Subgroups — C₅×#80980 #14458284

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	C₅×#5726	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5088	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4883	C₂	1	2	yes	maximal, complemented
7	C₅×#4882	C₂	1	2	yes	maximal, complemented
8	C₅×#4843	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4834	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4773	C₂	1	2	yes	maximal, complemented
11	C₅×D₃×#102	C₂	1	2	yes	maximal, complemented
12	C₅×#3294	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	—	2	1	no	—
14	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
15	C₂²×C₅×D₁₂	—	2	1	no	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₅×#946	—	2	1	no	—
19	C₂×C₅×#213	C₂²	1	1	yes	characteristic
20	C₅×#930	—	2	1	no	—
21	C₂×C₅×D₂₄	C₂²	1	2	yes	complemented
22	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
23	C₅×#895	C₂²	1	2	yes	—
24	C₅×#895	C₂²	1	2	yes	complemented
25	C₅×#894	—	2	2	no	—
26	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
27	C₅×#882	—	2	2	no	—
28	C₅×#874	C₂²	1	1	yes	characteristic
29	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
30	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#107	C₂²	1	2	yes	complemented
32	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#102	C₂²	1	2	yes	—
34	C₅×#832	C₂²	1	1	yes	characteristic
35	C₅×#821	C₂²	1	2	yes	complemented
36	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
37	C₅×#809	C₂²	1	1	yes	characteristic, complemented
38	C₅×#809	C₂²	1	2	yes	complemented
39	C₅×#809	C₂²	1	2	yes	complemented
40	C₅×#807	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	#80980	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#547	—	3	1	no	—
44	C₅×D₄²	—	3	1	no	—
45	C₅×#486	—	3	1	no	—
46	C₅×#480	—	3	2	no	—
47	C₅×#474	D₃	1	1	yes	characteristic, complemented
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	C₂×C₃×C₅×Q₈	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂×C₅×#67	—	2	2	no	—
59	C₅×#239	—	4	4	no	—
60	C₅×D₃×D₄	—	2	4	no	—
61	C₅×D₃×D₄	—	4	2	no	—
62	C₂×C₅×D₁₂	—	2	2	no	—
63	C₂×C₅×D₁₂	—	2	2	no	—
64	C₂×C₅×D₁₂	—	2	1	no	—
65	C₂×C₅×D₁₂	—	2	1	no	—
66	C₂×C₅×D₁₂	—	4	4	no	—
67	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
68	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
69	C₂×C₅×D₁₂	C₂³	1	2	yes	—
70	C₂×C₄×C₅×D₃	—	2	2	no	—
71	C₂×C₄×C₅×D₃	—	2	1	no	—
72	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#213	—	2	2	no	—
80	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
81	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
82	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
83	C₅×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
84	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
85	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
86	C₅×Dic₃⋊C₄	—	2	2	no	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₅×D₂₄	—	4	2	no	—
90	C₅×D₃×C₈	—	4	2	no	—
91	#5726	C₂×C₅	1	1	yes	characteristic, complemented
92	D₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
93	C₃×#474	C₂×C₅	1	1	yes	characteristic, complemented
