Subgroups — C₅×#79867 #14417330

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#5545	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#213	C₂	1	2	yes	maximal, complemented
6	C₅×#4869	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4860	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4770	C₂	1	2	yes	maximal, complemented
9	C₅×#4756	C₂	1	2	yes	maximal, complemented
10	C₅×#4711	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4708	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2948	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
16	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
17	C₂×C₅×#213	C₂²	1	2	yes	—
18	C₄×C₅×#67	—	2	2	no	—
19	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
20	C₅×D₃×D₈	C₄	1	8	yes	complemented
21	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
23	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
24	C₅×#893	C₂²	1	2	yes	complemented
25	C₅×#892	C₂²	1	2	yes	—
26	C₅×#67⋊C₄	—	2	2	no	—
27	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
28	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
29	C₅×#872	C₂²	1	1	yes	characteristic
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#102	C₂²	1	2	yes	complemented
32	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
33	C₅×#832	C₂²	1	2	yes	complemented
34	C₅×#821	C₂²	1	2	yes	complemented
35	C₅×#817	C₂²	1	1	yes	characteristic, complemented
36	C₅×#815	C₂²	1	1	yes	characteristic, complemented
37	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₅×#809	C₂²	1	2	yes	complemented
39	C₅×#807	C₂²	1	2	yes	complemented
40	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	#79867	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂²×C₅×D₈	—	3	1	no	—
43	C₅×#518	—	3	2	no	—
44	C₅×#442	—	3	1	no	—
45	C₅×#442	—	3	1	no	—
46	C₅×#442	—	3	1	no	—
47	C₅×#442	D₃	1	1	yes	characteristic, complemented
48	C₄×C₅×D₈	—	3	2	no	—
49	C₄×C₅×D₈	—	3	2	no	—
50	C₅×#427	—	3	1	no	—
51	C₅×#418	—	3	2	no	—
52	C₅×#405	—	3	1	no	—
53	C₂³×C₅×D₃	—	2	2	no	—
54	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₅×#67	—	2	2	no	—
57	C₂²×C₅×Dic₃	—	2	2	no	—
58	C₅×D₃×D₄	—	2	4	no	—
59	C₅×D₃×D₄	C₂×C₄	1	8	yes	complemented
60	C₂×C₅×D₁₂	C₂³	1	2	yes	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
64	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#217	—	2	2	no	—
71	C₅×#213	C₂×C₄	1	8	yes	complemented
72	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
73	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
74	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
75	C₅×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
76	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
77	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
78	C₄×C₅×Dic₃	—	2	2	no	—
79	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
83	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
84	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
85	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic
86	#5545	C₂×C₅	1	2	yes	complemented
87	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
