Subgroups — C₅×#68753 #14294478

Order 1920.

808 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	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4555	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4532	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1733	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₃×C₅×#117	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
14	C₅×#926	C₂²	1	1	yes	characteristic
15	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
16	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₅×#208	C₂²	1	1	yes	characteristic
18	C₅×D₃×M₁₆	—	2	2	no	—
19	C₅×D₃×M₁₆	C₄	1	4	yes	complemented
20	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
21	C₂×C₅×D₃×C₈	—	2	1	no	—
22	C₅×#892	C₄	1	2	yes	complemented
23	C₅×D₃×C₄⋊C₄	C₄	1	2	yes	complemented
24	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
25	C₅×#877	—	2	1	no	—
26	C₅×#872	—	2	2	no	—
27	C₅×#872	—	2	1	no	—
28	C₅×#872	C₄	1	4	yes	complemented
29	C₄²×C₅×D₃	—	2	1	no	—
30	#68753	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂²×C₅×M₁₆	—	3	1	no	—
32	C₂×C₅×#117	—	3	1	no	—
33	C₂×C₅×#117	—	3	1	no	—
34	C₅×#339	—	3	1	no	—
35	C₅×#339	—	3	1	no	—
36	C₅×#339	—	3	1	no	—
37	C₅×#339	D₃	1	1	yes	characteristic, complemented
38	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×Dic₃	—	2	1	no	—
42	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	—	2	2	no	—
44	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
45	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
46	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
49	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
50	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
51	C₂×C₄×C₅×D₃	Q₈	1	2	yes	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₃×C₄²×C₅	—	2	1	no	—
58	C₃×C₄²×C₅	—	2	1	no	—
59	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
60	C₅×#217	—	2	1	no	—
61	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
62	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
63	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
64	C₅×Dic₃⋊C₄	—	2	4	no	—
65	C₅×Dic₃⋊C₄	—	2	2	no	—
66	C₄×C₅×Dic₃	—	2	1	no	—
67	C₄×C₅×Dic₃	—	2	1	no	—
68	C₄×C₅×Dic₃	—	2	2	no	—
69	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	complemented
70	C₅×#208	—	2	1	no	—
71	C₅×#208	C₂×C₄	1	2	yes	complemented
72	C₂×C₅×C₃⋊C₈	—	2	1	no	—
73	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
74	C₅×D₃×C₈	—	2	4	no	—
75	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic
76	D₃×#117	C₂×C₅	1	1	yes	characteristic
77	C₂×#872	C₂×C₅	1	1	yes	characteristic
78	C₃×#339	C₂×C₅	1	1	yes	characteristic, complemented
79	#4555	C₂×C₅	1	1	yes	characteristic, complemented
80	#4532	C₂×C₅	1	1	yes	characteristic, complemented
81	#4523	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂³×C₄×C₅	—	3	1	no	—
83	C₂×C₅×M₁₆	—	3	1	no	—
84	C₂×C₅×M₁₆	—	3	4	no	—
85	C₂×C₅×M₁₆	—	6	1	no	—
86	C₂×C₅×M₁₆	—	6	2	no	—
87	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
88	C₂²×C₅×C₈	—	6	1	no	—
89	C₅×#117	—	3	4	no	—
90	C₅×#117	—	3	1	no	—
91	C₅×#117	—	3	2	no	—
92	C₅×#117	—	6	2	no	—
93	C₅×#117	—	6	1	no	—
94	C₅×#117	—	6	1	no	—
95	C₅×#117	C₂×D₃	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	—	3	2	no	—
97	C₂×C₅×C₄⋊C₄	—	6	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
