Subgroups — C₃×C₅×#3223 #14276257

Order 1920.

728 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	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#491	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#464	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#462	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#452	C₂	1	2	yes	maximal
10	C₃×C₅×#451	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3223	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×#126	—	2	2	no	—
23	C₃×C₅×#125	—	2	2	no	—
24	C₃×C₅×#125	C₂²	1	1	yes	characteristic
25	C₃×C₅×#124	C₂²	1	1	yes	characteristic
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic
27	C₃×C₅×#123	—	2	2	no	—
28	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
29	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
31	C₃×C₅×#117	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	2	yes	—
36	C₃×C₅×#102	C₂²	1	2	yes	—
37	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₃×C₅×#97	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₃×#3223	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#536	C₂×C₃	1	1	yes	characteristic
43	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#494	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#491	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#488	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#464	C₂×C₃	1	2	yes	complemented
48	C₅×#462	C₂×C₃	1	2	yes	complemented
49	C₅×#452	C₂×C₃	1	2	yes	—
50	C₅×#451	C₂×C₃	1	2	yes	complemented
51	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×C₅×#41	—	4	2	no	—
53	C₂×C₃×C₅×Q₈	—	2	1	no	—
54	C₂×C₃×C₅×Q₈	—	4	2	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₃×C₅×Q₁₆	—	4	2	no	—
65	C₃×C₅×Q₁₆	—	4	2	no	—
66	C₃×C₅×Q₁₆	—	4	2	no	—
67	C₃×C₅×SD₁₆	—	4	2	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	—	2	2	no	—
76	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
77	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
80	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
82	C₃×C₄²×C₅	—	2	2	no	—
83	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#536	C₂×C₅	1	1	yes	characteristic
87	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×#494	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#491	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#488	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×#464	C₂×C₅	1	2	yes	complemented
92	C₃×#462	C₂×C₅	1	2	yes	complemented
93	C₃×#452	C₂×C₅	1	2	yes	—
94	C₃×#451	C₂×C₅	1	2	yes	complemented
95	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
97	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
99	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
100	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
101	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
102	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
104	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₅×#126	—	2	2	no	—
106	C₅×#125	—	2	2	no	—
107	C₅×#125	C₂²×C₃	1	1	yes	characteristic
108	C₅×#124	C₂²×C₃	1	1	yes	characteristic
109	C₅×#124	C₂²×C₃	1	1	yes	characteristic
110	C₅×#123	—	2	2	no	—
111	C₅×C₂²⋊Q₈	—	2	2	no	—
112	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
113	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
114	C₅×#117	C₂²×C₃	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
116	C₅×#103	C₂²×C₃	1	2	yes	—
117	C₅×#103	C₂²×C₃	1	2	yes	—
118	C₅×#103	C₂²×C₃	1	2	yes	—
119	C₅×#102	C₂²×C₃	1	2	yes	—
120	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
121	C₅×#97	C₂²×C₃	1	1	yes	characteristic
122	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
123	#3223	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
124	C₂³×C₃×C₅	—	2	1	no	—
