Subgroups — C₅×#69453 #14300526

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5791	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#805	C₂	1	2	yes	maximal, complemented
5	C₅×#4523	C₂	1	2	yes	maximal, complemented
6	C₅×#1871	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₅×#235	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
10	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
11	C₅×#953	—	2	1	no	—
12	C₅×#930	C₄	1	1	yes	characteristic, complemented
13	C₅×#930	C₄	1	1	yes	characteristic, complemented
14	C₅×#929	—	2	1	no	—
15	C₄×C₅×#67	—	2	1	no	—
16	C₄×C₅×#67	—	2	1	no	—
17	C₅×#926	C₂²	1	1	yes	characteristic
18	C₅×#924	C₄	1	1	yes	characteristic, complemented
19	C₅×#924	C₄	1	1	yes	characteristic, complemented
20	C₂×C₅×#208	—	2	1	no	—
21	C₂×C₅×#208	—	2	4	no	—
22	C₂×C₅×#208	C₂²	1	2	yes	—
23	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
24	C₃×C₅×#95	—	2	1	no	—
25	C₅×#805	—	2	4	no	—
26	#69453	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂²×C₅×M₁₆	—	3	1	no	—
28	C₅×#525	—	3	1	no	—
29	C₂×C₅×#104	—	3	2	no	—
30	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
31	C₅×#339	—	3	2	no	—
32	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	—	2	2	no	—
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₅×#67	—	2	1	no	—
43	C₂×C₅×#67	—	2	1	no	—
44	C₂×C₅×#67	—	2	1	no	—
45	C₅×#235	—	2	2	no	—
46	C₅×#235	—	2	2	no	—
47	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	—	2	1	no	—
49	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
50	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
51	C₃×C₄²×C₅	—	2	2	no	—
52	C₃×C₄²×C₅	—	2	2	no	—
53	C₅×#217	—	2	1	no	—
54	C₅×#217	—	2	1	no	—
55	C₅×#217	—	2	1	no	—
56	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
57	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
58	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
60	C₅×Dic₃⋊C₄	—	2	1	no	—
61	C₅×Dic₃⋊C₄	—	2	1	no	—
62	C₄×C₅×Dic₃	—	2	1	no	—
63	C₅×#208	—	2	4	no	—
64	C₅×#208	—	2	2	no	—
65	C₅×#208	D₄	1	4	yes	complemented
66	C₂×C₅×C₃⋊C₈	—	2	4	no	—
67	C₂×C₅×C₃⋊C₈	—	2	2	no	—
68	#5791	C₂×C₅	1	1	yes	characteristic
69	C₂²×#208	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#805	C₂×C₅	1	2	yes	complemented
72	#4523	C₂×C₅	1	2	yes	complemented
73	C₂×C₅×#41	—	3	1	no	—
74	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
75	C₂×C₅×M₁₆	—	3	2	no	—
76	C₂×C₅×M₁₆	—	6	4	no	—
77	C₂×C₅×M₁₆	—	6	1	no	—
78	C₂²×C₅×C₈	—	6	1	no	—
79	C₅×#123	—	6	1	no	—
80	C₅×C₂²⋊Q₈	—	3	1	no	—
81	C₅×C₂²⋊Q₈	—	3	1	no	—
82	C₅×#121	—	3	1	no	—
83	C₅×#121	—	3	1	no	—
84	C₅×#120	—	6	1	no	—
85	C₄×C₅×D₄	—	6	1	no	—
86	C₄×C₅×D₄	—	6	1	no	—
87	C₅×#117	—	3	1	no	—
88	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
90	C₅×#104	—	6	4	no	—
91	C₅×#95	—	2	1	no	—
92	#1871	—	3	1	no	Sylow
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	4	1	no	—
96	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
97	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	—	2	1	no	—
