Subgroups — C₂×C₅×#5805 #14480374

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#953	C₂	1	4	yes	maximal, complemented
4	C₅×#5805	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#940	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#938	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#936	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#535	—	3	1	no	maximal, Hall
10	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	—	2	8	no	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	8	yes	complemented
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₅×#67	C₂²	1	2	yes	—
17	C₂²×C₅×#67	C₂²	1	8	yes	complemented
18	C₂×C₅×#235	—	2	8	no	—
19	C₂×C₅×#235	C₂²	1	8	yes	complemented
20	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
22	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
23	C₅×#953	C₂²	1	32	yes	complemented
24	C₂×C₅×#217	C₂²	1	2	yes	—
25	C₂×C₅×#217	C₂²	1	8	yes	complemented
26	C₅×#940	C₂²	1	16	yes	complemented
27	C₅×#938	C₂²	1	32	yes	complemented
28	C₅×#936	C₂²	1	16	yes	complemented
29	C₅×#926	C₂²	1	8	yes	complemented
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
31	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
32	C₂×#5805	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×#41	—	3	1	no	—
34	C₂³×C₅×D₄	D₃	1	1	yes	characteristic, complemented
35	C₅×#535	—	3	16	no	—
36	C₂×C₅×#127	—	3	2	no	—
37	C₂×C₅×#124	—	3	2	no	—
38	C₂×C₅×#121	—	3	4	no	—
39	C₂×C₅×#120	—	3	4	no	—
40	C₂×C₅×#117	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	8	no	—
42	C₂⁴×C₃×C₅	—	4	8	no	—
43	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
44	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
45	C₂⁴×C₃×C₅	C₂³	1	8	yes	—
46	C₂³×C₅×D₃	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	8	no	—
48	C₂×C₃×C₅×D₄	—	2	8	no	—
49	C₂×C₃×C₅×D₄	—	2	32	no	—
50	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
51	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
52	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
56	C₂×C₅×#67	—	2	8	no	—
57	C₂×C₅×#67	—	4	16	no	—
58	C₂×C₅×#67	C₂³	1	8	yes	—
59	C₂×C₅×#67	C₂³	1	32	yes	complemented
60	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
61	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
62	C₅×#235	—	2	32	no	—
63	C₂×C₅×D₁₂	—	2	4	no	—
64	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
65	C₂×C₄×C₅×D₃	—	2	8	no	—
66	C₂×C₄×C₅×D₃	C₂³	1	8	yes	complemented
67	C₂×C₅×Dic₆	—	2	4	no	—
68	C₂×C₅×Dic₆	C₂³	1	4	yes	complemented
69	C₅×#217	C₂³	1	8	yes	—
70	C₅×#217	C₂³	1	32	yes	complemented
71	C₅×C₄⋊Dic₃	C₂³	1	8	yes	complemented
72	C₄×C₅×Dic₃	C₂³	1	8	yes	complemented
73	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂²×#235	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#953	C₂×C₅	1	4	yes	complemented
76	#5805	C₂×C₅	1	16	yes	direct product factor
77	C₂×#940	C₂×C₅	1	2	yes	complemented
78	C₂×#938	C₂×C₅	1	4	yes	complemented
79	C₂×#936	C₂×C₅	1	2	yes	complemented
80	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂⁵×C₅	C₂×D₃	1	2	yes	—