88	#5152	C₂×C₅	1	1	yes	characteristic, complemented
89	C₄×#213	C₂×C₅	1	2	yes	complemented
90	#4869	C₂×C₅	1	1	yes	characteristic, complemented
91	#4860	C₂×C₅	1	1	yes	characteristic, complemented
92	#4770	C₂×C₅	1	2	yes	complemented
93	#4756	C₂×C₅	1	2	yes	complemented
94	#4711	C₂×C₅	1	1	yes	characteristic, complemented
95	#4708	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂²×C₅×D₄	—	3	2	no	—
97	C₂×C₅×D₈	—	3	2	no	—
98	C₂×C₅×D₈	—	3	8	no	—
99	C₂×C₅×D₈	—	3	1	no	—
100	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×M₁₆	—	3	1	no	—
102	C₂²×C₅×C₈	—	3	1	no	—
103	C₄×C₅×D₄	—	3	2	no	—
104	C₄×C₅×D₄	—	3	2	no	—
105	C₄×C₅×D₄	—	3	2	no	—
106	C₄×C₅×D₄	—	6	2	no	—
107	C₄×C₅×D₄	—	6	2	no	—
108	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
109	C₅×#117	—	3	1	no	—
110	C₅×#117	—	3	2	no	—
111	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
112	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
113	C₅×#107	—	3	2	no	—
114	C₅×#106	—	3	1	no	—
115	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
116	C₅×#102	—	3	2	no	—
117	C₅×#102	—	3	2	no	—
118	C₅×#102	—	3	2	no	—
119	C₅×#102	C₂×D₃	1	2	yes	complemented
120	C₅×#97	—	3	1	no	—
121	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
122	C₄×C₅×C₈	—	3	1	no	—
123	C₄×C₅×C₈	—	3	1	no	—
124	#2948	—	3	1	no	Sylow
125	C₂³×C₃×C₅	—	2	2	no	—
126	C₂²×C₅×D₃	—	2	2	no	—
127	C₂²×C₅×D₃	—	2	8	no	—
128	C₂²×C₅×D₃	—	8	2	no	—
129	C₂²×C₅×D₃	—	8	2	no	—
130	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
131	C₃×C₅×D₄	—	2	2	no	—
132	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	8	2	no	—
135	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₅×#67	—	2	8	no	—
138	C₂×C₅×Dic₃	—	2	2	no	—
139	C₂×C₅×Dic₃	—	8	2	no	—
140	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
141	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
142	C₅×D₁₂	—	2	2	no	—
143	C₅×D₁₂	C₂²×C₄	1	4	yes	—
144	C₄×C₅×D₃	—	8	2	no	—
145	C₄×C₅×D₃	—	8	2	no	—
146	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
147	C₄×C₅×D₃	#41	1	2	yes	—
148	C₃×C₅×C₈	—	2	1	no	—
149	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
150	C₅×C₃⋊C₈	—	2	1	no	—
151	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
153	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
154	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
155	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
156	C₂×#213	C₂²×C₅	1	2	yes	—
157	C₄×#67	—	2	2	no	—
158	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
159	D₃×D₈	C₄×C₅	1	8	yes	complemented
160	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
161	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
162	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
163	#893	C₂²×C₅	1	2	yes	complemented
164	#892	C₂²×C₅	1	2	yes	—
165	#67⋊C₄	—	2	2	no	—
166	D₃×C₂²⋊C₄	—	2	2	no	—
167	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
168	#872	C₂²×C₅	1	1	yes	characteristic
169	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
170	C₃×#102	C₂²×C₅	1	2	yes	complemented
171	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
