Subgroups — C₄×C₅×#535 #11956808

Order 1280.

3602 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2328	C₂	1	2	yes	maximal, complemented
5	C₅×#2326	C₂	1	2	yes	maximal, complemented
6	C₅×#2324	C₂	1	4	yes	maximal, complemented
7	C₅×#2321	C₂	1	4	yes	maximal, complemented
8	C₅×#2317	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2311	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2309	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#127	C₂	1	2	yes	maximal, complemented
12	C₄×C₅×#124	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×#121	C₂	1	4	yes	maximal, complemented
14	C₄×C₅×#120	C₂	1	4	yes	maximal, complemented
15	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₅	C₂²	1	2	yes	—
19	C₅×#535	C₄	1	16	yes	direct product factor
20	C₂×C₅×#127	C₂²	1	2	yes	—
21	C₂×C₅×#124	C₂²	1	2	yes	—
22	C₂×C₅×#121	C₂²	1	4	yes	—
23	C₂×C₅×#120	C₂²	1	4	yes	—
24	C₄×C₅×#41	—	2	8	no	—
25	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×C₅×D₄	—	2	8	no	—
28	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
29	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
33	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
34	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×C₅×D₄	C₂²	1	8	yes	complemented
37	C₂×C₅×#117	C₂²	1	1	yes	characteristic
38	C₂×C₅×#117	C₂²	1	1	yes	characteristic
39	C₂×C₅×#117	C₂²	1	1	yes	characteristic
40	C₂×C₅×#117	C₂²	1	2	yes	complemented
41	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
45	C₅×#391	C₂²	1	2	yes	complemented
46	C₅×#390	C₂²	1	4	yes	—
47	C₅×#390	C₂²	1	2	yes	—
48	C₅×#390	C₂²	1	2	yes	—
49	C₅×#390	C₂²	1	2	yes	complemented
50	C₅×#390	C₂²	1	8	yes	complemented
51	C₅×#389	C₂²	1	4	yes	complemented
52	C₅×#388	C₂²	1	8	yes	complemented
53	C₅×#388	C₂²	1	8	yes	complemented
54	C₅×#386	C₂²	1	4	yes	—
55	C₅×#386	C₂²	1	8	yes	complemented
56	C₅×#386	C₂²	1	8	yes	complemented
57	C₅×#385	C₂²	1	4	yes	—
58	C₅×#385	C₂²	1	8	yes	complemented
59	C₅×#384	C₂²	1	2	yes	complemented
60	C₅×#382	C₂²	1	2	yes	complemented
61	C₅×#380	C₂²	1	4	yes	complemented
62	C₅×#379	C₂²	1	4	yes	—
63	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
64	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
65	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
67	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
68	C₅×#376	C₂²	1	2	yes	complemented
69	C₄³×C₅	C₂²	1	2	yes	complemented
70	C₄×#535	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁵×C₅	C₂³	1	2	yes	—
72	C₂×C₅×#41	—	2	4	no	—
73	C₂×C₅×#41	—	2	4	no	—
74	C₂×C₅×#41	C₂×C₄	1	8	yes	complemented
75	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×D₄	—	2	4	no	—
77	C₂²×C₅×D₄	—	2	4	no	—
78	C₂²×C₅×D₄	C₂×C₄	1	8	yes	complemented
79	C₂²×C₅×D₄	C₂³	1	2	yes	—
80	C₂²×C₅×D₄	C₂³	1	2	yes	—
81	C₂²×C₅×D₄	C₂³	1	2	yes	—
82	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂²×C₅×D₄	C₂³	1	8	yes	—
84	C₂³×C₄×C₅	—	2	8	no	—
85	C₂³×C₄×C₅	—	4	8	no	—
86	C₂³×C₄×C₅	C₂³	1	4	yes	—
