Subgroups — C₃×C₅×#3054 #14276088

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#525	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#470	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#469	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#468	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#416	C₂	1	2	yes	maximal, complemented
9	C₅×#3054	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₃×C₅×#135	—	2	4	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×M₁₆	—	2	4	no	—
17	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
19	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×#123	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₃×C₅×#121	C₂²	1	4	yes	—
24	C₃×C₅×#120	—	2	2	no	—
25	C₃×C₄×C₅×D₄	—	2	4	no	—
26	C₃×C₅×#117	C₂²	1	2	yes	—
27	C₃×C₅×#107	C₂²	1	2	yes	complemented
28	C₃×C₅×#106	C₂²	1	2	yes	complemented
29	C₃×C₅×#103	C₂²	1	4	yes	complemented
30	C₃×C₅×#102	C₂²	1	4	yes	complemented
31	C₃×#3054	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#525	C₂×C₃	1	2	yes	complemented
35	C₅×#470	C₂×C₃	1	2	yes	complemented
36	C₅×#469	C₂×C₃	1	2	yes	complemented
37	C₅×#468	C₂×C₃	1	4	yes	complemented
38	C₅×#427	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#416	C₂×C₃	1	2	yes	complemented
40	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
41	C₃×C₅×#41	—	2	4	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	4	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	—	2	2	no	—
48	C₂²×C₃×C₄×C₅	—	2	2	no	—
49	C₂²×C₃×C₄×C₅	—	2	2	no	—
50	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₃×C₅×Q₁₆	—	2	2	no	—
55	C₃×C₅×SD₁₆	—	2	4	no	—
56	C₃×C₅×D₈	—	2	2	no	—
57	C₃×C₅×M₁₆	—	2	4	no	—
58	C₃×C₅×M₁₆	—	2	4	no	—
59	C₂×C₃×C₅×C₈	—	2	2	no	—
60	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	—	2	4	no	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×#525	C₂×C₅	1	2	yes	complemented
73	C₃×#470	C₂×C₅	1	2	yes	complemented
74	C₃×#469	C₂×C₅	1	2	yes	complemented
75	C₃×#468	C₂×C₅	1	4	yes	complemented
76	C₃×#427	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#416	C₂×C₅	1	2	yes	complemented
78	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
79	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
80	C₅×#135	—	2	4	no	—
81	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
83	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
84	C₂×C₅×M₁₆	—	2	4	no	—
85	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
86	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
87	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
89	C₅×#123	—	2	2	no	—
90	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
91	C₅×#121	C₂²×C₃	1	4	yes	—
92	C₅×#120	—	2	2	no	—
93	C₄×C₅×D₄	—	2	4	no	—
94	C₅×#117	C₂²×C₃	1	2	yes	—
95	C₅×#107	C₂²×C₃	1	2	yes	complemented
96	C₅×#106	C₂²×C₃	1	2	yes	complemented
97	C₅×#103	C₂²×C₃	1	4	yes	complemented
98	C₅×#102	C₂²×C₃	1	4	yes	complemented
99	#3054	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	2	2	no	—
102	C₂³×C₃×C₅	—	4	2	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
104	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
105	C₃×C₅×Q₈	—	2	2	no	—
106	C₃×C₅×Q₈	—	2	2	no	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	—	2	2	no	—
109	C₃×C₅×D₄	—	4	8	no	—
110	C₃×C₅×D₄	—	4	4	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	4	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	4	4	no	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	#41	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
123	C₃×C₅×C₈	—	2	2	no	—
124	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
125	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
126	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
127	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
128	C₃×#135	—	2	4	no	—
129	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