172	#832	C₂²×C₅	1	2	yes	complemented
173	#821	C₂²×C₅	1	2	yes	complemented
174	#817	C₂²×C₅	1	1	yes	characteristic, complemented
175	#815	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
177	#809	C₂²×C₅	1	2	yes	complemented
178	#807	C₂²×C₅	1	2	yes	complemented
179	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₂⁴×C₅	—	6	2	no	—
181	C₂×C₅×D₄	—	3	8	no	—
182	C₂×C₅×D₄	—	3	2	no	—
183	C₂×C₅×D₄	—	6	4	no	—
184	C₂×C₅×D₄	—	6	2	no	—
185	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
186	C₂²×C₄×C₅	—	2	2	no	—
187	C₂²×C₄×C₅	—	3	1	no	—
188	C₂²×C₄×C₅	—	6	2	no	—
189	C₂²×C₄×C₅	—	6	2	no	—
190	C₂²×C₄×C₅	—	6	2	no	—
191	C₅×D₈	—	3	8	no	—
192	C₅×D₈	—	3	4	no	—
193	C₅×D₈	C₄×D₃	1	4	yes	complemented
194	C₅×M₁₆	—	6	2	no	—
195	C₂×C₅×C₈	—	3	1	no	—
196	C₂×C₅×C₈	—	3	4	no	—
197	C₂×C₅×C₈	—	3	1	no	—
198	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
200	C₅×C₄⋊C₄	—	3	2	no	—
201	C₅×C₄⋊C₄	—	3	2	no	—
202	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
203	C₅×C₂²⋊C₄	—	2	2	no	—
204	C₅×C₂²⋊C₄	—	3	2	no	—
205	C₅×C₂²⋊C₄	—	6	2	no	—
206	C₅×C₂²⋊C₄	—	6	2	no	—
207	C₅×C₂²⋊C₄	—	6	2	no	—
208	C₅×C₂²⋊C₄	—	6	2	no	—
209	C₄²×C₅	—	3	1	no	—
210	C₄²×C₅	—	6	2	no	—
211	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
212	C₂²×D₈	—	3	1	no	—
213	#518	—	3	2	no	—
214	#442	—	3	1	no	—
215	#442	—	3	1	no	—
216	#442	—	3	1	no	—
217	#442	C₅×D₃	1	1	yes	characteristic, complemented
218	C₄×D₈	—	3	2	no	—
219	C₄×D₈	—	3	2	no	—
220	#427	—	3	1	no	—
221	#418	—	3	2	no	—
222	#405	—	3	1	no	—
223	C₂²×C₃×C₅	—	2	4	no	—
224	C₂²×C₃×C₅	—	4	2	no	—
225	C₂²×C₃×C₅	—	4	2	no	—
226	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₅×D₃	—	2	2	no	—
228	C₂×C₅×D₃	—	2	4	no	—
229	C₂×C₅×D₃	—	4	2	no	—
230	C₂×C₅×D₃	—	4	2	no	—
231	C₂×C₅×D₃	—	8	8	no	—
232	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	—	4	2	no	—
235	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
236	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	C₅×Dic₃	—	2	2	no	—
238	C₅×Dic₃	—	4	2	no	—
239	C₅×Dic₃	C₄×D₄	1	2	yes	—
240	C₂³×D₃	—	2	2	no	—
241	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
242	C₂²×C₃×C₄	—	2	2	no	—
243	C₂×#67	—	2	2	no	—
244	C₂²×Dic₃	—	2	2	no	—
245	D₃×D₄	—	2	4	no	—
246	D₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
247	C₂×D₁₂	C₂³×C₅	1	2	yes	—
248	C₂×C₄×D₃	—	2	2	no	—
249	C₂×C₄×D₃	—	2	2	no	—
250	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
251	C₃×D₈	C₂×C₄×C₅	1	4	yes	complemented
252	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
253	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
255	C₃×C₂²⋊C₄	—	2	2	no	—
256	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
257	#217	—	2	2	no	—
258	#213	C₂×C₄×C₅	1	8	yes	complemented
259	(C₂×D₃)⋊C₄	—	2	2	no	—
260	(C₂×D₃)⋊C₄	—	2	2	no	—
261	(C₂×D₃)⋊C₄	—	2	2	no	—
262	(C₂×D₃)⋊C₄	C₅×D₄	1	2	yes	—
263	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
264	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
265	C₄×Dic₃	—	2	2	no	—
266	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
267	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
