Subgroups — C₅×#73454 #14326172

Order 1920.

1744 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×Dic₆	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5212	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4957	C₂	1	4	yes	maximal, complemented
6	C₅×#4939	C₂	1	2	yes	maximal, complemented
7	C₅×#4667	C₂	1	2	yes	maximal, complemented
8	C₅×#4666	C₂	1	2	yes	maximal, complemented
9	C₅×#2341	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	C₂²	1	2	yes	—
12	C₂×C₅×#235	—	2	8	no	—
13	C₂×C₅×#235	C₄	1	8	yes	complemented
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
16	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
19	C₂×C₅×#217	C₂²	1	2	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
23	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
24	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	—
25	C₄×C₅×Dic₆	—	2	8	no	—
26	C₃×C₅×#95	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	1	yes	characteristic
28	C₅×C₃⋊#95	C₂²	1	2	yes	—
29	#73454	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂²×C₅×#41	—	3	1	no	—
31	C₂×C₄×C₅×Q₈	—	3	2	no	—
32	C₅×#390	—	3	4	no	—
33	C₅×#390	—	3	2	no	—
34	C₅×#380	—	3	2	no	—
35	C₅×#380	—	3	1	no	—
36	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
37	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
38	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
39	C₂³×C₅×D₃	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₅×#67	—	2	8	no	—
47	C₂×C₅×#67	C₂×C₄	1	8	yes	—
48	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
50	C₅×#235	—	2	32	no	—
51	C₂×C₅×D₁₂	—	2	4	no	—
52	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
53	C₂×C₄×C₅×D₃	—	2	8	no	—
54	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
55	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	—
56	C₂×C₅×Dic₆	D₄	1	8	yes	—
57	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₃×C₄²×C₅	—	2	4	no	—
59	C₅×#217	—	4	2	no	—
60	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
61	C₅×(C₂×D₃)⋊C₄	—	4	4	no	—
62	C₅×C₄⋊Dic₃	—	2	4	no	—
63	C₅×Dic₃⋊C₄	—	2	8	no	—
64	C₄×C₅×Dic₃	—	2	8	no	—
65	C₂²×#235	C₂×C₅	1	1	yes	characteristic
66	C₂×C₄×Dic₆	C₂×C₅	1	2	yes	complemented
67	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
68	#5212	C₂×C₅	1	1	yes	characteristic, complemented
69	#4957	C₂×C₅	1	4	yes	complemented
70	#4939	C₂×C₅	1	2	yes	complemented
71	#4667	C₂×C₅	1	2	yes	complemented
72	#4666	C₂×C₅	1	2	yes	complemented
73	C₂×C₅×#41	—	3	8	no	—
74	C₂×C₅×#41	—	6	8	no	—
75	C₂²×C₅×Q₈	—	3	1	no	—
76	C₂²×C₅×D₄	—	3	2	no	—
77	C₂²×C₅×D₄	—	3	1	no	—
78	C₂³×C₄×C₅	—	3	2	no	—
79	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
80	C₄×C₅×Q₈	—	6	8	no	—
81	C₂×C₅×C₄⋊C₄	—	3	4	no	—
82	C₂×C₅×C₄⋊C₄	—	3	2	no	—
83	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
84	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
85	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
86	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
87	C₂×C₄²×C₅	—	3	4	no	—
88	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
89	C₅×#95	—	3	2	no	—
90	C₅×#95	C₂×D₃	1	1	yes	characteristic
91	C₅×#95	C₂×D₃	1	1	yes	characteristic
92	#2341	—	3	1	no	Sylow
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	1	no	—
96	C₂³×C₃×C₅	—	2	1	no	—
97	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
98	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	2	4	no	—
100	C₂²×C₅×D₃	—	2	4	no	—
101	C₂²×C₅×D₃	—	2	2	no	—
102	C₂²×C₅×D₃	—	2	2	no	—
103	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	8	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
115	C₅×#67	—	2	16	no	—
116	C₂×C₅×Dic₃	—	2	4	no	—
117	C₂×C₅×Dic₃	—	2	4	no	—
118	C₂×C₅×Dic₃	—	2	4	no	—
119	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