125	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
126	C₃×C₅×Q₈	—	2	2	no	—
127	C₃×C₅×Q₈	—	2	2	no	—
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×Q₈	—	4	2	no	—
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	—	4	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	4	2	no	—
141	C₂×C₃×C₄×C₅	—	4	2	no	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₃×C₅×C₈	—	2	2	no	—
147	C₃×C₅×C₈	—	2	2	no	—
148	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
149	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
151	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
152	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
153	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
154	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
155	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
156	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
157	C₃×#126	—	2	2	no	—
158	C₃×#125	—	2	2	no	—
159	C₃×#125	C₂²×C₅	1	1	yes	characteristic
160	C₃×#124	C₂²×C₅	1	1	yes	characteristic
161	C₃×#124	C₂²×C₅	1	1	yes	characteristic
162	C₃×#123	—	2	2	no	—
163	C₃×C₂²⋊Q₈	—	2	2	no	—
164	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
165	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
166	C₃×#117	C₂²×C₅	1	1	yes	characteristic
167	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
168	C₃×#103	C₂²×C₅	1	2	yes	—
169	C₃×#103	C₂²×C₅	1	2	yes	—
170	C₃×#103	C₂²×C₅	1	2	yes	—
171	C₃×#102	C₂²×C₅	1	2	yes	—
172	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
173	C₃×#97	C₂²×C₅	1	1	yes	characteristic
174	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
175	C₅×#41	—	4	2	no	—
176	C₂×C₅×Q₈	—	2	1	no	—
177	C₂×C₅×Q₈	—	4	2	no	—
178	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
179	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₅×D₄	—	2	1	no	—
183	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
187	C₅×Q₁₆	—	4	2	no	—
188	C₅×Q₁₆	—	4	2	no	—
189	C₅×Q₁₆	—	4	2	no	—
190	C₅×SD₁₆	—	4	2	no	—
191	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
192	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	2	2	no	—
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
200	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₅×C₂²⋊C₄	—	2	2	no	—
203	C₅×C₂²⋊C₄	—	2	2	no	—
204	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
205	C₄²×C₅	—	2	2	no	—
206	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
208	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	#536	C₂×C₃×C₅	1	1	yes	characteristic
210	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
211	#494	C₂×C₃×C₅	1	1	yes	characteristic, complemented
212	#491	C₂×C₃×C₅	1	1	yes	characteristic, complemented
213	#488	C₂×C₃×C₅	1	1	yes	characteristic, complemented
214	#464	C₂×C₃×C₅	1	2	yes	complemented
215	#462	C₂×C₃×C₅	1	2	yes	complemented
216	#452	C₂×C₃×C₅	1	2	yes	—
217	#451	C₂×C₃×C₅	1	2	yes	complemented
218	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
219	C₂²×C₃×C₅	—	2	1	no	—
220	C₂²×C₃×C₅	—	2	2	no	—
221	C₂²×C₃×C₅	—	4	1	no	—
222	C₂²×C₃×C₅	—	4	2	no	—
223	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₃×C₄×C₅	—	2	1	no	—
225	C₃×C₄×C₅	—	2	2	no	—
226	C₃×C₄×C₅	—	2	2	no	—
227	C₃×C₄×C₅	—	4	1	no	—
228	C₃×C₄×C₅	—	4	1	no	—
229	C₃×C₄×C₅	—	4	1	no	—
230	C₃×C₄×C₅	—	4	2	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
233	C₃×#41	—	4	2	no	—
234	C₂×C₃×Q₈	—	2	1	no	—
235	C₂×C₃×Q₈	—	4	2	no	—
236	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
237	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
238	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
239	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
240	C₂×C₃×D₄	—	2	1	no	—
241	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
242	C₂²×C₃×C₄	—	2	1	no	—