269	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
270	ΓL(1,𝔽₂₅)	—	2	2	no	—
271	D₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
272	C₂³×C₅	—	2	2	no	—
273	C₂³×C₅	—	3	1	no	—
274	C₂³×C₅	—	6	8	no	—
275	C₂³×C₅	—	6	2	no	—
276	C₂³×C₅	—	24	2	no	—
277	C₂³×C₅	—	24	2	no	—
278	C₅×D₄	—	2	2	no	—
279	C₅×D₄	—	3	4	no	—
280	C₅×D₄	—	6	8	no	—
281	C₅×D₄	—	6	2	no	—
282	C₅×D₄	C₂×C₄×D₃	1	4	yes	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	3	1	no	—
285	C₂×C₄×C₅	—	3	2	no	—
286	C₂×C₄×C₅	—	3	2	no	—
287	C₂×C₄×C₅	—	3	2	no	—
288	C₂×C₄×C₅	—	6	2	no	—
289	C₂×C₄×C₅	—	8	2	no	—
290	C₂×C₄×C₅	—	24	2	no	—
291	C₂×C₄×C₅	—	24	2	no	—
292	C₂×C₄×C₅	—	24	2	no	—
293	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
294	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
295	C₅×C₈	—	2	1	no	—
296	C₅×C₈	—	3	2	no	—
297	C₅×C₈	—	6	1	no	—
298	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
299	C₂²×D₄	—	3	2	no	—
300	C₂×D₈	—	3	2	no	—
301	C₂×D₈	—	3	8	no	—
302	C₂×D₈	—	3	1	no	—
303	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
304	C₂×M₁₆	—	3	1	no	—
305	C₂²×C₈	—	3	1	no	—
306	C₄×D₄	—	3	2	no	—
307	C₄×D₄	—	3	2	no	—
308	C₄×D₄	—	3	2	no	—
309	C₄×D₄	—	6	2	no	—
310	C₄×D₄	—	6	2	no	—
311	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
312	#117	—	3	1	no	—
313	#117	—	3	2	no	—
314	C₂×C₂²⋊C₄	—	6	2	no	—
315	C₂×C₂²⋊C₄	—	6	2	no	—
316	#107	—	3	2	no	—
317	#106	—	3	1	no	—
318	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
319	#102	—	3	2	no	—
320	#102	—	3	2	no	—
321	#102	—	3	2	no	—
322	#102	C₂×C₅×D₃	1	2	yes	complemented
323	#97	—	3	1	no	—
324	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
325	C₄×C₈	—	3	1	no	—
326	C₄×C₈	—	3	1	no	—
327	C₂×C₃×C₅	—	4	4	no	—
328	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
329	C₂×C₃×C₅	#576	1	2	yes	—
330	C₅×D₃	—	2	2	no	—
331	C₅×D₃	—	4	4	no	—
332	C₂³×C₃	—	2	2	no	—
333	C₂²×D₃	—	2	2	no	—
334	C₂²×D₃	—	2	8	no	—
335	C₂²×D₃	—	8	2	no	—
336	C₂²×D₃	—	8	2	no	—
337	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
338	C₃×D₄	—	2	2	no	—
339	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	8	2	no	—
342	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
343	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
344	#67	—	2	8	no	—
345	C₂×Dic₃	—	2	2	no	—
346	C₂×Dic₃	—	8	2	no	—
347	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
348	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
349	D₁₂	—	2	2	no	—
350	D₁₂	C₂²×C₄×C₅	1	4	yes	—
351	C₄×D₃	—	8	2	no	—
352	C₄×D₃	—	8	2	no	—
353	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
354	C₄×D₃	C₅×#41	1	2	yes	—
355	C₃×C₈	—	2	1	no	—
356	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
357	C₃⋊C₈	—	2	1	no	—
358	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
359	C₂²×C₅	—	2	4	no	—
360	C₂²×C₅	—	3	2	no	—
361	C₂²×C₅	—	4	2	no	—
362	C₂²×C₅	—	4	2	no	—
363	C₂²×C₅	—	6	2	no	—
364	C₂²×C₅	—	6	4	no	—
365	C₂²×C₅	—	12	2	no	—
366	C₂²×C₅	—	12	2	no	—
367	C₂²×C₅	—	24	8	no	—
368	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
369	C₄×C₅	—	2	2	no	—
370	C₄×C₅	—	3	2	no	—
371	C₄×C₅	—	4	2	no	—
372	C₄×C₅	—	6	2	no	—
