Subgroups — C₂×C₅×#5535 #14481094

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#930	C₂	1	2	yes	maximal, complemented
3	C₅×#5535	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#894	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#884	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#874	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₅×D₁₂	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#540	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	C₂²	1	4	yes	—
12	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
13	C₂²×C₅×D₁₂	C₂²	1	4	yes	—
14	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
15	C₃×C₅×#117	C₂²	1	8	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₅×#930	C₂²	1	16	yes	complemented
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
24	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
25	C₅×#894	C₂²	1	32	yes	complemented
26	C₅×#884	C₂²	1	32	yes	complemented
27	C₅×#874	C₂²	1	8	yes	complemented
28	C₄×C₅×D₁₂	C₂²	1	16	yes	complemented
29	C₅×#870	C₂²	1	8	yes	complemented
30	C₂×#5535	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#540	—	3	16	no	—
32	C₂×C₅×#127	—	3	1	no	—
33	C₂×C₅×#125	—	3	1	no	—
34	C₂×C₅×#123	—	3	4	no	—
35	C₂×C₅×#121	—	3	2	no	—
36	C₂×C₅×#121	—	3	4	no	—
37	C₂×C₄×C₅×D₄	—	3	2	no	—
38	C₂×C₅×#117	D₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
40	C₂³×C₅×D₃	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
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	4	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₅×#67	—	4	8	no	—
48	C₂×C₅×#67	C₂³	1	16	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
50	C₂×C₅×D₁₂	—	2	8	no	—
51	C₂×C₅×D₁₂	—	4	8	no	—
52	C₂×C₅×D₁₂	C₂³	1	8	yes	—
53	C₂×C₅×D₁₂	C₂³	1	16	yes	—
54	C₂×C₄×C₅×D₃	—	4	8	no	—
55	C₂×C₄×C₅×D₃	C₂³	1	16	yes	—
56	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
57	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
58	C₃×C₄²×C₅	C₂³	1	4	yes	—
59	C₃×C₄²×C₅	C₂³	1	4	yes	—
60	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
61	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
62	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
63	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
64	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×#930	C₂×C₅	1	2	yes	complemented
66	#5535	C₂×C₅	1	16	yes	direct product factor
67	C₂×#894	C₂×C₅	1	4	yes	complemented
68	C₂×#884	C₂×C₅	1	4	yes	complemented
69	C₂×#874	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×C₄×D₁₂	C₂×C₅	1	2	yes	complemented
71	C₂×#870	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂²×C₅×D₄	—	3	4	no	—
73	C₂²×C₅×D₄	—	3	2	no	—
74	C₂²×C₅×D₄	—	3	4	no	—
75	C₂³×C₄×C₅	—	3	4	no	—
76	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
77	C₅×#127	—	3	8	no	—
78	C₅×#125	—	3	8	no	—
79	C₅×#123	—	3	32	no	—
80	C₅×#121	—	3	16	no	—
81	C₅×#121	—	3	32	no	—
82	C₄×C₅×D₄	—	3	16	no	—
83	C₅×#117	C₂×D₃	1	8	yes	complemented
84	C₂×C₅×C₄⋊C₄	—	3	4	no	—
85	C₂×C₅×C₄⋊C₄	—	3	2	no	—
86	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
87	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
88	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
89	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
90	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
92	C₂×#540	—	3	1	no	Sylow
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂²×C₅×D₃	—	2	8	no	—
98	C₂²×C₅×D₃	—	2	8	no	—
99	C₂²×C₅×D₃	—	2	8	no	—
100	C₂²×C₅×D₃	C₂⁴	1	8	yes	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	2	8	no	—
105	C₂×C₃×C₄×C₅	#41	1	4	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
107	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
