Subgroups — C₃×C₅×#3284 #14276318

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 564 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	2	yes	maximal, complemented
2	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3284	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
15	C₃×C₅×#135	—	2	8	no	—
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
19	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
21	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
22	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#127	—	2	1	no	—
24	C₃×C₅×#127	C₂²	1	1	yes	characteristic
25	C₃×C₅×#123	—	2	2	no	—
26	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₃×C₅×#121	—	2	1	no	—
28	C₃×C₅×#121	—	2	2	no	—
29	C₃×C₅×#121	C₂²	1	2	yes	—
30	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₃×C₄×C₅×D₄	—	2	1	no	—
32	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
35	C₃×C₅×#106	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₃×C₅×#103	C₂²	1	2	yes	—
38	C₃×C₅×#103	C₂²	1	1	yes	characteristic
39	C₃×C₅×#102	C₂²	1	1	yes	characteristic
40	C₃×C₅×#102	C₂²	1	2	yes	—
41	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
43	C₃×#3284	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂×C₅×#135	C₂×C₃	1	2	yes	complemented
45	C₅×#550	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#492	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#465	C₂×C₃	1	2	yes	complemented
49	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#452	C₂×C₃	1	2	yes	complemented
52	C₅×#449	C₂×C₃	1	2	yes	complemented
53	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×C₅×#41	—	2	4	no	—
56	C₃×C₅×#41	—	2	4	no	—
57	C₃×C₅×#41	—	4	2	no	—
58	C₃×C₅×#41	—	4	2	no	—
59	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	2	1	no	—
65	C₂×C₃×C₅×D₄	—	2	1	no	—
66	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
67	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
68	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	—	2	1	no	—
70	C₂²×C₃×C₄×C₅	—	2	2	no	—
71	C₂²×C₃×C₄×C₅	—	2	2	no	—
72	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
73	C₃×C₅×Q₁₆	—	2	4	no	—
74	C₃×C₅×SD₁₆	—	2	4	no	—
75	C₃×C₅×SD₁₆	—	4	2	no	—
76	C₃×C₅×SD₁₆	D₄	1	4	yes	complemented
77	C₃×C₅×D₈	—	2	4	no	—
78	C₂×C₃×C₅×C₈	—	2	4	no	—
79	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
80	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₃×C₅×C₄⋊C₄	—	2	1	no	—
83	C₃×C₅×C₄⋊C₄	—	2	2	no	—
84	C₃×C₅×C₄⋊C₄	—	2	1	no	—
85	C₃×C₅×C₄⋊C₄	—	2	1	no	—
86	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
90	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
91	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
93	C₃×C₄²×C₅	—	2	1	no	—
94	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₂×C₃×#135	C₂×C₅	1	2	yes	complemented
96	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#465	C₂×C₅	1	2	yes	complemented
100	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#452	C₂×C₅	1	2	yes	complemented
103	C₃×#449	C₂×C₅	1	2	yes	complemented
104	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
107	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
108	C₅×#135	—	2	8	no	—
109	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
110	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
111	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
112	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
114	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
115	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
116	C₅×#127	—	2	1	no	—
117	C₅×#127	C₂²×C₃	1	1	yes	characteristic
118	C₅×#123	—	2	2	no	—
119	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
120	C₅×#121	—	2	1	no	—
121	C₅×#121	—	2	2	no	—
122	C₅×#121	C₂²×C₃	1	2	yes	—
123	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
124	C₄×C₅×D₄	—	2	1	no	—
125	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
