Subgroups — C₅×#79025 #14430231

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₅×#5470	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5113	C₂	1	2	yes	maximal
5	C₅×#5106	C₂	1	2	yes	maximal, complemented
6	C₅×#4851	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4850	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4847	C₂	1	2	yes	maximal, complemented
9	C₅×#4846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4842	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4829	C₂	1	2	yes	maximal, complemented
12	C₅×#3076	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₄×C₅×#67	—	2	1	no	—
17	C₄×C₅×#67	—	2	1	no	—
18	C₅×#926	C₂²	1	2	yes	—
19	C₅×#926	C₂²	1	1	yes	characteristic
20	C₅×#924	—	2	1	no	—
21	C₅×#924	—	2	1	no	—
22	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
23	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
24	C₅×#872	—	2	1	no	—
25	C₄²×C₅×D₃	—	2	1	no	—
26	C₅×#870	C₂²	1	2	yes	—
27	C₅×#869	C₂²	1	1	yes	characteristic
28	C₅×#869	C₂²	1	1	yes	characteristic
29	C₄×C₅×Dic₆	—	2	1	no	—
30	C₄×C₅×Dic₆	—	2	1	no	—
31	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
32	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
34	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₅×#821	C₂²	1	2	yes	—
37	C₅×#821	C₂²	1	2	yes	—
38	C₅×#818	C₂²	1	2	yes	—
39	C₅×#818	C₂²	1	2	yes	—
40	C₅×#817	C₂²	1	2	yes	—
41	C₅×#817	C₂²	1	2	yes	—
42	C₅×#816	C₂²	1	2	yes	—
43	C₅×#816	C₂²	1	2	yes	—
44	#79025	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#533	—	3	1	no	—
46	C₄×C₅×#41	—	3	1	no	—
47	C₅×#479	—	3	2	no	—
48	C₅×#478	—	3	2	no	—
49	C₅×#477	—	3	1	no	—
50	C₅×#476	—	3	1	no	—
51	C₅×#475	—	3	1	no	—
52	C₅×#474	—	3	1	no	—
53	C₅×#427	—	3	2	no	—
54	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
55	C₅×#416	—	3	2	no	—
56	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	—	2	1	no	—
60	C₅×#235	—	2	2	no	—
61	C₅×#235	Q₈	1	4	yes	complemented
62	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	—	2	1	no	—
64	C₂×C₄×C₅×D₃	—	2	1	no	—
65	C₂×C₄×C₅×D₃	—	2	1	no	—
66	C₂×C₅×Dic₆	—	2	1	no	—
67	C₂×C₅×Dic₆	—	2	1	no	—
68	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	—	2	4	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#217	—	2	2	no	—
77	C₅×#217	—	2	1	no	—
78	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
79	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
80	C₅×C₄⋊Dic₃	—	2	1	no	—
81	C₅×C₄⋊Dic₃	—	2	1	no	—
82	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
85	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
86	C₅×Dic₃⋊C₄	—	2	2	no	—
87	C₅×Dic₃⋊C₄	—	2	2	no	—
88	C₅×Dic₃⋊C₄	—	2	1	no	—
89	C₅×Dic₃⋊C₄	—	2	1	no	—
90	C₄×C₅×Dic₃	—	2	2	no	—
91	C₄×C₅×Dic₃	—	2	1	no	—
92	C₄×C₅×Dic₃	—	2	1	no	—
93	C₄×C₅×Dic₃	—	2	1	no	—
94	C₄×#235	C₂×C₅	1	1	yes	characteristic
95	#5470	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
97	#5113	C₂×C₅	1	2	yes	—
98	#5106	C₂×C₅	1	2	yes	complemented
99	#4851	C₂×C₅	1	1	yes	characteristic, complemented
100	#4850	C₂×C₅	1	1	yes	characteristic, complemented
101	#4847	C₂×C₅	1	2	yes	complemented
102	#4846	C₂×C₅	1	1	yes	characteristic, complemented
103	#4842	C₂×C₅	1	1	yes	characteristic, complemented
104	#4829	C₂×C₅	1	2	yes	complemented
105	C₂×C₅×#41	—	3	1	no	—
106	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
107	C₅×C₄⋊Q₈	—	3	1	no	—
108	C₅×C₄⋊Q₈	—	3	1	no	—
109	C₅×#125	—	3	2	no	—