120	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	—
121	C₅×D₁₂	—	2	8	no	—
122	C₄×C₅×D₃	—	2	16	no	—
123	C₅×Dic₆	C₂²⋊C₄	1	16	yes	complemented
124	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
125	C₂²×#67	C₂²×C₅	1	2	yes	—
126	C₂×#235	—	2	8	no	—
127	C₂×#235	C₄×C₅	1	8	yes	complemented
128	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
129	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
130	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
133	C₂×#217	C₂²×C₅	1	2	yes	—
134	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
135	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
136	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
137	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
138	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	—
139	C₄×Dic₆	—	2	8	no	—
140	C₃×#95	C₂²×C₅	1	1	yes	characteristic
141	C₃×#95	C₂²×C₅	1	1	yes	characteristic
142	C₃⋊#95	C₂²×C₅	1	2	yes	—
143	C₂⁴×C₅	—	3	2	no	—
144	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₅×#41	—	6	32	no	—
146	C₂×C₅×Q₈	—	3	4	no	—
147	C₂×C₅×Q₈	—	3	8	no	—
148	C₂×C₅×D₄	—	3	8	no	—
149	C₂×C₅×D₄	—	3	4	no	—
150	C₂×C₅×D₄	—	6	8	no	—
151	C₂×C₅×D₄	—	6	4	no	—
152	C₂²×C₄×C₅	—	2	4	no	—
153	C₂²×C₄×C₅	—	3	2	no	—
154	C₂²×C₄×C₅	—	3	8	no	—
155	C₂²×C₄×C₅	—	3	4	no	—
156	C₂²×C₄×C₅	—	6	8	no	—
157	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
158	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
161	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
162	C₅×C₄⋊C₄	—	6	8	no	—
163	C₅×C₄⋊C₄	—	6	4	no	—
164	C₅×C₂²⋊C₄	—	2	4	no	—
165	C₅×C₂²⋊C₄	—	6	8	no	—
166	C₅×C₂²⋊C₄	—	12	4	no	—
167	C₅×C₂²⋊C₄	—	12	2	no	—
168	C₄²×C₅	—	2	4	no	—
169	C₄²×C₅	—	6	8	no	—
170	C₂²×#41	—	3	1	no	—
171	C₂×C₄×Q₈	—	3	2	no	—
172	#390	—	3	4	no	—
173	#390	—	3	2	no	—
174	#380	—	3	1	no	—
175	#380	—	3	2	no	—
176	C₄×C₂²⋊C₄	—	3	2	no	—
177	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
178	C₂²×C₃×C₅	—	2	2	no	—
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	—	4	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
185	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
186	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂×C₅×D₃	—	2	4	no	—
189	C₂×C₅×D₃	—	2	4	no	—
190	C₂×C₅×D₃	—	2	4	no	—
191	C₂×C₅×D₃	—	4	4	no	—
192	C₂×C₅×D₃	—	4	4	no	—
193	C₃×C₄×C₅	—	2	2	no	—
194	C₃×C₄×C₅	—	2	4	no	—
195	C₃×C₄×C₅	—	4	2	no	—
196	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
197	C₅×Dic₃	—	4	4	no	—
198	C₅×Dic₃	C₂×C₂²⋊C₄	1	8	yes	—
199	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
200	C₂³×D₃	C₂³×C₅	1	2	yes	—
201	C₂²×C₃×C₄	—	2	4	no	—
202	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
203	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂×#67	—	2	8	no	—
208	C₂×#67	C₂×C₄×C₅	1	8	yes	—
209	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
210	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
211	#235	—	2	32	no	—
212	C₂×D₁₂	—	2	4	no	—
213	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
214	C₂×C₄×D₃	—	2	8	no	—
215	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
216	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	—
217	C₂×Dic₆	C₅×D₄	1	8	yes	—
218	C₃×C₂²⋊C₄	—	2	4	no	—
219	C₃×C₄²	—	2	4	no	—
220	#217	—	4	2	no	—
221	(C₂×D₃)⋊C₄	—	2	8	no	—
222	(C₂×D₃)⋊C₄	—	4	4	no	—
223	C₄⋊Dic₃	—	2	4	no	—
224	Dic₃⋊C₄	—	2	8	no	—
225	C₄×Dic₃	—	2	8	no	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	2	1	no	—
229	C₂³×C₅	—	2	1	no	—
230	C₂³×C₅	—	3	4	no	—
231	C₂³×C₅	—	6	4	no	—
232	C₂³×C₅	—	6	4	no	—
233	C₂³×C₅	—	6	2	no	—
234	C₂³×C₅	—	6	2	no	—
235	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
236	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
237	C₅×Q₈	—	3	16	no	—
238	C₅×D₄	—	6	16	no	—
