Subgroups — C₅×#76298 #14324374

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4977	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4958	C₂	1	4	yes	maximal, complemented
7	C₅×#4956	C₂	1	4	yes	maximal, complemented
8	C₅×#4939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4932	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2328	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×#67	C₂²	1	4	yes	—
13	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×#217	C₂²	1	2	yes	—
20	C₅×#940	C₄	1	8	yes	complemented
21	C₅×D₄×Dic₃	—	2	4	no	—
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
27	C₅×#893	—	2	4	no	—
28	C₅×C₃⋊#95	C₂²	1	2	yes	—
29	C₅×C₃⋊#95	C₂²	1	2	yes	—
30	C₅×C₃⋊#95	C₂²	1	4	yes	—
31	#76298	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#127	—	3	1	no	—
33	C₂×C₄×C₅×D₄	—	3	1	no	—
34	C₂×C₄×C₅×D₄	—	3	1	no	—
35	C₅×#390	—	3	1	no	—
36	C₅×#390	D₃	1	1	yes	characteristic, complemented
37	C₅×#386	—	3	4	no	—
38	C₅×#386	—	3	4	no	—
39	C₅×#382	—	3	1	no	—
40	C₅×#376	—	3	1	no	—
41	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
42	C₂³×C₅×D₃	C₂³	1	2	yes	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₅×#67	—	4	4	no	—
50	C₂×C₅×#67	—	4	4	no	—
51	C₂×C₅×#67	C₂×C₄	1	16	yes	complemented
52	C₂²×C₅×Dic₃	—	2	4	no	—
53	C₂²×C₅×Dic₃	—	4	4	no	—
54	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
55	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
56	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
58	C₂×C₅×D₁₂	—	2	2	no	—
59	C₂×C₅×D₁₂	—	2	2	no	—
60	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
61	C₂×C₄×C₅×D₃	—	2	4	no	—
62	C₂×C₄×C₅×D₃	—	4	4	no	—
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
65	C₃×C₄²×C₅	—	2	2	no	—
66	C₅×#217	—	2	4	no	—
67	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
68	C₅×(C₂×D₃)⋊C₄	—	4	4	no	—
69	C₅×C₄⋊Dic₃	—	2	2	no	—
70	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
71	C₄×C₅×Dic₃	D₄	1	4	yes	complemented
72	C₂×#940	C₂×C₅	1	1	yes	characteristic
73	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
76	#4977	C₂×C₅	1	1	yes	characteristic, complemented
77	#4958	C₂×C₅	1	4	yes	complemented
78	#4956	C₂×C₅	1	4	yes	complemented
79	#4939	C₂×C₅	1	1	yes	characteristic, complemented
80	#4932	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂²×C₅×D₄	—	3	4	no	—
82	C₂²×C₅×D₄	—	3	1	no	—
83	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
84	C₂³×C₄×C₅	—	3	2	no	—
85	C₂³×C₄×C₅	—	3	2	no	—
86	C₅×#127	—	3	8	no	—
87	C₄×C₅×D₄	—	6	4	no	—
88	C₄×C₅×D₄	—	6	4	no	—
89	C₂×C₅×C₄⋊C₄	—	3	1	no	—
90	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
92	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
93	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
94	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	—
95	C₂×C₄²×C₅	—	3	1	no	—
96	C₂×C₄²×C₅	—	3	1	no	—
97	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
98	C₅×#95	—	3	2	no	—
99	C₅×#95	—	3	2	no	—
100	C₅×#95	—	3	4	no	—
101	#2328	—	3	1	no	Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	2	4	no	—
105	C₂³×C₃×C₅	—	2	4	no	—
106	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
107	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
108	C₂²×C₅×D₃	—	2	2	no	—
109	C₂²×C₅×D₃	—	2	2	no	—
110	C₂²×C₅×D₃	—	2	4	no	—
