Subgroups — C₅×#78989 #14418008

Order 1920.

912 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×#5822	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#907	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5124	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5005	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4824	C₂	1	4	yes	maximal, complemented
9	C₅×#4823	C₂	1	4	yes	maximal, complemented
10	C₅×#2955	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂×C₅×#235	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₅×#951	C₄	1	2	yes	complemented
16	C₅×#950	C₂²	1	4	yes	—
17	C₅×#949	C₄	1	2	yes	complemented
18	C₅×#948	—	2	1	no	—
19	C₅×#948	—	2	1	no	—
20	C₅×#948	C₂²	1	2	yes	complemented
21	C₅×#948	C₂²	1	2	yes	complemented
22	C₅×#942	C₄	1	2	yes	complemented
23	C₅×#932	C₄	1	2	yes	complemented
24	C₂×C₅×#208	—	2	1	no	—
25	C₂×C₅×#208	C₂²	1	1	yes	characteristic
26	C₂×C₅×#208	C₂²	1	1	yes	characteristic
27	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
28	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₅×#907	—	2	1	no	—
30	C₅×#907	—	2	1	no	—
31	C₅×#907	C₂²	1	2	yes	complemented
32	C₅×#907	C₂²	1	2	yes	complemented
33	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
34	C₂×C₅×D₃×C₈	—	2	1	no	—
35	C₃×C₅×#104	C₂²	1	4	yes	complemented
36	C₅×#822	C₂²	1	4	yes	complemented
37	C₅×#805	C₂²	1	4	yes	complemented
38	C₅×#803	C₂²	1	2	yes	complemented
39	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
40	#78989	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#575	—	3	1	no	—
42	C₂×C₅×#131	—	3	1	no	—
43	C₂×C₅×#131	—	3	1	no	—
44	C₅×#444	—	3	4	no	—
45	C₅×#443	—	3	4	no	—
46	C₅×#430	—	3	1	no	—
47	C₅×#421	—	3	1	no	—
48	C₅×#421	D₃	1	1	yes	characteristic, complemented
49	C₅×#405	—	3	1	no	—
50	C₃×C₅×#41	—	2	1	no	—
51	C₃×C₅×#41	—	2	1	no	—
52	C₃×C₅×#41	C₂×C₄	1	2	yes	—
53	C₃×C₅×#41	C₂³	1	2	yes	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	—	2	1	no	—
60	C₅×#235	—	2	1	no	—
61	C₅×#235	—	2	1	no	—
62	C₅×#235	C₂×C₄	1	2	yes	—
63	C₅×#235	C₂³	1	2	yes	—
64	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	—	2	1	no	—
66	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
67	C₃×C₅×M₁₆	—	2	1	no	—
68	C₃×C₅×M₁₆	C₂³	1	2	yes	—
69	C₂×C₃×C₅×C₈	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₃×C₄²×C₅	C₂³	1	2	yes	—
73	C₅×#216	C₂×C₄	1	4	yes	—
74	C₅×#215	C₂×C₄	1	4	yes	—
75	C₅×#214	C₂×C₄	1	4	yes	—
76	C₅×#213	C₂×C₄	1	4	yes	—
77	C₅×#208	—	2	1	no	—
78	C₅×#208	—	2	2	no	—
79	C₅×#208	—	2	2	no	—
80	C₅×#208	C₂×C₄	1	2	yes	—
81	C₅×#208	C₂×C₄	1	2	yes	—
82	C₅×#208	C₂³	1	2	yes	—
83	C₂×C₅×C₃⋊C₈	—	2	1	no	—
84	C₂×C₅×C₃⋊C₈	—	2	2	no	—
85	C₂×C₅×C₃⋊C₈	—	2	2	no	—
86	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
87	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
88	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
89	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
90	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
91	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
94	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
95	C₅×D₃×C₈	—	2	2	no	—