105	C₂×C₃×C₄×C₅	—	2	1	no	—
106	C₂×C₃×C₄×C₅	—	2	1	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	—	4	2	no	—
109	C₂×C₃×C₄×C₅	—	4	2	no	—
110	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	#41	1	2	yes	—
116	C₅×#67	—	4	2	no	—
117	C₅×#67	—	4	2	no	—
118	C₅×#67	—	4	2	no	—
119	C₂×C₅×Dic₃	—	2	1	no	—
120	C₂×C₅×Dic₃	—	2	1	no	—
121	C₂×C₅×Dic₃	—	2	1	no	—
122	C₅×D₁₂	—	2	2	no	—
123	C₄×C₅×D₃	—	4	1	no	—
124	C₄×C₅×D₃	—	4	1	no	—
125	C₅×Dic₆	—	2	2	no	—
126	C₅×C₃⋊C₈	—	2	4	no	—
127	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×#235	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
130	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
131	#953	—	2	1	no	—
132	#930	C₄×C₅	1	1	yes	characteristic, complemented
133	#930	C₄×C₅	1	1	yes	characteristic, complemented
134	#929	—	2	1	no	—
135	C₄×#67	—	2	1	no	—
136	C₄×#67	—	2	1	no	—
137	#926	C₂²×C₅	1	1	yes	characteristic
138	#924	C₄×C₅	1	1	yes	characteristic, complemented
139	#924	C₄×C₅	1	1	yes	characteristic, complemented
140	C₂×#208	—	2	1	no	—
141	C₂×#208	—	2	4	no	—
142	C₂×#208	C₂²×C₅	1	2	yes	—
143	C₂²×C₃⋊C₈	—	2	1	no	—
144	C₃×#95	—	2	1	no	—
145	#805	—	2	4	no	—
146	C₂⁴×C₅	#67	1	1	yes	characteristic
147	C₅×#41	—	6	2	no	—
148	C₅×#41	—	6	2	no	—
149	C₂×C₅×Q₈	—	3	1	no	—
150	C₂×C₅×D₄	—	3	1	no	—
151	C₂×C₅×D₄	—	6	1	no	—
152	C₂×C₅×D₄	—	6	1	no	—
153	C₂×C₅×D₄	—	6	1	no	—
154	C₂²×C₄×C₅	—	2	2	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	—	2	2	no	—
157	C₂²×C₄×C₅	—	6	1	no	—
158	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
160	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
161	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
162	C₂²×C₄×C₅	#67	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₅×M₁₆	—	3	4	no	—
165	C₅×M₁₆	—	6	4	no	—
166	C₅×M₁₆	—	6	2	no	—
167	C₂×C₅×C₈	—	6	4	no	—
168	C₂×C₅×C₈	—	6	2	no	—
169	C₅×C₄⋊C₄	—	3	1	no	—
170	C₅×C₄⋊C₄	—	3	1	no	—
171	C₅×C₄⋊C₄	—	6	1	no	—
172	C₅×C₄⋊C₄	—	6	1	no	—
173	C₅×C₂²⋊C₄	—	2	4	no	—
174	C₅×C₂²⋊C₄	—	6	1	no	—
175	C₅×C₂²⋊C₄	—	6	1	no	—
176	C₅×C₂²⋊C₄	—	6	1	no	—
177	C₅×C₂²⋊C₄	—	6	1	no	—
178	C₅×C₂²⋊C₄	—	6	1	no	—
179	C₄²×C₅	—	2	2	no	—
180	C₄²×C₅	—	2	2	no	—
181	C₄²×C₅	—	6	1	no	—
182	C₂²×M₁₆	—	3	1	no	—
183	#525	—	3	1	no	—
184	C₂×#104	—	3	2	no	—
185	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
186	#339	—	3	2	no	—
187	C₂²×C₃×C₅	—	2	1	no	—
188	C₂²×C₃×C₅	—	2	1	no	—
189	C₂²×C₃×C₅	—	2	1	no	—
190	C₂²×C₃×C₅	—	2	1	no	—
191	C₂²×C₃×C₅	—	2	1	no	—
192	C₂²×C₃×C₅	—	2	1	no	—
193	C₂²×C₃×C₅	—	2	1	no	—
194	C₂²×C₃×C₅	—	4	4	no	—
195	C₂²×C₃×C₅	#104	1	2	yes	complemented
196	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₃×C₅	#121	1	2	yes	—
198	C₂×C₅×D₃	—	4	1	no	—
199	C₂×C₅×D₃	—	4	1	no	—
200	C₂×C₅×D₃	—	4	1	no	—
201	C₃×C₄×C₅	—	2	1	no	—
202	C₃×C₄×C₅	—	2	1	no	—
203	C₃×C₄×C₅	—	4	4	no	—
204	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
205	C₃×C₄×C₅	#120	1	1	yes	characteristic
206	C₃×C₄×C₅	#123	1	1	yes	characteristic
207	C₅×Dic₃	—	4	1	no	—