111	C₂²×C₅×D₃	—	2	4	no	—
112	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
113	C₃×C₅×D₄	—	2	8	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	4	no	—
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	#41	1	2	yes	—
122	C₅×#67	—	4	16	no	—
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	—	2	2	no	—
125	C₂×C₅×Dic₃	—	2	2	no	—
126	C₂×C₅×Dic₃	—	2	2	no	—
127	C₂×C₅×Dic₃	—	2	2	no	—
128	C₂×C₅×Dic₃	—	2	4	no	—
129	C₂×C₅×Dic₃	—	4	8	no	—
130	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
131	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
132	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
133	C₅×D₁₂	—	2	8	no	—
134	C₄×C₅×D₃	—	4	8	no	—
135	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
136	C₂²×#67	C₂²×C₅	1	4	yes	—
137	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
138	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
139	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
142	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
143	C₂×#217	C₂²×C₅	1	2	yes	—
144	#940	C₄×C₅	1	8	yes	complemented
145	D₄×Dic₃	—	2	4	no	—
146	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
147	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
148	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
151	#893	—	2	4	no	—
152	C₃⋊#95	C₂²×C₅	1	2	yes	—
153	C₃⋊#95	C₂²×C₅	1	2	yes	—
154	C₃⋊#95	C₂²×C₅	1	4	yes	—
155	C₂⁴×C₅	—	3	2	no	—
156	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
157	C₂×C₅×D₄	—	2	2	no	—
158	C₂×C₅×D₄	—	2	2	no	—
159	C₂×C₅×D₄	—	3	16	no	—
160	C₂×C₅×D₄	—	3	4	no	—
161	C₂×C₅×D₄	—	6	2	no	—
162	C₂×C₅×D₄	—	6	2	no	—
163	C₂×C₅×D₄	—	12	4	no	—
164	C₂×C₅×D₄	—	12	4	no	—
165	C₂×C₅×D₄	C₄×D₃	1	4	yes	complemented
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	—	3	2	no	—
170	C₂²×C₄×C₅	—	6	4	no	—
171	C₂²×C₄×C₅	—	6	4	no	—
172	C₂²×C₄×C₅	—	12	4	no	—
173	C₂²×C₄×C₅	—	12	4	no	—
174	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
175	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
176	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
177	C₅×C₄⋊C₄	—	2	2	no	—
178	C₅×C₄⋊C₄	—	6	2	no	—
179	C₅×C₂²⋊C₄	—	4	4	no	—
180	C₅×C₂²⋊C₄	—	6	4	no	—
181	C₅×C₂²⋊C₄	—	6	4	no	—
182	C₅×C₂²⋊C₄	—	12	4	no	—
183	C₄²×C₅	—	2	2	no	—
184	C₄²×C₅	—	3	4	no	—
185	C₄²×C₅	—	3	4	no	—
186	C₂×#127	—	3	1	no	—
187	C₂×C₄×D₄	—	3	1	no	—
188	C₂×C₄×D₄	—	3	1	no	—
189	#390	—	3	1	no	—
190	#390	C₅×D₃	1	1	yes	characteristic, complemented
191	#386	—	3	4	no	—
192	#386	—	3	4	no	—
193	#382	—	3	1	no	—
194	#376	—	3	1	no	—
195	C₂²×C₃×C₅	—	2	4	no	—
196	C₂²×C₃×C₅	—	2	8	no	—
197	C₂²×C₃×C₅	—	4	2	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	—	4	4	no	—
200	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
201	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
202	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
203	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
204	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
205	C₂×C₅×D₃	—	2	4	no	—
206	C₂×C₅×D₃	—	2	8	no	—
207	C₂×C₅×D₃	—	4	2	no	—
208	C₂×C₅×D₃	—	4	2	no	—
209	C₂×C₅×D₃	—	4	4	no	—
210	C₃×C₄×C₅	—	4	2	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
213	C₅×Dic₃	—	2	4	no	—
214	C₅×Dic₃	—	2	2	no	—
215	C₅×Dic₃	—	2	2	no	—
216	C₅×Dic₃	—	4	2	no	—