94	#5088	C₂×C₅	1	1	yes	characteristic, complemented
95	C₄×#213	C₂×C₅	1	1	yes	characteristic, complemented
96	#4883	C₂×C₅	1	2	yes	complemented
97	#4882	C₂×C₅	1	2	yes	complemented
98	#4843	C₂×C₅	1	1	yes	characteristic, complemented
99	#4834	C₂×C₅	1	1	yes	characteristic, complemented
100	#4773	C₂×C₅	1	2	yes	complemented
101	D₃×#102	C₂×C₅	1	2	yes	complemented
102	C₂×C₅×#41	—	6	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	—	6	2	no	—
111	C₅×C₂²⋊Q₈	—	6	1	no	—
112	C₅×#121	—	3	2	no	—
113	C₅×#121	—	3	2	no	—
114	C₅×#121	—	6	1	no	—
115	C₅×#120	—	6	2	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	3	1	no	—
118	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
119	C₂×C₅×C₄⋊C₄	—	3	2	no	—
120	C₅×#107	—	3	1	no	—
121	C₅×#107	C₂×D₃	1	2	yes	complemented
122	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
123	C₅×#102	—	3	1	no	—
124	C₅×#102	—	3	2	no	—
125	C₅×#102	—	3	2	no	—
126	C₅×#102	—	3	1	no	—
127	C₅×#102	—	3	2	no	—
128	C₅×#102	C₂×D₃	1	2	yes	—
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	C₂²×C₅×D₃	—	2	1	no	—
134	C₂²×C₅×D₃	—	2	2	no	—
135	C₂²×C₅×D₃	—	4	4	no	—
136	C₂²×C₅×D₃	—	4	4	no	—
137	C₂²×C₅×D₃	—	8	2	no	—
138	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
139	C₃×C₅×Q₈	—	4	2	no	—
140	C₃×C₅×D₄	—	2	1	no	—
141	C₃×C₅×D₄	#41	1	2	yes	complemented
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	4	2	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₅×#67	—	4	4	no	—
149	C₂×C₅×Dic₃	—	2	1	no	—
150	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
151	C₅×D₁₂	—	2	1	no	—
152	C₅×D₁₂	—	2	2	no	—
153	C₅×D₁₂	—	2	1	no	—
154	C₅×D₁₂	—	2	2	no	—
155	C₅×D₁₂	—	4	4	no	—
156	C₅×D₁₂	—	4	4	no	—
157	C₅×D₁₂	—	4	2	no	—
158	C₅×D₁₂	—	8	1	no	—
159	C₅×D₁₂	D₈	1	4	yes	complemented
160	C₄×C₅×D₃	—	2	2	no	—
161	C₄×C₅×D₃	—	2	2	no	—
162	C₄×C₅×D₃	—	4	4	no	—
163	C₄×C₅×D₃	—	4	2	no	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₅×C₃⋊C₈	—	2	1	no	—
166	C₅×C₃⋊C₈	—	2	1	no	—
167	C₂×#239	—	2	1	no	—
168	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
169	C₂²×D₁₂	—	2	1	no	—
170	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
171	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
172	#946	—	2	1	no	—
173	C₂×#213	C₂²×C₅	1	1	yes	characteristic
174	#930	—	2	1	no	—
175	C₂×D₂₄	C₂²×C₅	1	2	yes	complemented
176	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
177	#895	C₂²×C₅	1	2	yes	—
178	#895	C₂²×C₅	1	2	yes	complemented
179	#894	—	2	2	no	—
180	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
181	#882	—	2	2	no	—
182	#874	C₂²×C₅	1	1	yes	characteristic
183	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
184	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
185	C₃×#107	C₂²×C₅	1	2	yes	complemented
186	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
187	C₃×#102	C₂²×C₅	1	2	yes	—
188	#832	C₂²×C₅	1	1	yes	characteristic
189	#821	C₂²×C₅	1	2	yes	complemented
190	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	complemented
191	#809	C₂²×C₅	1	2	yes	complemented
192	#809	C₂²×C₅	1	1	yes	characteristic, complemented
193	#809	C₂²×C₅	1	2	yes	complemented
