Subgroups — C₅×#78655 #14414923

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5828	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5126	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5102	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4728	C₂	1	4	yes	maximal, complemented
9	C₅×#67⋊C₈	C₂	1	4	yes	maximal, complemented
10	C₅×#2929	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#948	—	2	4	no	—
16	C₅×#946	C₄	1	2	yes	—
17	C₅×#938	C₄	1	2	yes	—
18	C₅×#937	C₄	1	2	yes	—
19	C₅×#935	C₄	1	2	yes	—
20	C₄×C₅×#67	C₂²	1	4	yes	—
21	C₅×#926	C₂²	1	1	yes	characteristic
22	C₂×C₅×#208	C₂²	1	1	yes	characteristic
23	C₂×C₅×#208	C₂²	1	2	yes	complemented
24	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
26	C₂×C₅×D₃×C₈	—	2	4	no	—
27	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
28	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
29	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
30	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
31	C₅×#815	C₂²	1	2	yes	complemented
32	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
33	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
34	#78655	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×#131	—	3	1	no	—
36	C₂³×C₅×C₈	—	3	1	no	—
37	C₅×#525	—	3	1	no	—
38	C₅×#435	—	3	4	no	—
39	C₅×C₈×D₄	—	3	4	no	—
40	C₅×#424	—	3	1	no	—
41	C₅×#408	D₃	1	1	yes	characteristic, complemented
42	C₅×#407	—	3	1	no	—
43	C₅×#405	—	3	1	no	—
44	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×#41	—	2	2	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₅×#67	C₂×C₄	1	4	yes	—
53	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×C₅×D₃	—	2	2	no	—
55	C₂×C₄×C₅×D₃	—	2	2	no	—
56	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
58	C₃×C₅×M₁₆	—	2	2	no	—
59	C₂×C₃×C₅×C₈	—	2	2	no	—
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₅×#217	C₂×C₄	1	2	yes	—
63	C₅×#217	C₂×C₄	1	4	yes	—
64	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
65	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
66	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
67	C₄×C₅×Dic₃	C₂³	1	2	yes	—
68	C₅×#208	—	2	2	no	—
69	C₅×#208	—	2	4	no	—
70	C₂×C₅×C₃⋊C₈	—	2	4	no	—
71	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
72	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
75	C₅×D₃×C₈	—	2	4	no	—
76	C₅×D₃×C₈	—	2	4	no	—
77	#5828	C₂×C₅	1	1	yes	characteristic
78	C₂×#948	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
81	#5126	C₂×C₅	1	1	yes	characteristic, complemented
82	#5122	C₂×C₅	1	1	yes	characteristic, complemented
83	#5102	C₂×C₅	1	1	yes	characteristic, complemented
84	#4728	C₂×C₅	1	4	yes	complemented
85	#67⋊C₈	C₂×C₅	1	4	yes	complemented
86	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
87	C₂³×C₄×C₅	—	3	1	no	—
88	C₅×#131	—	6	4	no	—
89	C₂×C₅×M₁₆	—	3	1	no	—
90	C₂×C₅×M₁₆	—	3	2	no	—
91	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
92	C₂²×C₅×C₈	—	3	1	no	—
93	C₂²×C₅×C₈	—	3	2	no	—
94	C₂²×C₅×C₈	—	3	2	no	—
95	C₂²×C₅×C₈	—	3	2	no	—
96	C₂²×C₅×C₈	—	6	4	no	—
97	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
98	C₅×#123	—	3	2	no	—
99	C₅×C₂²⋊Q₈	—	3	2	no	—
100	C₅×#121	—	3	2	no	—
101	C₅×#120	—	3	2	no	—
102	C₄×C₅×D₄	—	3	4	no	—
103	C₅×#117	—	3	1	no	—
104	C₅×C₄⋊C₈	—	3	4	no	—
105	C₅×C₂²⋊C₈	—	3	4	no	—
106	C₅×C₂²⋊C₈	C₂×D₃	1	4	yes	complemented
107	C₅×#97	—	3	2	no	—
108	C₄×C₅×C₈	—	3	2	no	—
109	#2929	—	3	1	no	Sylow
110	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
111	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₅×D₃	—	2	2	no	—
113	C₂²×C₅×D₃	—	2	4	no	—
114	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
115	C₃×C₅×Q₈	—	2	2	no	—
116	C₃×C₅×D₄	—	2	4	no	—
117	C₃×C₅×D₄	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	#41	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₅×#67	—	2	8	no	—
126	C₂×C₅×Dic₃	—	2	2	no	—
127	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
128	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
129	C₄×C₅×D₃	—	2	4	no	—
130	C₄×C₅×D₃	—	2	2	no	—
131	C₄×C₅×D₃	—	2	2	no	—
132	C₃×C₅×C₈	—	2	2	no	—