243	C₂²×C₃×C₄	—	2	1	no	—
244	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
245	C₃×Q₁₆	—	4	2	no	—
246	C₃×Q₁₆	—	4	2	no	—
247	C₃×Q₁₆	—	4	2	no	—
248	C₃×SD₁₆	—	4	2	no	—
249	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
250	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
251	C₃×C₄⋊C₄	—	2	2	no	—
252	C₃×C₄⋊C₄	—	2	2	no	—
253	C₃×C₄⋊C₄	—	2	2	no	—
254	C₃×C₄⋊C₄	—	2	2	no	—
255	C₃×C₄⋊C₄	—	2	2	no	—
256	C₃×C₄⋊C₄	—	2	2	no	—
257	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
258	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
259	C₃×C₂²⋊C₄	—	2	2	no	—
260	C₃×C₂²⋊C₄	—	2	2	no	—
261	C₃×C₂²⋊C₄	—	2	2	no	—
262	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
263	C₃×C₄²	—	2	2	no	—
264	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
265	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
266	C₂³×C₅	—	2	1	no	—
267	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
268	C₅×Q₈	—	2	2	no	—
269	C₅×Q₈	—	2	2	no	—
270	C₅×Q₈	—	2	2	no	—
271	C₅×Q₈	—	2	2	no	—
272	C₅×Q₈	—	2	2	no	—
273	C₅×Q₈	—	4	2	no	—
274	C₅×D₄	—	2	2	no	—
275	C₅×D₄	—	4	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	4	2	no	—
283	C₂×C₄×C₅	—	4	2	no	—
284	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
285	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
286	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
288	C₅×C₈	—	2	2	no	—
289	C₅×C₈	—	2	2	no	—
290	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
291	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
292	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
293	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
294	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
295	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
296	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
297	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
298	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
299	#126	—	2	2	no	—
300	#125	—	2	2	no	—
301	#125	C₂²×C₃×C₅	1	1	yes	characteristic
302	#124	C₂²×C₃×C₅	1	1	yes	characteristic
303	#124	C₂²×C₃×C₅	1	1	yes	characteristic
304	#123	—	2	2	no	—
305	C₂²⋊Q₈	—	2	2	no	—
306	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
307	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
308	#117	C₂²×C₃×C₅	1	1	yes	characteristic
309	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
310	#103	C₂²×C₃×C₅	1	2	yes	—
311	#103	C₂²×C₃×C₅	1	2	yes	—
312	#103	C₂²×C₃×C₅	1	2	yes	—
313	#102	C₂²×C₃×C₅	1	2	yes	—
314	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
315	#97	C₂²×C₃×C₅	1	1	yes	characteristic
316	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₂×C₃×C₅	—	4	1	no	—
318	C₂×C₃×C₅	—	8	1	no	—
319	C₂×C₃×C₅	#535	1	1	yes	characteristic
320	C₂×C₃×C₅	#578	1	2	yes	—
321	C₂³×C₃	—	2	1	no	—
322	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
323	C₃×Q₈	—	2	2	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	2	2	no	—
326	C₃×Q₈	—	2	2	no	—
327	C₃×Q₈	—	2	2	no	—
328	C₃×Q₈	—	4	2	no	—
329	C₃×D₄	—	2	2	no	—
330	C₃×D₄	—	4	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	4	2	no	—
338	C₂×C₃×C₄	—	4	2	no	—
339	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
340	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
341	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
343	C₃×C₈	—	2	2	no	—
344	C₃×C₈	—	2	2	no	—
345	C₂²×C₅	—	2	2	no	—
346	C₂²×C₅	—	2	1	no	—
347	C₂²×C₅	—	4	2	no	—
348	C₂²×C₅	—	4	1	no	—
349	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	2	2	no	—
352	C₄×C₅	—	2	1	no	—
353	C₄×C₅	—	4	2	no	—
354	C₄×C₅	—	4	1	no	—
355	C₄×C₅	—	4	1	no	—
356	C₄×C₅	—	4	1	no	—
357	C₄×C₅	—	4	2	no	—
358	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
359	#41	—	4	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