217	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
218	C₂³×D₃	C₂³×C₅	1	2	yes	—
219	C₂×C₃×D₄	—	2	2	no	—
220	C₂×C₃×D₄	—	2	2	no	—
221	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
222	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂×#67	—	4	4	no	—
226	C₂×#67	—	4	4	no	—
227	C₂×#67	C₂×C₄×C₅	1	16	yes	complemented
228	C₂²×Dic₃	—	2	4	no	—
229	C₂²×Dic₃	—	4	4	no	—
230	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
231	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
232	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
233	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
234	C₂×D₁₂	—	2	2	no	—
235	C₂×D₁₂	—	2	2	no	—
236	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
237	C₂×C₄×D₃	—	2	4	no	—
238	C₂×C₄×D₃	—	4	4	no	—
239	C₃×C₄⋊C₄	—	2	2	no	—
240	C₃×C₂²⋊C₄	—	4	4	no	—
241	C₃×C₄²	—	2	2	no	—
242	#217	—	2	4	no	—
243	(C₂×D₃)⋊C₄	—	2	4	no	—
244	(C₂×D₃)⋊C₄	—	4	4	no	—
245	C₄⋊Dic₃	—	2	2	no	—
246	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
247	C₄×Dic₃	C₅×D₄	1	4	yes	complemented
248	C₂³×C₅	—	2	2	no	—
249	C₂³×C₅	—	2	2	no	—
250	C₂³×C₅	—	2	4	no	—
251	C₂³×C₅	—	2	4	no	—
252	C₂³×C₅	—	3	4	no	—
253	C₂³×C₅	—	6	2	no	—
254	C₂³×C₅	—	6	2	no	—
255	C₂³×C₅	—	6	4	no	—
256	C₂³×C₅	—	6	4	no	—
257	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
258	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
259	C₅×D₄	—	2	8	no	—
260	C₅×D₄	—	6	8	no	—
261	C₅×D₄	—	12	16	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	4	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	3	4	no	—
268	C₂×C₄×C₅	—	3	2	no	—
269	C₂×C₄×C₅	—	3	2	no	—
270	C₂×C₄×C₅	—	6	2	no	—
271	C₂×C₄×C₅	—	6	2	no	—
272	C₂×C₄×C₅	—	6	2	no	—
273	C₂×C₄×C₅	—	6	2	no	—
274	C₂×C₄×C₅	—	6	2	no	—
275	C₂×C₄×C₅	—	6	4	no	—
276	C₂×C₄×C₅	—	12	8	no	—
277	C₂×C₄×C₅	—	12	8	no	—
278	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
279	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
280	C₂×C₄×C₅	#237	1	2	yes	—
281	C₂²×D₄	—	3	4	no	—
282	C₂²×D₄	—	3	1	no	—
283	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
284	C₂³×C₄	—	3	2	no	—
285	C₂³×C₄	—	3	2	no	—
286	#127	—	3	8	no	—
287	C₄×D₄	—	6	4	no	—
288	C₄×D₄	—	6	4	no	—
289	C₂×C₄⋊C₄	—	3	1	no	—
290	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	—	3	2	no	—
292	C₂×C₂²⋊C₄	—	3	2	no	—
293	C₂×C₂²⋊C₄	—	3	4	no	—
294	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	—
295	C₂×C₄²	—	3	1	no	—
296	C₂×C₄²	—	3	1	no	—
297	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
298	#95	—	3	2	no	—
299	#95	—	3	2	no	—
300	#95	—	3	4	no	—
301	C₂×C₃×C₅	—	4	4	no	—
302	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂×C₃×C₅	#518	1	2	yes	—
304	C₂×C₃×C₅	#535	1	1	yes	characteristic
305	C₂×C₃×C₅	#535	1	1	yes	characteristic
306	C₂×C₃×C₅	#540	1	2	yes	—
307	C₅×D₃	—	4	4	no	—
308	C₂³×C₃	—	2	2	no	—
309	C₂³×C₃	—	2	2	no	—
310	C₂³×C₃	—	2	4	no	—
311	C₂³×C₃	—	2	4	no	—
312	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
313	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
314	C₂²×D₃	—	2	2	no	—
315	C₂²×D₃	—	2	2	no	—
316	C₂²×D₃	—	2	4	no	—
317	C₂²×D₃	—	2	4	no	—
318	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
319	C₃×D₄	—	2	8	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	4	no	—
325	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