87	C₂³×C₄×C₅	C₂³	1	2	yes	—
88	C₂³×C₄×C₅	C₂³	1	2	yes	—
89	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₅	C₂³	1	2	yes	—
91	C₂³×C₄×C₅	C₂³	1	4	yes	—
92	C₂³×C₄×C₅	C₂³	1	2	yes	—
93	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₅×#127	C₂×C₄	1	16	yes	complemented
96	C₅×#124	C₂×C₄	1	16	yes	complemented
97	C₅×#121	C₂×C₄	1	32	yes	complemented
98	C₅×#120	C₂×C₄	1	32	yes	complemented
99	C₄×C₅×Q₈	—	2	4	no	—
100	C₄×C₅×Q₈	—	2	4	no	—
101	C₄×C₅×D₄	—	2	8	no	—
102	C₄×C₅×D₄	—	2	8	no	—
103	C₄×C₅×D₄	—	2	8	no	—
104	C₄×C₅×D₄	—	2	8	no	—
105	C₄×C₅×D₄	—	2	8	no	—
106	C₄×C₅×D₄	—	2	8	no	—
107	C₄×C₅×D₄	—	2	4	no	—
108	C₄×C₅×D₄	—	2	4	no	—
109	C₄×C₅×D₄	—	4	16	no	—
110	C₅×#117	—	2	4	no	—
111	C₅×#117	—	2	4	no	—
112	C₅×#117	—	2	8	no	—
113	C₅×#117	C₂×C₄	1	8	yes	complemented
114	C₂×C₅×C₄⋊C₄	—	2	4	no	—
115	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
123	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
125	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
132	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
133	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
134	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
136	C₂×C₄²×C₅	—	2	8	no	—
137	C₂×C₄²×C₅	D₄	1	8	yes	complemented
138	C₂×C₄²×C₅	C₂³	1	2	yes	—
139	C₂×C₄²×C₅	C₂³	1	2	yes	—
140	C₂×C₄²×C₅	C₂³	1	2	yes	—
141	C₂×C₄²×C₅	C₂³	1	4	yes	—
142	C₂×C₄²×C₅	C₂³	1	2	yes	—
143	C₂×C₄²×C₅	C₂³	1	4	yes	—
144	C₂×C₄²×C₅	C₂³	1	2	yes	—
145	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
149	C₅×#95	C₂³	1	4	yes	—
150	C₅×#95	C₂³	1	4	yes	—
151	C₅×#95	C₂³	1	8	yes	—
152	C₅×#95	C₂³	1	8	yes	—
153	C₂×#535	C₂×C₅	1	1	yes	characteristic
154	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂²×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
156	#2328	C₂×C₅	1	2	yes	complemented
157	#2326	C₂×C₅	1	2	yes	complemented
158	#2324	C₂×C₅	1	4	yes	complemented
159	#2321	C₂×C₅	1	4	yes	complemented
160	#2317	C₂×C₅	1	1	yes	characteristic, complemented
161	#2311	C₂×C₅	1	1	yes	characteristic, complemented
162	#2309	C₂×C₅	1	1	yes	characteristic, complemented
163	C₄×#127	C₂×C₅	1	2	yes	complemented
164	C₄×#124	C₂×C₅	1	2	yes	complemented
165	C₄×#121	C₂×C₅	1	4	yes	complemented
166	C₄×#120	C₂×C₅	1	4	yes	complemented
167	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
168	C₂⁴×C₅	—	2	4	no	—
169	C₂⁴×C₅	—	2	4	no	—
170	C₂⁴×C₅	—	4	4	no	—
171	C₂⁴×C₅	—	4	4	no	—
172	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
173	C₂⁴×C₅	C₂⁴	1	4	yes	—
174	C₂⁴×C₅	C₂⁴	1	2	yes	—
175	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
176	C₅×#41	—	2	32	no	—
177	C₂×C₅×Q₈	—	2	2	no	—
178	C₂×C₅×Q₈	—	2	2	no	—
179	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
180	C₂×C₅×D₄	—	2	4	no	—
181	C₂×C₅×D₄	—	2	4	no	—
182	C₂×C₅×D₄	—	2	32	no	—
183	C₂×C₅×D₄	—	2	4	no	—
184	C₂×C₅×D₄	—	2	4	no	—
185	C₂×C₅×D₄	—	2	2	no	—
186	C₂×C₅×D₄	—	2	4	no	—
187	C₂×C₅×D₄	—	2	4	no	—
188	C₂×C₅×D₄	—	2	2	no	—
189	C₂×C₅×D₄	—	4	8	no	—
190	C₂×C₅×D₄	—	4	8	no	—
