Subgroups — C₅×#83525 #14458275

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5038	C₂	1	2	yes	maximal, complemented
6	C₅×#5036	C₂	1	2	yes	maximal, complemented
7	C₅×#5015	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4967	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#809	C₂	1	2	yes	maximal, complemented
12	C₅×#3294	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	—	2	1	no	—
14	C₂×C₅×D₃×D₄	—	2	1	no	—
15	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₅×#123	—	2	2	no	—
18	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
19	C₃×C₅×#121	C₂²	1	2	yes	complemented
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
23	C₂×C₅×#213	C₂²	1	1	yes	characteristic
24	C₂×C₅×#213	C₂²	1	2	yes	complemented
25	C₅×#930	C₂²	1	2	yes	—
26	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
27	C₅×#895	—	2	1	no	—
28	C₅×#882	—	2	2	no	—
29	C₅×#874	C₂²	1	1	yes	characteristic
30	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
31	C₅×#832	C₂²	1	1	yes	characteristic, complemented
32	C₅×#830	C₂²	1	2	yes	complemented
33	C₅×#809	C₂²	1	1	yes	characteristic
34	C₅×#809	C₂²	1	2	yes	—
35	C₅×#809	C₂²	1	2	yes	complemented
36	C₅×#809	C₂²	1	2	yes	complemented
37	C₅×#809	C₂²	1	2	yes	complemented
38	C₅×#807	C₂²	1	1	yes	characteristic, complemented
39	C₅×#807	C₂²	1	2	yes	complemented
40	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	#83525	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#547	D₃	1	1	yes	characteristic, complemented
44	C₅×D₄²	—	3	1	no	—
45	C₅×#486	—	3	1	no	—
46	C₅×#480	—	3	2	no	—
47	C₅×#474	—	3	1	no	—
48	C₅×#466	—	3	2	no	—
49	C₅×#459	—	3	1	no	—
50	C₅×#447	—	3	2	no	—
51	C₄×C₅×D₈	—	3	1	no	—
52	C₅×C₈×D₄	—	3	1	no	—
53	C₂×C₅×#102	—	3	2	no	—
54	C₂³×C₅×D₃	—	2	2	no	—
55	C₃×C₅×#41	—	4	4	no	—
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×D₄	—	2	2	no	—
58	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂×C₅×#67	—	2	2	no	—
64	C₅×D₃×D₄	—	4	4	no	—
65	C₂×C₅×D₁₂	—	2	4	no	—
66	C₂×C₅×D₁₂	—	2	1	no	—
67	C₂×C₅×D₁₂	—	2	2	no	—
68	C₂×C₅×D₁₂	—	2	1	no	—
69	C₂×C₅×D₁₂	—	4	2	no	—
70	C₂×C₅×D₁₂	C₂³	1	2	yes	—
71	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
72	C₂×C₄×C₅×D₃	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
76	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
78	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
80	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₅×#213	—	2	2	no	—
83	C₅×#213	—	4	2	no	—
84	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
85	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
86	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₃⋊C₈	—	4	2	no	—
88	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
90	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
91	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
92	D₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
93	#5088	C₂×C₅	1	1	yes	characteristic, complemented
94	#5087	C₂×C₅	1	1	yes	characteristic, complemented
95	#5038	C₂×C₅	1	2	yes	complemented
96	#5036	C₂×C₅	1	2	yes	complemented
97	#5015	C₂×C₅	1	1	yes	characteristic, complemented
98	C₄×#213	C₂×C₅	1	1	yes	characteristic, complemented