126	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₄⋊C₄	—	2	1	no	—
128	C₅×#106	C₂²×C₃	1	1	yes	characteristic
129	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
130	C₅×#103	C₂²×C₃	1	1	yes	characteristic
131	C₅×#103	C₂²×C₃	1	2	yes	—
132	C₅×#102	C₂²×C₃	1	1	yes	characteristic
133	C₅×#102	C₂²×C₃	1	2	yes	—
134	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
135	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
136	#3284	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	—	2	2	no	—
139	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
140	C₃×C₅×Q₈	—	2	1	no	—
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	—	2	2	no	—
143	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
144	C₃×C₅×D₄	—	2	2	no	—
145	C₃×C₅×D₄	—	2	2	no	—
146	C₃×C₅×D₄	—	2	1	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	4	4	no	—
149	C₃×C₅×D₄	—	4	4	no	—
150	C₃×C₅×D₄	—	4	2	no	—
151	C₃×C₅×D₄	—	8	1	no	—
152	C₃×C₅×D₄	—	8	2	no	—
153	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	—	2	1	no	—
159	C₂×C₃×C₄×C₅	—	2	2	no	—
160	C₂×C₃×C₄×C₅	—	4	4	no	—
161	C₂×C₃×C₄×C₅	—	4	4	no	—
162	C₂×C₃×C₄×C₅	—	4	2	no	—
163	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
165	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
167	C₃×C₅×C₈	—	2	2	no	—
168	C₃×C₅×C₈	—	2	1	no	—
169	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
170	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
171	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
172	C₃×#135	—	2	8	no	—
173	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
174	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
175	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
176	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
178	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
179	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
180	C₃×#127	—	2	1	no	—
181	C₃×#127	C₂²×C₅	1	1	yes	characteristic
182	C₃×#123	—	2	2	no	—
183	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
184	C₃×#121	—	2	1	no	—
185	C₃×#121	—	2	2	no	—
186	C₃×#121	C₂²×C₅	1	2	yes	—
187	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
188	C₃×C₄×D₄	—	2	1	no	—
189	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
190	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	—	2	1	no	—
192	C₃×#106	C₂²×C₅	1	1	yes	characteristic
193	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
194	C₃×#103	C₂²×C₅	1	1	yes	characteristic
195	C₃×#103	C₂²×C₅	1	2	yes	—
196	C₃×#102	C₂²×C₅	1	1	yes	characteristic
197	C₃×#102	C₂²×C₅	1	2	yes	—
198	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
199	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
200	C₅×#41	—	2	4	no	—
201	C₅×#41	—	2	4	no	—
202	C₅×#41	—	4	2	no	—
203	C₅×#41	—	4	2	no	—
204	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
205	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₅×D₄	—	2	2	no	—
207	C₂×C₅×D₄	—	2	2	no	—
208	C₂×C₅×D₄	—	2	2	no	—
209	C₂×C₅×D₄	—	2	1	no	—
210	C₂×C₅×D₄	—	2	1	no	—
211	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
212	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
213	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
214	C₂²×C₄×C₅	—	2	1	no	—
215	C₂²×C₄×C₅	—	2	2	no	—
216	C₂²×C₄×C₅	—	2	2	no	—
217	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
218	C₅×Q₁₆	—	2	4	no	—
219	C₅×SD₁₆	—	2	4	no	—
220	C₅×SD₁₆	—	4	2	no	—
221	C₅×SD₁₆	C₃×D₄	1	4	yes	complemented
222	C₅×D₈	—	2	4	no	—
223	C₂×C₅×C₈	—	2	4	no	—
224	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
225	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
226	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	—	2	2	no	—
229	C₅×C₄⋊C₄	—	2	1	no	—
230	C₅×C₄⋊C₄	—	2	1	no	—
231	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
232	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
233	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