130	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
131	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
132	C₂×C₃×M₁₆	—	2	4	no	—
133	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
134	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
135	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
137	C₃×#123	—	2	2	no	—
138	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
139	C₃×#121	C₂²×C₅	1	4	yes	—
140	C₃×#120	—	2	2	no	—
141	C₃×C₄×D₄	—	2	4	no	—
142	C₃×#117	C₂²×C₅	1	2	yes	—
143	C₃×#107	C₂²×C₅	1	2	yes	complemented
144	C₃×#106	C₂²×C₅	1	2	yes	complemented
145	C₃×#103	C₂²×C₅	1	4	yes	complemented
146	C₃×#102	C₂²×C₅	1	4	yes	complemented
147	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
148	C₅×#41	—	2	4	no	—
149	C₅×#41	—	2	4	no	—
150	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
151	C₂×C₅×D₄	—	2	4	no	—
152	C₂×C₅×D₄	—	2	2	no	—
153	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	—	2	2	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	—	2	2	no	—
157	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
158	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
161	C₅×Q₁₆	—	2	2	no	—
162	C₅×SD₁₆	—	2	4	no	—
163	C₅×D₈	—	2	2	no	—
164	C₅×M₁₆	—	2	4	no	—
165	C₅×M₁₆	—	2	4	no	—
166	C₂×C₅×C₈	—	2	2	no	—
167	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
168	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
169	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
171	C₅×C₄⋊C₄	—	2	4	no	—
172	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
173	C₅×C₂²⋊C₄	—	2	2	no	—
174	C₅×C₂²⋊C₄	—	2	4	no	—
175	C₅×C₂²⋊C₄	—	2	4	no	—
176	C₄²×C₅	—	2	2	no	—
177	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
178	C₂²×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
179	#525	C₂×C₃×C₅	1	2	yes	complemented
180	#470	C₂×C₃×C₅	1	2	yes	complemented
181	#469	C₂×C₃×C₅	1	2	yes	complemented
182	#468	C₂×C₃×C₅	1	4	yes	complemented
183	#427	C₂×C₃×C₅	1	1	yes	characteristic, complemented
184	#416	C₂×C₃×C₅	1	2	yes	complemented
185	C₂²×C₃×C₅	—	2	2	no	—
186	C₂²×C₃×C₅	—	2	2	no	—
187	C₂²×C₃×C₅	—	2	4	no	—
188	C₂²×C₃×C₅	—	4	4	no	—
189	C₂²×C₃×C₅	—	4	2	no	—
190	C₂²×C₃×C₅	—	4	4	no	—
191	C₂²×C₃×C₅	#121	1	2	yes	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₃×C₄×C₅	—	2	2	no	—
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	—	4	4	no	—
196	C₃×C₄×C₅	#121	1	2	yes	—
197	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
198	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
199	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
200	C₃×#41	—	2	4	no	—
201	C₃×#41	—	2	4	no	—
202	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
203	C₂×C₃×D₄	—	2	4	no	—
204	C₂×C₃×D₄	—	2	2	no	—
205	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	—	2	2	no	—
207	C₂²×C₃×C₄	—	2	2	no	—
208	C₂²×C₃×C₄	—	2	2	no	—
209	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
210	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
212	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
213	C₃×Q₁₆	—	2	2	no	—
214	C₃×SD₁₆	—	2	4	no	—
215	C₃×D₈	—	2	2	no	—
216	C₃×M₁₆	—	2	4	no	—
217	C₃×M₁₆	—	2	4	no	—
218	C₂×C₃×C₈	—	2	2	no	—
219	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
220	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
221	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
222	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
223	C₃×C₄⋊C₄	—	2	4	no	—
224	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
225	C₃×C₂²⋊C₄	—	2	2	no	—
226	C₃×C₂²⋊C₄	—	2	4	no	—
227	C₃×C₂²⋊C₄	—	2	4	no	—
228	C₃×C₄²	—	2	2	no	—
229	C₂³×C₅	—	2	2	no	—
230	C₂³×C₅	—	2	2	no	—
231	C₂³×C₅	—	4	2	no	—
232	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
233	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
234	C₅×Q₈	—	2	2	no	—
235	C₅×Q₈	—	2	2	no	—
236	C₅×D₄	—	2	2	no	—