208	C₅×Dic₃	—	4	1	no	—
209	C₅×Dic₃	—	4	1	no	—
210	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
211	C₂²×C₃×C₄	—	2	2	no	—
212	C₂²×C₃×C₄	—	2	2	no	—
213	C₂²×C₃×C₄	—	2	2	no	—
214	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
220	C₂×#67	—	2	1	no	—
221	C₂×#67	—	2	1	no	—
222	C₂×#67	—	2	1	no	—
223	#235	—	2	2	no	—
224	#235	—	2	2	no	—
225	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
226	C₂×C₄×D₃	—	2	1	no	—
227	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
228	C₃×C₂²⋊C₄	—	2	4	no	—
229	C₃×C₄²	—	2	2	no	—
230	C₃×C₄²	—	2	2	no	—
231	#217	—	2	1	no	—
232	#217	—	2	1	no	—
233	#217	—	2	1	no	—
234	(C₂×D₃)⋊C₄	—	2	1	no	—
235	(C₂×D₃)⋊C₄	—	2	1	no	—
236	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
237	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
238	Dic₃⋊C₄	—	2	1	no	—
239	Dic₃⋊C₄	—	2	1	no	—
240	C₄×Dic₃	—	2	1	no	—
241	#208	—	2	4	no	—
242	#208	—	2	2	no	—
243	#208	C₅×D₄	1	4	yes	complemented
244	C₂×C₃⋊C₈	—	2	4	no	—
245	C₂×C₃⋊C₈	—	2	2	no	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	4	1	no	—
249	C₂³×C₅	—	6	1	no	—
250	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
251	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
252	C₂³×C₅	C₂×#67	1	1	yes	characteristic
253	C₅×Q₈	—	6	2	no	—
254	C₅×D₄	—	6	2	no	—
255	C₅×D₄	—	12	2	no	—
256	C₅×D₄	—	12	2	no	—
257	C₅×D₄	—	12	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	1	no	—
265	C₂×C₄×C₅	—	2	4	no	—
266	C₂×C₄×C₅	—	4	2	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	—	6	1	no	—
269	C₂×C₄×C₅	—	6	1	no	—
270	C₂×C₄×C₅	—	6	1	no	—
271	C₂×C₄×C₅	—	12	1	no	—
272	C₂×C₄×C₅	—	12	1	no	—
273	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
277	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
278	C₂×C₄×C₅	#237	1	2	yes	—
279	C₅×C₈	—	6	4	no	—
280	C₂×#41	—	3	1	no	—
281	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
282	C₂×M₁₆	—	3	2	no	—
283	C₂×M₁₆	—	6	4	no	—
284	C₂×M₁₆	—	6	1	no	—
285	C₂²×C₈	—	6	1	no	—
286	#123	—	6	1	no	—
287	C₂²⋊Q₈	—	3	1	no	—
288	C₂²⋊Q₈	—	3	1	no	—
289	#121	—	3	1	no	—
290	#121	—	3	1	no	—
291	#120	—	6	1	no	—
292	C₄×D₄	—	6	1	no	—
293	C₄×D₄	—	6	1	no	—
294	#117	—	3	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
297	#104	—	6	4	no	—
298	#95	—	2	1	no	—
299	C₂×C₃×C₅	—	2	2	no	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	—	4	1	no	—
302	C₂×C₃×C₅	#386	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
304	C₂×C₃×C₅	#421	1	1	yes	characteristic
305	C₅×D₃	—	8	1	no	—
306	C₂³×C₃	—	2	2	no	—
307	C₂³×C₃	—	2	2	no	—
308	C₂³×C₃	—	4	1	no	—
309	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
310	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
311	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂²×D₃	—	2	1	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	4	no	—
321	C₂×C₃×C₄	—	4	2	no	—
322	C₂×C₃×C₄	—	4	2	no	—
323	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
324	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