100	C₂×C₄²×C₅	—	3	1	no	—
101	C₂×C₄²×C₅	—	6	1	no	—
102	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
103	#1733	—	3	1	no	Sylow
104	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₅×D₃	—	4	2	no	—
106	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₅×D₃	C₄⋊C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	4	2	no	—
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₂×C₅×Dic₃	—	4	2	no	—
122	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
124	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
126	C₄×C₅×D₃	—	4	4	no	—
127	C₄×C₅×D₃	C₄²	1	2	yes	—
128	C₄×C₅×D₃	C₄²	1	2	yes	—
129	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
130	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
131	C₄×C₅×D₃	C₄⋊C₄	1	2	yes	—
132	C₄×C₅×D₃	C₄⋊C₄	1	2	yes	—
133	C₄×C₅×D₃	C₄⋊C₄	1	2	yes	—
134	C₄×C₅×D₃	C₄⋊C₄	1	2	yes	—
135	C₃×C₅×C₈	—	2	2	no	—
136	C₅×C₃⋊C₈	—	2	2	no	—
137	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
139	C₃×#117	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
141	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
142	#926	C₂²×C₅	1	1	yes	characteristic
143	C₂×Dic₃⋊C₄	—	2	1	no	—
144	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
145	C₂×#208	C₂²×C₅	1	1	yes	characteristic
146	D₃×M₁₆	—	2	2	no	—
147	D₃×M₁₆	C₄×C₅	1	4	yes	complemented
148	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
149	C₂×D₃×C₈	—	2	1	no	—
150	#892	C₄×C₅	1	2	yes	complemented
151	D₃×C₄⋊C₄	C₄×C₅	1	2	yes	complemented
152	D₃×C₂²⋊C₄	—	2	1	no	—
153	#877	—	2	1	no	—
154	#872	—	2	2	no	—
155	#872	—	2	1	no	—
156	#872	C₄×C₅	1	4	yes	complemented
157	C₄²×D₃	—	2	1	no	—
158	C₂⁴×C₅	—	3	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	3	1	no	—
161	C₂²×C₄×C₅	—	3	1	no	—
162	C₂²×C₄×C₅	—	3	1	no	—
163	C₂²×C₄×C₅	—	3	2	no	—
164	C₂²×C₄×C₅	—	3	2	no	—
165	C₂²×C₄×C₅	—	3	2	no	—
166	C₂²×C₄×C₅	—	3	1	no	—
167	C₂²×C₄×C₅	—	3	1	no	—
168	C₂²×C₄×C₅	—	3	2	no	—
169	C₂²×C₄×C₅	—	6	2	no	—
170	C₂²×C₄×C₅	—	6	1	no	—
171	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₅×M₁₆	—	2	1	no	—
173	C₅×M₁₆	—	3	2	no	—
174	C₅×M₁₆	—	6	4	no	—
175	C₅×M₁₆	—	6	1	no	—
176	C₅×M₁₆	C₄×D₃	1	2	yes	complemented
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	6	4	no	—
179	C₂×C₅×C₈	—	6	1	no	—
180	C₅×C₄⋊C₄	—	3	2	no	—
181	C₅×C₄⋊C₄	—	6	2	no	—
182	C₅×C₄⋊C₄	—	6	4	no	—
183	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
184	C₅×C₂²⋊C₄	—	2	1	no	—
185	C₅×C₂²⋊C₄	—	6	2	no	—
186	C₅×C₂²⋊C₄	—	6	4	no	—
187	C₅×C₂²⋊C₄	—	6	1	no	—
188	C₄²×C₅	—	2	1	no	—
189	C₄²×C₅	—	2	1	no	—
190	C₄²×C₅	—	3	2	no	—
191	C₄²×C₅	—	6	2	no	—
192	C₄²×C₅	—	6	1	no	—
193	C₄²×C₅	—	6	1	no	—
194	C₄²×C₅	C₄×D₃	1	2	yes	complemented
195	C₂²×M₁₆	—	3	1	no	—
196	C₂×#117	—	3	1	no	—
197	C₂×#117	—	3	1	no	—
198	#339	—	3	1	no	—
199	#339	—	3	1	no	—
200	#339	—	3	1	no	—
201	#339	C₅×D₃	1	1	yes	characteristic, complemented
202	C₂²×C₃×C₅	—	2	2	no	—
203	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₅×D₃	—	2	2	no	—
207	C₂×C₅×D₃	—	2	2	no	—
208	C₂×C₅×D₃	—	4	2	no	—
209	C₂×C₅×D₃	—	4	2	no	—
210	C₂×C₅×D₃	#95	1	2	yes	—
211	C₂×C₅×D₃	#95	1	2	yes	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₃×C₄×C₅	—	4	2	no	—
214	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
215	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₅×Dic₃	—	4	2	no	—