96	C₅×D₃×C₈	—	2	2	no	—
97	#5822	C₂×C₅	1	1	yes	characteristic
98	C₂×#948	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×#907	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#421	C₂×C₅	1	1	yes	characteristic, complemented
101	#5124	C₂×C₅	1	1	yes	characteristic, complemented
102	#5005	C₂×C₅	1	1	yes	characteristic, complemented
103	#4997	C₂×C₅	1	1	yes	characteristic, complemented
104	#4824	C₂×C₅	1	4	yes	complemented
105	#4823	C₂×C₅	1	4	yes	complemented
106	C₂×C₅×#41	—	3	1	no	—
107	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
108	C₅×#137	—	3	2	no	—
109	C₅×#137	—	3	2	no	—
110	C₅×AGL(1,ℤ/8)	—	3	2	no	—
111	C₅×AGL(1,ℤ/8)	—	3	2	no	—
112	C₅×#135	—	3	4	no	—
113	C₅×#131	—	3	2	no	—
114	C₅×#131	—	3	2	no	—
115	C₅×#131	—	3	2	no	—
116	C₅×#131	—	3	2	no	—
117	C₅×#131	—	6	1	no	—
118	C₅×#131	—	6	1	no	—
119	C₅×#131	—	6	1	no	—
120	C₅×#131	—	6	1	no	—
121	C₂×C₅×M₁₆	—	3	1	no	—
122	C₂×C₅×M₁₆	—	3	1	no	—
123	C₂×C₅×M₁₆	—	6	1	no	—
124	C₂×C₅×M₁₆	—	6	1	no	—
125	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
126	C₂²×C₅×C₈	—	3	1	no	—
127	C₂²×C₅×C₈	—	6	1	no	—
128	C₂²×C₅×C₈	—	6	1	no	—
129	C₅×#117	C₂×D₃	1	1	yes	characteristic
130	C₅×#108	—	3	4	no	—
131	C₅×#104	—	3	4	no	—
132	C₅×#104	C₂×D₃	1	4	yes	complemented
133	C₅×#97	—	3	2	no	—
134	C₄×C₅×C₈	—	3	2	no	—
135	#2955	—	3	1	no	Sylow
136	C₂³×C₃×C₅	—	2	1	no	—
137	C₂³×C₃×C₅	#41	1	1	yes	characteristic
138	C₂²×C₅×D₃	—	2	1	no	—
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₅×#67	—	2	2	no	—
156	C₅×#67	—	2	2	no	—
157	C₂×C₅×Dic₃	—	2	1	no	—
158	C₅×D₁₂	—	2	1	no	—
159	C₅×D₁₂	C₂²×C₄	1	2	yes	—
160	C₄×C₅×D₃	—	2	2	no	—
161	C₄×C₅×D₃	—	2	2	no	—
162	C₅×Dic₆	—	2	1	no	—
163	C₅×Dic₆	C₂²×C₄	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₅×C₃⋊C₈	—	2	2	no	—
166	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
167	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
168	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
169	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
172	C₂×#235	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
174	C₃×#117	C₂²×C₅	1	1	yes	characteristic
175	#951	C₄×C₅	1	2	yes	complemented
176	#950	C₂²×C₅	1	4	yes	—
177	#949	C₄×C₅	1	2	yes	complemented
178	#948	—	2	1	no	—
179	#948	—	2	1	no	—
180	#948	C₂²×C₅	1	2	yes	complemented
181	#948	C₂²×C₅	1	2	yes	complemented
182	#942	C₄×C₅	1	2	yes	complemented
183	#932	C₄×C₅	1	2	yes	complemented
184	C₂×#208	—	2	1	no	—
185	C₂×#208	C₂²×C₅	1	1	yes	characteristic
186	C₂×#208	C₂²×C₅	1	1	yes	characteristic
187	C₂²×C₃⋊C₈	—	2	1	no	—
188	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
189	#907	—	2	1	no	—
190	#907	—	2	1	no	—
191	#907	C₂²×C₅	1	2	yes	complemented
192	#907	C₂²×C₅	1	2	yes	complemented
193	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
194	C₂×D₃×C₈	—	2	1	no	—
195	C₃×#104	C₂²×C₅	1	4	yes	complemented
196	#822	C₂²×C₅	1	4	yes	complemented
197	#805	C₂²×C₅	1	4	yes	complemented
198	#803	C₂²×C₅	1	2	yes	complemented
199	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
200	C₅×#41	—	2	1	no	—
201	C₅×#41	—	2	1	no	—
202	C₅×#41	—	3	2	no	—
203	C₅×#41	—	3	2	no	—