328	C₂×C₃×C₄	C₅×#41	1	2	yes	—
329	#67	—	4	2	no	—
330	#67	—	4	2	no	—
331	#67	—	4	2	no	—
332	C₂×Dic₃	—	2	1	no	—
333	C₂×Dic₃	—	2	1	no	—
334	C₂×Dic₃	—	2	1	no	—
335	D₁₂	—	2	2	no	—
336	C₄×D₃	—	4	1	no	—
337	C₄×D₃	—	4	1	no	—
338	Dic₆	—	2	2	no	—
339	C₃⋊C₈	—	2	4	no	—
340	C₂²×C₅	—	2	1	no	—
341	C₂²×C₅	—	2	1	no	—
342	C₂²×C₅	—	2	1	no	—
343	C₂²×C₅	—	2	1	no	—
344	C₂²×C₅	—	2	1	no	—
345	C₂²×C₅	—	2	1	no	—
346	C₂²×C₅	—	2	1	no	—
347	C₂²×C₅	—	4	4	no	—
348	C₂²×C₅	—	12	1	no	—
349	C₂²×C₅	—	12	1	no	—
350	C₂²×C₅	—	12	1	no	—
351	C₂²×C₅	#805	1	2	yes	complemented
352	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
353	C₂²×C₅	#939	1	2	yes	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	4	4	no	—
357	C₄×C₅	—	12	1	no	—
358	C₄×C₅	—	12	1	no	—
359	C₄×C₅	—	12	1	no	—
360	C₄×C₅	#67⋊C₄	1	2	yes	—
361	C₄×C₅	#882	1	1	yes	characteristic
362	C₄×C₅	#886	1	1	yes	characteristic
363	C₂⁴	C₅×#67	1	1	yes	characteristic
364	#41	—	6	2	no	—
365	#41	—	6	2	no	—
366	C₂×Q₈	—	3	1	no	—
367	C₂×D₄	—	3	1	no	—
368	C₂×D₄	—	6	1	no	—
369	C₂×D₄	—	6	1	no	—
370	C₂×D₄	—	6	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	6	1	no	—
375	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
376	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
377	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
378	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
379	C₂²×C₄	C₅×#67	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
381	M₁₆	—	3	4	no	—
382	M₁₆	—	6	4	no	—
383	M₁₆	—	6	2	no	—
384	C₂×C₈	—	6	4	no	—
385	C₂×C₈	—	6	2	no	—
386	C₄⋊C₄	—	3	1	no	—
387	C₄⋊C₄	—	3	1	no	—
388	C₄⋊C₄	—	6	1	no	—
389	C₄⋊C₄	—	6	1	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	6	1	no	—
392	C₂²⋊C₄	—	6	1	no	—
393	C₂²⋊C₄	—	6	1	no	—
394	C₂²⋊C₄	—	6	1	no	—
395	C₂²⋊C₄	—	6	1	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	6	1	no	—
399	C₃×C₅	#1871	1	1	yes	characteristic, complemented, Hall
400	C₂²×C₃	—	2	1	no	—
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	—	2	1	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	4	4	no	—
408	C₂²×C₃	C₅×#104	1	2	yes	complemented
409	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
410	C₂²×C₃	C₅×#121	1	2	yes	—
411	C₂×D₃	—	4	1	no	—
412	C₂×D₃	—	4	1	no	—
413	C₂×D₃	—	4	1	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	4	4	no	—
417	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
418	C₃×C₄	C₅×#120	1	1	yes	characteristic
419	C₃×C₄	C₅×#123	1	1	yes	characteristic
420	Dic₃	—	4	1	no	—
421	Dic₃	—	4	1	no	—
422	Dic₃	—	4	1	no	—
423	C₂×C₅	—	2	2	no	—
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	—	4	1	no	—
426	C₂×C₅	—	24	1	no	—
427	C₂×C₅	C₂×#805	1	1	yes	characteristic
428	C₂×C₅	#4958	1	1	yes	characteristic
429	C₂×C₅	#5005	1	1	yes	characteristic
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	6	1	no	—
434	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
435	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
436	C₂³	C₂×C₅×#67	1	1	yes	characteristic
437	Q₈	—	6	2	no	—