191	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
192	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
193	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
194	C₂×C₅×D₄	C₂²×C₄	1	4	yes	complemented
195	C₂×C₅×D₄	C₂²×C₄	1	32	yes	complemented
196	C₂²×C₄×C₅	—	2	4	no	—
197	C₂²×C₄×C₅	—	2	4	no	—
198	C₂²×C₄×C₅	—	2	4	no	—
199	C₂²×C₄×C₅	—	2	4	no	—
200	C₂²×C₄×C₅	—	2	4	no	—
201	C₂²×C₄×C₅	—	2	4	no	—
202	C₂²×C₄×C₅	—	2	8	no	—
203	C₂²×C₄×C₅	—	2	8	no	—
204	C₂²×C₄×C₅	—	2	8	no	—
205	C₂²×C₄×C₅	—	2	16	no	—
206	C₂²×C₄×C₅	—	4	8	no	—
207	C₂²×C₄×C₅	—	4	4	no	—
208	C₂²×C₄×C₅	—	4	2	no	—
209	C₂²×C₄×C₅	—	4	4	no	—
210	C₂²×C₄×C₅	—	4	32	no	—
211	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
212	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	complemented
213	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
216	C₂²×C₄×C₅	#41	1	4	yes	—
217	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
229	C₅×C₄⋊C₄	—	2	4	no	—
230	C₅×C₄⋊C₄	—	2	4	no	—
231	C₅×C₄⋊C₄	—	2	4	no	—
232	C₅×C₄⋊C₄	—	2	4	no	—
233	C₅×C₄⋊C₄	—	2	2	no	—
234	C₅×C₄⋊C₄	—	2	2	no	—
235	C₅×C₄⋊C₄	—	2	4	no	—
236	C₅×C₄⋊C₄	—	4	8	no	—
237	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
238	C₅×C₂²⋊C₄	—	2	4	no	—
239	C₅×C₂²⋊C₄	—	2	4	no	—
240	C₅×C₂²⋊C₄	—	2	8	no	—
241	C₅×C₂²⋊C₄	—	2	8	no	—
242	C₅×C₂²⋊C₄	—	2	4	no	—
243	C₅×C₂²⋊C₄	—	2	4	no	—
244	C₅×C₂²⋊C₄	—	4	8	no	—
245	C₅×C₂²⋊C₄	—	4	8	no	—
246	C₅×C₂²⋊C₄	—	4	8	no	—
247	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
248	C₅×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
249	C₄²×C₅	—	2	4	no	—
250	C₄²×C₅	—	2	4	no	—
251	C₄²×C₅	—	2	4	no	—
252	C₄²×C₅	—	2	4	no	—
253	C₄²×C₅	—	2	8	no	—
254	C₄²×C₅	—	4	4	no	—
255	C₄²×C₅	C₂²×C₄	1	8	yes	complemented
256	C₄²×C₅	C₂×D₄	1	4	yes	—
257	C₄²×C₅	C₂×D₄	1	4	yes	—
258	C₄²×C₅	C₂×D₄	1	4	yes	—
259	C₄²×C₅	C₂×D₄	1	4	yes	—
260	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
261	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
262	C₂⁴×C₄	C₂²×C₅	1	2	yes	—
263	#535	C₄×C₅	1	16	yes	direct product factor
264	C₂×#127	C₂²×C₅	1	2	yes	—
265	C₂×#124	C₂²×C₅	1	2	yes	—
266	C₂×#121	C₂²×C₅	1	4	yes	—
267	C₂×#120	C₂²×C₅	1	4	yes	—
268	C₄×#41	—	2	8	no	—
269	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂×C₄×D₄	—	2	8	no	—
272	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
273	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
274	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
275	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
276	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
277	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
278	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₂×C₄×D₄	C₂²×C₅	1	8	yes	complemented
281	C₂×#117	C₂²×C₅	1	1	yes	characteristic
282	C₂×#117	C₂²×C₅	1	1	yes	characteristic
283	C₂×#117	C₂²×C₅	1	1	yes	characteristic
284	C₂×#117	C₂²×C₅	1	2	yes	complemented
285	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