110	C₅×C₂²⋊Q₈	—	6	1	no	—
111	C₅×C₂²⋊Q₈	—	6	1	no	—
112	C₄×C₅×Q₈	—	3	1	no	—
113	C₄×C₅×Q₈	—	3	1	no	—
114	C₄×C₅×Q₈	—	6	1	no	—
115	C₄×C₅×Q₈	—	6	1	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	3	1	no	—
118	C₄×C₅×D₄	—	6	1	no	—
119	C₄×C₅×D₄	—	6	1	no	—
120	C₅×#117	—	3	2	no	—
121	C₅×#117	—	3	1	no	—
122	C₅×#117	—	6	1	no	—
123	C₂×C₄²×C₅	—	6	1	no	—
124	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
125	C₅×#107	—	3	2	no	—
126	C₅×#107	—	3	2	no	—
127	C₅×#106	—	3	2	no	—
128	C₅×#106	—	3	2	no	—
129	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
130	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
131	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
132	C₅×#103	—	3	2	no	—
133	C₅×#103	—	3	2	no	—
134	C₅×#102	—	3	2	no	—
135	C₅×#102	—	3	2	no	—
136	#3076	—	3	1	no	Sylow
137	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₅×D₃	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	4	1	no	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
147	C₂×C₃×C₄×C₅	#41	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₅×#67	—	2	4	no	—
150	C₂×C₅×Dic₃	—	2	1	no	—
151	C₂×C₅×Dic₃	—	2	1	no	—
152	C₂×C₅×Dic₃	—	2	1	no	—
153	C₂×C₅×Dic₃	—	2	2	no	—
154	C₂×C₅×Dic₃	—	2	2	no	—
155	C₅×D₁₂	—	2	1	no	—
156	C₅×D₁₂	C₂×Q₈	1	2	yes	—
157	C₄×C₅×D₃	—	2	4	no	—
158	C₄×C₅×D₃	—	4	2	no	—
159	C₄×C₅×D₃	—	4	2	no	—
160	C₅×Dic₆	—	2	1	no	—
161	C₅×Dic₆	—	4	2	no	—
162	C₅×Dic₆	—	4	2	no	—
163	C₅×Dic₆	C₂×Q₈	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×C₅×C₈	—	2	2	no	—
166	C₂×#235	C₂²×C₅	1	1	yes	characteristic
167	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
168	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
169	C₄×#67	—	2	1	no	—
170	C₄×#67	—	2	1	no	—
171	#926	C₂²×C₅	1	2	yes	—
172	#926	C₂²×C₅	1	1	yes	characteristic
173	#924	—	2	1	no	—
174	#924	—	2	1	no	—
175	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
176	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
177	#872	—	2	1	no	—
178	C₄²×D₃	—	2	1	no	—
179	#870	C₂²×C₅	1	2	yes	—
180	#869	C₂²×C₅	1	1	yes	characteristic
181	#869	C₂²×C₅	1	1	yes	characteristic
182	C₄×Dic₆	—	2	1	no	—
183	C₄×Dic₆	—	2	1	no	—
184	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
185	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
186	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
187	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
188	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
189	#821	C₂²×C₅	1	2	yes	—
190	#821	C₂²×C₅	1	2	yes	—
191	#818	C₂²×C₅	1	2	yes	—
192	#818	C₂²×C₅	1	2	yes	—
193	#817	C₂²×C₅	1	2	yes	—
194	#817	C₂²×C₅	1	2	yes	—
195	#816	C₂²×C₅	1	2	yes	—
196	#816	C₂²×C₅	1	2	yes	—
197	C₅×#41	—	3	4	no	—
198	C₅×#41	—	6	2	no	—
199	C₂×C₅×Q₈	—	3	1	no	—
200	C₂×C₅×Q₈	—	6	1	no	—
201	C₂×C₅×Q₈	—	6	1	no	—
202	C₂×C₅×D₄	—	3	1	no	—
203	C₂×C₅×D₄	—	6	1	no	—
204	C₂²×C₄×C₅	—	6	1	no	—
205	C₂²×C₄×C₅	—	6	1	no	—
206	C₂²×C₄×C₅	—	6	1	no	—
207	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
208	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₂×C₅×C₈	—	2	4	no	—
211	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
212	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
213	C₅×C₄⋊C₄	—	3	1	no	—
214	C₅×C₄⋊C₄	—	3	1	no	—
215	C₅×C₄⋊C₄	—	3	2	no	—
216	C₅×C₄⋊C₄	—	3	2	no	—
217	C₅×C₄⋊C₄	—	6	1	no	—
218	C₅×C₄⋊C₄	—	6	1	no	—
219	C₅×C₄⋊C₄	—	6	2	no	—
220	C₅×C₄⋊C₄	—	6	2	no	—
221	C₅×C₄⋊C₄	—	6	1	no	—
222	C₅×C₄⋊C₄	—	6	1	no	—