234	C₅×C₂²⋊C₄	—	2	2	no	—
235	C₅×C₂²⋊C₄	—	2	2	no	—
236	C₅×C₂²⋊C₄	—	2	1	no	—
237	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
238	C₄²×C₅	—	2	1	no	—
239	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
240	C₂×#135	C₂×C₃×C₅	1	2	yes	complemented
241	#550	C₂×C₃×C₅	1	1	yes	characteristic, complemented
242	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
243	#492	C₂×C₃×C₅	1	1	yes	characteristic, complemented
244	#465	C₂×C₃×C₅	1	2	yes	complemented
245	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
246	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
247	#452	C₂×C₃×C₅	1	2	yes	complemented
248	#449	C₂×C₃×C₅	1	2	yes	complemented
249	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
250	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	—	2	2	no	—
254	C₂²×C₃×C₅	—	2	2	no	—
255	C₂²×C₃×C₅	—	4	1	no	—
256	C₂²×C₃×C₅	—	4	1	no	—
257	C₂²×C₃×C₅	—	4	2	no	—
258	C₂²×C₃×C₅	—	4	2	no	—
259	C₂²×C₃×C₅	—	4	2	no	—
260	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₃×C₄×C₅	—	2	2	no	—
262	C₃×C₄×C₅	—	2	2	no	—
263	C₃×C₄×C₅	—	2	1	no	—
264	C₃×C₄×C₅	—	4	2	no	—
265	C₃×C₄×C₅	—	4	1	no	—
266	C₃×C₄×C₅	—	4	1	no	—
267	C₃×C₄×C₅	#135	1	2	yes	complemented
268	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
269	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
270	C₃×#41	—	2	4	no	—
271	C₃×#41	—	2	4	no	—
272	C₃×#41	—	4	2	no	—
273	C₃×#41	—	4	2	no	—
274	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
275	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₃×D₄	—	2	2	no	—
277	C₂×C₃×D₄	—	2	2	no	—
278	C₂×C₃×D₄	—	2	2	no	—
279	C₂×C₃×D₄	—	2	1	no	—
280	C₂×C₃×D₄	—	2	1	no	—
281	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
282	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
283	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
284	C₂²×C₃×C₄	—	2	1	no	—
285	C₂²×C₃×C₄	—	2	2	no	—
286	C₂²×C₃×C₄	—	2	2	no	—
287	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
288	C₃×Q₁₆	—	2	4	no	—
289	C₃×SD₁₆	—	2	4	no	—
290	C₃×SD₁₆	—	4	2	no	—
291	C₃×SD₁₆	C₅×D₄	1	4	yes	complemented
292	C₃×D₈	—	2	4	no	—
293	C₂×C₃×C₈	—	2	4	no	—
294	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
295	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
296	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
297	C₃×C₄⋊C₄	—	2	1	no	—
298	C₃×C₄⋊C₄	—	2	2	no	—
299	C₃×C₄⋊C₄	—	2	1	no	—
300	C₃×C₄⋊C₄	—	2	1	no	—
301	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
302	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
303	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
304	C₃×C₂²⋊C₄	—	2	2	no	—
305	C₃×C₂²⋊C₄	—	2	2	no	—
306	C₃×C₂²⋊C₄	—	2	1	no	—
307	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
308	C₃×C₄²	—	2	1	no	—
309	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
310	C₂³×C₅	—	2	1	no	—
311	C₂³×C₅	—	2	2	no	—
312	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
313	C₅×Q₈	—	2	1	no	—
314	C₅×Q₈	—	2	2	no	—
315	C₅×Q₈	—	2	2	no	—
316	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
317	C₅×D₄	—	2	2	no	—
318	C₅×D₄	—	2	2	no	—
319	C₅×D₄	—	2	1	no	—
320	C₅×D₄	—	2	2	no	—
321	C₅×D₄	—	4	4	no	—
322	C₅×D₄	—	4	4	no	—
323	C₅×D₄	—	4	2	no	—
324	C₅×D₄	—	8	1	no	—
325	C₅×D₄	—	8	2	no	—
326	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	4	4	no	—
334	C₂×C₄×C₅	—	4	4	no	—
335	C₂×C₄×C₅	—	4	2	no	—
336	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
338	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
340	C₅×C₈	—	2	2	no	—
341	C₅×C₈	—	2	1	no	—
342	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
343	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
344	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
345	#135	—	2	8	no	—
346	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
347	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
348	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