99	D₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
100	#4967	C₂×C₅	1	2	yes	complemented
101	C₂×#809	C₂×C₅	1	2	yes	complemented
102	C₂×C₅×#41	—	2	1	no	—
103	C₂²×C₅×D₄	—	3	2	no	—
104	C₂²×C₅×D₄	—	6	1	no	—
105	C₂×C₅×D₈	—	3	1	no	—
106	C₂×C₅×D₈	—	3	2	no	—
107	C₂²×C₅×C₈	—	3	2	no	—
108	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
109	C₅×#127	—	3	1	no	—
110	C₅×#123	—	2	2	no	—
111	C₅×C₂²⋊Q₈	—	2	1	no	—
112	C₅×#121	—	3	2	no	—
113	C₅×#121	—	6	1	no	—
114	C₅×#121	C₂×D₃	1	2	yes	complemented
115	C₅×#120	—	6	2	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
118	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
119	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
120	C₅×#107	—	3	1	no	—
121	C₅×#107	—	3	2	no	—
122	C₅×C₄⋊C₈	—	3	1	no	—
123	C₅×#102	—	3	1	no	—
124	C₅×#102	—	3	1	no	—
125	C₅×#102	—	3	2	no	—
126	C₅×#102	—	3	2	no	—
127	C₅×#102	—	3	2	no	—
128	C₅×#102	—	3	2	no	—
129	C₅×C₂²⋊C₈	—	3	2	no	—
130	C₄×C₅×C₈	—	3	1	no	—
131	#3294	—	3	1	no	Sylow
132	C₂³×C₃×C₅	—	2	1	no	—
133	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
134	C₂²×C₅×D₃	—	2	1	no	—
135	C₂²×C₅×D₃	—	2	2	no	—
136	C₂²×C₅×D₃	—	4	4	no	—
137	C₂²×C₅×D₃	—	4	4	no	—
138	C₂²×C₅×D₃	—	8	2	no	—
139	C₃×C₅×Q₈	—	4	2	no	—
140	C₃×C₅×D₄	—	2	1	no	—
141	C₃×C₅×D₄	—	2	1	no	—
142	C₃×C₅×D₄	—	4	4	no	—
143	C₃×C₅×D₄	D₈	1	4	yes	complemented
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	4	4	no	—
149	C₂×C₃×C₄×C₅	—	4	2	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₅×#67	—	4	4	no	—
155	C₂×C₅×Dic₃	—	2	1	no	—
156	C₅×D₁₂	—	2	2	no	—
157	C₅×D₁₂	—	2	1	no	—
158	C₅×D₁₂	—	2	2	no	—
159	C₅×D₁₂	—	4	4	no	—
160	C₅×D₁₂	—	4	2	no	—
161	C₅×D₁₂	—	8	1	no	—
162	C₅×D₁₂	#41	1	2	yes	complemented
163	C₄×C₅×D₃	—	4	2	no	—
164	C₅×C₃⋊C₈	—	2	1	no	—
165	C₅×C₃⋊C₈	—	2	1	no	—
166	C₅×C₃⋊C₈	—	2	2	no	—
167	C₂×C₃×#41	—	2	1	no	—
168	C₂×D₃×D₄	—	2	1	no	—
169	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
170	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
171	C₃×#123	—	2	2	no	—
172	C₃×C₂²⋊Q₈	—	2	1	no	—
173	C₃×#121	C₂²×C₅	1	2	yes	complemented
174	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
175	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
177	C₂×#213	C₂²×C₅	1	1	yes	characteristic
178	C₂×#213	C₂²×C₅	1	2	yes	complemented
179	#930	C₂²×C₅	1	2	yes	—
180	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
181	#895	—	2	1	no	—
182	#882	—	2	2	no	—
183	#874	C₂²×C₅	1	1	yes	characteristic
184	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
185	#832	C₂²×C₅	1	1	yes	characteristic, complemented
186	#830	C₂²×C₅	1	2	yes	complemented
187	#809	C₂²×C₅	1	1	yes	characteristic
188	#809	C₂²×C₅	1	2	yes	—
189	#809	C₂²×C₅	1	2	yes	complemented
190	#809	C₂²×C₅	1	2	yes	complemented
191	#809	C₂²×C₅	1	2	yes	complemented
192	#807	C₂²×C₅	1	1	yes	characteristic, complemented
193	#807	C₂²×C₅	1	2	yes	complemented
194	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
196	C₂⁴×C₅	—	6	2	no	—
197	C₅×#41	—	4	4	no	—
198	C₂×C₅×Q₈	—	2	1	no	—
199	C₂×C₅×D₄	—	2	2	no	—
200	C₂×C₅×D₄	—	3	1	no	—
201	C₂×C₅×D₄	—	3	2	no	—
202	C₂×C₅×D₄	—	6	4	no	—
203	C₂×C₅×D₄	—	6	2	no	—
204	C₂×C₅×D₄	—	6	2	no	—
205	C₂×C₅×D₄	—	6	1	no	—
206	C₂×C₅×D₄	—	6	1	no	—
207	C₂×C₅×D₄	—	12	2	no	—