110	C₅×#67	—	4	16	no	—
111	C₂×C₅×Dic₃	—	2	8	no	—
112	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
113	C₅×D₁₂	—	2	16	no	—
114	C₅×D₁₂	—	4	16	no	—
115	C₄×C₅×D₃	—	4	16	no	—
116	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
117	C₂²×#67	C₂²×C₅	1	4	yes	—
118	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
119	C₂²×D₁₂	C₂²×C₅	1	4	yes	—
120	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
121	C₃×#117	C₂²×C₅	1	8	yes	complemented
122	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
123	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
124	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
126	#930	C₂²×C₅	1	16	yes	complemented
127	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
128	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
129	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
130	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
131	#894	C₂²×C₅	1	32	yes	complemented
132	#884	C₂²×C₅	1	32	yes	complemented
133	#874	C₂²×C₅	1	8	yes	complemented
134	C₄×D₁₂	C₂²×C₅	1	16	yes	complemented
135	#870	C₂²×C₅	1	8	yes	complemented
136	C₂⁴×C₅	—	3	4	no	—
137	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
138	C₂×C₅×D₄	—	3	16	no	—
139	C₂×C₅×D₄	—	3	8	no	—
140	C₂×C₅×D₄	—	3	16	no	—
141	C₂×C₅×D₄	—	6	8	no	—
142	C₂×C₅×D₄	—	12	8	no	—
143	C₂×C₅×D₄	—	12	8	no	—
144	C₂²×C₄×C₅	—	2	4	no	—
145	C₂²×C₄×C₅	—	3	4	no	—
146	C₂²×C₄×C₅	—	3	16	no	—
147	C₂²×C₄×C₅	—	12	8	no	—
148	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
149	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
150	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
151	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₅×C₄⋊C₄	—	3	8	no	—
154	C₅×C₄⋊C₄	—	3	16	no	—
155	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
156	C₅×C₂²⋊C₄	—	3	16	no	—
157	C₅×C₂²⋊C₄	—	3	16	no	—
158	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
159	C₄²×C₅	C₂²×D₃	1	4	yes	—
160	C₄²×C₅	C₂²×D₃	1	4	yes	—
161	#540	—	3	16	no	—
162	C₂×#127	—	3	1	no	—
163	C₂×#125	—	3	1	no	—
164	C₂×#123	—	3	4	no	—
165	C₂×#121	—	3	2	no	—
166	C₂×#121	—	3	4	no	—
167	C₂×C₄×D₄	—	3	2	no	—
168	C₂×#117	C₅×D₃	1	1	yes	characteristic, complemented
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	—	2	4	no	—
171	C₂²×C₃×C₅	—	4	4	no	—
172	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
173	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
174	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
175	C₂×C₅×D₃	—	2	8	no	—
176	C₂×C₅×D₃	—	2	8	no	—
177	C₂×C₅×D₃	—	2	8	no	—
178	C₂×C₅×D₃	—	4	16	no	—
179	C₃×C₄×C₅	—	2	2	no	—
180	C₃×C₄×C₅	—	2	4	no	—
181	C₃×C₄×C₅	—	2	4	no	—
182	C₃×C₄×C₅	C₂×#41	1	4	yes	—
183	C₅×Dic₃	—	2	8	no	—
184	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
185	C₂³×D₃	C₂³×C₅	1	4	yes	—
186	C₂²×C₃×C₄	—	2	4	no	—
187	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
188	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
190	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
191	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂×#67	—	4	8	no	—
193	C₂×#67	C₂³×C₅	1	16	yes	—
194	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
195	C₂×D₁₂	—	2	8	no	—
196	C₂×D₁₂	—	4	8	no	—
197	C₂×D₁₂	C₂³×C₅	1	8	yes	—
198	C₂×D₁₂	C₂³×C₅	1	16	yes	—
199	C₂×C₄×D₃	—	4	8	no	—
200	C₂×C₄×D₃	C₂³×C₅	1	16	yes	—
201	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
202	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
203	C₃×C₄²	C₂³×C₅	1	4	yes	—
204	C₃×C₄²	C₂³×C₅	1	4	yes	—
205	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
206	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
207	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
