Subgroups — C₃×C₅×#3222 #14276256

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 492 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×#535	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#490	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×#460	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#450	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3222	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#127	C₂²	1	1	yes	characteristic
21	C₃×C₅×#127	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, complemented
25	C₃×C₅×#124	C₂²	1	1	yes	characteristic
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₃×C₅×#121	—	2	2	no	—
29	C₃×C₅×#120	—	2	2	no	—
30	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
31	C₃×C₅×#117	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
33	C₃×C₅×#103	C₂²	1	2	yes	complemented
34	C₃×C₅×#102	C₂²	1	2	yes	—
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₃×C₅×#102	C₂²	1	2	yes	complemented
37	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3222	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#535	C₂×C₃	1	1	yes	characteristic
43	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#492	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#490	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×#460	C₂×C₃	1	2	yes	complemented
49	C₅×#452	C₂×C₃	1	2	yes	complemented
50	C₅×#450	C₂×C₃	1	2	yes	complemented
51	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂⁴×C₃×C₅	—	2	1	no	—
53	C₃×C₅×#41	—	4	2	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	—	2	1	no	—
57	C₂×C₃×C₅×D₄	—	2	1	no	—
58	C₂×C₃×C₅×D₄	—	2	2	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	4	2	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₅×Q₁₆	—	4	2	no	—
67	C₃×C₅×SD₁₆	—	4	2	no	—
68	C₃×C₅×SD₁₆	—	4	2	no	—
69	C₃×C₅×SD₁₆	—	4	2	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
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×#535	C₂×C₅	1	1	yes	characteristic
87	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#490	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×#460	C₂×C₅	1	2	yes	complemented
93	C₃×#452	C₂×C₅	1	2	yes	complemented
94	C₃×#450	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×D₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
99	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
100	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
101	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
102	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
103	C₅×#127	C₂²×C₃	1	1	yes	characteristic
104	C₅×#127	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, complemented
108	C₅×#124	C₂²×C₃	1	1	yes	characteristic
109	C₅×#124	C₂²×C₃	1	1	yes	characteristic
110	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
111	C₅×#121	—	2	2	no	—
112	C₅×#120	—	2	2	no	—
113	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
114	C₅×#117	C₂²×C₃	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
116	C₅×#103	C₂²×C₃	1	2	yes	complemented
117	C₅×#102	C₂²×C₃	1	2	yes	—
118	C₅×#102	C₂²×C₃	1	2	yes	—
119	C₅×#102	C₂²×C₃	1	2	yes	complemented
120	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
121	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
123	#3222	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
124	C₂³×C₃×C₅	—	2	1	no	—
125	C₂³×C₃×C₅	—	2	1	no	—
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	—	4	2	no	—
128	C₂³×C₃×C₅	—	8	2	no	—
129	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×Q₈	—	2	2	no	—
132	C₃×C₅×Q₈	—	2	2	no	—
133	C₃×C₅×D₄	—	2	2	no	—
134	C₃×C₅×D₄	—	2	2	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	—	4	2	no	—
137	C₃×C₅×D₄	—	4	2	no	—
138	C₃×C₅×D₄	—	8	2	no	—
139	C₃×C₅×D₄	—	8	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	4	2	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₃×C₅×C₈	—	2	2	no	—
150	C₃×C₅×C₈	—	2	2	no	—
151	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
154	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
155	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
156	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
157	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
158	C₃×#127	C₂²×C₅	1	1	yes	characteristic
159	C₃×#127	C₂²×C₅	1	1	yes	characteristic