204	C₅×#41	—	6	1	no	—
205	C₅×#41	—	6	1	no	—
206	C₅×#41	C₄×D₃	1	2	yes	—
207	C₅×#41	C₂²×D₃	1	2	yes	—
208	C₂×C₅×Q₈	—	3	1	no	—
209	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
210	C₂×C₅×D₄	—	2	1	no	—
211	C₂×C₅×D₄	—	3	1	no	—
212	C₂×C₅×D₄	—	6	1	no	—
213	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
214	C₂²×C₄×C₅	—	2	1	no	—
215	C₂²×C₄×C₅	—	6	1	no	—
216	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
217	C₅×Q₁₆	—	3	4	no	—
218	C₅×SD₁₆	—	3	4	no	—
219	C₅×SD₁₆	—	3	4	no	—
220	C₅×D₈	—	3	4	no	—
221	C₅×M₁₆	—	2	1	no	—
222	C₅×M₁₆	—	3	2	no	—
223	C₅×M₁₆	—	3	2	no	—
224	C₅×M₁₆	—	3	2	no	—
225	C₅×M₁₆	—	6	2	no	—
226	C₅×M₁₆	—	6	2	no	—
227	C₅×M₁₆	—	6	2	no	—
228	C₅×M₁₆	—	6	2	no	—
229	C₅×M₁₆	—	6	1	no	—
230	C₅×M₁₆	C₂²×D₃	1	2	yes	—
231	C₂×C₅×C₈	—	2	1	no	—
232	C₂×C₅×C₈	—	3	1	no	—
233	C₂×C₅×C₈	—	3	1	no	—
234	C₂×C₅×C₈	—	3	1	no	—
235	C₂×C₅×C₈	—	3	1	no	—
236	C₂×C₅×C₈	—	3	1	no	—
237	C₂×C₅×C₈	—	3	1	no	—
238	C₂×C₅×C₈	—	3	2	no	—
239	C₂×C₅×C₈	—	6	2	no	—
240	C₂×C₅×C₈	—	6	2	no	—
241	C₂×C₅×C₈	—	6	2	no	—
242	C₂×C₅×C₈	—	6	2	no	—
243	C₂×C₅×C₈	—	6	1	no	—
244	C₅×C₄⋊C₄	—	2	1	no	—
245	C₅×C₂²⋊C₄	—	2	1	no	—
246	C₄²×C₅	C₂²×D₃	1	2	yes	—
247	#575	—	3	1	no	—
248	C₂×#131	—	3	1	no	—
249	C₂×#131	—	3	1	no	—
250	#444	—	3	4	no	—
251	#443	—	3	4	no	—
252	#430	—	3	1	no	—
253	#421	—	3	1	no	—
254	#421	C₅×D₃	1	1	yes	characteristic, complemented
255	#405	—	3	1	no	—
256	C₂²×C₃×C₅	—	2	2	no	—
257	C₂²×C₃×C₅	—	4	1	no	—
258	C₂²×C₃×C₅	—	4	2	no	—
259	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
260	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
261	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
262	C₂×C₅×D₃	—	2	2	no	—
263	C₂×C₅×D₃	—	4	2	no	—
264	C₃×C₄×C₅	—	2	2	no	—
265	C₃×C₄×C₅	—	4	2	no	—
266	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
267	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
268	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
269	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₅×Dic₃	—	2	2	no	—
271	C₃×#41	—	2	1	no	—
272	C₃×#41	—	2	1	no	—
273	C₃×#41	C₂×C₄×C₅	1	2	yes	—
274	C₃×#41	C₂³×C₅	1	2	yes	—
275	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂×C₃×D₄	—	2	1	no	—
277	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂²×C₃×C₄	—	2	1	no	—
279	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
280	C₂×#67	—	2	1	no	—
281	#235	—	2	1	no	—
282	#235	—	2	1	no	—
283	#235	C₂×C₄×C₅	1	2	yes	—
284	#235	C₂³×C₅	1	2	yes	—
285	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
286	C₂×C₄×D₃	—	2	1	no	—
287	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
288	C₃×M₁₆	—	2	1	no	—
289	C₃×M₁₆	C₂³×C₅	1	2	yes	—
290	C₂×C₃×C₈	—	2	1	no	—
291	C₃×C₄⋊C₄	—	2	1	no	—
292	C₃×C₂²⋊C₄	—	2	1	no	—
293	C₃×C₄²	C₂³×C₅	1	2	yes	—
294	#216	C₂×C₄×C₅	1	4	yes	—
295	#215	C₂×C₄×C₅	1	4	yes	—
296	#214	C₂×C₄×C₅	1	4	yes	—
297	#213	C₂×C₄×C₅	1	4	yes	—
298	#208	—	2	1	no	—
299	#208	—	2	2	no	—
300	#208	—	2	2	no	—
301	#208	C₂×C₄×C₅	1	2	yes	—
302	#208	C₂×C₄×C₅	1	2	yes	—
303	#208	C₂³×C₅	1	2	yes	—
304	C₂×C₃⋊C₈	—	2	1	no	—
305	C₂×C₃⋊C₈	—	2	2	no	—
306	C₂×C₃⋊C₈	—	2	2	no	—
307	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