286	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
287	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
288	C₂²×C₄²	C₂²×C₅	1	2	yes	complemented
289	#391	C₂²×C₅	1	2	yes	complemented
290	#390	C₂²×C₅	1	2	yes	—
291	#390	C₂²×C₅	1	4	yes	—
292	#390	C₂²×C₅	1	2	yes	—
293	#390	C₂²×C₅	1	2	yes	complemented
294	#390	C₂²×C₅	1	8	yes	complemented
295	#389	C₂²×C₅	1	4	yes	complemented
296	#388	C₂²×C₅	1	8	yes	complemented
297	#388	C₂²×C₅	1	8	yes	complemented
298	#386	C₂²×C₅	1	4	yes	—
299	#386	C₂²×C₅	1	8	yes	complemented
300	#386	C₂²×C₅	1	8	yes	complemented
301	#385	C₂²×C₅	1	4	yes	—
302	#385	C₂²×C₅	1	8	yes	complemented
303	#384	C₂²×C₅	1	2	yes	complemented
304	#382	C₂²×C₅	1	2	yes	complemented
305	#380	C₂²×C₅	1	4	yes	complemented
306	#379	C₂²×C₅	1	4	yes	—
307	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
308	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
309	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
310	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
312	#376	C₂²×C₅	1	2	yes	complemented
313	C₄³	C₂²×C₅	1	2	yes	complemented
314	C₂³×C₅	—	2	2	no	—
315	C₂³×C₅	—	2	2	no	—
316	C₂³×C₅	—	2	16	no	—
317	C₂³×C₅	—	2	2	no	—
318	C₂³×C₅	—	2	4	no	—
319	C₂³×C₅	—	2	2	no	—
320	C₂³×C₅	—	2	4	no	—
321	C₂³×C₅	—	2	4	no	—
322	C₂³×C₅	—	2	8	no	—
323	C₂³×C₅	—	2	8	no	—
324	C₂³×C₅	—	2	4	no	—
325	C₂³×C₅	—	4	16	no	—
326	C₂³×C₅	—	4	8	no	—
327	C₂³×C₅	—	4	8	no	—
328	C₂³×C₅	—	4	16	no	—
329	C₂³×C₅	C₂³×C₄	1	8	yes	—
330	C₂³×C₅	C₂³×C₄	1	4	yes	—
331	C₂³×C₅	C₂³×C₄	1	2	yes	—
332	C₂³×C₅	C₂²×D₄	1	2	yes	—
333	C₂³×C₅	C₂×#41	1	2	yes	—
334	C₂³×C₅	C₂⁵	1	1	yes	characteristic
335	C₅×Q₈	—	2	8	no	—
336	C₅×D₄	—	2	16	no	—
337	C₅×D₄	—	2	16	no	—
338	C₅×D₄	—	2	16	no	—
339	C₅×D₄	—	2	8	no	—
340	C₅×D₄	—	4	32	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	4	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	2	4	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	16	no	—
349	C₂×C₄×C₅	—	2	8	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	2	2	no	—
352	C₂×C₄×C₅	—	2	4	no	—
353	C₂×C₄×C₅	—	2	4	no	—
354	C₂×C₄×C₅	—	2	4	no	—
355	C₂×C₄×C₅	—	2	4	no	—
356	C₂×C₄×C₅	—	2	8	no	—
357	C₂×C₄×C₅	—	2	4	no	—
358	C₂×C₄×C₅	—	2	4	no	—
359	C₂×C₄×C₅	—	4	4	no	—
360	C₂×C₄×C₅	—	4	8	no	—
361	C₂×C₄×C₅	—	4	16	no	—
362	C₂×C₄×C₅	—	4	8	no	—
363	C₂×C₄×C₅	—	4	8	no	—
364	C₂×C₄×C₅	—	4	16	no	—
365	C₂×C₄×C₅	C₄×D₄	1	16	yes	complemented
366	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
367	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
368	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
369	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
370	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₅	C₂×#41	1	2	yes	—
377	C₂×C₄×C₅	C₂×#41	1	2	yes	—
378	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
379	C₂⁵	C₂³×C₅	1	2	yes	—
380	C₂×#41	—	2	4	no	—
381	C₂×#41	—	2	4	no	—
382	C₂×#41	C₂×C₄×C₅	1	8	yes	complemented
383	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
384	C₂²×D₄	—	2	4	no	—