160	C₃×#126	—	2	2	no	—
161	C₃×#125	—	2	2	no	—
162	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
163	C₃×#124	C₂²×C₅	1	1	yes	characteristic
164	C₃×#124	C₂²×C₅	1	1	yes	characteristic
165	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
166	C₃×#121	—	2	2	no	—
167	C₃×#120	—	2	2	no	—
168	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
169	C₃×#117	C₂²×C₅	1	1	yes	characteristic
170	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
171	C₃×#103	C₂²×C₅	1	2	yes	complemented
172	C₃×#102	C₂²×C₅	1	2	yes	—
173	C₃×#102	C₂²×C₅	1	2	yes	—
174	C₃×#102	C₂²×C₅	1	2	yes	complemented
175	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
176	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
177	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₂⁴×C₅	—	2	1	no	—
179	C₅×#41	—	4	2	no	—
180	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
181	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₅×D₄	—	2	1	no	—
183	C₂×C₅×D₄	—	2	1	no	—
184	C₂×C₅×D₄	—	2	2	no	—
185	C₂×C₅×D₄	—	2	2	no	—
186	C₂×C₅×D₄	—	4	2	no	—
187	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
192	C₅×Q₁₆	—	4	2	no	—
193	C₅×SD₁₆	—	4	2	no	—
194	C₅×SD₁₆	—	4	2	no	—
195	C₅×SD₁₆	—	4	2	no	—
196	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
197	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	—	2	2	no	—
200	C₅×C₄⋊C₄	—	2	2	no	—
201	C₅×C₄⋊C₄	—	2	2	no	—
202	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
203	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
204	C₅×C₂²⋊C₄	—	2	2	no	—
205	C₅×C₂²⋊C₄	—	2	2	no	—
206	C₅×C₂²⋊C₄	—	2	2	no	—
207	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
208	C₄²×C₅	—	2	2	no	—
209	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
211	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
212	#535	C₂×C₃×C₅	1	1	yes	characteristic
213	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
214	#492	C₂×C₃×C₅	1	1	yes	characteristic, complemented
215	#490	C₂×C₃×C₅	1	1	yes	characteristic, complemented
216	#488	C₂×C₃×C₅	1	1	yes	characteristic, complemented
217	#464	C₂×C₃×C₅	1	2	yes	complemented
218	#460	C₂×C₃×C₅	1	2	yes	complemented
219	#452	C₂×C₃×C₅	1	2	yes	complemented
220	#450	C₂×C₃×C₅	1	2	yes	complemented
221	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
222	C₂²×C₃×C₅	—	2	1	no	—
223	C₂²×C₃×C₅	—	2	2	no	—
224	C₂²×C₃×C₅	—	4	1	no	—
225	C₂²×C₃×C₅	—	4	1	no	—
226	C₂²×C₃×C₅	—	4	1	no	—
227	C₂²×C₃×C₅	—	4	2	no	—
228	C₂²×C₃×C₅	—	4	2	no	—
229	C₂²×C₃×C₅	—	4	2	no	—
230	C₂²×C₃×C₅	—	8	4	no	—
231	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₃×C₄×C₅	—	2	1	no	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	—	2	2	no	—
235	C₃×C₄×C₅	—	4	1	no	—
236	C₃×C₄×C₅	—	4	2	no	—
237	C₃×C₄×C₅	—	4	2	no	—
238	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
239	C₂⁴×C₃	—	2	1	no	—
240	C₃×#41	—	4	2	no	—
241	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
243	C₂×C₃×D₄	—	2	1	no	—
244	C₂×C₃×D₄	—	2	1	no	—
245	C₂×C₃×D₄	—	2	2	no	—
246	C₂×C₃×D₄	—	2	2	no	—
247	C₂×C₃×D₄	—	4	2	no	—
248	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₃×C₄	—	2	1	no	—
252	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
253	C₃×Q₁₆	—	4	2	no	—
254	C₃×SD₁₆	—	4	2	no	—
255	C₃×SD₁₆	—	4	2	no	—
256	C₃×SD₁₆	—	4	2	no	—
257	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
258	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
259	C₃×C₄⋊C₄	—	2	2	no	—
260	C₃×C₄⋊C₄	—	2	2	no	—
261	C₃×C₄⋊C₄	—	2	2	no	—
262	C₃×C₄⋊C₄	—	2	2	no	—
263	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
264	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
265	C₃×C₂²⋊C₄	—	2	2	no	—
266	C₃×C₂²⋊C₄	—	2	2	no	—
267	C₃×C₂²⋊C₄	—	2	2	no	—
268	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
269	C₃×C₄²	—	2	2	no	—
270	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
271	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	2	1	no	—
275	C₂³×C₅	—	4	2	no	—
276	C₂³×C₅	—	8	2	no	—
277	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
278	C₅×Q₈	—	2	2	no	—
279	C₅×Q₈	—	2	2	no	—
280	C₅×Q₈	—	2	2	no	—
281	C₅×D₄	—	2	2	no	—
282	C₅×D₄	—	2	2	no	—
283	C₅×D₄	—	2	2	no	—
284	C₅×D₄	—	4	2	no	—
285	C₅×D₄	—	4	2	no	—
286	C₅×D₄	—	8	2	no	—
287	C₅×D₄	—	8	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	4	2	no	—