208	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	—	2	4	no	—
211	C₂³×C₅	—	3	8	no	—
212	C₂³×C₅	—	6	8	no	—
213	C₂³×C₅	—	6	8	no	—
214	C₂³×C₅	—	6	8	no	—
215	C₂³×C₅	C₂³×D₃	1	2	yes	—
216	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
217	C₅×D₄	—	6	16	no	—
218	C₅×D₄	—	12	16	no	—
219	C₅×D₄	—	12	16	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	4	no	—
222	C₂×C₄×C₅	—	2	4	no	—
223	C₂×C₄×C₅	—	2	8	no	—
224	C₂×C₄×C₅	—	3	8	no	—
225	C₂×C₄×C₅	—	6	8	no	—
226	C₂×C₄×C₅	—	12	16	no	—
227	C₂×C₄×C₅	#235	1	4	yes	—
228	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
229	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
230	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
231	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
232	C₂²×D₄	—	3	4	no	—
233	C₂²×D₄	—	3	2	no	—
234	C₂²×D₄	—	3	4	no	—
235	C₂³×C₄	—	3	4	no	—
236	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
237	#127	—	3	8	no	—
238	#125	—	3	8	no	—
239	#123	—	3	32	no	—
240	#121	—	3	16	no	—
241	#121	—	3	32	no	—
242	C₄×D₄	—	3	16	no	—
243	#117	C₂×C₅×D₃	1	8	yes	complemented
244	C₂×C₄⋊C₄	—	3	2	no	—
245	C₂×C₄⋊C₄	—	3	4	no	—
246	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
247	C₂×C₂²⋊C₄	—	3	4	no	—
248	C₂×C₂²⋊C₄	—	3	4	no	—
249	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
250	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
252	C₂×C₃×C₅	—	4	2	no	—
253	C₂×C₃×C₅	#540	1	4	yes	complemented
254	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
255	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
256	C₅×D₃	—	4	8	no	—
257	C₂³×C₃	—	2	2	no	—
258	C₂³×C₃	—	2	4	no	—
259	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
260	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
261	C₂²×D₃	—	2	8	no	—
262	C₂²×D₃	—	2	8	no	—
263	C₂²×D₃	—	2	8	no	—
264	C₂²×D₃	C₂⁴×C₅	1	8	yes	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	4	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	C₅×#41	1	4	yes	—
270	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
271	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
272	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
273	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
274	#67	—	4	16	no	—
275	C₂×Dic₃	—	2	8	no	—
276	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
277	D₁₂	—	2	16	no	—
278	D₁₂	—	4	16	no	—
279	C₄×D₃	—	4	16	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	2	4	no	—
282	C₂²×C₅	—	4	4	no	—
283	C₂²×C₅	—	6	8	no	—
284	C₂²×C₅	—	6	8	no	—
285	C₂²×C₅	—	6	8	no	—
286	C₂²×C₅	—	12	16	no	—
287	C₂²×C₅	C₂×#235	1	2	yes	—
288	C₂²×C₅	#1009	1	4	yes	—
289	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	2	4	no	—
292	C₄×C₅	—	2	4	no	—
293	C₄×C₅	—	6	8	no	—
294	C₄×C₅	C₂×#235	1	4	yes	—
295	C₂⁴	—	3	4	no	—
296	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
297	C₂×D₄	—	3	16	no	—
298	C₂×D₄	—	3	8	no	—
299	C₂×D₄	—	3	16	no	—
300	C₂×D₄	—	6	8	no	—
301	C₂×D₄	—	12	8	no	—
302	C₂×D₄	—	12	8	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	3	4	no	—
305	C₂²×C₄	—	3	16	no	—
306	C₂²×C₄	—	12	8	no	—
307	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
308	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
309	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
311	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
312	C₄⋊C₄	—	3	8	no	—
313	C₄⋊C₄	—	3	16	no	—
314	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
315	C₂²⋊C₄	—	3	16	no	—
316	C₂²⋊C₄	—	3	16	no	—
317	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
318	C₄²	C₂²×C₅×D₃	1	4	yes	—
319	C₄²	C₂²×C₅×D₃	1	4	yes	—
320	C₃×C₅	C₂×#540	1	1	yes	characteristic, complemented, Hall
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	2	4	no	—
323	C₂²×C₃	—	4	4	no	—