82	C₂×C₅×#41	—	3	8	no	—
83	C₂×C₅×#41	—	6	8	no	—
84	C₂²×C₅×Q₈	—	3	1	no	—
85	C₂²×C₅×D₄	—	2	8	no	—
86	C₂²×C₅×D₄	—	3	2	no	—
87	C₂²×C₅×D₄	—	3	8	no	—
88	C₂²×C₅×D₄	—	3	1	no	—
89	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
90	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
91	C₂²×C₅×D₄	C₂×D₃	1	8	yes	complemented
92	C₂³×C₄×C₅	—	3	2	no	—
93	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
94	C₅×#127	—	3	16	no	—
95	C₅×#124	—	3	16	no	—
96	C₅×#121	—	3	32	no	—
97	C₅×#120	—	3	32	no	—
98	C₅×#117	—	3	8	no	—
99	C₂×C₅×C₄⋊C₄	—	3	2	no	—
100	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
101	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
102	C₂×C₄²×C₅	—	3	2	no	—
103	C₂×#535	—	3	1	no	Sylow
104	C₂³×C₃×C₅	—	2	4	no	—
105	C₂³×C₃×C₅	—	2	16	no	—
106	C₂³×C₃×C₅	—	2	8	no	—
107	C₂³×C₃×C₅	—	2	16	no	—
108	C₂³×C₃×C₅	—	4	16	no	—
109	C₂³×C₃×C₅	—	4	32	no	—
110	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
111	C₂³×C₃×C₅	C₂⁴	1	8	yes	—
112	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
113	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
114	C₂²×C₅×D₃	—	2	4	no	—
115	C₂²×C₅×D₃	—	2	8	no	—
116	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
117	C₃×C₅×D₄	—	2	16	no	—
118	C₃×C₅×D₄	—	2	16	no	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	complemented
122	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
124	C₅×#67	—	2	16	no	—
125	C₅×#67	—	4	32	no	—
126	C₂×C₅×Dic₃	—	2	4	no	—
127	C₂×C₅×Dic₃	—	2	8	no	—
128	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
129	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
130	C₅×D₁₂	—	2	8	no	—
131	C₄×C₅×D₃	—	2	16	no	—
132	C₅×Dic₆	—	2	8	no	—
133	C₂⁵×C₃	C₂²×C₅	1	2	yes	—
134	C₂²×C₃×D₄	—	2	8	no	—
135	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
136	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
137	C₂²×C₃×D₄	C₂²×C₅	1	8	yes	complemented
138	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
139	C₂²×#67	C₂²×C₅	1	2	yes	—
140	C₂²×#67	C₂²×C₅	1	8	yes	complemented
141	C₂×#235	—	2	8	no	—
142	C₂×#235	C₂²×C₅	1	8	yes	complemented
143	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
144	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
145	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
146	#953	C₂²×C₅	1	32	yes	complemented
147	C₂×#217	C₂²×C₅	1	2	yes	—
148	C₂×#217	C₂²×C₅	1	8	yes	complemented
149	#940	C₂²×C₅	1	16	yes	complemented
150	#938	C₂²×C₅	1	32	yes	complemented
151	#936	C₂²×C₅	1	16	yes	complemented
152	#926	C₂²×C₅	1	8	yes	complemented
153	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
154	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
155	C₂⁴×C₅	—	2	8	no	—
156	C₂⁴×C₅	—	3	2	no	—
157	C₂⁴×C₅	—	4	8	no	—
158	C₂⁴×C₅	C₂²×D₃	1	4	yes	—
159	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₂⁴×C₅	C₂²×D₃	1	8	yes	—
161	C₅×#41	—	6	32	no	—
162	C₂×C₅×Q₈	—	3	4	no	—
163	C₂×C₅×Q₈	—	6	4	no	—
164	C₂×C₅×D₄	—	2	8	no	—
165	C₂×C₅×D₄	—	2	8	no	—
166	C₂×C₅×D₄	—	2	32	no	—