293	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
294	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
295	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
297	C₅×C₈	—	2	2	no	—
298	C₅×C₈	—	2	2	no	—
299	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
300	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
301	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	complemented
302	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
303	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
304	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
305	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
306	#127	C₂²×C₃×C₅	1	1	yes	characteristic
307	#127	C₂²×C₃×C₅	1	1	yes	characteristic
308	#126	—	2	2	no	—
309	#125	—	2	2	no	—
310	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
311	#124	C₂²×C₃×C₅	1	1	yes	characteristic
312	#124	C₂²×C₃×C₅	1	1	yes	characteristic
313	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
314	#121	—	2	2	no	—
315	#120	—	2	2	no	—
316	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
317	#117	C₂²×C₃×C₅	1	1	yes	characteristic
318	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
319	#103	C₂²×C₃×C₅	1	2	yes	complemented
320	#102	C₂²×C₃×C₅	1	2	yes	—
321	#102	C₂²×C₃×C₅	1	2	yes	—
322	#102	C₂²×C₃×C₅	1	2	yes	complemented
323	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
324	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
325	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
326	C₂×C₃×C₅	—	4	1	no	—
327	C₂×C₃×C₅	—	8	1	no	—
328	C₂×C₃×C₅	—	8	1	no	—
329	C₂×C₃×C₅	—	8	1	no	—
330	C₂×C₃×C₅	#535	1	1	yes	characteristic
331	C₂×C₃×C₅	#577	1	2	yes	—
332	C₂³×C₃	—	2	1	no	—
333	C₂³×C₃	—	2	1	no	—
334	C₂³×C₃	—	2	1	no	—
335	C₂³×C₃	—	4	2	no	—
336	C₂³×C₃	—	8	2	no	—
337	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
338	C₃×Q₈	—	2	2	no	—
339	C₃×Q₈	—	2	2	no	—
340	C₃×Q₈	—	2	2	no	—
341	C₃×D₄	—	2	2	no	—
342	C₃×D₄	—	2	2	no	—
343	C₃×D₄	—	2	2	no	—
344	C₃×D₄	—	4	2	no	—
345	C₃×D₄	—	4	2	no	—
346	C₃×D₄	—	8	2	no	—
347	C₃×D₄	—	8	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	4	2	no	—
353	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
354	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
355	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
357	C₃×C₈	—	2	2	no	—
358	C₃×C₈	—	2	2	no	—
359	C₂²×C₅	—	2	2	no	—
360	C₂²×C₅	—	2	1	no	—
361	C₂²×C₅	—	4	2	no	—
362	C₂²×C₅	—	4	2	no	—
363	C₂²×C₅	—	4	2	no	—
364	C₂²×C₅	—	4	1	no	—
365	C₂²×C₅	—	4	1	no	—
366	C₂²×C₅	—	4	1	no	—
367	C₂²×C₅	—	8	4	no	—
368	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
369	C₄×C₅	—	2	2	no	—
370	C₄×C₅	—	2	2	no	—
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	4	2	no	—
373	C₄×C₅	—	4	1	no	—
374	C₄×C₅	—	4	2	no	—
375	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
376	C₂⁴	—	2	1	no	—
377	#41	—	4	2	no	—
378	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
379	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
386	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
387	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
390	Q₁₆	—	4	2	no	—
391	SD₁₆	—	4	2	no	—
392	SD₁₆	—	4	2	no	—
393	SD₁₆	—	4	2	no	—
394	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
395	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
401	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
406	C₄²	—	2	2	no	—
407	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
408	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
409	C₃×C₅	#3222	1	1	yes	characteristic, direct product factor, Hall
410	C₂²×C₃	—	2	1	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	4	1	no	—
413	C₂²×C₃	—	4	1	no	—
414	C₂²×C₃	—	4	1	no	—
415	C₂²×C₃	—	4	2	no	—
416	C₂²×C₃	—	4	2	no	—
417	C₂²×C₃	—	4	2	no	—
418	C₂²×C₃	—	8	4	no	—
419	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
420	C₃×C₄	—	2	1	no	—
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	2	2	no	—
423	C₃×C₄	—	4	1	no	—
424	C₃×C₄	—	4	2	no	—
425	C₃×C₄	—	4	2	no	—
426	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
427	C₂×C₅	—	4	1	no	—
428	C₂×C₅	—	8	1	no	—
429	C₂×C₅	—	8	1	no	—
430	C₂×C₅	—	8	1	no	—
431	C₂×C₅	C₃×#535	1	1	yes	characteristic
432	C₂×C₅	C₃×#577	1	2	yes	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	8	2	no	—