194	#807	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	—	12	4	no	—
198	C₂×C₅×Q₈	—	2	1	no	—
199	C₂×C₅×D₄	—	3	1	no	—
200	C₂×C₅×D₄	—	3	1	no	—
201	C₂×C₅×D₄	—	3	2	no	—
202	C₂×C₅×D₄	—	6	2	no	—
203	C₂×C₅×D₄	—	6	2	no	—
204	C₂×C₅×D₄	—	6	2	no	—
205	C₂×C₅×D₄	—	6	4	no	—
206	C₂×C₅×D₄	—	6	1	no	—
207	C₂×C₅×D₄	—	6	1	no	—
208	C₂×C₅×D₄	—	12	4	no	—
209	C₂×C₅×D₄	—	12	2	no	—
210	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	—	2	1	no	—
212	C₂²×C₄×C₅	—	3	2	no	—
213	C₂²×C₄×C₅	—	6	2	no	—
214	C₂²×C₄×C₅	—	6	1	no	—
215	C₅×D₈	—	6	2	no	—
216	C₅×D₈	—	12	2	no	—
217	C₂×C₅×C₈	—	3	1	no	—
218	C₂×C₅×C₈	—	3	1	no	—
219	C₂×C₅×C₈	—	12	2	no	—
220	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	3	1	no	—
223	C₅×C₄⋊C₄	—	3	1	no	—
224	C₅×C₄⋊C₄	—	6	2	no	—
225	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
226	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	3	2	no	—
229	C₅×C₂²⋊C₄	—	6	2	no	—
230	C₅×C₂²⋊C₄	—	6	2	no	—
231	C₅×C₂²⋊C₄	—	6	1	no	—
232	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
233	#547	—	3	1	no	—
234	D₄²	—	3	1	no	—
235	#486	—	3	1	no	—
236	#480	—	3	2	no	—
237	#474	C₅×D₃	1	1	yes	characteristic, complemented
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	—	4	1	no	—
246	C₂²×C₃×C₅	—	4	1	no	—
247	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₅×D₃	—	2	2	no	—
249	C₂×C₅×D₃	—	2	2	no	—
250	C₂×C₅×D₃	—	4	2	no	—
251	C₂×C₅×D₃	—	4	1	no	—
252	C₂×C₅×D₃	—	4	1	no	—
253	C₂×C₅×D₃	—	4	2	no	—
254	C₂×C₅×D₃	—	4	2	no	—
255	C₂×C₅×D₃	—	4	1	no	—
256	C₂×C₅×D₃	—	8	8	no	—
257	C₂×C₅×D₃	C₂×D₈	1	4	yes	—
258	C₃×C₄×C₅	—	2	1	no	—
259	C₃×C₄×C₅	—	4	2	no	—
260	C₃×C₄×C₅	—	4	1	no	—
261	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
262	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
264	C₅×Dic₃	—	2	2	no	—
265	C₅×Dic₃	—	4	1	no	—
266	C₂³×D₃	—	2	2	no	—
267	C₂×C₃×Q₈	—	2	1	no	—
268	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂×#67	—	2	2	no	—
271	#239	—	4	4	no	—
272	D₃×D₄	—	2	4	no	—
273	D₃×D₄	—	4	2	no	—
274	C₂×D₁₂	—	2	2	no	—
275	C₂×D₁₂	—	2	2	no	—
276	C₂×D₁₂	—	2	1	no	—
277	C₂×D₁₂	—	2	1	no	—
278	C₂×D₁₂	—	4	4	no	—
279	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
280	C₂×D₁₂	C₂³×C₅	1	2	yes	—
281	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
282	C₂×C₄×D₃	—	2	2	no	—
283	C₂×C₄×D₃	—	2	1	no	—
284	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
285	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
288	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
289	C₃×C₂²⋊C₄	—	2	1	no	—
290	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
291	#213	—	2	2	no	—
292	(C₂×D₃)⋊C₄	—	2	1	no	—
293	(C₂×D₃)⋊C₄	—	2	2	no	—
294	(C₂×D₃)⋊C₄	—	2	2	no	—
295	(C₂×D₃)⋊C₄	C₅×D₄	1	2	yes	—
296	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
297	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
298	Dic₃⋊C₄	—	2	2	no	—
299	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
300	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
301	D₂₄	—	4	2	no	—
302	D₃×C₈	—	4	2	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	3	2	no	—
305	C₂³×C₅	—	6	1	no	—
306	C₂³×C₅	—	6	2	no	—