385	C₂²×D₄	—	2	4	no	—
386	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
387	C₂²×D₄	C₂³×C₅	1	2	yes	—
388	C₂²×D₄	C₂³×C₅	1	2	yes	—
389	C₂²×D₄	C₂³×C₅	1	2	yes	—
390	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
391	C₂²×D₄	C₂³×C₅	1	8	yes	—
392	C₂³×C₄	—	2	8	no	—
393	C₂³×C₄	—	4	8	no	—
394	C₂³×C₄	C₂³×C₅	1	4	yes	—
395	C₂³×C₄	C₂³×C₅	1	2	yes	—
396	C₂³×C₄	C₂³×C₅	1	2	yes	—
397	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₅	1	2	yes	—
399	C₂³×C₄	C₂³×C₅	1	4	yes	—
400	C₂³×C₄	C₂³×C₅	1	2	yes	—
401	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
403	#127	C₂×C₄×C₅	1	16	yes	complemented
404	#124	C₂×C₄×C₅	1	16	yes	complemented
405	#121	C₂×C₄×C₅	1	32	yes	complemented
406	#120	C₂×C₄×C₅	1	32	yes	complemented
407	C₄×Q₈	—	2	4	no	—
408	C₄×Q₈	—	2	4	no	—
409	C₄×D₄	—	2	8	no	—
410	C₄×D₄	—	2	8	no	—
411	C₄×D₄	—	2	8	no	—
412	C₄×D₄	—	2	8	no	—
413	C₄×D₄	—	2	8	no	—
414	C₄×D₄	—	2	8	no	—
415	C₄×D₄	—	2	4	no	—
416	C₄×D₄	—	2	4	no	—
417	C₄×D₄	—	4	16	no	—
418	#117	—	2	4	no	—
419	#117	—	2	4	no	—
420	#117	—	2	8	no	—
421	#117	C₂×C₄×C₅	1	8	yes	complemented
422	C₂×C₄⋊C₄	—	2	4	no	—
423	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
431	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
432	C₂×C₂²⋊C₄	—	2	8	no	—
433	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
444	C₂×C₄²	—	2	8	no	—
445	C₂×C₄²	C₅×D₄	1	8	yes	complemented
446	C₂×C₄²	C₂³×C₅	1	2	yes	—
447	C₂×C₄²	C₂³×C₅	1	2	yes	—
448	C₂×C₄²	C₂³×C₅	1	2	yes	—
449	C₂×C₄²	C₂³×C₅	1	2	yes	—
450	C₂×C₄²	C₂³×C₅	1	4	yes	—
451	C₂×C₄²	C₂³×C₅	1	4	yes	—
452	C₂×C₄²	C₂³×C₅	1	2	yes	—
453	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
457	#95	C₂³×C₅	1	4	yes	—
458	#95	C₂³×C₅	1	4	yes	—
459	#95	C₂³×C₅	1	8	yes	—
460	#95	C₂³×C₅	1	8	yes	—
461	C₂²×C₅	—	2	4	no	—
462	C₂²×C₅	—	2	2	no	—
463	C₂²×C₅	—	2	2	no	—
464	C₂²×C₅	—	2	4	no	—
465	C₂²×C₅	—	2	4	no	—
466	C₂²×C₅	—	2	8	no	—
467	C₂²×C₅	—	2	8	no	—
468	C₂²×C₅	—	2	16	no	—
469	C₂²×C₅	—	4	32	no	—
470	C₂²×C₅	—	4	4	no	—
471	C₂²×C₅	—	4	2	no	—
472	C₂²×C₅	—	4	2	no	—
473	C₂²×C₅	—	4	4	no	—
474	C₂²×C₅	—	4	4	no	—
475	C₂²×C₅	—	4	8	no	—
476	C₂²×C₅	C₂×C₄×D₄	1	4	yes	—
477	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
478	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
479	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
480	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
481	C₂²×C₅	#585	1	2	yes	—
482	C₄×C₅	—	2	4	no	—
483	C₄×C₅	—	2	8	no	—
484	C₄×C₅	—	2	2	no	—
485	C₄×C₅	—	2	2	no	—
486	C₄×C₅	—	2	2	no	—
487	C₄×C₅	—	4	2	no	—
488	C₄×C₅	—	4	4	no	—
489	C₄×C₅	—	4	2	no	—
490	C₄×C₅	—	4	4	no	—
491	C₄×C₅	C₂×C₄×D₄	1	4	yes	—
492	C₄×C₅	C₂×C₄×D₄	1	4	yes	—
493	C₄×C₅	#535	1	4	yes	direct product factor
494	C₂⁴	—	2	4	no	—
495	C₂⁴	—	2	4	no	—
496	C₂⁴	—	4	4	no	—
497	C₂⁴	—	4	4	no	—
498	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
499	C₂⁴	C₂⁴×C₅	1	4	yes	—
500	C₂⁴	C₂⁴×C₅	1	2	yes	—
501	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
502	#41	—	2	32	no	—
503	C₂×Q₈	—	2	2	no	—