133	C₃×C₅×C₈	—	2	2	no	—
134	C₅×C₃⋊C₈	—	2	2	no	—
135	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
136	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
137	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
138	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
140	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
141	#948	—	2	4	no	—
142	#946	C₄×C₅	1	2	yes	—
143	#938	C₄×C₅	1	2	yes	—
144	#937	C₄×C₅	1	2	yes	—
145	#935	C₄×C₅	1	2	yes	—
146	C₄×#67	C₂²×C₅	1	4	yes	—
147	#926	C₂²×C₅	1	1	yes	characteristic
148	C₂×#208	C₂²×C₅	1	1	yes	characteristic
149	C₂×#208	C₂²×C₅	1	2	yes	complemented
150	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
151	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
152	C₂×D₃×C₈	—	2	4	no	—
153	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
154	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
155	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	complemented
156	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	—
157	#815	C₂²×C₅	1	2	yes	complemented
158	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
159	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
160	C₂⁴×C₅	—	3	1	no	—
161	C₅×#41	—	2	2	no	—
162	C₅×#41	—	2	2	no	—
163	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
164	C₂×C₅×D₄	—	3	4	no	—
165	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
166	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	—	3	1	no	—
168	C₂²×C₄×C₅	—	3	2	no	—
169	C₂²×C₄×C₅	—	3	2	no	—
170	C₂²×C₄×C₅	—	6	2	no	—
171	C₂²×C₄×C₅	—	6	2	no	—
172	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
173	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₅×M₁₆	—	2	2	no	—
175	C₅×M₁₆	—	6	4	no	—
176	C₅×M₁₆	—	6	2	no	—
177	C₂×C₅×C₈	—	2	2	no	—
178	C₂×C₅×C₈	—	3	4	no	—
179	C₂×C₅×C₈	—	3	1	no	—
180	C₂×C₅×C₈	—	3	1	no	—
181	C₂×C₅×C₈	—	3	2	no	—
182	C₂×C₅×C₈	—	6	4	no	—
183	C₂×C₅×C₈	—	6	4	no	—
184	C₂×C₅×C₈	—	6	4	no	—
185	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
186	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
187	C₅×C₄⋊C₄	—	3	2	no	—
188	C₅×C₄⋊C₄	—	3	4	no	—
189	C₅×C₂²⋊C₄	—	3	2	no	—
190	C₅×C₂²⋊C₄	—	3	4	no	—
191	C₅×C₂²⋊C₄	—	3	4	no	—
192	C₄²×C₅	—	3	2	no	—
193	C₂×#131	—	3	1	no	—
194	C₂³×C₈	—	3	1	no	—
195	#525	—	3	1	no	—
196	#435	—	3	4	no	—
197	C₈×D₄	—	3	4	no	—
198	#424	—	3	1	no	—
199	#408	C₅×D₃	1	1	yes	characteristic, complemented
200	#407	—	3	1	no	—
201	#405	—	3	1	no	—
202	C₂²×C₃×C₅	—	2	2	no	—
203	C₂²×C₃×C₅	—	2	2	no	—
204	C₂²×C₃×C₅	—	2	4	no	—
205	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
206	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₅×D₃	—	2	8	no	—
208	C₂×C₅×D₃	—	2	2	no	—
209	C₂×C₅×D₃	—	2	2	no	—
210	C₂×C₅×D₃	#131	1	4	yes	complemented
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
213	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
215	C₅×Dic₃	—	2	2	no	—
216	C₅×Dic₃	—	2	4	no	—
217	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
218	C₃×#41	—	2	2	no	—
219	C₃×#41	—	2	2	no	—
220	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
222	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂×#67	C₂×C₄×C₅	1	4	yes	—
226	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
227	C₂×C₄×D₃	—	2	2	no	—
228	C₂×C₄×D₃	—	2	2	no	—
229	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
230	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
231	C₃×M₁₆	—	2	2	no	—
232	C₂×C₃×C₈	—	2	2	no	—
233	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
234	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
235	#217	C₂×C₄×C₅	1	2	yes	—
236	#217	C₂×C₄×C₅	1	4	yes	—
237	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
238	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
239	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
240	C₄×Dic₃	C₂³×C₅	1	2	yes	—
241	#208	—	2	2	no	—
242	#208	—	2	4	no	—
243	C₂×C₃⋊C₈	—	2	4	no	—
244	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
245	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
246	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
248	D₃×C₈	—	2	4	no	—