438	D₄	—	6	2	no	—
439	D₄	—	12	2	no	—
440	D₄	—	12	2	no	—
441	D₄	—	12	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	6	1	no	—
453	C₂×C₄	—	6	1	no	—
454	C₂×C₄	—	6	1	no	—
455	C₂×C₄	—	12	1	no	—
456	C₂×C₄	—	12	1	no	—
457	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
458	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
459	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
460	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
461	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
462	C₂×C₄	C₅×#237	1	2	yes	—
463	C₈	—	6	4	no	—
464	C₂×C₃	—	2	2	no	—
465	C₂×C₃	—	2	2	no	—
466	C₂×C₃	—	4	1	no	—
467	C₂×C₃	C₅×#386	1	1	yes	characteristic
468	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
469	C₂×C₃	C₅×#421	1	1	yes	characteristic
470	D₃	—	8	1	no	—
471	C₅	#69453	1	1	yes	characteristic, direct product factor, Sylow
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	12	1	no	—
481	C₂²	—	12	1	no	—
482	C₂²	—	12	1	no	—
483	C₂²	C₅×#805	1	2	yes	complemented
484	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
485	C₂²	C₅×#939	1	2	yes	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	4	no	—
489	C₄	—	12	1	no	—
490	C₄	—	12	1	no	—
491	C₄	—	12	1	no	—
492	C₄	C₅×#67⋊C₄	1	2	yes	—
493	C₄	C₅×#882	1	1	yes	characteristic
494	C₄	C₅×#886	1	1	yes	characteristic
495	C₃	C₅×#1871	1	1	yes	characteristic, complemented, Sylow
496	C₂	—	2	2	no	—
497	C₂	—	2	2	no	—
498	C₂	—	4	1	no	—
499	C₂	—	24	1	no	—
500	C₂	C₂×C₅×#805	1	1	yes	characteristic
501	C₂	C₅×#4958	1	1	yes	characteristic
502	C₂	C₅×#5005	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#5791	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₄×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₅×#1871
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₄×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#208	C₂	semidirect
3. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
4. C₂×C₅×#805	C₂	semidirect
5. C₅×#4523	C₂	semidirect
12. C₅×#930	C₄	semidirect
13. C₅×#930	C₄	semidirect
18. C₅×#924	C₄	semidirect
19. C₅×#924	C₄	semidirect
26. #69453	C₅	direct (N × H)
30. C₄×C₅×C₂²⋊C₄	D₃	semidirect
65. C₅×#208	D₄	semidirect
69. C₂²×#208	C₂×C₅	semidirect
70. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
71. C₂×#805	C₂×C₅	semidirect
72. #4523	C₂×C₅	semidirect
132. #930	C₄×C₅	semidirect
133. #930	C₄×C₅	semidirect
138. #924	C₄×C₅	semidirect
139. #924	C₄×C₅	semidirect
185. C₄×C₂²⋊C₄	C₅×D₃	semidirect
195. C₂²×C₃×C₅	#104	semidirect
243. #208	C₅×D₄	semidirect
351. C₂²×C₅	#805	semidirect
399. C₃×C₅	#1871	semidirect
408. C₂²×C₃	C₅×#104	semidirect
471. C₅	#69453	direct (N × H)
483. C₂²	C₅×#805	semidirect
495. C₃	C₅×#1871	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5791	2
C₂²×C₅×#208	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₂×C₅×#805	2
C₅×#4523	2
C₅×#1871	3
#69453	5

Subgroups — C5×#69453 #14300526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69453 #14300526