223	C₅×C₂²⋊C₄	—	6	1	no	—
224	C₅×C₂²⋊C₄	—	6	2	no	—
225	C₅×C₂²⋊C₄	—	6	1	no	—
226	C₅×C₂²⋊C₄	—	6	1	no	—
227	C₄²×C₅	—	6	1	no	—
228	C₄²×C₅	—	6	1	no	—
229	C₄²×C₅	—	6	1	no	—
230	C₄²×C₅	—	6	2	no	—
231	C₄²×C₅	D₁₂	1	1	yes	characteristic
232	C₄²×C₅	D₁₂	1	1	yes	characteristic
233	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
234	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
235	#533	—	3	1	no	—
236	C₄×#41	—	3	1	no	—
237	#479	—	3	2	no	—
238	#478	—	3	2	no	—
239	#477	—	3	1	no	—
240	#476	—	3	1	no	—
241	#475	—	3	1	no	—
242	#474	—	3	1	no	—
243	#427	—	3	2	no	—
244	C₂×C₄⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
245	#416	—	3	2	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₅×D₃	—	2	2	no	—
251	C₂×C₅×D₃	—	4	1	no	—
252	C₂×C₅×D₃	—	4	1	no	—
253	C₃×C₄×C₅	—	2	1	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
257	C₃×C₄×C₅	#135	1	2	yes	—
258	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
259	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₅×Dic₃	—	2	2	no	—
261	C₅×Dic₃	—	4	2	no	—
262	C₅×Dic₃	—	4	1	no	—
263	C₅×Dic₃	—	4	2	no	—
264	C₅×Dic₃	—	4	1	no	—
265	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂×#67	—	2	1	no	—
269	#235	—	2	2	no	—
270	#235	C₅×Q₈	1	4	yes	complemented
271	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₄×D₃	—	2	1	no	—
273	C₂×C₄×D₃	—	2	1	no	—
274	C₂×C₄×D₃	—	2	1	no	—
275	C₂×Dic₆	—	2	1	no	—
276	C₂×Dic₆	—	2	1	no	—
277	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₃×C₈	—	2	4	no	—
279	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
280	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
281	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
282	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
283	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
284	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
285	#217	—	2	2	no	—
286	#217	—	2	1	no	—
287	(C₂×D₃)⋊C₄	—	2	1	no	—
288	(C₂×D₃)⋊C₄	—	2	1	no	—
289	C₄⋊Dic₃	—	2	1	no	—
290	C₄⋊Dic₃	—	2	1	no	—
291	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
292	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
293	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
294	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
295	Dic₃⋊C₄	—	2	2	no	—
296	Dic₃⋊C₄	—	2	2	no	—
297	Dic₃⋊C₄	—	2	1	no	—
298	Dic₃⋊C₄	—	2	1	no	—
299	C₄×Dic₃	—	2	2	no	—
300	C₄×Dic₃	—	2	1	no	—
301	C₄×Dic₃	—	2	1	no	—
302	C₄×Dic₃	—	2	1	no	—
303	C₂³×C₅	—	6	1	no	—
304	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
305	C₅×Q₈	—	3	2	no	—
306	C₅×Q₈	—	6	1	no	—
307	C₅×Q₈	—	12	2	no	—
308	C₅×Q₈	—	12	2	no	—
309	C₅×D₄	—	3	2	no	—
310	C₅×D₄	—	6	4	no	—
311	C₅×D₄	—	6	1	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	6	1	no	—
315	C₂×C₄×C₅	—	6	4	no	—
316	C₂×C₄×C₅	—	6	1	no	—
317	C₂×C₄×C₅	—	6	1	no	—
318	C₂×C₄×C₅	—	6	2	no	—
319	C₂×C₄×C₅	—	6	2	no	—
320	C₂×C₄×C₅	—	12	2	no	—
321	C₂×C₄×C₅	—	12	2	no	—
322	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
324	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
327	C₂×C₄×C₅	#237	1	2	yes	—
328	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
329	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
330	C₅×C₈	—	2	2	no	—
331	C₅×C₈	—	2	2	no	—
332	C₂×#41	—	3	1	no	—
333	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
334	C₄⋊Q₈	—	3	1	no	—
335	C₄⋊Q₈	—	3	1	no	—
336	#125	—	3	2	no	—
337	C₂²⋊Q₈	—	6	1	no	—