167	C₂×C₅×D₄	—	3	8	no	—
168	C₂×C₅×D₄	—	3	32	no	—
169	C₂×C₅×D₄	—	3	4	no	—
170	C₂×C₅×D₄	—	6	8	no	—
171	C₂×C₅×D₄	—	6	4	no	—
172	C₂×C₅×D₄	—	12	16	no	—
173	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
174	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
175	C₂²×C₄×C₅	—	3	4	no	—
176	C₂²×C₄×C₅	—	3	2	no	—
177	C₂²×C₄×C₅	—	3	8	no	—
178	C₂²×C₄×C₅	—	6	8	no	—
179	C₂²×C₄×C₅	#67	1	8	yes	complemented
180	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
183	C₅×C₄⋊C₄	—	3	8	no	—
184	C₅×C₂²⋊C₄	—	3	8	no	—
185	C₅×C₂²⋊C₄	—	3	32	no	—
186	C₄²×C₅	—	3	8	no	—
187	C₂²×#41	—	3	1	no	—
188	C₂³×D₄	C₅×D₃	1	1	yes	characteristic, complemented
189	#535	—	3	16	no	—
190	C₂×#127	—	3	2	no	—
191	C₂×#124	—	3	2	no	—
192	C₂×#121	—	3	4	no	—
193	C₂×#120	—	3	4	no	—
194	C₂×#117	—	3	1	no	—
195	C₂²×C₃×C₅	—	2	8	no	—
196	C₂²×C₃×C₅	—	2	4	no	—
197	C₂²×C₃×C₅	—	2	8	no	—
198	C₂²×C₃×C₅	—	2	16	no	—
199	C₂²×C₃×C₅	—	4	32	no	—
200	C₂²×C₃×C₅	—	4	16	no	—
201	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
202	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
203	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
204	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
205	C₂×C₅×D₃	—	2	4	no	—
206	C₂×C₅×D₃	—	2	8	no	—
207	C₂×C₅×D₃	—	4	8	no	—
208	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
209	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
210	C₅×Dic₃	—	2	4	no	—
211	C₅×Dic₃	—	2	8	no	—
212	C₂⁴×C₃	—	2	8	no	—
213	C₂⁴×C₃	—	4	8	no	—
214	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
215	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
216	C₂⁴×C₃	C₂³×C₅	1	8	yes	—
217	C₂³×D₃	C₂³×C₅	1	2	yes	—
218	C₂×C₃×D₄	—	2	8	no	—
219	C₂×C₃×D₄	—	2	8	no	—
220	C₂×C₃×D₄	—	2	32	no	—
221	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
222	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
223	C₂²×C₃×C₄	C₅×D₄	1	8	yes	complemented
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
227	C₂×#67	—	2	8	no	—
228	C₂×#67	—	4	16	no	—
229	C₂×#67	C₂³×C₅	1	8	yes	—
230	C₂×#67	C₂³×C₅	1	32	yes	complemented
231	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
232	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
233	#235	—	2	32	no	—
234	C₂×D₁₂	—	2	4	no	—
235	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
236	C₂×C₄×D₃	—	2	8	no	—
237	C₂×C₄×D₃	C₂³×C₅	1	8	yes	complemented
238	C₂×Dic₆	—	2	4	no	—
239	C₂×Dic₆	C₂³×C₅	1	4	yes	complemented
240	#217	C₂³×C₅	1	8	yes	—
241	#217	C₂³×C₅	1	32	yes	complemented
242	C₄⋊Dic₃	C₂³×C₅	1	8	yes	complemented
243	C₄×Dic₃	C₂³×C₅	1	8	yes	complemented
244	C₂³×C₅	—	2	4	no	—
245	C₂³×C₅	—	2	16	no	—
246	C₂³×C₅	—	2	16	no	—
247	C₂³×C₅	—	2	8	no	—
248	C₂³×C₅	—	3	4	no	—
249	C₂³×C₅	—	4	16	no	—
250	C₂³×C₅	—	4	32	no	—
251	C₂³×C₅	—	6	8	no	—
252	C₂³×C₅	—	6	4	no	—
253	C₂³×C₅	C₂×#67	1	4	yes	—
254	C₂³×C₅	C₂³×D₃	1	8	yes	—
255	C₂³×C₅	C₂³×D₃	1	2	yes	—
256	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
257	C₅×Q₈	—	6	8	no	—
258	C₅×D₄	—	2	16	no	—
259	C₅×D₄	—	2	16	no	—
260	C₅×D₄	—	6	16	no	—
261	C₅×D₄	—	6	8	no	—