373	C₄×C₅	—	12	2	no	—
374	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
375	C₄×C₅	D₃×#41	1	1	yes	characteristic
376	C₂⁴	—	6	2	no	—
377	C₂×D₄	—	3	8	no	—
378	C₂×D₄	—	3	2	no	—
379	C₂×D₄	—	6	4	no	—
380	C₂×D₄	—	6	2	no	—
381	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	3	1	no	—
384	C₂²×C₄	—	6	2	no	—
385	C₂²×C₄	—	6	2	no	—
386	C₂²×C₄	—	6	2	no	—
387	D₈	—	3	8	no	—
388	D₈	—	3	4	no	—
389	D₈	C₄×C₅×D₃	1	4	yes	complemented
390	M₁₆	—	6	2	no	—
391	C₂×C₈	—	3	1	no	—
392	C₂×C₈	—	3	4	no	—
393	C₂×C₈	—	3	1	no	—
394	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
395	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
396	C₄⋊C₄	—	3	2	no	—
397	C₄⋊C₄	—	3	2	no	—
398	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	3	2	no	—
401	C₂²⋊C₄	—	6	2	no	—
402	C₂²⋊C₄	—	6	2	no	—
403	C₂²⋊C₄	—	6	2	no	—
404	C₂²⋊C₄	—	6	2	no	—
405	C₄²	—	3	1	no	—
406	C₄²	—	6	2	no	—
407	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
408	C₃×C₅	#2948	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	—	2	4	no	—
410	C₂²×C₃	—	4	2	no	—
411	C₂²×C₃	—	4	2	no	—
412	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
413	C₂×D₃	—	2	2	no	—
414	C₂×D₃	—	2	4	no	—
415	C₂×D₃	—	4	2	no	—
416	C₂×D₃	—	4	2	no	—
417	C₂×D₃	—	8	8	no	—
418	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	4	2	no	—
421	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
422	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
423	Dic₃	—	2	2	no	—
424	Dic₃	—	4	2	no	—
425	Dic₃	C₄×C₅×D₄	1	2	yes	—
426	C₂×C₅	—	4	4	no	—
427	C₂×C₅	—	6	2	no	—
428	C₂×C₅	—	12	4	no	—
429	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
430	C₂×C₅	#5774	1	2	yes	—
431	C₂³	—	2	2	no	—
432	C₂³	—	3	1	no	—
433	C₂³	—	6	8	no	—
434	C₂³	—	6	2	no	—
435	C₂³	—	24	2	no	—
436	C₂³	—	24	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	3	4	no	—
439	D₄	—	6	8	no	—
440	D₄	—	6	2	no	—
441	D₄	C₂×C₄×C₅×D₃	1	4	yes	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	3	1	no	—
444	C₂×C₄	—	3	2	no	—
445	C₂×C₄	—	3	2	no	—
446	C₂×C₄	—	3	2	no	—
447	C₂×C₄	—	6	2	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	—	24	2	no	—
450	C₂×C₄	—	24	2	no	—
451	C₂×C₄	—	24	2	no	—
452	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
453	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
454	C₈	—	2	1	no	—
455	C₈	—	3	2	no	—
456	C₈	—	6	1	no	—
457	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
458	C₂×C₃	—	4	4	no	—
459	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
460	C₂×C₃	C₅×#576	1	2	yes	—
461	D₃	—	2	2	no	—
462	D₃	—	4	4	no	—
463	C₅	#79867	1	1	yes	characteristic, direct product factor, Sylow
464	C₂²	—	2	4	no	—
465	C₂²	—	3	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	6	2	no	—
469	C₂²	—	6	4	no	—
470	C₂²	—	12	2	no	—
471	C₂²	—	12	2	no	—
472	C₂²	—	24	8	no	—
473	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	3	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	6	2	no	—
478	C₄	—	12	2	no	—
479	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
480	C₄	C₅×D₃×#41	1	1	yes	characteristic
481	C₃	C₅×#2948	1	1	yes	characteristic, complemented, Sylow