249	D₃×C₈	—	2	4	no	—
250	C₂³×C₅	—	3	2	no	—
251	C₂³×C₅	—	6	4	no	—
252	C₂³×C₅	—	6	2	no	—
253	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
254	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
255	C₅×Q₈	—	2	2	no	—
256	C₅×D₄	—	2	4	no	—
257	C₅×D₄	—	2	2	no	—
258	C₅×D₄	—	6	8	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	3	4	no	—
262	C₂×C₄×C₅	—	3	2	no	—
263	C₂×C₄×C₅	—	6	2	no	—
264	C₂×C₄×C₅	—	6	4	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	6	2	no	—
267	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
268	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
269	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
270	C₂×C₄×C₅	#237	1	2	yes	—
271	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
272	C₅×C₈	—	2	2	no	—
273	C₅×C₈	—	2	2	no	—
274	C₅×C₈	—	3	2	no	—
275	C₅×C₈	—	3	2	no	—
276	C₅×C₈	—	6	2	no	—
277	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
278	C₂³×C₄	—	3	1	no	—
279	#131	—	6	4	no	—
280	C₂×M₁₆	—	3	1	no	—
281	C₂×M₁₆	—	3	2	no	—
282	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
283	C₂²×C₈	—	3	1	no	—
284	C₂²×C₈	—	3	2	no	—
285	C₂²×C₈	—	3	2	no	—
286	C₂²×C₈	—	3	2	no	—
287	C₂²×C₈	—	6	4	no	—
288	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
289	#123	—	3	2	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	#121	—	3	2	no	—
292	#120	—	3	2	no	—
293	C₄×D₄	—	3	4	no	—
294	#117	—	3	1	no	—
295	C₄⋊C₈	—	3	4	no	—
296	C₂²⋊C₈	—	3	4	no	—
297	C₂²⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
298	#97	—	3	2	no	—
299	C₄×C₈	—	3	2	no	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	—	4	2	no	—
302	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×#131	1	2	yes	—
304	C₅×D₃	—	2	4	no	—
305	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
306	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
307	C₂²×D₃	—	2	2	no	—
308	C₂²×D₃	—	2	4	no	—
309	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×D₄	—	2	4	no	—
312	C₃×D₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
316	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
318	C₂×C₃×C₄	C₅×#41	1	2	yes	—
319	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
320	#67	—	2	8	no	—
321	C₂×Dic₃	—	2	2	no	—
322	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
323	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
324	C₄×D₃	—	2	4	no	—
325	C₄×D₃	—	2	2	no	—
326	C₄×D₃	—	2	2	no	—
327	C₃×C₈	—	2	2	no	—
328	C₃×C₈	—	2	2	no	—
329	C₃⋊C₈	—	2	2	no	—
330	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
331	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
332	C₂²×C₅	—	2	2	no	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	2	4	no	—
335	C₂²×C₅	—	3	4	no	—
336	C₂²×C₅	—	6	8	no	—
337	C₂²×C₅	—	6	2	no	—
338	C₂²×C₅	—	6	2	no	—
339	C₂²×C₅	#67⋊C₄	1	2	yes	—
340	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	6	2	no	—
343	C₄×C₅	—	6	4	no	—
344	C₄×C₅	#67⋊C₄	1	2	yes	—
345	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
346	C₄×C₅	C₂×#237	1	1	yes	characteristic
347	C₂⁴	—	3	1	no	—
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
351	C₂×D₄	—	3	4	no	—
352	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
353	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
354	C₂²×C₄	—	3	1	no	—
355	C₂²×C₄	—	3	2	no	—
356	C₂²×C₄	—	3	2	no	—
357	C₂²×C₄	—	6	2	no	—
358	C₂²×C₄	—	6	2	no	—
359	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
360	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
361	M₁₆	—	2	2	no	—
362	M₁₆	—	6	4	no	—
363	M₁₆	—	6	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	3	4	no	—
366	C₂×C₈	—	3	1	no	—
367	C₂×C₈	—	3	1	no	—
368	C₂×C₈	—	3	2	no	—
369	C₂×C₈	—	6	4	no	—
370	C₂×C₈	—	6	4	no	—
371	C₂×C₈	—	6	4	no	—
372	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
373	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
374	C₄⋊C₄	—	3	2	no	—
375	C₄⋊C₄	—	3	4	no	—
376	C₂²⋊C₄	—	3	2	no	—
377	C₂²⋊C₄	—	3	4	no	—
378	C₂²⋊C₄	—	3	4	no	—
379	C₄²	—	3	2	no	—
380	C₃×C₅	#2929	1	1	yes	characteristic, complemented, Hall
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	4	no	—