239	C₅×D₄	—	6	8	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	8	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	3	4	no	—
248	C₂×C₄×C₅	—	3	8	no	—
249	C₂×C₄×C₅	—	6	16	no	—
250	C₂×C₄×C₅	—	6	4	no	—
251	C₂×C₄×C₅	—	6	4	no	—
252	C₂×C₄×C₅	—	6	4	no	—
253	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
254	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
255	C₂×C₄×C₅	#235	1	4	yes	complemented
256	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
257	C₂×#41	—	3	8	no	—
258	C₂×#41	—	6	8	no	—
259	C₂²×Q₈	—	3	1	no	—
260	C₂²×D₄	—	3	2	no	—
261	C₂²×D₄	—	3	1	no	—
262	C₂³×C₄	—	3	2	no	—
263	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
264	C₄×Q₈	—	6	8	no	—
265	C₂×C₄⋊C₄	—	3	4	no	—
266	C₂×C₄⋊C₄	—	3	2	no	—
267	C₂×C₂²⋊C₄	—	3	4	no	—
268	C₂×C₂²⋊C₄	—	3	2	no	—
269	C₂×C₂²⋊C₄	—	3	4	no	—
270	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
271	C₂×C₄²	—	3	4	no	—
272	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
273	#95	—	3	2	no	—
274	#95	C₂×C₅×D₃	1	1	yes	characteristic
275	#95	C₂×C₅×D₃	1	1	yes	characteristic
276	C₂×C₃×C₅	—	4	2	no	—
277	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
279	C₂×C₃×C₅	#520	1	1	yes	characteristic
280	C₂×C₃×C₅	#548	1	2	yes	—
281	C₂×C₃×C₅	#550	1	2	yes	—
282	C₅×D₃	—	4	4	no	—
283	C₂³×C₃	—	2	2	no	—
284	C₂³×C₃	—	2	2	no	—
285	C₂³×C₃	—	2	1	no	—
286	C₂³×C₃	—	2	1	no	—
287	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
288	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
289	C₂²×D₃	—	2	4	no	—
290	C₂²×D₃	—	2	4	no	—
291	C₂²×D₃	—	2	2	no	—
292	C₂²×D₃	—	2	2	no	—
293	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	8	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
302	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
304	C₂×C₃×C₄	C₅×#41	1	4	yes	complemented
305	#67	—	2	16	no	—
306	C₂×Dic₃	—	2	4	no	—
307	C₂×Dic₃	—	2	4	no	—
308	C₂×Dic₃	—	2	4	no	—
309	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
310	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	—
311	D₁₂	—	2	8	no	—
312	C₄×D₃	—	2	16	no	—
313	Dic₆	C₅×C₂²⋊C₄	1	16	yes	complemented
314	C₂²×C₅	—	2	2	no	—
315	C₂²×C₅	—	2	2	no	—
316	C₂²×C₅	—	2	2	no	—
317	C₂²×C₅	—	4	2	no	—
318	C₂²×C₅	—	4	2	no	—
319	C₂²×C₅	—	6	4	no	—
320	C₂²×C₅	—	6	4	no	—
321	C₂²×C₅	—	6	4	no	—
322	C₂²×C₅	—	12	4	no	—
323	C₂²×C₅	—	12	4	no	—
324	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
325	C₂²×C₅	C₂×#235	1	2	yes	—
326	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
327	C₂²×C₅	#1009	1	1	yes	characteristic
328	C₂²×C₅	#1010	1	1	yes	characteristic
329	C₄×C₅	—	2	2	no	—
330	C₄×C₅	—	2	4	no	—
331	C₄×C₅	—	3	8	no	—
332	C₄×C₅	—	4	2	no	—
333	C₄×C₅	—	12	4	no	—
334	C₄×C₅	D₃×C₂²⋊C₄	1	4	yes	—
335	C₂⁴	—	3	2	no	—
336	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
337	#41	—	6	32	no	—
338	C₂×Q₈	—	3	4	no	—
339	C₂×Q₈	—	3	8	no	—
340	C₂×D₄	—	3	8	no	—
341	C₂×D₄	—	3	4	no	—
342	C₂×D₄	—	6	8	no	—
343	C₂×D₄	—	6	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	3	2	no	—
346	C₂²×C₄	—	3	8	no	—
347	C₂²×C₄	—	3	4	no	—
348	C₂²×C₄	—	6	8	no	—
349	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
350	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
351	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
353	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
354	C₄⋊C₄	—	6	8	no	—
355	C₄⋊C₄	—	6	4	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	6	8	no	—
358	C₂²⋊C₄	—	12	4	no	—
359	C₂²⋊C₄	—	12	2	no	—
360	C₄²	—	2	4	no	—
361	C₄²	—	6	8	no	—
362	C₃×C₅	#2341	1	1	yes	characteristic, complemented, Hall
363	C₂²×C₃	—	2	2	no	—
364	C₂²×C₃	—	2	2	no	—
365	C₂²×C₃	—	2	2	no	—
366	C₂²×C₃	—	4	2	no	—
367	C₂²×C₃	—	4	2	no	—
368	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
369	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