208	C₂×C₅×D₄	—	12	4	no	—
209	C₂×C₅×D₄	#67	1	1	yes	characteristic
210	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	—	2	2	no	—
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	6	1	no	—
214	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
215	C₅×D₈	—	6	2	no	—
216	C₅×D₈	—	12	2	no	—
217	C₂×C₅×C₈	—	3	1	no	—
218	C₂×C₅×C₈	—	3	2	no	—
219	C₂×C₅×C₈	—	3	1	no	—
220	C₂×C₅×C₈	—	12	2	no	—
221	C₅×C₄⋊C₄	—	2	2	no	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	3	1	no	—
224	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
225	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
226	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	2	2	no	—
229	C₅×C₂²⋊C₄	—	6	1	no	—
230	C₅×C₂²⋊C₄	—	6	2	no	—
231	C₅×C₂²⋊C₄	#67	1	2	yes	—
232	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
233	#547	C₅×D₃	1	1	yes	characteristic, complemented
234	D₄²	—	3	1	no	—
235	#486	—	3	1	no	—
236	#480	—	3	2	no	—
237	#474	—	3	1	no	—
238	#466	—	3	2	no	—
239	#459	—	3	1	no	—
240	#447	—	3	2	no	—
241	C₄×D₈	—	3	1	no	—
242	C₈×D₄	—	3	1	no	—
243	C₂×#102	—	3	2	no	—
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	—	2	2	no	—
246	C₂²×C₃×C₅	—	4	1	no	—
247	C₂²×C₃×C₅	—	4	1	no	—
248	C₂²×C₃×C₅	—	4	1	no	—
249	C₂²×C₃×C₅	C₂×D₈	1	4	yes	—
250	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₅×D₃	—	2	2	no	—
252	C₂×C₅×D₃	—	4	1	no	—
253	C₂×C₅×D₃	—	4	1	no	—
254	C₂×C₅×D₃	—	4	2	no	—
255	C₂×C₅×D₃	—	4	2	no	—
256	C₂×C₅×D₃	—	4	2	no	—
257	C₂×C₅×D₃	—	8	8	no	—
258	C₃×C₄×C₅	—	2	2	no	—
259	C₃×C₄×C₅	—	2	1	no	—
260	C₃×C₄×C₅	—	4	1	no	—
261	C₃×C₄×C₅	—	4	2	no	—
262	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
263	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
264	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
265	C₅×Dic₃	—	4	1	no	—
266	C₂³×D₃	—	2	2	no	—
267	C₃×#41	—	4	4	no	—
268	C₂×C₃×Q₈	—	2	1	no	—
269	C₂×C₃×D₄	—	2	2	no	—
270	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
271	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	—	2	2	no	—
273	C₂²×C₃×C₄	—	2	1	no	—
274	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
275	C₂×#67	—	2	2	no	—
276	D₃×D₄	—	4	4	no	—
277	C₂×D₁₂	—	2	4	no	—
278	C₂×D₁₂	—	2	1	no	—
279	C₂×D₁₂	—	2	2	no	—
280	C₂×D₁₂	—	2	1	no	—
281	C₂×D₁₂	—	4	2	no	—
282	C₂×D₁₂	C₂³×C₅	1	2	yes	—
283	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
284	C₂×C₄×D₃	—	2	1	no	—
285	C₃×C₄⋊C₄	—	2	2	no	—
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
288	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
289	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
290	C₃×C₂²⋊C₄	—	2	1	no	—
291	C₃×C₂²⋊C₄	—	2	2	no	—
292	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
293	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
294	#213	—	2	2	no	—
295	#213	—	4	2	no	—
296	(C₂×D₃)⋊C₄	—	2	1	no	—
297	(C₂×D₃)⋊C₄	—	2	2	no	—
298	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
299	C₂×C₃⋊C₈	—	4	2	no	—
300	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
301	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	6	1	no	—
305	C₂³×C₅	—	6	2	no	—
306	C₂³×C₅	—	12	4	no	—
307	C₂³×C₅	—	12	4	no	—
308	C₂³×C₅	—	24	2	no	—
309	C₂³×C₅	C₂×#67	1	2	yes	—
310	C₅×Q₈	—	4	2	no	—