219	C₅×Dic₃	—	4	2	no	—
220	C₅×Dic₃	#95	1	2	yes	—
221	C₅×Dic₃	#95	1	2	yes	—
222	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂²×Dic₃	—	2	1	no	—
226	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
227	C₂×C₄×D₃	—	2	2	no	—
228	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
229	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
230	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
231	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
233	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
234	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
235	C₂×C₄×D₃	C₅×Q₈	1	2	yes	—
236	C₃×M₁₆	—	2	1	no	—
237	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	complemented
238	C₂×C₃×C₈	—	2	1	no	—
239	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
240	C₃×C₂²⋊C₄	—	2	1	no	—
241	C₃×C₄²	—	2	1	no	—
242	C₃×C₄²	—	2	1	no	—
243	C₃×C₄²	C₂×C₄×C₅	1	2	yes	complemented
244	#217	—	2	1	no	—
245	(C₂×D₃)⋊C₄	—	2	4	no	—
246	(C₂×D₃)⋊C₄	—	2	2	no	—
247	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
248	Dic₃⋊C₄	—	2	4	no	—
249	Dic₃⋊C₄	—	2	2	no	—
250	C₄×Dic₃	—	2	1	no	—
251	C₄×Dic₃	—	2	1	no	—
252	C₄×Dic₃	—	2	2	no	—
253	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	complemented
254	#208	—	2	1	no	—
255	#208	C₂×C₄×C₅	1	2	yes	complemented
256	C₂×C₃⋊C₈	—	2	1	no	—
257	ΓL(1,𝔽₂₅)	—	2	4	no	—
258	D₃×C₈	—	2	4	no	—
259	C₂³×C₅	—	3	1	no	—
260	C₂³×C₅	—	3	1	no	—
261	C₂³×C₅	—	3	2	no	—
262	C₂³×C₅	—	3	2	no	—
263	C₂³×C₅	—	12	2	no	—
264	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	3	1	no	—
268	C₂×C₄×C₅	—	3	2	no	—
269	C₂×C₄×C₅	—	3	1	no	—
270	C₂×C₄×C₅	—	3	2	no	—
271	C₂×C₄×C₅	—	3	2	no	—
272	C₂×C₄×C₅	—	3	2	no	—
273	C₂×C₄×C₅	—	3	2	no	—
274	C₂×C₄×C₅	—	3	2	no	—
275	C₂×C₄×C₅	—	3	2	no	—
276	C₂×C₄×C₅	—	3	2	no	—
277	C₂×C₄×C₅	—	3	2	no	—
278	C₂×C₄×C₅	—	3	2	no	—
279	C₂×C₄×C₅	—	4	2	no	—
280	C₂×C₄×C₅	—	6	2	no	—
281	C₂×C₄×C₅	—	6	2	no	—
282	C₂×C₄×C₅	—	12	4	no	—
283	C₂×C₄×C₅	—	12	2	no	—
284	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
287	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
288	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
290	C₅×C₈	—	2	2	no	—
291	C₅×C₈	—	6	2	no	—
292	C₂³×C₄	—	3	1	no	—
293	C₂×M₁₆	—	3	1	no	—
294	C₂×M₁₆	—	3	4	no	—
295	C₂×M₁₆	—	6	1	no	—
296	C₂×M₁₆	—	6	2	no	—
297	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
298	C₂²×C₈	—	6	1	no	—
299	#117	—	3	4	no	—
300	#117	—	3	1	no	—
301	#117	—	3	2	no	—
302	#117	—	6	1	no	—
303	#117	—	6	2	no	—
304	#117	—	6	1	no	—
305	#117	C₂×C₅×D₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	—	3	2	no	—
307	C₂×C₄⋊C₄	—	6	1	no	—
308	C₂×C₂²⋊C₄	—	6	1	no	—
309	C₂×C₂²⋊C₄	—	6	1	no	—
310	C₂×C₄²	—	3	1	no	—
311	C₂×C₄²	—	6	1	no	—
312	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
313	C₂×C₃×C₅	—	2	1	no	—
314	C₂×C₃×C₅	—	2	1	no	—
315	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
316	C₂×C₃×C₅	#421	1	2	yes	—
317	C₅×D₃	—	2	2	no	—
318	C₅×D₃	—	2	2	no	—
319	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂²×D₃	—	4	2	no	—
321	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
323	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
324	C₂²×D₃	C₅×C₄⋊C₄	1	2	yes	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	4	2	no	—
328	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