307	C₂³×C₅	—	12	4	no	—
308	C₂³×C₅	—	12	4	no	—
309	C₂³×C₅	—	24	2	no	—
310	C₅×Q₈	—	4	2	no	—
311	C₅×D₄	—	2	1	no	—
312	C₅×D₄	—	3	4	no	—
313	C₅×D₄	—	6	1	no	—
314	C₅×D₄	—	6	2	no	—
315	C₅×D₄	—	6	1	no	—
316	C₅×D₄	—	6	2	no	—
317	C₅×D₄	—	12	4	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	#239	1	2	yes	complemented
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	3	2	no	—
326	C₂×C₄×C₅	—	4	2	no	—
327	C₂×C₄×C₅	—	6	2	no	—
328	C₂×C₄×C₅	—	6	2	no	—
329	C₂×C₄×C₅	—	6	1	no	—
330	C₂×C₄×C₅	—	12	4	no	—
331	C₂×C₄×C₅	—	12	2	no	—
332	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
333	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
335	C₅×C₈	—	2	2	no	—
336	C₅×C₈	—	6	1	no	—
337	C₅×C₈	—	6	1	no	—
338	C₂×#41	—	6	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	—	6	2	no	—
347	C₂²⋊Q₈	—	6	1	no	—
348	#121	—	3	2	no	—
349	#121	—	3	2	no	—
350	#121	—	6	1	no	—
351	#120	—	6	2	no	—
352	C₄×D₄	—	3	1	no	—
353	C₄×D₄	—	3	1	no	—
354	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	—	3	2	no	—
356	#107	—	3	1	no	—
357	#107	C₂×C₅×D₃	1	2	yes	complemented
358	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
359	#102	—	3	1	no	—
360	#102	—	3	2	no	—
361	#102	—	3	2	no	—
362	#102	—	3	1	no	—
363	#102	—	3	2	no	—
364	#102	C₂×C₅×D₃	1	2	yes	—
365	C₂²⋊C₈	—	3	2	no	—
366	C₄×C₈	—	3	1	no	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	#546	1	1	yes	characteristic
369	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
370	C₂×C₃×C₅	#577	1	1	yes	characteristic
371	C₅×D₃	—	2	4	no	—
372	C₅×D₃	—	8	1	no	—
373	C₅×D₃	—	8	2	no	—
374	C₂³×C₃	—	2	1	no	—
375	C₂²×D₃	—	2	1	no	—
376	C₂²×D₃	—	2	2	no	—
377	C₂²×D₃	—	4	4	no	—
378	C₂²×D₃	—	4	4	no	—
379	C₂²×D₃	—	8	2	no	—
380	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
381	C₃×Q₈	—	4	2	no	—
382	C₃×D₄	—	2	1	no	—
383	C₃×D₄	C₅×#41	1	2	yes	complemented
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	4	2	no	—
387	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
390	#67	—	4	4	no	—
391	C₂×Dic₃	—	2	1	no	—
392	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
393	D₁₂	—	2	1	no	—
394	D₁₂	—	2	2	no	—
395	D₁₂	—	2	1	no	—
396	D₁₂	—	2	2	no	—
397	D₁₂	—	4	4	no	—
398	D₁₂	—	4	4	no	—
399	D₁₂	—	4	2	no	—
400	D₁₂	—	8	1	no	—
401	D₁₂	C₅×D₈	1	4	yes	complemented
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	2	2	no	—
404	C₄×D₃	—	4	4	no	—
405	C₄×D₃	—	4	2	no	—
406	C₃×C₈	—	2	2	no	—
407	C₃⋊C₈	—	2	1	no	—
408	C₃⋊C₈	—	2	1	no	—
409	C₂²×C₅	—	2	2	no	—
410	C₂²×C₅	—	3	4	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	—	4	1	no	—
413	C₂²×C₅	—	6	2	no	—
414	C₂²×C₅	—	6	2	no	—
415	C₂²×C₅	—	12	1	no	—
416	C₂²×C₅	—	12	2	no	—
417	C₂²×C₅	—	12	2	no	—
418	C₂²×C₅	—	12	1	no	—
419	C₂²×C₅	—	12	2	no	—
420	C₂²×C₅	—	12	1	no	—
421	C₂²×C₅	—	24	8	no	—
422	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	4	1	no	—
425	C₄×C₅	—	4	2	no	—
426	C₄×C₅	—	6	2	no	—
427	C₄×C₅	—	12	1	no	—
428	C₄×C₅	D₃×D₈	1	2	yes	—
429	C₄×C₅	C₂×#239	1	1	yes	characteristic
430	C₄×C₅	#1009	1	1	yes	characteristic
431	C₂⁴	—	6	2	no	—
432	#41	—	12	4	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×D₄	—	3	1	no	—