504	C₂×Q₈	—	2	2	no	—
505	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	complemented
506	C₂×D₄	—	2	4	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	32	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	4	8	no	—
516	C₂×D₄	—	4	8	no	—
517	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
518	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
519	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
520	C₂×D₄	C₂²×C₄×C₅	1	4	yes	complemented
521	C₂×D₄	C₂²×C₄×C₅	1	32	yes	complemented
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	—	2	8	no	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	2	8	no	—
531	C₂²×C₄	—	2	16	no	—
532	C₂²×C₄	—	4	8	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	4	no	—
536	C₂²×C₄	—	4	32	no	—
537	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
538	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	complemented
539	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
540	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
541	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
542	C₂²×C₄	C₅×#41	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
546	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	4	8	no	—
563	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	8	no	—
567	C₂²⋊C₄	—	2	8	no	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	4	8	no	—
571	C₂²⋊C₄	—	4	8	no	—
572	C₂²⋊C₄	—	4	8	no	—
573	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₅	1	32	yes	complemented
575	C₄²	—	2	4	no	—
576	C₄²	—	2	4	no	—
577	C₄²	—	2	4	no	—
578	C₄²	—	2	4	no	—
579	C₄²	—	2	8	no	—
580	C₄²	—	4	4	no	—
581	C₄²	C₂²×C₄×C₅	1	8	yes	complemented
582	C₄²	C₂×C₅×D₄	1	4	yes	—
583	C₄²	C₂×C₅×D₄	1	4	yes	—
584	C₄²	C₂×C₅×D₄	1	4	yes	—
585	C₄²	C₂×C₅×D₄	1	4	yes	—
586	C₂×C₅	—	2	4	no	—
587	C₂×C₅	—	4	4	no	—
588	C₂×C₅	—	4	8	no	—
589	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
590	C₂×C₅	C₄×H(5,𝔽₂)	1	2	yes	—
591	C₂×C₅	C₂×#535	1	1	yes	characteristic
592	C₂×C₅	#3449	1	1	yes	characteristic
593	C₂×C₅	#3460	1	2	yes	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	16	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	4	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	4	no	—
601	C₂³	—	2	4	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	2	8	no	—
604	C₂³	—	2	4	no	—
605	C₂³	—	4	16	no	—
606	C₂³	—	4	8	no	—
607	C₂³	—	4	8	no	—
608	C₂³	—	4	16	no	—
609	C₂³	C₂³×C₄×C₅	1	8	yes	—
610	C₂³	C₂³×C₄×C₅	1	4	yes	—
611	C₂³	C₂³×C₄×C₅	1	2	yes	—
612	C₂³	C₂²×C₅×D₄	1	2	yes	—
613	C₂³	C₂×C₅×#41	1	2	yes	—
614	C₂³	C₂⁵×C₅	1	1	yes	characteristic
615	Q₈	—	2	8	no	—
616	D₄	—	2	16	no	—
617	D₄	—	2	16	no	—
618	D₄	—	2	16	no	—
619	D₄	—	2	8	no	—
620	D₄	—	4	32	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	16	no	—
629	C₂×C₄	—	2	8	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	8	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	16	no	—
641	C₂×C₄	—	4	8	no	—
642	C₂×C₄	—	4	8	no	—