338	C₂²⋊Q₈	—	6	1	no	—
339	C₄×Q₈	—	3	1	no	—
340	C₄×Q₈	—	3	1	no	—
341	C₄×Q₈	—	6	1	no	—
342	C₄×Q₈	—	6	1	no	—
343	C₄×D₄	—	3	1	no	—
344	C₄×D₄	—	3	1	no	—
345	C₄×D₄	—	6	1	no	—
346	C₄×D₄	—	6	1	no	—
347	#117	—	3	1	no	—
348	#117	—	3	2	no	—
349	#117	—	6	1	no	—
350	C₂×C₄²	—	6	1	no	—
351	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
352	#107	—	3	2	no	—
353	#107	—	3	2	no	—
354	#106	—	3	2	no	—
355	#106	—	3	2	no	—
356	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
357	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
358	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	—
359	#103	—	3	2	no	—
360	#103	—	3	2	no	—
361	#102	—	3	2	no	—
362	#102	—	3	2	no	—
363	C₂×C₃×C₅	—	2	2	no	—
364	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
366	C₂×C₃×C₅	#575	1	1	yes	characteristic
367	C₅×D₃	—	4	2	no	—
368	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂²×D₃	—	2	1	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	4	1	no	—
372	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
378	C₂×C₃×C₄	C₅×#41	1	2	yes	—
379	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
380	#67	—	2	4	no	—
381	C₂×Dic₃	—	2	1	no	—
382	C₂×Dic₃	—	2	1	no	—
383	C₂×Dic₃	—	2	1	no	—
384	C₂×Dic₃	—	2	2	no	—
385	C₂×Dic₃	—	2	2	no	—
386	D₁₂	—	2	1	no	—
387	D₁₂	C₂×C₅×Q₈	1	2	yes	—
388	C₄×D₃	—	2	4	no	—
389	C₄×D₃	—	4	2	no	—
390	C₄×D₃	—	4	2	no	—
391	Dic₆	—	2	1	no	—
392	Dic₆	—	4	2	no	—
393	Dic₆	—	4	2	no	—
394	Dic₆	C₂×C₅×Q₈	1	2	yes	—
395	C₃×C₈	—	2	2	no	—
396	C₃×C₈	—	2	2	no	—
397	C₂²×C₅	—	2	1	no	—
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	6	2	no	—
400	C₂²×C₅	—	12	1	no	—
401	C₂²×C₅	—	12	1	no	—
402	C₂²×C₅	#897	1	2	yes	—
403	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	—	6	2	no	—
408	C₄×C₅	—	12	1	no	—
409	C₄×C₅	—	12	2	no	—
410	C₄×C₅	—	12	1	no	—
411	C₄×C₅	—	12	2	no	—
412	C₄×C₅	#897	1	2	yes	—
413	C₄×C₅	#904	1	2	yes	—
414	C₄×C₅	C₂×#237	1	1	yes	characteristic
415	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
416	#41	—	3	4	no	—
417	#41	—	6	2	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	6	1	no	—
420	C₂×Q₈	—	6	1	no	—
421	C₂×D₄	—	3	1	no	—
422	C₂×D₄	—	6	1	no	—
423	C₂²×C₄	—	6	1	no	—
424	C₂²×C₄	—	6	1	no	—
425	C₂²×C₄	—	6	1	no	—
426	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
427	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
431	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
432	C₄⋊C₄	—	3	2	no	—
433	C₄⋊C₄	—	3	2	no	—
434	C₄⋊C₄	—	3	1	no	—
435	C₄⋊C₄	—	3	1	no	—
436	C₄⋊C₄	—	6	1	no	—
437	C₄⋊C₄	—	6	1	no	—
438	C₄⋊C₄	—	6	2	no	—
439	C₄⋊C₄	—	6	2	no	—
440	C₄⋊C₄	—	6	1	no	—
441	C₄⋊C₄	—	6	1	no	—
442	C₂²⋊C₄	—	6	1	no	—
443	C₂²⋊C₄	—	6	2	no	—
444	C₂²⋊C₄	—	6	1	no	—
445	C₂²⋊C₄	—	6	1	no	—
446	C₄²	—	6	1	no	—
447	C₄²	—	6	1	no	—
448	C₄²	—	6	1	no	—
449	C₄²	—	6	2	no	—
450	C₄²	C₅×D₁₂	1	1	yes	characteristic
451	C₄²	C₅×D₁₂	1	1	yes	characteristic
452	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
453	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
454	C₃×C₅	#3076	1	1	yes	characteristic, complemented, Hall
455	C₂²×C₃	—	2	1	no	—
456	C₂²×C₃	—	2	1	no	—
457	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
458	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₂×D₃	—	2	2	no	—
460	C₂×D₃	—	4	1	no	—
461	C₂×D₃	—	4	1	no	—
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	2	1	no	—
464	C₃×C₄	—	2	1	no	—
465	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