435	C₂×D₄	—	3	2	no	—
436	C₂×D₄	—	3	1	no	—
437	C₂×D₄	—	6	2	no	—
438	C₂×D₄	—	6	2	no	—
439	C₂×D₄	—	6	2	no	—
440	C₂×D₄	—	6	4	no	—
441	C₂×D₄	—	6	1	no	—
442	C₂×D₄	—	6	1	no	—
443	C₂×D₄	—	12	4	no	—
444	C₂×D₄	—	12	2	no	—
445	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	6	2	no	—
449	C₂²×C₄	—	6	1	no	—
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	—	12	2	no	—
455	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	3	1	no	—
458	C₄⋊C₄	—	3	1	no	—
459	C₄⋊C₄	—	6	2	no	—
460	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
461	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	3	2	no	—
464	C₂²⋊C₄	—	6	2	no	—
465	C₂²⋊C₄	—	6	2	no	—
466	C₂²⋊C₄	—	6	1	no	—
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	—	4	1	no	—
471	C₂²×C₃	—	4	1	no	—
472	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
473	C₂×D₃	—	2	2	no	—
474	C₂×D₃	—	2	2	no	—
475	C₂×D₃	—	4	2	no	—
476	C₂×D₃	—	4	1	no	—
477	C₂×D₃	—	4	1	no	—
478	C₂×D₃	—	4	2	no	—
479	C₂×D₃	—	4	2	no	—
480	C₂×D₃	—	4	1	no	—
481	C₂×D₃	—	8	8	no	—
482	C₂×D₃	C₂×C₅×D₈	1	4	yes	—
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	4	2	no	—
485	C₃×C₄	—	4	1	no	—
486	C₃×C₄	C₂×C₅×D₈	1	2	yes	—
487	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
488	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
489	Dic₃	—	2	2	no	—
490	Dic₃	—	4	1	no	—
491	C₂×C₅	—	4	2	no	—
492	C₂×C₅	—	6	4	no	—
493	C₂×C₅	—	24	2	no	—
494	C₂×C₅	—	24	1	no	—
495	C₂×C₅	#5630	1	1	yes	characteristic
496	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
497	C₂×C₅	#5778	1	1	yes	characteristic
498	C₂³	—	2	1	no	—
499	C₂³	—	3	2	no	—
500	C₂³	—	6	1	no	—
501	C₂³	—	6	2	no	—
502	C₂³	—	12	4	no	—
503	C₂³	—	12	4	no	—
504	C₂³	—	24	2	no	—
505	Q₈	—	4	2	no	—
506	D₄	—	2	1	no	—
507	D₄	—	3	4	no	—
508	D₄	—	6	1	no	—
509	D₄	—	6	2	no	—
510	D₄	—	6	1	no	—
511	D₄	—	6	2	no	—
512	D₄	—	12	4	no	—
513	D₄	—	12	4	no	—
514	D₄	—	12	4	no	—
515	D₄	—	12	2	no	—
516	D₄	—	24	1	no	—
517	D₄	C₅×#239	1	2	yes	complemented
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	3	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	6	2	no	—
523	C₂×C₄	—	6	2	no	—
524	C₂×C₄	—	6	1	no	—
525	C₂×C₄	—	12	4	no	—
526	C₂×C₄	—	12	2	no	—
527	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
528	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
529	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
530	C₈	—	2	2	no	—
531	C₈	—	6	1	no	—
532	C₈	—	6	1	no	—
533	C₂×C₃	—	4	2	no	—
534	C₂×C₃	C₅×#546	1	1	yes	characteristic
535	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
536	C₂×C₃	C₅×#577	1	1	yes	characteristic
537	D₃	—	2	4	no	—
538	D₃	—	8	2	no	—
539	D₃	—	8	1	no	—
540	C₅	#80980	1	1	yes	characteristic, direct product factor, Sylow
541	C₂²	—	2	2	no	—
542	C₂²	—	3	4	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	6	2	no	—
546	C₂²	—	6	2	no	—
547	C₂²	—	12	1	no	—
548	C₂²	—	12	2	no	—
549	C₂²	—	12	2	no	—
550	C₂²	—	12	1	no	—
551	C₂²	—	12	2	no	—
552	C₂²	—	12	1	no	—
553	C₂²	—	24	8	no	—
554	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
555	C₄	—	2	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	2	no	—
558	C₄	—	6	2	no	—