438	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
439	Q₈	—	2	2	no	—
440	Q₈	—	2	2	no	—
441	Q₈	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	8	2	no	—
448	D₄	—	8	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
455	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
456	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
457	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
458	C₈	—	2	2	no	—
459	C₈	—	2	2	no	—
460	C₂×C₃	—	4	1	no	—
461	C₂×C₃	—	8	1	no	—
462	C₂×C₃	—	8	1	no	—
463	C₂×C₃	—	8	1	no	—
464	C₂×C₃	C₅×#535	1	1	yes	characteristic
465	C₂×C₃	C₅×#577	1	2	yes	—
466	C₅	C₃×#3222	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²	—	2	1	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	8	4	no	—
476	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
484	C₃	C₅×#3222	1	1	yes	characteristic, direct product factor, Sylow
485	C₂	—	4	1	no	—
486	C₂	—	8	1	no	—
487	C₂	—	8	1	no	—
488	C₂	—	8	1	no	—
489	C₂	C₃×C₅×#535	1	1	yes	characteristic
490	C₂	C₃×C₅×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#535	C₂
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×#492	C₂	semidirect
5. C₃×C₅×#490	C₂	semidirect
6. C₃×C₅×#488	C₂	semidirect
7. C₃×C₅×#464	C₂	semidirect
8. C₃×C₅×#460	C₂	semidirect
9. C₃×C₅×#452	C₂	semidirect
10. C₃×C₅×#450	C₂	semidirect
11. C₃×C₅×#433	C₂	semidirect
12. C₅×#3222	C₃	direct (N × H)
15. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
18. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
24. C₃×C₅×#125	C₂²	semidirect
30. C₃×C₄×C₅×Q₈	C₂²	semidirect
32. C₃×C₅×C₄⋊C₈	C₂²	semidirect
33. C₃×C₅×#103	C₂²	semidirect
36. C₃×C₅×#102	C₂²	semidirect
38. C₃×C₅×#97	C₂²	semidirect
39. C₃×C₄×C₅×C₈	C₂²	semidirect
40. C₃×#3222	C₅	direct (N × H)
41. C₅×#541	C₂×C₃	semidirect
43. C₅×#497	C₂×C₃	semidirect
44. C₅×#492	C₂×C₃	semidirect
45. C₅×#490	C₂×C₃	semidirect
46. C₅×#488	C₂×C₃	semidirect
47. C₅×#464	C₂×C₃	semidirect
48. C₅×#460	C₂×C₃	semidirect
49. C₅×#452	C₂×C₃	semidirect
50. C₅×#450	C₂×C₃	semidirect
51. C₅×#433	C₂×C₃	semidirect
85. C₃×#541	C₂×C₅	semidirect
87. C₃×#497	C₂×C₅	semidirect
88. C₃×#492	C₂×C₅	semidirect
89. C₃×#490	C₂×C₅	semidirect
90. C₃×#488	C₂×C₅	semidirect
91. C₃×#464	C₂×C₅	semidirect
92. C₃×#460	C₂×C₅	semidirect
93. C₃×#452	C₂×C₅	semidirect
94. C₃×#450	C₂×C₅	semidirect
95. C₃×#433	C₂×C₅	semidirect
98. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
101. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
102. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
107. C₅×#125	C₂²×C₃	semidirect
113. C₄×C₅×Q₈	C₂²×C₃	semidirect
115. C₅×C₄⋊C₈	C₂²×C₃	semidirect
116. C₅×#103	C₂²×C₃	semidirect
119. C₅×#102	C₂²×C₃	semidirect
121. C₅×#97	C₂²×C₃	semidirect
122. C₄×C₅×C₈	C₂²×C₃	semidirect
123. #3222	C₃×C₅	direct (N × H)
153. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
156. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
157. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
162. C₃×#125	C₂²×C₅	semidirect
168. C₃×C₄×Q₈	C₂²×C₅	semidirect
170. C₃×C₄⋊C₈	C₂²×C₅	semidirect
171. C₃×#103	C₂²×C₅	semidirect
174. C₃×#102	C₂²×C₅	semidirect
176. C₃×#97	C₂²×C₅	semidirect
177. C₃×C₄×C₈	C₂²×C₅	semidirect
211. #541	C₂×C₃×C₅	semidirect
213. #497	C₂×C₃×C₅	semidirect
214. #492	C₂×C₃×C₅	semidirect
215. #490	C₂×C₃×C₅	semidirect
216. #488	C₂×C₃×C₅	semidirect
217. #464	C₂×C₃×C₅	semidirect
218. #460	C₂×C₃×C₅	semidirect
219. #452	C₂×C₃×C₅	semidirect
220. #450	C₂×C₃×C₅	semidirect
221. #433	C₂×C₃×C₅	semidirect
301. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
304. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
305. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
310. #125	C₂²×C₃×C₅	semidirect
316. C₄×Q₈	C₂²×C₃×C₅	semidirect
318. C₄⋊C₈	C₂²×C₃×C₅	semidirect
319. #103	C₂²×C₃×C₅	semidirect
322. #102	C₂²×C₃×C₅	semidirect
324. #97	C₂²×C₃×C₅	semidirect
325. C₄×C₈	C₂²×C₃×C₅	semidirect
409. C₃×C₅	#3222	direct (N × H)
466. C₅	C₃×#3222	direct (N × H)
484. C₃	C₅×#3222	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×#535	2
C₃×C₅×#497	2
C₃×C₅×#492	2
C₃×C₅×#490	2
C₃×C₅×#488	2
C₃×C₅×#464	2
C₃×C₅×#460	2
C₃×C₅×#452	2
C₃×C₅×#450	2
C₃×C₅×#433	2
C₅×#3222	3
C₃×#3222	5

Subgroups — C3×C5×#3222 #14276256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3222 #14276256