482	C₂	—	4	4	no	—
483	C₂	—	6	2	no	—
484	C₂	—	12	4	no	—
485	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
486	C₂	C₅×#5774	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#442	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₈	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#442	D₃
hypocenter	C₃	C₅×#2948
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#442

Complements

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

N	H ≅ G/N	type
2. C₅×#5545	C₂	semidirect
3. C₃×C₅×#442	C₂	semidirect
4. C₅×#5152	C₂	semidirect
5. C₄×C₅×#213	C₂	semidirect
6. C₅×#4869	C₂	semidirect
7. C₅×#4860	C₂	semidirect
8. C₅×#4770	C₂	semidirect
9. C₅×#4756	C₂	semidirect
10. C₅×#4711	C₂	semidirect
11. C₅×#4708	C₂	semidirect
15. C₃×C₄×C₅×D₄	C₂²	semidirect
16. C₅×D₄×Dic₃	C₂²	semidirect
20. C₅×D₃×D₈	C₄	semidirect
24. C₅×#893	C₂²	semidirect
28. C₄×C₅×D₁₂	C₂²	semidirect
30. C₃×C₅×#106	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
32. C₃×C₅×#97	C₂²	semidirect
33. C₅×#832	C₂²	semidirect
34. C₅×#821	C₂²	semidirect
35. C₅×#817	C₂²	semidirect
36. C₅×#815	C₂²	semidirect
37. C₅×C₈×Dic₃	C₂²	semidirect
38. C₅×#809	C₂²	semidirect
39. C₅×#807	C₂²	semidirect
40. C₄×C₅×C₃⋊C₈	C₂²	semidirect
41. #79867	C₅	direct (N × H)
47. C₅×#442	D₃	semidirect
59. C₅×D₃×D₄	C₂×C₄	semidirect
64. C₃×C₅×D₈	C₂×C₄	semidirect
71. C₅×#213	C₂×C₄	semidirect
82. C₅×D₂₄	C₂×C₄	semidirect
84. C₅×D₃×C₈	C₂×C₄	semidirect
86. #5545	C₂×C₅	semidirect
87. C₃×#442	C₂×C₅	semidirect
88. #5152	C₂×C₅	semidirect
89. C₄×#213	C₂×C₅	semidirect
90. #4869	C₂×C₅	semidirect
91. #4860	C₂×C₅	semidirect
92. #4770	C₂×C₅	semidirect
93. #4756	C₂×C₅	semidirect
94. #4711	C₂×C₅	semidirect
95. #4708	C₂×C₅	semidirect
108. C₄×C₅×D₄	C₂×D₃	semidirect
115. C₅×#106	C₂×D₃	semidirect
119. C₅×#102	C₂×D₃	semidirect
121. C₅×#97	C₂×D₃	semidirect
154. C₃×C₄×D₄	C₂²×C₅	semidirect
155. D₄×Dic₃	C₂²×C₅	semidirect
159. D₃×D₈	C₄×C₅	semidirect
163. #893	C₂²×C₅	semidirect
167. C₄×D₁₂	C₂²×C₅	semidirect
169. C₃×#106	C₂²×C₅	semidirect
170. C₃×#102	C₂²×C₅	semidirect
171. C₃×#97	C₂²×C₅	semidirect
172. #832	C₂²×C₅	semidirect
173. #821	C₂²×C₅	semidirect
174. #817	C₂²×C₅	semidirect
175. #815	C₂²×C₅	semidirect
176. C₈×Dic₃	C₂²×C₅	semidirect
177. #809	C₂²×C₅	semidirect
178. #807	C₂²×C₅	semidirect
179. C₄×C₃⋊C₈	C₂²×C₅	semidirect
193. C₅×D₈	C₄×D₃	semidirect
217. #442	C₅×D₃	semidirect
246. D₃×D₄	C₂×C₄×C₅	semidirect
251. C₃×D₈	C₂×C₄×C₅	semidirect
258. #213	C₂×C₄×C₅	semidirect
269. D₂₄	C₂×C₄×C₅	semidirect
271. D₃×C₈	C₂×C₄×C₅	semidirect
311. C₄×D₄	C₂×C₅×D₃	semidirect
318. #106	C₂×C₅×D₃	semidirect
322. #102	C₂×C₅×D₃	semidirect
324. #97	C₂×C₅×D₃	semidirect
389. D₈	C₄×C₅×D₃	semidirect
408. C₃×C₅	#2948	semidirect
463. C₅	#79867	direct (N × H)
481. C₃	C₅×#2948	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×D₈	2
C₅×#5545	2
C₃×C₅×#442	2
C₅×#5152	2
C₄×C₅×#213	2
C₅×#4869	2
C₅×#4860	2
C₅×#4770	2
C₅×#4756	2
C₅×#4711	2
C₅×#4708	2
C₅×#2948	3
#79867	5

Subgroups — C5×#79867 #14417330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79867 #14417330