559	C₄	—	12	1	no	—
560	C₄	C₅×D₃×D₈	1	2	yes	—
561	C₄	C₂×C₅×#239	1	1	yes	characteristic
562	C₄	C₅×#1009	1	1	yes	characteristic
563	C₃	C₅×#3294	1	1	yes	characteristic, complemented, Sylow
564	C₂	—	4	2	no	—
565	C₂	—	6	4	no	—
566	C₂	—	24	2	no	—
567	C₂	—	24	1	no	—
568	C₂	C₅×#5630	1	1	yes	characteristic
569	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
570	C₂	C₅×#5778	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#474	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#474	D₃
hypocenter	C₃	C₅×#3294
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#474

Complements

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

N	H ≅ G/N	type
1. C₅×#5726	C₂	semidirect
2. C₅×D₄×D₁₂	C₂	semidirect
3. C₃×C₅×#474	C₂	semidirect
4. C₅×#5088	C₂	semidirect
5. C₄×C₅×#213	C₂	semidirect
6. C₅×#4883	C₂	semidirect
7. C₅×#4882	C₂	semidirect
8. C₅×#4843	C₂	semidirect
9. C₅×#4834	C₂	semidirect
10. C₅×#4773	C₂	semidirect
11. C₅×D₃×#102	C₂	semidirect
16. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₅×D₂₄	C₂²	semidirect
22. C₂×C₅×D₃×C₈	C₂²	semidirect
24. C₅×#895	C₂²	semidirect
26. C₅×D₃×C₄⋊C₄	C₂²	semidirect
30. C₄×C₅×D₁₂	C₂²	semidirect
31. C₃×C₅×#107	C₂²	semidirect
32. C₃×C₅×C₄⋊C₈	C₂²	semidirect
35. C₅×#821	C₂²	semidirect
36. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
37. C₅×#809	C₂²	semidirect
38. C₅×#809	C₂²	semidirect
39. C₅×#809	C₂²	semidirect
40. C₅×#807	C₂²	semidirect
41. C₄×C₅×C₃⋊C₈	C₂²	semidirect
42. #80980	C₅	direct (N × H)
47. C₅×#474	D₃	semidirect
91. #5726	C₂×C₅	semidirect
92. D₄×D₁₂	C₂×C₅	semidirect
93. C₃×#474	C₂×C₅	semidirect
94. #5088	C₂×C₅	semidirect
95. C₄×#213	C₂×C₅	semidirect
96. #4883	C₂×C₅	semidirect
97. #4882	C₂×C₅	semidirect
98. #4843	C₂×C₅	semidirect
99. #4834	C₂×C₅	semidirect
100. #4773	C₂×C₅	semidirect
101. D₃×#102	C₂×C₅	semidirect
108. C₅×C₄⋊Q₈	C₂×D₃	semidirect
121. C₅×#107	C₂×D₃	semidirect
122. C₅×C₄⋊C₈	C₂×D₃	semidirect
141. C₃×C₅×D₄	#41	semidirect
159. C₅×D₁₂	D₈	semidirect
170. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
175. C₂×D₂₄	C₂²×C₅	semidirect
176. C₂×D₃×C₈	C₂²×C₅	semidirect
178. #895	C₂²×C₅	semidirect
180. D₃×C₄⋊C₄	C₂²×C₅	semidirect
184. C₄×D₁₂	C₂²×C₅	semidirect
185. C₃×#107	C₂²×C₅	semidirect
186. C₃×C₄⋊C₈	C₂²×C₅	semidirect
189. #821	C₂²×C₅	semidirect
190. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
191. #809	C₂²×C₅	semidirect
192. #809	C₂²×C₅	semidirect
193. #809	C₂²×C₅	semidirect
194. #807	C₂²×C₅	semidirect
195. C₄×C₃⋊C₈	C₂²×C₅	semidirect
237. #474	C₅×D₃	semidirect
322. C₅×D₄	#239	semidirect
344. C₄⋊Q₈	C₂×C₅×D₃	semidirect
357. #107	C₂×C₅×D₃	semidirect
358. C₄⋊C₈	C₂×C₅×D₃	semidirect
383. C₃×D₄	C₅×#41	semidirect
401. D₁₂	C₅×D₈	semidirect
468. C₃×C₅	#3294	semidirect
517. D₄	C₅×#239	semidirect
540. C₅	#80980	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
C₅×#5726	2
C₅×D₄×D₁₂	2
C₃×C₅×#474	2
C₅×#5088	2
C₄×C₅×#213	2
C₅×#4883	2
C₅×#4882	2
C₅×#4843	2
C₅×#4834	2
C₅×#4773	2
C₅×D₃×#102	2
C₅×#3294	3
#80980	5

Subgroups — C5×#80980 #14458284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80980 #14458284