334	C₂×Dic₃	—	2	2	no	—
335	C₂×Dic₃	—	2	2	no	—
336	C₂×Dic₃	—	4	2	no	—
337	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
339	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
340	C₂×Dic₃	C₅×C₄⋊C₄	1	2	yes	—
341	C₄×D₃	—	4	4	no	—
342	C₄×D₃	C₄²×C₅	1	2	yes	—
343	C₄×D₃	C₄²×C₅	1	2	yes	—
344	C₄×D₃	C₅×C₂²⋊C₄	1	2	yes	—
345	C₄×D₃	C₅×C₂²⋊C₄	1	2	yes	—
346	C₄×D₃	C₅×C₄⋊C₄	1	2	yes	—
347	C₄×D₃	C₅×C₄⋊C₄	1	2	yes	—
348	C₄×D₃	C₅×C₄⋊C₄	1	2	yes	—
349	C₄×D₃	C₅×C₄⋊C₄	1	2	yes	—
350	C₃×C₈	—	2	2	no	—
351	C₃⋊C₈	—	2	2	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	—	3	2	no	—
354	C₂²×C₅	—	3	2	no	—
355	C₂²×C₅	—	6	2	no	—
356	C₂²×C₅	—	6	2	no	—
357	C₂²×C₅	—	12	2	no	—
358	C₂²×C₅	—	12	2	no	—
359	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
360	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
361	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
362	C₄×C₅	—	3	2	no	—
363	C₄×C₅	—	3	2	no	—
364	C₄×C₅	—	4	2	no	—
365	C₄×C₅	—	4	2	no	—
366	C₄×C₅	—	12	2	no	—
367	C₄×C₅	—	12	2	no	—
368	C₄×C₅	C₄²×D₃	1	1	yes	characteristic
369	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
370	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
371	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
372	C₂⁴	—	3	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	3	1	no	—
375	C₂²×C₄	—	3	1	no	—
376	C₂²×C₄	—	3	1	no	—
377	C₂²×C₄	—	3	2	no	—
378	C₂²×C₄	—	3	2	no	—
379	C₂²×C₄	—	3	1	no	—
380	C₂²×C₄	—	3	1	no	—
381	C₂²×C₄	—	3	2	no	—
382	C₂²×C₄	—	3	2	no	—
383	C₂²×C₄	—	6	2	no	—
384	C₂²×C₄	—	6	1	no	—
385	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
386	M₁₆	—	2	1	no	—
387	M₁₆	—	3	2	no	—
388	M₁₆	—	6	4	no	—
389	M₁₆	—	6	1	no	—
390	M₁₆	C₄×C₅×D₃	1	2	yes	complemented
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	6	4	no	—
393	C₂×C₈	—	6	1	no	—
394	C₄⋊C₄	—	3	2	no	—
395	C₄⋊C₄	—	6	2	no	—
396	C₄⋊C₄	—	6	4	no	—
397	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	6	2	no	—
400	C₂²⋊C₄	—	6	4	no	—
401	C₂²⋊C₄	—	6	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	3	2	no	—
405	C₄²	—	6	2	no	—
406	C₄²	—	6	1	no	—
407	C₄²	—	6	1	no	—
408	C₄²	C₄×C₅×D₃	1	2	yes	complemented
409	C₃×C₅	#1733	1	1	yes	characteristic, complemented, Hall
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
412	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
413	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
414	C₂×D₃	—	2	2	no	—
415	C₂×D₃	—	2	2	no	—
416	C₂×D₃	—	4	2	no	—
417	C₂×D₃	—	4	2	no	—
418	C₂×D₃	C₅×#95	1	2	yes	—
419	C₂×D₃	C₅×#95	1	2	yes	—
420	C₃×C₄	—	4	2	no	—
421	C₃×C₄	—	4	2	no	—
422	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
423	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
424	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
425	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
426	Dic₃	—	4	2	no	—
427	Dic₃	—	4	2	no	—
428	Dic₃	C₅×#95	1	2	yes	—
429	Dic₃	C₅×#95	1	2	yes	—
430	C₂×C₅	—	2	1	no	—
431	C₂×C₅	—	2	1	no	—
432	C₂×C₅	—	6	2	no	—
433	C₂×C₅	—	6	2	no	—
434	C₂×C₅	D₃×#95	1	1	yes	characteristic
435	C₂×C₅	#4821	1	2	yes	—
436	C₂³	—	3	1	no	—
437	C₂³	—	3	1	no	—
438	C₂³	—	3	2	no	—
439	C₂³	—	3	2	no	—
440	C₂³	—	12	2	no	—
441	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	3	1	no	—
445	C₂×C₄	—	3	2	no	—
446	C₂×C₄	—	3	1	no	—
447	C₂×C₄	—	3	2	no	—
448	C₂×C₄	—	3	2	no	—