363	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
364	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
365	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
371	Q₁₆	—	4	2	no	—
372	Q₁₆	—	4	2	no	—
373	Q₁₆	—	4	2	no	—
374	SD₁₆	—	4	2	no	—
375	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
376	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
384	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
389	C₄²	—	2	2	no	—
390	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
391	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
392	C₃×C₅	#3223	1	1	yes	characteristic, direct product factor, Hall
393	C₂²×C₃	—	2	1	no	—
394	C₂²×C₃	—	2	2	no	—
395	C₂²×C₃	—	4	1	no	—
396	C₂²×C₃	—	4	2	no	—
397	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
398	C₃×C₄	—	2	1	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	4	1	no	—
402	C₃×C₄	—	4	1	no	—
403	C₃×C₄	—	4	1	no	—
404	C₃×C₄	—	4	2	no	—
405	C₃×C₄	—	4	2	no	—
406	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
407	C₂×C₅	—	4	1	no	—
408	C₂×C₅	—	8	1	no	—
409	C₂×C₅	C₃×#535	1	1	yes	characteristic
410	C₂×C₅	C₃×#578	1	2	yes	—
411	C₂³	—	2	1	no	—
412	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
413	Q₈	—	2	2	no	—
414	Q₈	—	2	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	4	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	4	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
430	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
431	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
432	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₂×C₃	—	4	1	no	—
436	C₂×C₃	—	8	1	no	—
437	C₂×C₃	C₅×#535	1	1	yes	characteristic
438	C₂×C₃	C₅×#578	1	2	yes	—
439	C₅	C₃×#3223	1	1	yes	characteristic, direct product factor, Sylow
440	C₂²	—	2	1	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	2	no	—
444	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
454	C₃	C₅×#3223	1	1	yes	characteristic, direct product factor, Sylow
455	C₂	—	4	1	no	—
456	C₂	—	8	1	no	—
457	C₂	C₃×C₅×#535	1	1	yes	characteristic
458	C₂	C₃×C₅×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#541	C₂	semidirect
3. C₃×C₅×#497	C₂	semidirect
4. C₃×C₅×#494	C₂	semidirect
5. C₃×C₅×#491	C₂	semidirect
6. C₃×C₅×#488	C₂	semidirect
7. C₃×C₅×#464	C₂	semidirect
8. C₃×C₅×#462	C₂	semidirect
10. C₃×C₅×#451	C₂	semidirect
11. C₃×C₅×#433	C₂	semidirect
12. C₅×#3223	C₃	direct (N × H)
40. C₃×#3223	C₅	direct (N × H)
41. C₅×#541	C₂×C₃	semidirect
43. C₅×#497	C₂×C₃	semidirect
44. C₅×#494	C₂×C₃	semidirect
45. C₅×#491	C₂×C₃	semidirect
46. C₅×#488	C₂×C₃	semidirect
47. C₅×#464	C₂×C₃	semidirect
48. C₅×#462	C₂×C₃	semidirect
50. C₅×#451	C₂×C₃	semidirect
51. C₅×#433	C₂×C₃	semidirect
85. C₃×#541	C₂×C₅	semidirect
87. C₃×#497	C₂×C₅	semidirect
88. C₃×#494	C₂×C₅	semidirect
89. C₃×#491	C₂×C₅	semidirect
90. C₃×#488	C₂×C₅	semidirect
91. C₃×#464	C₂×C₅	semidirect
92. C₃×#462	C₂×C₅	semidirect
94. C₃×#451	C₂×C₅	semidirect
95. C₃×#433	C₂×C₅	semidirect
123. #3223	C₃×C₅	direct (N × H)
208. #541	C₂×C₃×C₅	semidirect
210. #497	C₂×C₃×C₅	semidirect
211. #494	C₂×C₃×C₅	semidirect
212. #491	C₂×C₃×C₅	semidirect
213. #488	C₂×C₃×C₅	semidirect
214. #464	C₂×C₃×C₅	semidirect
215. #462	C₂×C₃×C₅	semidirect
217. #451	C₂×C₃×C₅	semidirect
218. #433	C₂×C₃×C₅	semidirect
392. C₃×C₅	#3223	direct (N × H)
439. C₅	C₃×#3223	direct (N × H)
454. C₃	C₅×#3223	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#541	2
C₃×C₅×#536	2
C₃×C₅×#497	2
C₃×C₅×#494	2
C₃×C₅×#491	2
C₃×C₅×#488	2
C₃×C₅×#464	2
C₃×C₅×#462	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₅×#433	2
C₅×#3223	3
C₃×#3223	5

Subgroups — C3×C5×#3223 #14276257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3223 #14276257