384	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
385	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
386	C₂×D₃	—	2	8	no	—
387	C₂×D₃	—	2	2	no	—
388	C₂×D₃	—	2	2	no	—
389	C₂×D₃	C₅×#131	1	4	yes	complemented
390	C₃×C₄	—	2	2	no	—
391	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
392	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
393	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
394	Dic₃	—	2	2	no	—
395	Dic₃	—	2	4	no	—
396	C₂×C₅	—	2	2	no	—
397	C₂×C₅	—	4	2	no	—
398	C₂×C₅	—	6	4	no	—
399	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
400	C₂×C₅	D₃×#131	1	2	yes	—
401	C₂³	—	3	2	no	—
402	C₂³	—	6	4	no	—
403	C₂³	—	6	2	no	—
404	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
405	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
406	Q₈	—	2	2	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	2	no	—
409	D₄	—	6	8	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	3	4	no	—
413	C₂×C₄	—	3	2	no	—
414	C₂×C₄	—	6	2	no	—
415	C₂×C₄	—	6	4	no	—
416	C₂×C₄	—	6	2	no	—
417	C₂×C₄	—	6	2	no	—
418	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
419	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
420	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
421	C₂×C₄	C₅×#237	1	2	yes	—
422	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	2	2	no	—
425	C₈	—	3	2	no	—
426	C₈	—	3	2	no	—
427	C₈	—	6	2	no	—
428	C₂×C₃	—	2	2	no	—
429	C₂×C₃	—	4	2	no	—
430	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
431	C₂×C₃	C₂×C₅×#131	1	2	yes	—
432	D₃	—	2	4	no	—
433	C₅	#78655	1	1	yes	characteristic, direct product factor, Sylow
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	3	4	no	—
438	C₂²	—	6	8	no	—
439	C₂²	—	6	2	no	—
440	C₂²	—	6	2	no	—
441	C₂²	C₅×#67⋊C₄	1	2	yes	—
442	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	6	2	no	—
445	C₄	—	6	4	no	—
446	C₄	C₅×#67⋊C₄	1	2	yes	—
447	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
448	C₄	C₂×C₅×#237	1	1	yes	characteristic
449	C₃	C₅×#2929	1	1	yes	characteristic, complemented, Sylow
450	C₂	—	2	2	no	—
451	C₂	—	4	2	no	—
452	C₂	—	6	4	no	—
453	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
454	C₂	C₅×D₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#408	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₅×#5828	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#408	D₃
hypocenter	C₃	C₅×#2929
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#408

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#948	C₂	semidirect
3. C₂²×C₅×D₃×C₈	C₂	semidirect
4. C₃×C₅×#408	C₂	semidirect
5. C₅×#5126	C₂	semidirect
6. C₅×#5122	C₂	semidirect
7. C₅×#5102	C₂	semidirect
8. C₅×#4728	C₂	semidirect
9. C₅×#67⋊C₈	C₂	semidirect
23. C₂×C₅×#208	C₂²	semidirect
25. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
29. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
31. C₅×#815	C₂²	semidirect
32. C₅×Dic₃⋊C₈	C₂²	semidirect
33. C₅×C₈×Dic₃	C₂²	semidirect
34. #78655	C₅	direct (N × H)
41. C₅×#408	D₃	semidirect
71. C₂×C₅×C₃⋊C₈	D₄	semidirect
78. C₂×#948	C₂×C₅	semidirect
79. C₂²×D₃×C₈	C₂×C₅	semidirect
80. C₃×#408	C₂×C₅	semidirect
81. #5126	C₂×C₅	semidirect
82. #5122	C₂×C₅	semidirect
83. #5102	C₂×C₅	semidirect
84. #4728	C₂×C₅	semidirect
85. #67⋊C₈	C₂×C₅	semidirect
106. C₅×C₂²⋊C₈	C₂×D₃	semidirect
149. C₂×#208	C₂²×C₅	semidirect
151. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
155. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
157. #815	C₂²×C₅	semidirect
158. Dic₃⋊C₈	C₂²×C₅	semidirect
159. C₈×Dic₃	C₂²×C₅	semidirect
199. #408	C₅×D₃	semidirect
210. C₂×C₅×D₃	#131	semidirect
244. C₂×C₃⋊C₈	C₅×D₄	semidirect
297. C₂²⋊C₈	C₂×C₅×D₃	semidirect
380. C₃×C₅	#2929	semidirect
389. C₂×D₃	C₅×#131	semidirect
433. C₅	#78655	direct (N × H)
449. C₃	C₅×#2929	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5828	2
C₂×C₅×#948	2
C₂²×C₅×D₃×C₈	2
C₃×C₅×#408	2
C₅×#5126	2
C₅×#5122	2
C₅×#5102	2
C₅×#4728	2
C₅×#67⋊C₈	2
C₅×#2929	3
#78655	5

Subgroups — C5×#78655 #14414923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78655 #14414923