308	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
309	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
310	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
311	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
312	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
313	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
314	ΓL(1,𝔽₂₅)	—	2	2	no	—
315	ΓL(1,𝔽₂₅)	—	2	2	no	—
316	D₃×C₈	—	2	2	no	—
317	D₃×C₈	—	2	2	no	—
318	C₂³×C₅	—	2	1	no	—
319	C₂³×C₅	—	6	1	no	—
320	C₂³×C₅	#237	1	1	yes	characteristic
321	C₅×Q₈	—	2	1	no	—
322	C₅×Q₈	—	3	2	no	—
323	C₅×Q₈	—	6	1	no	—
324	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
325	C₅×D₄	—	2	2	no	—
326	C₅×D₄	—	2	2	no	—
327	C₅×D₄	—	2	1	no	—
328	C₅×D₄	—	3	2	no	—
329	C₅×D₄	—	6	2	no	—
330	C₅×D₄	—	6	2	no	—
331	C₅×D₄	—	6	1	no	—
332	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	6	1	no	—
338	C₂×C₄×C₅	—	6	2	no	—
339	C₂×C₄×C₅	—	6	2	no	—
340	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
342	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
344	C₂×C₄×C₅	#237	1	1	yes	characteristic
345	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
346	C₅×C₈	—	2	2	no	—
347	C₅×C₈	—	3	4	no	—
348	C₅×C₈	—	3	1	no	—
349	C₅×C₈	—	3	1	no	—
350	C₅×C₈	—	3	1	no	—
351	C₅×C₈	—	3	1	no	—
352	C₅×C₈	—	6	2	no	—
353	C₂×#41	—	3	1	no	—
354	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
355	#137	—	3	2	no	—
356	#137	—	3	2	no	—
357	AGL(1,ℤ/8)	—	3	2	no	—
358	AGL(1,ℤ/8)	—	3	2	no	—
359	#135	—	3	4	no	—
360	#131	—	3	2	no	—
361	#131	—	3	2	no	—
362	#131	—	3	2	no	—
363	#131	—	3	2	no	—
364	#131	—	6	1	no	—
365	#131	—	6	1	no	—
366	#131	—	6	1	no	—
367	#131	—	6	1	no	—
368	C₂×M₁₆	—	3	1	no	—
369	C₂×M₁₆	—	3	1	no	—
370	C₂×M₁₆	—	6	1	no	—
371	C₂×M₁₆	—	6	1	no	—
372	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
373	C₂²×C₈	—	3	1	no	—
374	C₂²×C₈	—	6	1	no	—
375	C₂²×C₈	—	6	1	no	—
376	#117	C₂×C₅×D₃	1	1	yes	characteristic
377	#108	—	3	4	no	—
378	#104	—	3	4	no	—
379	#104	C₂×C₅×D₃	1	4	yes	complemented
380	#97	—	3	2	no	—
381	C₄×C₈	—	3	2	no	—
382	C₂×C₃×C₅	—	2	1	no	—
383	C₂×C₃×C₅	—	2	1	no	—
384	C₂×C₃×C₅	—	2	1	no	—
385	C₂×C₃×C₅	—	4	2	no	—
386	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
387	C₅×D₃	—	4	2	no	—
388	C₂³×C₃	—	2	1	no	—
389	C₂³×C₃	C₅×#41	1	1	yes	characteristic
390	C₂²×D₃	—	2	1	no	—
391	C₃×Q₈	—	2	1	no	—
392	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
393	C₃×D₄	—	2	2	no	—
394	C₃×D₄	—	2	2	no	—
395	C₃×D₄	—	2	1	no	—
396	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
407	#67	—	2	2	no	—
408	#67	—	2	2	no	—
409	C₂×Dic₃	—	2	1	no	—
410	D₁₂	—	2	1	no	—
411	D₁₂	C₂²×C₄×C₅	1	2	yes	—
412	C₄×D₃	—	2	2	no	—
413	C₄×D₃	—	2	2	no	—
414	Dic₆	—	2	1	no	—
415	Dic₆	C₂²×C₄×C₅	1	2	yes	—
416	C₃×C₈	—	2	2	no	—
417	C₃⋊C₈	—	2	2	no	—
418	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
419	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
420	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
421	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
422	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	2	no	—
426	C₂²×C₅	—	6	2	no	—