262	C₅×D₄	—	12	32	no	—
263	C₂×C₄×C₅	—	3	8	no	—
264	C₂×C₄×C₅	—	3	4	no	—
265	C₂×C₄×C₅	—	6	8	no	—
266	C₂×C₄×C₅	—	6	4	no	—
267	C₂×C₄×C₅	—	6	16	no	—
268	C₂×C₄×C₅	C₂×#67	1	4	yes	—
269	C₂×C₄×C₅	C₂×#67	1	4	yes	—
270	C₂×C₄×C₅	C₂×#67	1	16	yes	complemented
271	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
272	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
273	C₂⁵	C₂×C₅×D₃	1	2	yes	—
274	C₂×#41	—	3	8	no	—
275	C₂×#41	—	6	8	no	—
276	C₂²×Q₈	—	3	1	no	—
277	C₂²×D₄	—	2	8	no	—
278	C₂²×D₄	—	3	2	no	—
279	C₂²×D₄	—	3	8	no	—
280	C₂²×D₄	—	3	1	no	—
281	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
282	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
283	C₂²×D₄	C₂×C₅×D₃	1	8	yes	complemented
284	C₂³×C₄	—	3	2	no	—
285	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
286	#127	—	3	16	no	—
287	#124	—	3	16	no	—
288	#121	—	3	32	no	—
289	#120	—	3	32	no	—
290	#117	—	3	8	no	—
291	C₂×C₄⋊C₄	—	3	2	no	—
292	C₂×C₂²⋊C₄	—	3	2	no	—
293	C₂×C₂²⋊C₄	—	3	8	no	—
294	C₂×C₄²	—	3	2	no	—
295	C₂×C₃×C₅	—	2	4	no	—
296	C₂×C₃×C₅	—	4	8	no	—
297	C₂×C₃×C₅	#535	1	4	yes	complemented
298	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
299	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
300	C₅×D₃	—	4	4	no	—
301	C₂³×C₃	—	2	4	no	—
302	C₂³×C₃	—	2	16	no	—
303	C₂³×C₃	—	2	8	no	—
304	C₂³×C₃	—	2	16	no	—
305	C₂³×C₃	—	4	16	no	—
306	C₂³×C₃	—	4	32	no	—
307	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
308	C₂³×C₃	C₂⁴×C₅	1	8	yes	—
309	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
310	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
311	C₂²×D₃	—	2	4	no	—
312	C₂²×D₃	—	2	8	no	—
313	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
314	C₃×D₄	—	2	16	no	—
315	C₃×D₄	—	2	16	no	—
316	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
317	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
318	C₂×C₃×C₄	C₂×C₅×D₄	1	16	yes	complemented
319	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
320	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
321	#67	—	2	16	no	—
322	#67	—	4	32	no	—
323	C₂×Dic₃	—	2	4	no	—
324	C₂×Dic₃	—	2	8	no	—
325	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
326	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
327	D₁₂	—	2	8	no	—
328	C₄×D₃	—	2	16	no	—
329	Dic₆	—	2	8	no	—
330	C₂²×C₅	—	2	4	no	—
331	C₂²×C₅	—	2	8	no	—
332	C₂²×C₅	—	2	16	no	—
333	C₂²×C₅	—	2	8	no	—
334	C₂²×C₅	—	4	32	no	—
335	C₂²×C₅	—	4	16	no	—
336	C₂²×C₅	—	6	8	no	—
337	C₂²×C₅	—	6	4	no	—
338	C₂²×C₅	—	12	8	no	—
339	C₂²×C₅	#1004	1	4	yes	—
340	C₂²×C₅	C₂²×#67	1	4	yes	—
341	C₂²×C₅	C₂²×#67	1	2	yes	—
342	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
343	C₄×C₅	—	6	8	no	—
344	C₄×C₅	—	6	4	no	—
345	C₄×C₅	C₂²×#67	1	4	yes	—
346	C₄×C₅	C₂²×#67	1	4	yes	—
347	C₂⁴	—	2	8	no	—
348	C₂⁴	—	3	2	no	—
349	C₂⁴	—	4	8	no	—
350	C₂⁴	C₂²×C₅×D₃	1	4	yes	—
351	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
352	C₂⁴	C₂²×C₅×D₃	1	8	yes	—
353	#41	—	6	32	no	—
354	C₂×Q₈	—	3	4	no	—
355	C₂×Q₈	—	6	4	no	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	32	no	—