311	C₅×D₄	—	2	1	no	—
312	C₅×D₄	—	2	1	no	—
313	C₅×D₄	—	3	2	no	—
314	C₅×D₄	—	4	4	no	—
315	C₅×D₄	—	6	2	no	—
316	C₅×D₄	—	6	1	no	—
317	C₅×D₄	—	6	2	no	—
318	C₅×D₄	—	12	4	no	—
319	C₅×D₄	—	12	4	no	—
320	C₅×D₄	—	12	2	no	—
321	C₅×D₄	—	24	1	no	—
322	C₅×D₄	#213	1	4	yes	complemented
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	4	4	no	—
328	C₂×C₄×C₅	—	4	2	no	—
329	C₂×C₄×C₅	—	6	1	no	—
330	C₂×C₄×C₅	—	12	2	no	—
331	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×#67	1	2	yes	—
333	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
335	C₅×C₈	—	6	1	no	—
336	C₅×C₈	—	6	1	no	—
337	C₅×C₈	—	6	2	no	—
338	C₂×#41	—	2	1	no	—
339	C₂²×D₄	—	3	2	no	—
340	C₂²×D₄	—	6	1	no	—
341	C₂×D₈	—	3	1	no	—
342	C₂×D₈	—	3	2	no	—
343	C₂²×C₈	—	3	2	no	—
344	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
345	#127	—	3	1	no	—
346	#123	—	2	2	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	#121	—	3	2	no	—
349	#121	—	6	1	no	—
350	#121	C₂×C₅×D₃	1	2	yes	complemented
351	#120	—	6	2	no	—
352	C₄×D₄	—	3	1	no	—
353	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
354	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
355	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
356	#107	—	3	1	no	—
357	#107	—	3	2	no	—
358	C₄⋊C₈	—	3	1	no	—
359	#102	—	3	1	no	—
360	#102	—	3	1	no	—
361	#102	—	3	2	no	—
362	#102	—	3	2	no	—
363	#102	—	3	2	no	—
364	#102	—	3	2	no	—
365	C₂²⋊C₈	—	3	2	no	—
366	C₄×C₈	—	3	1	no	—
367	C₂×C₃×C₅	—	2	4	no	—
368	C₂×C₃×C₅	—	8	1	no	—
369	C₂×C₃×C₅	#546	1	1	yes	characteristic
370	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
371	C₂×C₃×C₅	#577	1	1	yes	characteristic
372	C₅×D₃	—	4	2	no	—
373	C₅×D₃	—	8	2	no	—
374	C₂³×C₃	—	2	1	no	—
375	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
376	C₂²×D₃	—	2	1	no	—
377	C₂²×D₃	—	2	2	no	—
378	C₂²×D₃	—	4	4	no	—
379	C₂²×D₃	—	4	4	no	—
380	C₂²×D₃	—	8	2	no	—
381	C₃×Q₈	—	4	2	no	—
382	C₃×D₄	—	2	1	no	—
383	C₃×D₄	—	2	1	no	—
384	C₃×D₄	—	4	4	no	—
385	C₃×D₄	C₅×D₈	1	4	yes	complemented
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	4	4	no	—
391	C₂×C₃×C₄	—	4	2	no	—
392	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
394	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
396	#67	—	4	4	no	—
397	C₂×Dic₃	—	2	1	no	—
398	D₁₂	—	2	2	no	—
399	D₁₂	—	2	1	no	—
400	D₁₂	—	2	2	no	—
401	D₁₂	—	4	4	no	—
402	D₁₂	—	4	2	no	—
403	D₁₂	—	8	1	no	—
404	D₁₂	C₅×#41	1	2	yes	complemented
405	C₄×D₃	—	4	2	no	—
406	C₃⋊C₈	—	2	1	no	—
407	C₃⋊C₈	—	2	1	no	—
408	C₃⋊C₈	—	2	2	no	—
409	C₂²×C₅	—	2	2	no	—
410	C₂²×C₅	—	2	2	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	—	4	1	no	—
413	C₂²×C₅	—	4	1	no	—
414	C₂²×C₅	—	6	2	no	—
415	C₂²×C₅	—	12	1	no	—
416	C₂²×C₅	—	12	1	no	—
417	C₂²×C₅	—	12	2	no	—
418	C₂²×C₅	—	12	2	no	—
419	C₂²×C₅	—	12	2	no	—
420	C₂²×C₅	—	24	8	no	—
421	C₂²×C₅	C₂×#213	1	4	yes	—
422	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
423	C₄×C₅	—	2	2	no	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	4	1	no	—
426	C₄×C₅	—	4	2	no	—
427	C₄×C₅	—	12	1	no	—
428	C₄×C₅	C₂×#213	1	2	yes	—
429	C₄×C₅	D₃×#41	1	1	yes	characteristic
430	C₄×C₅	#1009	1	1	yes	characteristic
431	C₂⁴	—	6	2	no	—
432	#41	—	4	4	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	3	2	no	—