349	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
350	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
351	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
352	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
353	#127	—	2	1	no	—
354	#127	C₂²×C₃×C₅	1	1	yes	characteristic
355	#123	—	2	2	no	—
356	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
357	#121	—	2	1	no	—
358	#121	—	2	2	no	—
359	#121	C₂²×C₃×C₅	1	2	yes	—
360	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
363	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
364	C₂×C₄⋊C₄	—	2	1	no	—
365	#106	C₂²×C₃×C₅	1	1	yes	characteristic
366	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
367	#103	C₂²×C₃×C₅	1	1	yes	characteristic
368	#103	C₂²×C₃×C₅	1	2	yes	—
369	#102	C₂²×C₃×C₅	1	1	yes	characteristic
370	#102	C₂²×C₃×C₅	1	2	yes	—
371	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
372	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
373	C₂×C₃×C₅	—	4	2	no	—
374	C₂×C₃×C₅	—	4	2	no	—
375	C₂×C₃×C₅	—	8	2	no	—
376	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
377	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
378	C₂×C₃×C₅	#577	1	1	yes	characteristic
379	C₂³×C₃	—	2	1	no	—
380	C₂³×C₃	—	2	2	no	—
381	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
382	C₃×Q₈	—	2	1	no	—
383	C₃×Q₈	—	2	2	no	—
384	C₃×Q₈	—	2	2	no	—
385	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
386	C₃×D₄	—	2	2	no	—
387	C₃×D₄	—	2	2	no	—
388	C₃×D₄	—	2	1	no	—
389	C₃×D₄	—	2	2	no	—
390	C₃×D₄	—	4	4	no	—
391	C₃×D₄	—	4	4	no	—
392	C₃×D₄	—	4	2	no	—
393	C₃×D₄	—	8	1	no	—
394	C₃×D₄	—	8	2	no	—
395	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	4	4	no	—
403	C₂×C₃×C₄	—	4	4	no	—
404	C₂×C₃×C₄	—	4	2	no	—
405	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
407	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
408	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
409	C₃×C₈	—	2	2	no	—
410	C₃×C₈	—	2	1	no	—
411	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
412	C₂²×C₅	—	2	2	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	4	1	no	—
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	—	4	2	no	—
419	C₂²×C₅	—	4	2	no	—
420	C₂²×C₅	—	4	2	no	—
421	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	2	2	no	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	4	1	no	—
426	C₄×C₅	—	4	1	no	—
427	C₄×C₅	—	4	2	no	—
428	C₄×C₅	C₃×#135	1	2	yes	complemented
429	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
430	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
431	#41	—	2	4	no	—
432	#41	—	2	4	no	—
433	#41	—	4	2	no	—
434	#41	—	4	2	no	—
435	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
436	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
443	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
444	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
449	Q₁₆	—	2	4	no	—
450	SD₁₆	—	2	4	no	—
451	SD₁₆	—	4	2	no	—
452	SD₁₆	C₃×C₅×D₄	1	4	yes	complemented
453	D₈	—	2	4	no	—
454	C₂×C₈	—	2	4	no	—
455	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
456	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
457	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
463	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
464	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
469	C₄²	—	2	1	no	—
470	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
471	C₃×C₅	#3284	1	1	yes	characteristic, direct product factor, Hall
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	4	1	no	—
477	C₂²×C₃	—	4	1	no	—
478	C₂²×C₃	—	4	2	no	—
479	C₂²×C₃	—	4	2	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
482	C₃×C₄	—	2	2	no	—
483	C₃×C₄	—	2	2	no	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	4	2	no	—
486	C₃×C₄	—	4	1	no	—
487	C₃×C₄	—	4	1	no	—
488	C₃×C₄	C₅×#135	1	2	yes	complemented
489	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