359	C₂×D₄	—	3	8	no	—
360	C₂×D₄	—	3	32	no	—
361	C₂×D₄	—	3	4	no	—
362	C₂×D₄	—	6	8	no	—
363	C₂×D₄	—	6	4	no	—
364	C₂×D₄	—	12	16	no	—
365	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
366	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
367	C₂²×C₄	—	3	4	no	—
368	C₂²×C₄	—	3	2	no	—
369	C₂²×C₄	—	3	8	no	—
370	C₂²×C₄	—	6	8	no	—
371	C₂²×C₄	C₅×#67	1	8	yes	complemented
372	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
375	C₄⋊C₄	—	3	8	no	—
376	C₂²⋊C₄	—	3	8	no	—
377	C₂²⋊C₄	—	3	32	no	—
378	C₄²	—	3	8	no	—
379	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	—	2	8	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	2	8	no	—
383	C₂²×C₃	—	2	16	no	—
384	C₂²×C₃	—	4	32	no	—
385	C₂²×C₃	—	4	16	no	—
386	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
387	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
388	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
389	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
390	C₂×D₃	—	2	4	no	—
391	C₂×D₃	—	2	8	no	—
392	C₂×D₃	—	4	8	no	—
393	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
394	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
395	Dic₃	—	2	4	no	—
396	Dic₃	—	2	8	no	—
397	C₂×C₅	—	2	4	no	—
398	C₂×C₅	—	4	8	no	—
399	C₂×C₅	—	12	4	no	—
400	C₂×C₅	#5805	1	4	yes	direct product factor
401	C₂×C₅	C₂×#1004	1	2	yes	—
402	C₂×C₅	C₂³×#67	1	1	yes	characteristic
403	C₂³	—	2	4	no	—
404	C₂³	—	2	16	no	—
405	C₂³	—	2	16	no	—
406	C₂³	—	2	8	no	—
407	C₂³	—	3	4	no	—
408	C₂³	—	4	16	no	—
409	C₂³	—	4	32	no	—
410	C₂³	—	6	8	no	—
411	C₂³	—	6	4	no	—
412	C₂³	C₂×C₅×#67	1	4	yes	—
413	C₂³	C₂³×C₅×D₃	1	8	yes	—
414	C₂³	C₂³×C₅×D₃	1	2	yes	—
415	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
416	Q₈	—	6	8	no	—
417	D₄	—	2	16	no	—
418	D₄	—	2	16	no	—
419	D₄	—	6	16	no	—
420	D₄	—	6	8	no	—
421	D₄	—	12	32	no	—
422	C₂×C₄	—	3	8	no	—
423	C₂×C₄	—	3	4	no	—
424	C₂×C₄	—	6	8	no	—
425	C₂×C₄	—	6	4	no	—
426	C₂×C₄	—	6	16	no	—
427	C₂×C₄	C₂×C₅×#67	1	4	yes	—
428	C₂×C₄	C₂×C₅×#67	1	4	yes	—
429	C₂×C₄	C₂×C₅×#67	1	16	yes	complemented
430	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
431	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
432	C₂×C₃	—	2	4	no	—
433	C₂×C₃	—	4	8	no	—
434	C₂×C₃	C₅×#535	1	4	yes	complemented
435	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
436	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
437	D₃	—	4	4	no	—
438	C₅	C₂×#5805	1	1	yes	characteristic, direct product factor, Sylow
439	C₂²	—	2	4	no	—
440	C₂²	—	2	8	no	—
441	C₂²	—	2	16	no	—
442	C₂²	—	2	8	no	—
443	C₂²	—	4	32	no	—
444	C₂²	—	4	16	no	—
445	C₂²	—	6	8	no	—
446	C₂²	—	6	4	no	—
447	C₂²	—	12	8	no	—
448	C₂²	C₅×#1004	1	4	yes	—
449	C₂²	C₂²×C₅×#67	1	4	yes	—
450	C₂²	C₂²×C₅×#67	1	2	yes	—
451	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
452	C₄	—	6	8	no	—
453	C₄	—	6	4	no	—
454	C₄	C₂²×C₅×#67	1	4	yes	—
455	C₄	C₂²×C₅×#67	1	4	yes	—
456	C₃	C₂×C₅×#535	1	1	yes	characteristic, complemented, Sylow
457	C₂	—	2	4	no	—
458	C₂	—	4	8	no	—
