²×C₅	1	1	yes	characteristic
176	#340	C₂²×C₅	1	2	yes	—
177	#340	C₂²×C₅	1	1	yes	characteristic
178	#340	C₂²×C₅	1	2	yes	—
179	C₂³×C₅	—	2	1	no	—
180	C₂³×C₅	—	2	2	no	—
181	C₂³×C₅	—	2	2	no	—
182	C₂³×C₅	—	2	1	no	—
183	C₂³×C₅	—	2	1	no	—
184	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₅×Q₈	—	2	4	no	—
186	C₅×Q₈	—	2	4	no	—
187	C₅×Q₈	—	4	2	no	—
188	C₅×Q₈	—	4	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	2	4	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	#121	1	2	yes	—
215	C₂×C₄×C₅	#121	1	2	yes	—
216	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×#41	1	2	yes	—
218	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×#41	1	2	yes	—
220	C₅×C₈	—	2	2	no	—
221	C₅×C₈	—	2	2	no	—
222	C₅×C₈	—	4	1	no	—
223	C₅×C₈	—	4	1	no	—
224	C₂²×Q₈	C₂³×C₅	1	2	yes	—
225	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂×Q₁₆	—	2	4	no	—
227	C₂×Q₁₆	—	2	2	no	—
228	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
232	C₂²⋊Q₈	—	2	4	no	—
233	C₂²⋊Q₈	—	2	4	no	—
234	C₄×Q₈	—	2	4	no	—
235	C₄×Q₈	—	2	4	no	—
236	#117	—	2	2	no	—
237	#117	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
254	#107	—	2	2	no	—
255	#106	—	2	4	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	#103	—	2	4	no	—
259	#103	—	2	4	no	—
260	#103	—	2	4	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	#97	—	2	2	no	—
264	C₄×C₈	C₅×D₄	1	4	yes	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	4	2	no	—
272	C₂²×C₅	—	4	1	no	—
273	C₂²×C₅	—	4	1	no	—
274	C₂²×C₅	—	4	1	no	—
275	C₂²×C₅	C₂×#121	1	1	yes	characteristic
276	C₂²×C₅	#525	1	2	yes	—
277	C₂²×C₅	#577	1	2	yes	—
278	C₂²×C₅	#578	1	1	yes	characteristic
279	C₂²×C₅	#578	1	1	yes	characteristic
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	—	2	2	no	—
282	C₄×C₅	—	4	4	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	—	4	4	no	—
285	C₄×C₅	—	4	1	no	—
286	C₄×C₅	—	4	1	no	—
287	C₄×C₅	—	8	2	no	—
288	C₄×C₅	—	8	2	no	—
289	C₄×C₅	#525	1	1	yes	characteristic
290	C₄×C₅	#529	1	2	yes	—
291	C₄×C₅	#532	1	1	yes	characteristic
292	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	C₅×#41	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
313	Q₁₆	—	2	8	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
321	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	8	2	no	—
332	C₄⋊C₄	C₅×#41	1	4	yes	—
333	C₂²⋊C₄	—	2	8	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	8	2	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	4	4	no	—
340	C₄²	—	8	2	no	—
341	C₄²	C₂×C₅×D₄	1	2	yes	—
342	C₄²	C₅×#41	1	2	yes	—
343	C₂×C₅	—	8	1	no	—
344	C₂×C₅	#2392	1	1	yes	characteristic
345	C₂×C₅	#3059	1	1	yes	characteristic
346	C₂×C₅	#3060	1	1	yes	characteristic
347	C₂×C₅	#3120	1	2	yes	—
348	C₂×C₅	#3121	1	2	yes	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
355	Q₈	—	2	4	no	—
356	Q₈	—	2	4	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	C₂×C₄	—	2	2	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	—	2	1	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	C₅×#121	1	2	yes	—
385	C₂×C₄	C₅×#121	1	2	yes	—
386	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
387	C₂×C₄	C₂×C₅×#41	1	2	yes	—
388	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
389	C₂×C₄	C₂×C₅×#41	1	2	yes	—
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₅	#23704	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	C₂×C₅×#121	1	1	yes	characteristic
401	C₂²	C₅×#525	1	2	yes	—
402	C₂²	C₅×#577	1	2	yes	—
403	C₂²	C₅×#578	1	1	yes	characteristic
404	C₂²	C₅×#578	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₅×#525	1	1	yes	characteristic
415	C₄	C₅×#529	1	2	yes	—
416	C₄	C₅×#532	1	1	yes	characteristic
417	C₂	—	8	1	no	—
418	C₂	C₅×#2392	1	1	yes	characteristic
419	C₂	C₅×#3059	1	1	yes	characteristic
420	C₂	C₅×#3060	1	1	yes	characteristic
421	C₂	C₅×#3120	1	2	yes	—
422	C₂	C₅×#3121	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₅×Q₁₆	C₂	semidirect
4. C₅×#2087	C₂	semidirect
6. C₅×#2066	C₂	semidirect
7. C₅×#2056	C₂	semidirect
10. C₄×C₅×#106	C₂	semidirect
11. C₅×#1763	C₂	semidirect
41. #23704	C₅	direct (N × H)
88. C₂×C₄×Q₁₆	C₂×C₅	semidirect
91. #2087	C₂×C₅	semidirect
93. #2066	C₂×C₅	semidirect
94. #2056	C₂×C₅	semidirect
97. C₄×#106	C₂×C₅	semidirect
98. #1763	C₂×C₅	semidirect
394. C₅	#23704	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×Q₁₆	2
C₂×C₅×#433	2
C₅×#2323	2
C₅×#2087	2
C₅×#2076	2
C₅×#2066	2
C₅×#2056	2
C₅×#2035	2
C₅×#2001	2
C₄×C₅×#106	2
C₅×#1763	2
#23704	5

Subgroups — C5×#23704 #11946424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23704 #11946424