370	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
371	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
373	C₂×D₃	—	2	4	no	—
374	C₂×D₃	—	2	4	no	—
375	C₂×D₃	—	2	4	no	—
376	C₂×D₃	—	4	4	no	—
377	C₂×D₃	—	4	4	no	—
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	—	2	4	no	—
380	C₃×C₄	—	4	2	no	—
381	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
382	Dic₃	—	4	4	no	—
383	Dic₃	C₂×C₅×C₂²⋊C₄	1	8	yes	—
384	C₂×C₅	—	4	2	no	—
385	C₂×C₅	—	12	4	no	—
386	C₂×C₅	C₄×#235	1	1	yes	characteristic
387	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
388	C₂×C₅	#5523	1	1	yes	characteristic
389	C₂×C₅	#5552	1	2	yes	—
390	C₂×C₅	#5553	1	2	yes	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	3	4	no	—
396	C₂³	—	6	4	no	—
397	C₂³	—	6	4	no	—
398	C₂³	—	6	2	no	—
399	C₂³	—	6	2	no	—
400	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
401	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
402	Q₈	—	3	16	no	—
403	D₄	—	6	16	no	—
404	D₄	—	6	8	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	3	4	no	—
413	C₂×C₄	—	3	8	no	—
414	C₂×C₄	—	6	16	no	—
415	C₂×C₄	—	6	4	no	—
416	C₂×C₄	—	6	4	no	—
417	C₂×C₄	—	6	4	no	—
418	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
419	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
420	C₂×C₄	C₅×#235	1	4	yes	complemented
421	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
422	C₂×C₃	—	4	2	no	—
423	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
424	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
425	C₂×C₃	C₅×#520	1	1	yes	characteristic
426	C₂×C₃	C₅×#548	1	2	yes	—
427	C₂×C₃	C₅×#550	1	2	yes	—
428	D₃	—	4	4	no	—
429	C₅	#73454	1	1	yes	characteristic, direct product factor, Sylow
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	6	4	no	—
436	C₂²	—	6	4	no	—
437	C₂²	—	6	4	no	—
438	C₂²	—	12	4	no	—
439	C₂²	—	12	4	no	—
440	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
441	C₂²	C₂×C₅×#235	1	2	yes	—
442	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
443	C₂²	C₅×#1009	1	1	yes	characteristic
444	C₂²	C₅×#1010	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	—	3	8	no	—
448	C₄	—	4	2	no	—
449	C₄	—	12	4	no	—
450	C₄	C₅×D₃×C₂²⋊C₄	1	4	yes	—
451	C₃	C₅×#2341	1	1	yes	characteristic, complemented, Sylow
452	C₂	—	4	2	no	—
453	C₂	—	12	4	no	—
454	C₂	C₄×C₅×#235	1	1	yes	characteristic
455	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
456	C₂	C₅×#5523	1	1	yes	characteristic
457	C₂	C₅×#5552	1	2	yes	—
458	C₂	C₅×#5553	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₅×#2341
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×Dic₆	C₂	semidirect
3. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
4. C₅×#5212	C₂	semidirect
5. C₅×#4957	C₂	semidirect
6. C₅×#4939	C₂	semidirect
7. C₅×#4667	C₂	semidirect
8. C₅×#4666	C₂	semidirect
13. C₂×C₅×#235	C₄	semidirect
29. #73454	C₅	direct (N × H)
37. C₄×C₅×C₂²⋊C₄	D₃	semidirect
66. C₂×C₄×Dic₆	C₂×C₅	semidirect
67. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
68. #5212	C₂×C₅	semidirect
69. #4957	C₂×C₅	semidirect
70. #4939	C₂×C₅	semidirect
71. #4667	C₂×C₅	semidirect
72. #4666	C₂×C₅	semidirect
114. C₂×C₃×C₄×C₅	#41	semidirect
123. C₅×Dic₆	C₂²⋊C₄	semidirect
127. C₂×#235	C₄×C₅	semidirect
177. C₄×C₂²⋊C₄	C₅×D₃	semidirect
255. C₂×C₄×C₅	#235	semidirect
304. C₂×C₃×C₄	C₅×#41	semidirect
313. Dic₆	C₅×C₂²⋊C₄	semidirect
362. C₃×C₅	#2341	semidirect
420. C₂×C₄	C₅×#235	semidirect
429. C₅	#73454	direct (N × H)
451. C₃	C₅×#2341	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#235	2
C₂×C₄×C₅×Dic₆	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#5212	2
C₅×#4957	2
C₅×#4939	2
C₅×#4667	2
C₅×#4666	2
C₅×#2341	3
#73454	5

Subgroups — C5×#73454 #14326172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73454 #14326172