437	C₂×D₄	—	6	4	no	—
438	C₂×D₄	—	6	2	no	—
439	C₂×D₄	—	6	2	no	—
440	C₂×D₄	—	6	1	no	—
441	C₂×D₄	—	6	1	no	—
442	C₂×D₄	—	12	2	no	—
443	C₂×D₄	—	12	4	no	—
444	C₂×D₄	C₅×#67	1	1	yes	characteristic
445	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	6	1	no	—
449	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
450	D₈	—	6	2	no	—
451	D₈	—	12	2	no	—
452	C₂×C₈	—	3	1	no	—
453	C₂×C₈	—	3	1	no	—
454	C₂×C₈	—	3	2	no	—
455	C₂×C₈	—	12	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	3	1	no	—
459	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
460	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	6	1	no	—
465	C₂²⋊C₄	—	6	2	no	—
466	C₂²⋊C₄	C₅×#67	1	2	yes	—
467	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
468	C₃×C₅	#3294	1	1	yes	characteristic, complemented, Hall
469	C₂²×C₃	—	2	2	no	—
470	C₂²×C₃	—	2	2	no	—
471	C₂²×C₃	—	4	1	no	—
472	C₂²×C₃	—	4	1	no	—
473	C₂²×C₃	—	4	1	no	—
474	C₂²×C₃	C₂×C₅×D₈	1	4	yes	—
475	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
476	C₂×D₃	—	2	2	no	—
477	C₂×D₃	—	4	1	no	—
478	C₂×D₃	—	4	1	no	—
479	C₂×D₃	—	4	2	no	—
480	C₂×D₃	—	4	2	no	—
481	C₂×D₃	—	4	2	no	—
482	C₂×D₃	—	8	8	no	—
483	C₃×C₄	—	2	2	no	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	4	1	no	—
486	C₃×C₄	—	4	2	no	—
487	C₃×C₄	C₂×C₅×D₈	1	2	yes	—
488	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
489	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
490	Dic₃	—	4	1	no	—
491	C₂×C₅	—	2	4	no	—
492	C₂×C₅	—	8	1	no	—
493	C₂×C₅	—	12	2	no	—
494	C₂×C₅	—	24	2	no	—
495	C₂×C₅	C₂²×#213	1	1	yes	characteristic
496	C₂×C₅	#5829	1	1	yes	characteristic
497	C₂×C₅	#5837	1	1	yes	characteristic
498	C₂³	—	2	1	no	—
499	C₂³	—	6	1	no	—
500	C₂³	—	6	2	no	—
501	C₂³	—	12	4	no	—
502	C₂³	—	12	4	no	—
503	C₂³	—	24	2	no	—
504	C₂³	C₂×C₅×#67	1	2	yes	—
505	Q₈	—	4	2	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	3	2	no	—
509	D₄	—	4	4	no	—
510	D₄	—	6	2	no	—
511	D₄	—	6	1	no	—
512	D₄	—	6	2	no	—
513	D₄	—	12	4	no	—
514	D₄	—	12	4	no	—
515	D₄	—	12	2	no	—
516	D₄	—	24	1	no	—
517	D₄	C₅×#213	1	4	yes	complemented
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	6	1	no	—
525	C₂×C₄	—	12	2	no	—
526	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
527	C₂×C₄	C₂×C₅×#67	1	2	yes	—
528	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
529	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
530	C₈	—	6	1	no	—
531	C₈	—	6	1	no	—
532	C₈	—	6	2	no	—
533	C₂×C₃	—	2	4	no	—
534	C₂×C₃	—	8	1	no	—
535	C₂×C₃	C₅×#546	1	1	yes	characteristic
536	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
537	C₂×C₃	C₅×#577	1	1	yes	characteristic
538	D₃	—	4	2	no	—
539	D₃	—	8	2	no	—
540	C₅	#83525	1	1	yes	characteristic, direct product factor, Sylow
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	6	2	no	—
547	C₂²	—	12	1	no	—
548	C₂²	—	12	1	no	—
549	C₂²	—	12	2	no	—
550	C₂²	—	12	2	no	—
551	C₂²	—	12	2	no	—
552	C₂²	—	24	8	no	—
553	C₂²	C₂×C₅×#213	1	4	yes	—
554	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
555	C₄	—	2	2	no	—
556	C₄	—	2	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	2	no	—
559	C₄	—	12	1	no	—
560	C₄	C₂×C₅×#213	1	2	yes	—
561	C₄	C₅×D₃×#41	1	1	yes	characteristic