326	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
327	C₂×C₃×C₄	C₅×#41	1	2	yes	—
328	#67	—	4	16	no	—
329	C₂×Dic₃	—	2	2	no	—
330	C₂×Dic₃	—	2	2	no	—
331	C₂×Dic₃	—	2	2	no	—
332	C₂×Dic₃	—	2	2	no	—
333	C₂×Dic₃	—	2	2	no	—
334	C₂×Dic₃	—	2	4	no	—
335	C₂×Dic₃	—	4	8	no	—
336	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
337	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
338	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
339	D₁₂	—	2	8	no	—
340	C₄×D₃	—	4	8	no	—
341	C₂²×C₅	—	2	4	no	—
342	C₂²×C₅	—	2	8	no	—
343	C₂²×C₅	—	4	2	no	—
344	C₂²×C₅	—	4	2	no	—
345	C₂²×C₅	—	4	4	no	—
346	C₂²×C₅	—	6	4	no	—
347	C₂²×C₅	—	6	8	no	—
348	C₂²×C₅	—	12	2	no	—
349	C₂²×C₅	—	12	2	no	—
350	C₂²×C₅	—	12	4	no	—
351	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
352	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
353	C₂²×C₅	C₂×#237	1	1	yes	characteristic
354	C₂²×C₅	#1004	1	2	yes	—
355	C₂²×C₅	#1009	1	2	yes	—
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	—	4	2	no	—
358	C₄×C₅	—	6	2	no	—
359	C₄×C₅	—	6	2	no	—
360	C₄×C₅	—	6	4	no	—
361	C₄×C₅	—	12	2	no	—
362	C₄×C₅	#67⋊C₄	1	4	yes	—
363	C₂⁴	—	3	2	no	—
364	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	3	16	no	—
368	C₂×D₄	—	3	4	no	—
369	C₂×D₄	—	6	2	no	—
370	C₂×D₄	—	6	2	no	—
371	C₂×D₄	—	12	4	no	—
372	C₂×D₄	—	12	4	no	—
373	C₂×D₄	C₄×C₅×D₃	1	4	yes	complemented
374	C₂²×C₄	—	3	2	no	—
375	C₂²×C₄	—	3	1	no	—
376	C₂²×C₄	—	3	1	no	—
377	C₂²×C₄	—	3	2	no	—
378	C₂²×C₄	—	6	4	no	—
379	C₂²×C₄	—	6	4	no	—
380	C₂²×C₄	—	12	4	no	—
381	C₂²×C₄	—	12	4	no	—
382	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
383	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
384	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	6	2	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	6	4	no	—
389	C₂²⋊C₄	—	6	4	no	—
390	C₂²⋊C₄	—	12	4	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	3	4	no	—
393	C₄²	—	3	4	no	—
394	C₃×C₅	#2328	1	1	yes	characteristic, complemented, Hall
395	C₂²×C₃	—	2	4	no	—
396	C₂²×C₃	—	2	8	no	—
397	C₂²×C₃	—	4	2	no	—
398	C₂²×C₃	—	4	2	no	—
399	C₂²×C₃	—	4	4	no	—
400	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
401	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
402	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
403	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
404	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
405	C₂×D₃	—	2	4	no	—
406	C₂×D₃	—	2	8	no	—
407	C₂×D₃	—	4	2	no	—
408	C₂×D₃	—	4	2	no	—
409	C₂×D₃	—	4	4	no	—
410	C₃×C₄	—	4	2	no	—
411	C₃×C₄	—	4	2	no	—
412	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
413	Dic₃	—	2	4	no	—
414	Dic₃	—	2	2	no	—
415	Dic₃	—	2	2	no	—
416	Dic₃	—	4	2	no	—
417	C₂×C₅	—	4	4	no	—
418	C₂×C₅	—	12	4	no	—
419	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
420	C₂×C₅	#5545	1	2	yes	—
421	C₂×C₅	#5619	1	2	yes	—
422	C₂×C₅	#5674	1	1	yes	characteristic
423	C₂×C₅	#5715	1	1	yes	characteristic
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	3	4	no	—
429	C₂³	—	6	2	no	—
430	C₂³	—	6	2	no	—
431	C₂³	—	6	4	no	—
432	C₂³	—	6	4	no	—
433	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
434	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
435	D₄	—	2	8	no	—
436	D₄	—	6	8	no	—