459	C₂	—	12	4	no	—
460	C₂	C₅×#5805	1	4	yes	direct product factor
461	C₂	C₂×C₅×#1004	1	2	yes	—
462	C₂	C₂³×C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂³×C₃×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂³×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂²×C₅×#235	C₂	semidirect
3. C₂×C₅×#953	C₂	semidirect
4. C₅×#5805	C₂	direct (N × H)
5. C₂×C₅×#940	C₂	semidirect
6. C₂×C₅×#938	C₂	semidirect
7. C₂×C₅×#936	C₂	semidirect
8. C₂×C₅×#926	C₂	semidirect
14. C₂²×C₃×C₅×D₄	C₂²	semidirect
17. C₂²×C₅×#67	C₂²	semidirect
19. C₂×C₅×#235	C₂²	semidirect
20. C₂²×C₅×D₁₂	C₂²	semidirect
21. C₂²×C₄×C₅×D₃	C₂²	semidirect
22. C₂²×C₅×Dic₆	C₂²	semidirect
23. C₅×#953	C₂²	semidirect
25. C₂×C₅×#217	C₂²	semidirect
26. C₅×#940	C₂²	semidirect
27. C₅×#938	C₂²	semidirect
28. C₅×#936	C₂²	semidirect
29. C₅×#926	C₂²	semidirect
30. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
31. C₂×C₄×C₅×Dic₃	C₂²	semidirect
32. C₂×#5805	C₅	direct (N × H)
34. C₂³×C₅×D₄	D₃	semidirect
52. C₂²×C₃×C₄×C₅	D₄	semidirect
59. C₂×C₅×#67	C₂³	semidirect
64. C₂×C₅×D₁₂	C₂³	semidirect
66. C₂×C₄×C₅×D₃	C₂³	semidirect
68. C₂×C₅×Dic₆	C₂³	semidirect
70. C₅×#217	C₂³	semidirect
71. C₅×C₄⋊Dic₃	C₂³	semidirect
72. C₄×C₅×Dic₃	C₂³	semidirect
73. C₂³×C₃×D₄	C₂×C₅	semidirect
74. C₂²×#235	C₂×C₅	semidirect
75. C₂×#953	C₂×C₅	semidirect
76. #5805	C₂×C₅	direct (N × H)
77. C₂×#940	C₂×C₅	semidirect
78. C₂×#938	C₂×C₅	semidirect
79. C₂×#936	C₂×C₅	semidirect
80. C₂×#926	C₂×C₅	semidirect
91. C₂²×C₅×D₄	C₂×D₃	semidirect
121. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
137. C₂²×C₃×D₄	C₂²×C₅	semidirect
140. C₂²×#67	C₂²×C₅	semidirect
142. C₂×#235	C₂²×C₅	semidirect
143. C₂²×D₁₂	C₂²×C₅	semidirect
144. C₂²×C₄×D₃	C₂²×C₅	semidirect
145. C₂²×Dic₆	C₂²×C₅	semidirect
146. #953	C₂²×C₅	semidirect
148. C₂×#217	C₂²×C₅	semidirect
149. #940	C₂²×C₅	semidirect
150. #938	C₂²×C₅	semidirect
151. #936	C₂²×C₅	semidirect
152. #926	C₂²×C₅	semidirect
153. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
154. C₂×C₄×Dic₃	C₂²×C₅	semidirect
179. C₂²×C₄×C₅	#67	semidirect
188. C₂³×D₄	C₅×D₃	semidirect
223. C₂²×C₃×C₄	C₅×D₄	semidirect
230. C₂×#67	C₂³×C₅	semidirect
235. C₂×D₁₂	C₂³×C₅	semidirect
237. C₂×C₄×D₃	C₂³×C₅	semidirect
239. C₂×Dic₆	C₂³×C₅	semidirect
241. #217	C₂³×C₅	semidirect
242. C₄⋊Dic₃	C₂³×C₅	semidirect
243. C₄×Dic₃	C₂³×C₅	semidirect
270. C₂×C₄×C₅	C₂×#67	semidirect
283. C₂²×D₄	C₂×C₅×D₃	semidirect
297. C₂×C₃×C₅	#535	semidirect
318. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
371. C₂²×C₄	C₅×#67	semidirect
379. C₃×C₅	C₂×#535	semidirect
400. C₂×C₅	#5805	direct (N × H)
429. C₂×C₄	C₂×C₅×#67	semidirect
434. C₂×C₃	C₅×#535	semidirect
438. C₅	C₂×#5805	direct (N × H)
456. C₃	C₂×C₅×#535	semidirect
460. C₂	C₅×#5805	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂²×C₅×#235	2
C₂×C₅×#953	2
C₅×#5805	2
C₂×C₅×#940	2
C₂×C₅×#938	2
C₂×C₅×#936	2
C₂×C₅×#926	2
C₂×C₅×#535	3
C₂×#5805	5

Subgroups — C2×C5×#5805 #14480374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5805 #14480374