643	C₂×C₄	—	4	16	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	C₄×C₅×D₄	1	16	yes	complemented
646	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
647	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
648	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
649	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
650	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
651	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
652	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
653	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
654	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
655	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
656	C₂×C₄	C₂×C₅×#41	1	2	yes	—
657	C₂×C₄	C₂×C₅×#41	1	2	yes	—
658	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
659	C₅	C₄×#535	1	1	yes	characteristic, direct product factor, Sylow
660	C₂²	—	2	4	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	8	no	—
666	C₂²	—	2	8	no	—
667	C₂²	—	2	16	no	—
668	C₂²	—	4	32	no	—
669	C₂²	—	4	4	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	4	8	no	—
674	C₂²	—	4	4	no	—
675	C₂²	C₂×C₄×C₅×D₄	1	4	yes	—
676	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
677	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
678	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
679	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
680	C₂²	C₅×#585	1	2	yes	—
681	C₄	—	2	4	no	—
682	C₄	—	2	8	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	4	4	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	4	no	—
690	C₄	C₂×C₄×C₅×D₄	1	4	yes	—
691	C₄	C₂×C₄×C₅×D₄	1	4	yes	—
692	C₄	C₅×#535	1	4	yes	direct product factor
693	C₂	—	2	4	no	—
694	C₂	—	4	8	no	—
695	C₂	—	4	4	no	—
696	C₂	C₂²×C₄×C₅×D₄	1	1	yes	characteristic
697	C₂	C₄×C₅×H(5,𝔽₂)	1	2	yes	—
698	C₂	C₂×C₅×#535	1	1	yes	characteristic
699	C₂	C₅×#3449	1	1	yes	characteristic
700	C₂	C₅×#3460	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₂×C₅×#535	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×#41	C₂	semidirect
3. C₂²×C₄×C₅×D₄	C₂	semidirect
4. C₅×#2328	C₂	semidirect
5. C₅×#2326	C₂	semidirect
6. C₅×#2324	C₂	semidirect
7. C₅×#2321	C₂	semidirect
8. C₅×#2317	C₂	semidirect
9. C₅×#2311	C₂	semidirect
10. C₅×#2309	C₂	semidirect
11. C₄×C₅×#127	C₂	semidirect
12. C₄×C₅×#124	C₂	semidirect
13. C₄×C₅×#121	C₂	semidirect
14. C₄×C₅×#120	C₂	semidirect
15. C₄×C₅×#117	C₂	semidirect
19. C₅×#535	C₄	direct (N × H)
25. C₂×C₄×C₅×Q₈	C₂²	semidirect
26. C₂×C₄×C₅×Q₈	C₂²	semidirect
34. C₂×C₄×C₅×D₄	C₂²	semidirect
35. C₂×C₄×C₅×D₄	C₂²	semidirect
36. C₂×C₄×C₅×D₄	C₂²	semidirect
40. C₂×C₅×#117	C₂²	semidirect
44. C₂²×C₄²×C₅	C₂²	semidirect
45. C₅×#391	C₂²	semidirect
49. C₅×#390	C₂²	semidirect
50. C₅×#390	C₂²	semidirect
51. C₅×#389	C₂²	semidirect
52. C₅×#388	C₂²	semidirect
53. C₅×#388	C₂²	semidirect
55. C₅×#386	C₂²	semidirect
56. C₅×#386	C₂²	semidirect
58. C₅×#385	C₂²	semidirect
59. C₅×#384	C₂²	semidirect
60. C₅×#382	C₂²	semidirect