237	C₅×D₄	—	2	2	no	—
238	C₅×D₄	—	4	8	no	—
239	C₅×D₄	—	4	4	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	4	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	4	4	no	—
247	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
248	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
250	C₂×C₄×C₅	C₃×#41	1	2	yes	—
251	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
254	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
255	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
256	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
257	#135	—	2	4	no	—
258	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
259	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
260	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
263	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
264	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
266	#123	—	2	2	no	—
267	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
268	#121	C₂²×C₃×C₅	1	4	yes	—
269	#120	—	2	2	no	—
270	C₄×D₄	—	2	4	no	—
271	#117	C₂²×C₃×C₅	1	2	yes	—
272	#107	C₂²×C₃×C₅	1	2	yes	complemented
273	#106	C₂²×C₃×C₅	1	2	yes	complemented
274	#103	C₂²×C₃×C₅	1	4	yes	complemented
275	#102	C₂²×C₃×C₅	1	4	yes	complemented
276	C₂×C₃×C₅	—	2	2	no	—
277	C₂×C₃×C₅	—	4	2	no	—
278	C₂×C₃×C₅	—	8	2	no	—
279	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
280	C₂×C₃×C₅	#575	1	2	yes	—
281	C₂³×C₃	—	2	2	no	—
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	—	4	2	no	—
284	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
285	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
286	C₃×Q₈	—	2	2	no	—
287	C₃×Q₈	—	2	2	no	—
288	C₃×D₄	—	2	2	no	—
289	C₃×D₄	—	2	2	no	—
290	C₃×D₄	—	4	8	no	—
291	C₃×D₄	—	4	4	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	4	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	4	4	no	—
299	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
302	C₂×C₃×C₄	C₅×#41	1	2	yes	—
303	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
304	C₃×C₈	—	2	2	no	—
305	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
306	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	4	4	no	—
311	C₂²×C₅	—	4	4	no	—
312	C₂²×C₅	—	4	2	no	—
313	C₂²×C₅	C₃×#121	1	2	yes	—
314	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	—	4	4	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	C₃×#121	1	2	yes	—
319	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
320	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
321	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
322	#41	—	2	4	no	—
323	#41	—	2	4	no	—
324	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
332	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
334	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
335	Q₁₆	—	2	2	no	—
336	SD₁₆	—	2	4	no	—
337	D₈	—	2	2	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	2	4	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
342	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
343	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
344	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₄²	—	2	2	no	—
351	C₃×C₅	#3054	1	1	yes	characteristic, direct product factor, Hall
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	—	4	4	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	—	4	4	no	—
358	C₂²×C₃	C₅×#121	1	2	yes	—
359	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	—	4	4	no	—
363	C₃×C₄	C₅×#121	1	2	yes	—
364	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
365	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
366	C₂×C₅	—	2	2	no	—
367	C₂×C₅	—	4	2	no	—
368	C₂×C₅	—	8	2	no	—
369	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
370	C₂×C₅	C₃×#575	1	2	yes	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
375	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