466	C₃×C₄	C₅×#135	1	2	yes	—
467	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
468	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
469	Dic₃	—	2	2	no	—
470	Dic₃	—	4	2	no	—
471	Dic₃	—	4	1	no	—
472	Dic₃	—	4	2	no	—
473	Dic₃	—	4	1	no	—
474	C₂×C₅	—	2	2	no	—
475	C₂×C₅	—	12	2	no	—
476	C₂×C₅	C₂×#897	1	1	yes	characteristic
477	C₂×C₅	C₂×#904	1	1	yes	characteristic
478	C₂×C₅	#5748	1	1	yes	characteristic
479	C₂³	—	6	1	no	—
480	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
481	Q₈	—	3	2	no	—
482	Q₈	—	6	1	no	—
483	Q₈	—	12	2	no	—
484	Q₈	—	12	2	no	—
485	D₄	—	3	2	no	—
486	D₄	—	6	4	no	—
487	D₄	—	6	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	6	1	no	—
491	C₂×C₄	—	6	4	no	—
492	C₂×C₄	—	6	1	no	—
493	C₂×C₄	—	6	1	no	—
494	C₂×C₄	—	6	2	no	—
495	C₂×C₄	—	6	2	no	—
496	C₂×C₄	—	12	2	no	—
497	C₂×C₄	—	12	2	no	—
498	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
499	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
500	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
501	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
502	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
503	C₂×C₄	C₅×#237	1	2	yes	—
504	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
505	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₂×C₃	—	2	2	no	—
509	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
510	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
511	C₂×C₃	C₅×#575	1	1	yes	characteristic
512	D₃	—	4	2	no	—
513	C₅	#79025	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	6	2	no	—
517	C₂²	—	12	1	no	—
518	C₂²	—	12	1	no	—
519	C₂²	C₅×#897	1	2	yes	—
520	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	6	2	no	—
525	C₄	—	12	1	no	—
526	C₄	—	12	2	no	—
527	C₄	—	12	1	no	—
528	C₄	—	12	2	no	—
529	C₄	C₅×#897	1	2	yes	—
530	C₄	C₅×#904	1	2	yes	—
531	C₄	C₂×C₅×#237	1	1	yes	characteristic
532	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
533	C₃	C₅×#3076	1	1	yes	characteristic, complemented, Sylow
534	C₂	—	2	2	no	—
535	C₂	—	12	2	no	—
536	C₂	C₂×C₅×#897	1	1	yes	characteristic
537	C₂	C₂×C₅×#904	1	1	yes	characteristic
538	C₂	C₅×#5748	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#235	C₂²
hypercenter	C₂×C₅×C₄⋊C₈	D₃
hypocenter	C₃	C₅×#3076
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₅×#5470	C₂	semidirect
3. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. C₅×#5106	C₂	semidirect
6. C₅×#4851	C₂	semidirect
7. C₅×#4850	C₂	semidirect
8. C₅×#4847	C₂	semidirect
9. C₅×#4846	C₂	semidirect
10. C₅×#4842	C₂	semidirect
11. C₅×#4829	C₂	semidirect
44. #79025	C₅	direct (N × H)
54. C₂×C₅×C₄⋊C₈	D₃	semidirect
61. C₅×#235	Q₈	semidirect
95. #5470	C₂×C₅	semidirect
96. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
98. #5106	C₂×C₅	semidirect
99. #4851	C₂×C₅	semidirect
100. #4850	C₂×C₅	semidirect
101. #4847	C₂×C₅	semidirect
102. #4846	C₂×C₅	semidirect
103. #4842	C₂×C₅	semidirect
104. #4829	C₂×C₅	semidirect
244. C₂×C₄⋊C₈	C₅×D₃	semidirect
270. #235	C₅×Q₈	semidirect
454. C₃×C₅	#3076	semidirect
513. C₅	#79025	direct (N × H)
533. C₃	C₅×#3076	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#235	2
C₅×#5470	2
C₂×C₃×C₅×C₄⋊C₈	2
C₅×#5113	2
C₅×#5106	2
C₅×#4851	2
C₅×#4850	2
C₅×#4847	2
C₅×#4846	2
C₅×#4842	2
C₅×#4829	2
C₅×#3076	3
#79025	5

Subgroups — C5×#79025 #14430231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79025 #14430231