449	C₂×C₄	—	3	2	no	—
450	C₂×C₄	—	3	2	no	—
451	C₂×C₄	—	3	2	no	—
452	C₂×C₄	—	3	2	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	3	2	no	—
455	C₂×C₄	—	3	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	6	2	no	—
458	C₂×C₄	—	6	2	no	—
459	C₂×C₄	—	12	4	no	—
460	C₂×C₄	—	12	2	no	—
461	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
462	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
463	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
464	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
465	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
466	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	6	2	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	2	1	no	—
471	C₂×C₃	C₂×C₅×#95	1	1	yes	characteristic
472	C₂×C₃	C₅×#421	1	2	yes	—
473	D₃	—	2	2	no	—
474	D₃	—	2	2	no	—
475	C₅	#68753	1	1	yes	characteristic, direct product factor, Sylow
476	C₂²	—	2	2	no	—
477	C₂²	—	3	2	no	—
478	C₂²	—	3	2	no	—
479	C₂²	—	6	2	no	—
480	C₂²	—	6	2	no	—
481	C₂²	—	12	2	no	—
482	C₂²	—	12	2	no	—
483	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
484	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
485	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
486	C₄	—	3	2	no	—
487	C₄	—	3	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	12	2	no	—
491	C₄	—	12	2	no	—
492	C₄	C₄²×C₅×D₃	1	1	yes	characteristic
493	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
494	C₄	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
495	C₄	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
496	C₃	C₅×#1733	1	1	yes	characteristic, complemented, Sylow
497	C₂	—	2	1	no	—
498	C₂	—	2	1	no	—
499	C₂	—	6	2	no	—
500	C₂	—	6	2	no	—
501	C₂	C₅×D₃×#95	1	1	yes	characteristic
502	C₂	C₅×#4821	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#339	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₅×D₃	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#339	D₃
hypocenter	C₃	C₅×#1733
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#339

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#339	C₂	semidirect
5. C₅×#4555	C₂	semidirect
6. C₅×#4532	C₂	semidirect
7. C₅×#4523	C₂	semidirect
19. C₅×D₃×M₁₆	C₄	semidirect
22. C₅×#892	C₄	semidirect
23. C₅×D₃×C₄⋊C₄	C₄	semidirect
28. C₅×#872	C₄	semidirect
30. #68753	C₅	direct (N × H)
37. C₅×#339	D₃	semidirect
53. C₃×C₅×M₁₆	C₂×C₄	semidirect
59. C₃×C₄²×C₅	C₂×C₄	semidirect
69. C₄×C₅×Dic₃	C₂×C₄	semidirect
71. C₅×#208	C₂×C₄	semidirect
78. C₃×#339	C₂×C₅	semidirect
79. #4555	C₂×C₅	semidirect
80. #4532	C₂×C₅	semidirect
81. #4523	C₂×C₅	semidirect
147. D₃×M₁₆	C₄×C₅	semidirect
150. #892	C₄×C₅	semidirect
151. D₃×C₄⋊C₄	C₄×C₅	semidirect
156. #872	C₄×C₅	semidirect
176. C₅×M₁₆	C₄×D₃	semidirect
194. C₄²×C₅	C₄×D₃	semidirect
201. #339	C₅×D₃	semidirect
237. C₃×M₁₆	C₂×C₄×C₅	semidirect
243. C₃×C₄²	C₂×C₄×C₅	semidirect
253. C₄×Dic₃	C₂×C₄×C₅	semidirect
255. #208	C₂×C₄×C₅	semidirect
390. M₁₆	C₄×C₅×D₃	semidirect
408. C₄²	C₄×C₅×D₃	semidirect
409. C₃×C₅	#1733	semidirect
475. C₅	#68753	direct (N × H)
496. C₃	C₅×#1733	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₅×D₃×#117	2
C₂×C₅×#872	2
C₃×C₅×#339	2
C₅×#4555	2
C₅×#4532	2
C₅×#4523	2
C₅×#1733	3
#68753	5

Subgroups — C5×#68753 #14294478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68753 #14294478