324	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
325	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
326	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
327	C₂×D₃	—	2	8	no	—
328	C₂×D₃	—	2	8	no	—
329	C₂×D₃	—	2	8	no	—
330	C₂×D₃	—	4	16	no	—
331	C₃×C₄	—	2	2	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	4	no	—
334	C₃×C₄	C₂×C₅×#41	1	4	yes	—
335	Dic₃	—	2	8	no	—
336	C₂×C₅	—	4	2	no	—
337	C₂×C₅	—	12	8	no	—
338	C₂×C₅	#5535	1	4	yes	direct product factor
339	C₂×C₅	C₂²×#235	1	1	yes	characteristic
340	C₂×C₅	C₂×#1009	1	2	yes	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	3	8	no	—
344	C₂³	—	6	8	no	—
345	C₂³	—	6	8	no	—
346	C₂³	—	6	8	no	—
347	C₂³	C₂³×C₅×D₃	1	2	yes	—
348	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
349	D₄	—	6	16	no	—
350	D₄	—	12	16	no	—
351	D₄	—	12	16	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	3	8	no	—
357	C₂×C₄	—	6	8	no	—
358	C₂×C₄	—	12	16	no	—
359	C₂×C₄	C₅×#235	1	4	yes	—
360	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
361	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
362	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
363	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
364	C₂×C₃	—	4	2	no	—
365	C₂×C₃	C₅×#540	1	4	yes	complemented
366	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
367	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
368	D₃	—	4	8	no	—
369	C₅	C₂×#5535	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²	—	2	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	6	8	no	—
374	C₂²	—	6	8	no	—
375	C₂²	—	6	8	no	—
376	C₂²	—	12	16	no	—
377	C₂²	C₂×C₅×#235	1	2	yes	—
378	C₂²	C₅×#1009	1	4	yes	—
379	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	4	no	—
382	C₄	—	2	4	no	—
383	C₄	—	6	8	no	—
384	C₄	C₂×C₅×#235	1	4	yes	—
385	C₃	C₂×C₅×#540	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	4	2	no	—
387	C₂	—	12	8	no	—
388	C₂	C₅×#5535	1	4	yes	direct product factor
389	C₂	C₂²×C₅×#235	1	1	yes	characteristic
390	C₂	C₂×C₅×#1009	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₂×C₅×#540
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#117	C₂	semidirect
2. C₂×C₅×#930	C₂	semidirect
3. C₅×#5535	C₂	direct (N × H)
4. C₂×C₅×#894	C₂	semidirect
5. C₂×C₅×#884	C₂	semidirect
6. C₂×C₅×#874	C₂	semidirect
7. C₂×C₄×C₅×D₁₂	C₂	semidirect
8. C₂×C₅×#870	C₂	semidirect
15. C₃×C₅×#117	C₂²	semidirect
20. C₅×#930	C₂²	semidirect
25. C₅×#894	C₂²	semidirect
26. C₅×#884	C₂²	semidirect
27. C₅×#874	C₂²	semidirect
28. C₄×C₅×D₁₂	C₂²	semidirect
29. C₅×#870	C₂²	semidirect
30. C₂×#5535	C₅	direct (N × H)
38. C₂×C₅×#117	D₃	semidirect
64. C₂×C₃×#117	C₂×C₅	semidirect
65. C₂×#930	C₂×C₅	semidirect
66. #5535	C₂×C₅	direct (N × H)
67. C₂×#894	C₂×C₅	semidirect
68. C₂×#884	C₂×C₅	semidirect
69. C₂×#874	C₂×C₅	semidirect
70. C₂×C₄×D₁₂	C₂×C₅	semidirect
71. C₂×#870	C₂×C₅	semidirect
83. C₅×#117	C₂×D₃	semidirect
121. C₃×#117	C₂²×C₅	semidirect
126. #930	C₂²×C₅	semidirect
131. #894	C₂²×C₅	semidirect
132. #884	C₂²×C₅	semidirect
133. #874	C₂²×C₅	semidirect
134. C₄×D₁₂	C₂²×C₅	semidirect
135. #870	C₂²×C₅	semidirect
168. C₂×#117	C₅×D₃	semidirect
243. #117	C₂×C₅×D₃	semidirect
253. C₂×C₃×C₅	#540	semidirect
320. C₃×C₅	C₂×#540	semidirect
338. C₂×C₅	#5535	direct (N × H)
365. C₂×C₃	C₅×#540	semidirect
369. C₅	C₂×#5535	direct (N × H)
385. C₃	C₂×C₅×#540	semidirect
388. C₂	C₅×#5535	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#117	2
C₂×C₅×#930	2
C₅×#5535	2
C₂×C₅×#894	2
C₂×C₅×#884	2
C₂×C₅×#874	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#870	2
C₂×C₅×#540	3
C₂×#5535	5

Subgroups — C2×C5×#5535 #14481094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5535 #14481094