427	C₂²×C₅	—	12	2	no	—
428	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
429	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
430	C₂²×C₅	C₂×#237	1	1	yes	characteristic
431	C₄×C₅	—	2	2	no	—
432	C₄×C₅	—	4	2	no	—
433	C₄×C₅	—	6	2	no	—
434	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
435	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
436	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
437	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
438	#41	—	2	1	no	—
439	#41	—	2	1	no	—
440	#41	—	3	2	no	—
441	#41	—	3	2	no	—
442	#41	—	6	1	no	—
443	#41	—	6	1	no	—
444	#41	C₄×C₅×D₃	1	2	yes	—
445	#41	C₂²×C₅×D₃	1	2	yes	—
446	C₂×Q₈	—	3	1	no	—
447	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	3	1	no	—
450	C₂×D₄	—	6	1	no	—
451	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	6	1	no	—
454	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
455	Q₁₆	—	3	4	no	—
456	SD₁₆	—	3	4	no	—
457	SD₁₆	—	3	4	no	—
458	D₈	—	3	4	no	—
459	M₁₆	—	2	1	no	—
460	M₁₆	—	3	2	no	—
461	M₁₆	—	3	2	no	—
462	M₁₆	—	3	2	no	—
463	M₁₆	—	6	2	no	—
464	M₁₆	—	6	2	no	—
465	M₁₆	—	6	2	no	—
466	M₁₆	—	6	2	no	—
467	M₁₆	—	6	1	no	—
468	M₁₆	C₂²×C₅×D₃	1	2	yes	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	3	1	no	—
471	C₂×C₈	—	3	1	no	—
472	C₂×C₈	—	3	1	no	—
473	C₂×C₈	—	3	1	no	—
474	C₂×C₈	—	3	1	no	—
475	C₂×C₈	—	3	2	no	—
476	C₂×C₈	—	3	1	no	—
477	C₂×C₈	—	6	2	no	—
478	C₂×C₈	—	6	2	no	—
479	C₂×C₈	—	6	2	no	—
480	C₂×C₈	—	6	2	no	—
481	C₂×C₈	—	6	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₄²	C₂²×C₅×D₃	1	2	yes	—
485	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
486	C₂²×C₃	—	2	2	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	2	no	—
489	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
490	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
491	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
492	C₂×D₃	—	2	2	no	—
493	C₂×D₃	—	4	2	no	—
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	4	2	no	—
496	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
497	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
498	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
499	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
500	Dic₃	—	2	2	no	—
501	C₂×C₅	—	2	1	no	—
502	C₂×C₅	—	2	1	no	—
503	C₂×C₅	—	2	1	no	—
504	C₂×C₅	—	4	2	no	—
505	C₂×C₅	—	12	2	no	—
506	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
507	C₂³	—	2	1	no	—
508	C₂³	—	6	1	no	—
509	C₂³	C₅×#237	1	1	yes	characteristic
510	Q₈	—	2	1	no	—
511	Q₈	—	3	2	no	—
512	Q₈	—	6	1	no	—
513	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	1	no	—
517	D₄	—	3	2	no	—
518	D₄	—	6	2	no	—
519	D₄	—	6	2	no	—
520	D₄	—	6	1	no	—
521	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	6	1	no	—
527	C₂×C₄	—	6	2	no	—
528	C₂×C₄	—	6	2	no	—
529	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
530	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
531	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
532	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
533	C₂×C₄	C₅×#237	1	1	yes	characteristic