437	D₄	—	12	16	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	3	4	no	—
444	C₂×C₄	—	3	2	no	—
445	C₂×C₄	—	3	2	no	—
446	C₂×C₄	—	6	2	no	—
447	C₂×C₄	—	6	2	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	6	2	no	—
450	C₂×C₄	—	6	2	no	—
451	C₂×C₄	—	6	4	no	—
452	C₂×C₄	—	12	8	no	—
453	C₂×C₄	—	12	8	no	—
454	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
455	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
456	C₂×C₄	C₅×#237	1	2	yes	—
457	C₂×C₃	—	4	4	no	—
458	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
459	C₂×C₃	C₅×#518	1	2	yes	—
460	C₂×C₃	C₅×#535	1	1	yes	characteristic
461	C₂×C₃	C₅×#535	1	1	yes	characteristic
462	C₂×C₃	C₅×#540	1	2	yes	—
463	D₃	—	4	4	no	—
464	C₅	#76298	1	1	yes	characteristic, direct product factor, Sylow
465	C₂²	—	2	4	no	—
466	C₂²	—	2	8	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	6	4	no	—
471	C₂²	—	6	8	no	—
472	C₂²	—	12	2	no	—
473	C₂²	—	12	2	no	—
474	C₂²	—	12	4	no	—
475	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
476	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
477	C₂²	C₂×C₅×#237	1	1	yes	characteristic
478	C₂²	C₅×#1004	1	2	yes	—
479	C₂²	C₅×#1009	1	2	yes	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	6	2	no	—
483	C₄	—	6	2	no	—
484	C₄	—	6	4	no	—
485	C₄	—	12	2	no	—
486	C₄	C₅×#67⋊C₄	1	4	yes	—
487	C₃	C₅×#2328	1	1	yes	characteristic, complemented, Sylow
488	C₂	—	4	4	no	—
489	C₂	—	12	4	no	—
490	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
491	C₂	C₅×#5545	1	2	yes	—
492	C₂	C₅×#5619	1	2	yes	—
493	C₂	C₅×#5674	1	1	yes	characteristic
494	C₂	C₅×#5715	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#390	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#940	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#390	D₃
hypocenter	C₃	C₅×#2328
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#390

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₄×Dic₃	C₂	semidirect
3. C₂×C₅×#893	C₂	semidirect
4. C₃×C₅×#390	C₂	semidirect
5. C₅×#4977	C₂	semidirect
6. C₅×#4958	C₂	semidirect
7. C₅×#4956	C₂	semidirect
8. C₅×#4939	C₂	semidirect
9. C₅×#4932	C₂	semidirect
20. C₅×#940	C₄	semidirect
31. #76298	C₅	direct (N × H)
36. C₅×#390	D₃	semidirect
45. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
51. C₂×C₅×#67	C₂×C₄	semidirect
60. C₂×C₅×D₁₂	C₂×C₄	semidirect
70. C₄×C₅×Dic₃	C₂×C₄	semidirect
71. C₄×C₅×Dic₃	D₄	semidirect
73. C₂×D₄×Dic₃	C₂×C₅	semidirect
74. C₂×#893	C₂×C₅	semidirect
75. C₃×#390	C₂×C₅	semidirect
76. #4977	C₂×C₅	semidirect
77. #4958	C₂×C₅	semidirect
78. #4956	C₂×C₅	semidirect
79. #4939	C₂×C₅	semidirect
80. #4932	C₂×C₅	semidirect
144. #940	C₄×C₅	semidirect
165. C₂×C₅×D₄	C₄×D₃	semidirect
190. #390	C₅×D₃	semidirect
221. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
227. C₂×#67	C₂×C₄×C₅	semidirect
236. C₂×D₁₂	C₂×C₄×C₅	semidirect
246. C₄×Dic₃	C₂×C₄×C₅	semidirect
247. C₄×Dic₃	C₅×D₄	semidirect
373. C₂×D₄	C₄×C₅×D₃	semidirect
394. C₃×C₅	#2328	semidirect
464. C₅	#76298	direct (N × H)
487. C₃	C₅×#2328	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#940	2
C₂×C₅×D₄×Dic₃	2
C₂×C₅×#893	2
C₃×C₅×#390	2
C₅×#4977	2
C₅×#4958	2
C₅×#4956	2
C₅×#4939	2
C₅×#4932	2
C₅×#2328	3
#76298	5

Subgroups — C5×#76298 #14324374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#76298 #14324374