376	Q₈	—	2	2	no	—
377	Q₈	—	2	2	no	—
378	D₄	—	2	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	8	no	—
381	D₄	—	4	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
390	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
391	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
392	C₂×C₄	C₃×C₅×#41	1	2	yes	—
393	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
396	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
397	C₂×C₃	—	2	2	no	—
398	C₂×C₃	—	4	2	no	—
399	C₂×C₃	—	8	2	no	—
400	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
401	C₂×C₃	C₅×#575	1	2	yes	—
402	C₅	C₃×#3054	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	4	no	—
409	C₂²	C₃×C₅×#121	1	2	yes	—
410	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	4	no	—
414	C₄	C₃×C₅×#121	1	2	yes	—
415	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
416	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
417	C₃	C₅×#3054	1	1	yes	characteristic, direct product factor, Sylow
418	C₂	—	2	2	no	—
419	C₂	—	4	2	no	—
420	C₂	—	8	2	no	—
421	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
422	C₂	C₃×C₅×#575	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
socle	C₂²×C₃×C₅	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₃×C₅×#525	C₂	semidirect
4. C₃×C₅×#470	C₂	semidirect
5. C₃×C₅×#469	C₂	semidirect
6. C₃×C₅×#468	C₂	semidirect
7. C₃×C₅×#427	C₂	semidirect
8. C₃×C₅×#416	C₂	semidirect
9. C₅×#3054	C₃	direct (N × H)
13. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
14. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₂×C₃×C₅×D₈	C₂²	semidirect
27. C₃×C₅×#107	C₂²	semidirect
28. C₃×C₅×#106	C₂²	semidirect
29. C₃×C₅×#103	C₂²	semidirect
30. C₃×C₅×#102	C₂²	semidirect
31. C₃×#3054	C₅	direct (N × H)
32. C₂×C₅×#135	C₂×C₃	semidirect
33. C₂²×C₅×M₁₆	C₂×C₃	semidirect
34. C₅×#525	C₂×C₃	semidirect
35. C₅×#470	C₂×C₃	semidirect
36. C₅×#469	C₂×C₃	semidirect
37. C₅×#468	C₂×C₃	semidirect
38. C₅×#427	C₂×C₃	semidirect
39. C₅×#416	C₂×C₃	semidirect
60. C₂×C₃×C₅×C₈	D₄	semidirect
70. C₂×C₃×#135	C₂×C₅	semidirect
71. C₂²×C₃×M₁₆	C₂×C₅	semidirect
72. C₃×#525	C₂×C₅	semidirect
73. C₃×#470	C₂×C₅	semidirect
74. C₃×#469	C₂×C₅	semidirect
75. C₃×#468	C₂×C₅	semidirect
76. C₃×#427	C₂×C₅	semidirect
77. C₃×#416	C₂×C₅	semidirect
81. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
82. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
83. C₂×C₅×D₈	C₂²×C₃	semidirect
95. C₅×#107	C₂²×C₃	semidirect
96. C₅×#106	C₂²×C₃	semidirect
97. C₅×#103	C₂²×C₃	semidirect
98. C₅×#102	C₂²×C₃	semidirect
99. #3054	C₃×C₅	direct (N × H)
129. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
130. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
131. C₂×C₃×D₈	C₂²×C₅	semidirect
143. C₃×#107	C₂²×C₅	semidirect
144. C₃×#106	C₂²×C₅	semidirect
145. C₃×#103	C₂²×C₅	semidirect
146. C₃×#102	C₂²×C₅	semidirect
167. C₂×C₅×C₈	C₃×D₄	semidirect
177. C₂×#135	C₂×C₃×C₅	semidirect
178. C₂²×M₁₆	C₂×C₃×C₅	semidirect
179. #525	C₂×C₃×C₅	semidirect
180. #470	C₂×C₃×C₅	semidirect
181. #469	C₂×C₃×C₅	semidirect
182. #468	C₂×C₃×C₅	semidirect
183. #427	C₂×C₃×C₅	semidirect
184. #416	C₂×C₃×C₅	semidirect
219. C₂×C₃×C₈	C₅×D₄	semidirect
258. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
259. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
260. C₂×D₈	C₂²×C₃×C₅	semidirect
272. #107	C₂²×C₃×C₅	semidirect
273. #106	C₂²×C₃×C₅	semidirect
274. #103	C₂²×C₃×C₅	semidirect
275. #102	C₂²×C₃×C₅	semidirect
341. C₂×C₈	C₃×C₅×D₄	semidirect
351. C₃×C₅	#3054	direct (N × H)
402. C₅	C₃×#3054	direct (N × H)
417. C₃	C₅×#3054	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×#135	2
C₂²×C₃×C₅×M₁₆	2
C₃×C₅×#525	2
C₃×C₅×#470	2
C₃×C₅×#469	2
C₃×C₅×#468	2
C₃×C₅×#427	2
C₃×C₅×#416	2
C₅×#3054	3
C₃×#3054	5

Subgroups — C3×C5×#3054 #14276088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3054 #14276088