562	C₄	C₅×#1009	1	1	yes	characteristic
563	C₃	C₅×#3294	1	1	yes	characteristic, complemented, Sylow
564	C₂	—	2	4	no	—
565	C₂	—	8	1	no	—
566	C₂	—	12	2	no	—
567	C₂	—	24	2	no	—
568	C₂	C₂²×C₅×#213	1	1	yes	characteristic
569	C₂	C₅×#5829	1	1	yes	characteristic
570	C₂	C₅×#5837	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#547	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#547	D₃
hypocenter	C₃	C₅×#3294
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×#547

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#547	C₂	semidirect
2. C₅×D₄×D₁₂	C₂	semidirect
3. C₅×#5088	C₂	semidirect
4. C₅×#5087	C₂	semidirect
5. C₅×#5038	C₂	semidirect
6. C₅×#5036	C₂	semidirect
7. C₅×#5015	C₂	semidirect
8. C₄×C₅×#213	C₂	semidirect
9. C₅×D₄×C₃⋊C₈	C₂	semidirect
10. C₅×#4967	C₂	semidirect
11. C₂×C₅×#809	C₂	semidirect
16. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
19. C₃×C₅×#121	C₂²	semidirect
21. C₃×C₄×C₅×D₄	C₂²	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₅×#213	C₂²	semidirect
26. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
31. C₅×#832	C₂²	semidirect
32. C₅×#830	C₂²	semidirect
35. C₅×#809	C₂²	semidirect
36. C₅×#809	C₂²	semidirect
37. C₅×#809	C₂²	semidirect
38. C₅×#807	C₂²	semidirect
39. C₅×#807	C₂²	semidirect
40. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
41. C₄×C₅×C₃⋊C₈	C₂²	semidirect
42. #83525	C₅	direct (N × H)
43. C₅×#547	D₃	semidirect
91. C₃×#547	C₂×C₅	semidirect
92. D₄×D₁₂	C₂×C₅	semidirect
93. #5088	C₂×C₅	semidirect
94. #5087	C₂×C₅	semidirect
95. #5038	C₂×C₅	semidirect
96. #5036	C₂×C₅	semidirect
97. #5015	C₂×C₅	semidirect
98. C₄×#213	C₂×C₅	semidirect
99. D₄×C₃⋊C₈	C₂×C₅	semidirect
100. #4967	C₂×C₅	semidirect
101. C₂×#809	C₂×C₅	semidirect
108. C₅×C₄⋊Q₈	C₂×D₃	semidirect
114. C₅×#121	C₂×D₃	semidirect
118. C₄×C₅×D₄	C₂×D₃	semidirect
119. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
143. C₃×C₅×D₄	D₈	semidirect
162. C₅×D₁₂	#41	semidirect
170. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
173. C₃×#121	C₂²×C₅	semidirect
175. C₃×C₄×D₄	C₂²×C₅	semidirect
176. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
178. C₂×#213	C₂²×C₅	semidirect
180. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
185. #832	C₂²×C₅	semidirect
186. #830	C₂²×C₅	semidirect
189. #809	C₂²×C₅	semidirect
190. #809	C₂²×C₅	semidirect
191. #809	C₂²×C₅	semidirect
192. #807	C₂²×C₅	semidirect
193. #807	C₂²×C₅	semidirect
194. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
195. C₄×C₃⋊C₈	C₂²×C₅	semidirect
233. #547	C₅×D₃	semidirect
322. C₅×D₄	#213	semidirect
344. C₄⋊Q₈	C₂×C₅×D₃	semidirect
350. #121	C₂×C₅×D₃	semidirect
354. C₄×D₄	C₂×C₅×D₃	semidirect
355. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
385. C₃×D₄	C₅×D₈	semidirect
404. D₁₂	C₅×#41	semidirect
468. C₃×C₅	#3294	semidirect
517. D₄	C₅×#213	semidirect
540. C₅	#83525	direct (N × H)
563. C₃	C₅×#3294	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#547	2
C₅×D₄×D₁₂	2
C₅×#5088	2
C₅×#5087	2
C₅×#5038	2
C₅×#5036	2
C₅×#5015	2
C₄×C₅×#213	2
C₅×D₄×C₃⋊C₈	2
C₅×#4967	2
C₂×C₅×#809	2
C₅×#3294	3
#83525	5

Subgroups — C5×#83525 #14458275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83525 #14458275