490	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂×C₅	—	4	2	no	—
492	C₂×C₅	—	4	2	no	—
493	C₂×C₅	—	8	2	no	—
494	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
495	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
496	C₂×C₅	C₃×#577	1	1	yes	characteristic
497	C₂³	—	2	1	no	—
498	C₂³	—	2	2	no	—
499	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
500	Q₈	—	2	1	no	—
501	Q₈	—	2	2	no	—
502	Q₈	—	2	2	no	—
503	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
504	D₄	—	2	2	no	—
505	D₄	—	2	1	no	—
506	D₄	—	2	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	4	4	no	—
509	D₄	—	4	4	no	—
510	D₄	—	4	2	no	—
511	D₄	—	8	1	no	—
512	D₄	—	8	2	no	—
513	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
525	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
526	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
527	C₈	—	2	2	no	—
528	C₈	—	2	1	no	—
529	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
530	C₂×C₃	—	4	2	no	—
531	C₂×C₃	—	4	2	no	—
532	C₂×C₃	—	8	2	no	—
533	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
534	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
535	C₂×C₃	C₅×#577	1	1	yes	characteristic
536	C₅	C₃×#3284	1	1	yes	characteristic, direct product factor, Sylow
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	C₃×C₅×#135	1	2	yes	complemented
554	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
555	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
556	C₃	C₅×#3284	1	1	yes	characteristic, direct product factor, Sylow
557	C₂	—	4	2	no	—
558	C₂	—	4	2	no	—
559	C₂	—	8	2	no	—
560	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
561	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
562	C₂	C₃×C₅×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ 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. C₃×C₅×#550	C₂	semidirect
3. C₃×C₅×#547	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₃×C₅×#465	C₂	semidirect
6. C₃×C₅×#462	C₂	semidirect
7. C₃×C₅×#459	C₂	semidirect
8. C₃×C₅×#452	C₂	semidirect
9. C₃×C₅×#449	C₂	semidirect
10. C₃×C₄×C₅×SD₁₆	C₂	semidirect
11. C₃×C₅×C₈×D₄	C₂	semidirect
12. C₅×#3284	C₃	direct (N × H)
43. C₃×#3284	C₅	direct (N × H)
44. C₂×C₅×#135	C₂×C₃	semidirect
45. C₅×#550	C₂×C₃	semidirect
46. C₅×#547	C₂×C₃	semidirect
47. C₅×#492	C₂×C₃	semidirect
48. C₅×#465	C₂×C₃	semidirect
49. C₅×#462	C₂×C₃	semidirect
50. C₅×#459	C₂×C₃	semidirect
51. C₅×#452	C₂×C₃	semidirect
52. C₅×#449	C₂×C₃	semidirect
53. C₄×C₅×SD₁₆	C₂×C₃	semidirect
54. C₅×C₈×D₄	C₂×C₃	semidirect
76. C₃×C₅×SD₁₆	D₄	semidirect
95. C₂×C₃×#135	C₂×C₅	semidirect
96. C₃×#550	C₂×C₅	semidirect
97. C₃×#547	C₂×C₅	semidirect
98. C₃×#492	C₂×C₅	semidirect
99. C₃×#465	C₂×C₅	semidirect
100. C₃×#462	C₂×C₅	semidirect
101. C₃×#459	C₂×C₅	semidirect
102. C₃×#452	C₂×C₅	semidirect
103. C₃×#449	C₂×C₅	semidirect
104. C₃×C₄×SD₁₆	C₂×C₅	semidirect
105. C₃×C₈×D₄	C₂×C₅	semidirect
136. #3284	C₃×C₅	direct (N × H)
221. C₅×SD₁₆	C₃×D₄	semidirect
240. C₂×#135	C₂×C₃×C₅	semidirect
241. #550	C₂×C₃×C₅	semidirect
242. #547	C₂×C₃×C₅	semidirect
243. #492	C₂×C₃×C₅	semidirect
244. #465	C₂×C₃×C₅	semidirect
245. #462	C₂×C₃×C₅	semidirect
246. #459	C₂×C₃×C₅	semidirect
247. #452	C₂×C₃×C₅	semidirect
248. #449	C₂×C₃×C₅	semidirect
249. C₄×SD₁₆	C₂×C₃×C₅	semidirect
250. C₈×D₄	C₂×C₃×C₅	semidirect
267. C₃×C₄×C₅	#135	semidirect
291. C₃×SD₁₆	C₅×D₄	semidirect
428. C₄×C₅	C₃×#135	semidirect
452. SD₁₆	C₃×C₅×D₄	semidirect
471. C₃×C₅	#3284	direct (N × H)
488. C₃×C₄	C₅×#135	semidirect
536. C₅	C₃×#3284	direct (N × H)
553. C₄	C₃×C₅×#135	semidirect
556. C₃	C₅×#3284	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
C₃×C₅×#550	2
C₃×C₅×#547	2
C₃×C₅×#492	2
C₃×C₅×#465	2
C₃×C₅×#462	2
C₃×C₅×#459	2
C₃×C₅×#452	2
C₃×C₅×#449	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×C₈×D₄	2
C₅×#3284	3
C₃×#3284	5

Subgroups — C3×C5×#3284 #14276318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3284 #14276318