61. C₅×#380	C₂²	semidirect
63. C₄×C₅×C₄⋊C₄	C₂²	semidirect
64. C₄×C₅×C₄⋊C₄	C₂²	semidirect
67. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
68. C₅×#376	C₂²	semidirect
69. C₄³×C₅	C₂²	semidirect
70. C₄×#535	C₅	direct (N × H)
74. C₂×C₅×#41	C₂×C₄	semidirect
78. C₂²×C₅×D₄	C₂×C₄	semidirect
95. C₅×#127	C₂×C₄	semidirect
96. C₅×#124	C₂×C₄	semidirect
97. C₅×#121	C₂×C₄	semidirect
98. C₅×#120	C₂×C₄	semidirect
113. C₅×#117	C₂×C₄	semidirect
137. C₂×C₄²×C₅	D₄	semidirect
154. C₂×C₄×#41	C₂×C₅	semidirect
155. C₂²×C₄×D₄	C₂×C₅	semidirect
156. #2328	C₂×C₅	semidirect
157. #2326	C₂×C₅	semidirect
158. #2324	C₂×C₅	semidirect
159. #2321	C₂×C₅	semidirect
160. #2317	C₂×C₅	semidirect
161. #2311	C₂×C₅	semidirect
162. #2309	C₂×C₅	semidirect
163. C₄×#127	C₂×C₅	semidirect
164. C₄×#124	C₂×C₅	semidirect
165. C₄×#121	C₂×C₅	semidirect
166. C₄×#120	C₂×C₅	semidirect
167. C₄×#117	C₂×C₅	semidirect
179. C₂×C₅×Q₈	C₂²×C₄	semidirect
194. C₂×C₅×D₄	C₂²×C₄	semidirect
195. C₂×C₅×D₄	C₂²×C₄	semidirect
212. C₂²×C₄×C₅	C₂²×C₄	semidirect
237. C₅×C₄⋊C₄	C₂²×C₄	semidirect
248. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
255. C₄²×C₅	C₂²×C₄	semidirect
263. #535	C₄×C₅	direct (N × H)
269. C₂×C₄×Q₈	C₂²×C₅	semidirect
270. C₂×C₄×Q₈	C₂²×C₅	semidirect
278. C₂×C₄×D₄	C₂²×C₅	semidirect
279. C₂×C₄×D₄	C₂²×C₅	semidirect
280. C₂×C₄×D₄	C₂²×C₅	semidirect
284. C₂×#117	C₂²×C₅	semidirect
288. C₂²×C₄²	C₂²×C₅	semidirect
289. #391	C₂²×C₅	semidirect
293. #390	C₂²×C₅	semidirect
294. #390	C₂²×C₅	semidirect
295. #389	C₂²×C₅	semidirect
296. #388	C₂²×C₅	semidirect
297. #388	C₂²×C₅	semidirect
299. #386	C₂²×C₅	semidirect
300. #386	C₂²×C₅	semidirect
302. #385	C₂²×C₅	semidirect
303. #384	C₂²×C₅	semidirect
304. #382	C₂²×C₅	semidirect
305. #380	C₂²×C₅	semidirect
307. C₄×C₄⋊C₄	C₂²×C₅	semidirect
308. C₄×C₄⋊C₄	C₂²×C₅	semidirect
311. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
312. #376	C₂²×C₅	semidirect
313. C₄³	C₂²×C₅	semidirect
365. C₂×C₄×C₅	C₄×D₄	semidirect
382. C₂×#41	C₂×C₄×C₅	semidirect
386. C₂²×D₄	C₂×C₄×C₅	semidirect
403. #127	C₂×C₄×C₅	semidirect
404. #124	C₂×C₄×C₅	semidirect
405. #121	C₂×C₄×C₅	semidirect
406. #120	C₂×C₄×C₅	semidirect
421. #117	C₂×C₄×C₅	semidirect
445. C₂×C₄²	C₅×D₄	semidirect
493. C₄×C₅	#535	direct (N × H)
505. C₂×Q₈	C₂²×C₄×C₅	semidirect
520. C₂×D₄	C₂²×C₄×C₅	semidirect
521. C₂×D₄	C₂²×C₄×C₅	semidirect
538. C₂²×C₄	C₂²×C₄×C₅	semidirect
563. C₄⋊C₄	C₂²×C₄×C₅	semidirect
574. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
581. C₄²	C₂²×C₄×C₅	semidirect
645. C₂×C₄	C₄×C₅×D₄	semidirect
659. C₅	C₄×#535	direct (N × H)
692. C₄	C₅×#535	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×C₅×#535	2
C₂×C₄×C₅×#41	2
C₂²×C₄×C₅×D₄	2
C₅×#2328	2
C₅×#2326	2
C₅×#2324	2
C₅×#2321	2
C₅×#2317	2
C₅×#2311	2
C₅×#2309	2
C₄×C₅×#127	2
C₄×C₅×#124	2
C₄×C₅×#121	2
C₄×C₅×#120	2
C₄×C₅×#117	2
C₄×#535	5

Subgroups — C4×C5×#535 #11956808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#535 #11956808