534	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
535	C₈	—	2	2	no	—
536	C₈	—	3	4	no	—
537	C₈	—	3	1	no	—
538	C₈	—	3	1	no	—
539	C₈	—	3	1	no	—
540	C₈	—	3	1	no	—
541	C₈	—	6	2	no	—
542	C₂×C₃	—	2	1	no	—
543	C₂×C₃	—	2	1	no	—
544	C₂×C₃	—	2	1	no	—
545	C₂×C₃	—	4	2	no	—
546	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
547	D₃	—	4	2	no	—
548	C₅	#78989	1	1	yes	characteristic, direct product factor, Sylow
549	C₂²	—	2	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	6	2	no	—
553	C₂²	—	12	2	no	—
554	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
555	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
556	C₂²	C₂×C₅×#237	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	6	2	no	—
560	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
561	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
562	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
563	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
564	C₃	C₅×#2955	1	1	yes	characteristic, complemented, Sylow
565	C₂	—	2	1	no	—
566	C₂	—	2	1	no	—
567	C₂	—	2	1	no	—
568	C₂	—	4	2	no	—
569	C₂	—	12	2	no	—
570	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#421	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₅×#5822	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#421	D₃
hypocenter	C₃	C₅×#2955
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#421

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#948	C₂	semidirect
3. C₂×C₅×#907	C₂	semidirect
4. C₃×C₅×#421	C₂	semidirect
5. C₅×#5124	C₂	semidirect
6. C₅×#5005	C₂	semidirect
7. C₅×#4997	C₂	semidirect
8. C₅×#4824	C₂	semidirect
9. C₅×#4823	C₂	semidirect
15. C₅×#951	C₄	semidirect
17. C₅×#949	C₄	semidirect
20. C₅×#948	C₂²	semidirect
21. C₅×#948	C₂²	semidirect
22. C₅×#942	C₄	semidirect
23. C₅×#932	C₄	semidirect
31. C₅×#907	C₂²	semidirect
32. C₅×#907	C₂²	semidirect
35. C₃×C₅×#104	C₂²	semidirect
36. C₅×#822	C₂²	semidirect
37. C₅×#805	C₂²	semidirect
38. C₅×#803	C₂²	semidirect
39. C₄×C₅×C₃⋊C₈	C₂²	semidirect
40. #78989	C₅	direct (N × H)
48. C₅×#421	D₃	semidirect
98. C₂×#948	C₂×C₅	semidirect
99. C₂×#907	C₂×C₅	semidirect
100. C₃×#421	C₂×C₅	semidirect
101. #5124	C₂×C₅	semidirect
102. #5005	C₂×C₅	semidirect
103. #4997	C₂×C₅	semidirect
104. #4824	C₂×C₅	semidirect
105. #4823	C₂×C₅	semidirect
132. C₅×#104	C₂×D₃	semidirect
175. #951	C₄×C₅	semidirect
177. #949	C₄×C₅	semidirect
180. #948	C₂²×C₅	semidirect
181. #948	C₂²×C₅	semidirect
182. #942	C₄×C₅	semidirect
183. #932	C₄×C₅	semidirect
191. #907	C₂²×C₅	semidirect
192. #907	C₂²×C₅	semidirect
195. C₃×#104	C₂²×C₅	semidirect
196. #822	C₂²×C₅	semidirect
197. #805	C₂²×C₅	semidirect
198. #803	C₂²×C₅	semidirect
199. C₄×C₃⋊C₈	C₂²×C₅	semidirect
254. #421	C₅×D₃	semidirect
379. #104	C₂×C₅×D₃	semidirect
485. C₃×C₅	#2955	semidirect
548. C₅	#78989	direct (N × H)
564. C₃	C₅×#2955	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5822	2
C₂×C₅×#948	2
C₂×C₅×#907	2
C₃×C₅×#421	2
C₅×#5124	2
C₅×#5005	2
C₅×#4997	2
C₅×#4824	2
C₅×#4823	2
C₅×#2955	3
#78989	5

Subgroups — C5×#78989 #14418008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78989 #14418008