Subgroups — C₃×C₅×#3295 #14276329

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₄²	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#481	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#450	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal, complemented
12	C₅×#3295	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×D₄	—	2	1	no	—
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic
20	C₃×C₅×#125	—	2	1	no	—
21	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
23	C₃×C₅×#121	—	2	1	no	—
24	C₃×C₅×#121	C₂²	1	2	yes	—
25	C₃×C₅×#120	—	2	2	no	—
26	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₄×C₅×D₄	—	2	1	no	—
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₃×C₅×#106	C₂²	1	2	yes	complemented
32	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₃×C₅×#102	C₂²	1	1	yes	characteristic
37	C₃×C₅×#102	C₂²	1	2	yes	complemented
38	C₃×C₅×#102	C₂²	1	2	yes	complemented
39	C₃×C₅×#102	C₂²	1	2	yes	complemented
40	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
42	C₃×#3295	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#554	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×D₄²	C₂×C₃	1	1	yes	characteristic
45	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#481	C₂×C₃	1	2	yes	complemented
47	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#465	C₂×C₃	1	2	yes	complemented
49	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#450	C₂×C₃	1	2	yes	complemented
51	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₅×#102	C₂×C₃	1	2	yes	complemented
54	C₂⁴×C₃×C₅	—	2	2	no	—
55	C₂×C₃×C₅×Q₈	—	2	1	no	—
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	—	2	4	no	—
58	C₂×C₃×C₅×D₄	—	2	2	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	4	2	no	—
63	C₂×C₃×C₅×D₄	—	4	4	no	—
64	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
65	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
66	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	—	2	2	no	—
68	C₂²×C₃×C₄×C₅	—	2	1	no	—
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₃×C₅×SD₁₆	—	2	2	no	—
71	C₃×C₅×SD₁₆	—	4	2	no	—
72	C₂×C₃×C₅×C₈	—	4	2	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
75	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	—	2	2	no	—
80	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
88	C₃×C₄²×C₅	—	2	1	no	—
89	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×D₄²	C₂×C₅	1	1	yes	characteristic
92	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
93	C₃×#481	C₂×C₅	1	2	yes	complemented
94	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×#465	C₂×C₅	1	2	yes	complemented
96	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#450	C₂×C₅	1	2	yes	complemented
98	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×C₃×#102	C₂×C₅	1	2	yes	complemented
101	C₂²×C₅×D₄	—	2	1	no	—
102	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
103	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
105	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
106	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₅×#127	C₂²×C₃	1	1	yes	characteristic
108	C₅×#125	—	2	1	no	—
109	C₅×C₂²⋊Q₈	—	2	2	no	—
110	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
111	C₅×#121	—	2	1	no	—
112	C₅×#121	C₂²×C₃	1	2	yes	—
113	C₅×#120	—	2	2	no	—
114	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₄×C₅×D₄	—	2	1	no	—
116	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
119	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₅×#106	C₂²×C₃	1	2	yes	complemented
121	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₅×#102	C₂²×C₃	1	1	yes	characteristic
124	C₅×#102	C₂²×C₃	1	2	yes	—
125	C₅×#102	C₂²×C₃	1	2	yes	complemented
126	C₅×#102	C₂²×C₃	1	2	yes	complemented
127	C₅×#102	C₂²×C₃	1	2	yes	complemented
128	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
129	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
130	#3295	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	—	2	2	no	—
133	C₂³×C₃×C₅	—	4	4	no	—
134	C₂³×C₃×C₅	—	4	4	no	—
135	C₂³×C₃×C₅	—	8	2	no	—
136	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
137	C₃×C₅×Q₈	—	2	1	no	—
138	C₃×C₅×Q₈	—	2	1	no	—
139	C₃×C₅×Q₈	—	8	1	no	—
140	C₃×C₅×D₄	—	2	2	no	—
141	C₃×C₅×D₄	—	2	1	no	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	—	4	4	no	—
144	C₃×C₅×D₄	—	4	4	no	—
145	C₃×C₅×D₄	—	4	2	no	—
146	C₃×C₅×D₄	—	8	1	no	—
147	C₃×C₅×D₄	SD₁₆	1	4	yes	complemented
148	C₃×C₅×D₄	#41	1	2	yes	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	4	2	no	—
156	C₂×C₃×C₄×C₅	—	8	2	no	—
157	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃×C₅×C₈	—	2	1	no	—
163	C₃×C₅×C₈	—	2	2	no	—
164	C₂²×C₃×D₄	—	2	1	no	—
165	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
166	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
168	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
169	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
170	C₃×#127	C₂²×C₅	1	1	yes	characteristic
171	C₃×#125	—	2	1	no	—
172	C₃×C₂²⋊Q₈	—	2	2	no	—
173	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
174	C₃×#121	—	2	1	no	—
175	C₃×#121	C₂²×C₅	1	2	yes	—
176	C₃×#120	—	2	2	no	—
177	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₃×C₄×D₄	—	2	1	no	—
179	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
180	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
182	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₃×#106	C₂²×C₅	1	2	yes	complemented
184	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
185	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
186	C₃×#102	C₂²×C₅	1	1	yes	characteristic
187	C₃×#102	C₂²×C₅	1	2	yes	—
188	C₃×#102	C₂²×C₅	1	2	yes	complemented
189	C₃×#102	C₂²×C₅	1	2	yes	complemented
190	C₃×#102	C₂²×C₅	1	2	yes	complemented
191	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
192	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₂⁴×C₅	—	2	2	no	—
194	C₂×C₅×Q₈	—	2	1	no	—
195	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₅×D₄	—	2	4	no	—
197	C₂×C₅×D₄	—	2	2	no	—
198	C₂×C₅×D₄	—	2	2	no	—
199	C₂×C₅×D₄	—	2	1	no	—
200	C₂×C₅×D₄	—	2	1	no	—
201	C₂×C₅×D₄	—	4	2	no	—
202	C₂×C₅×D₄	—	4	4	no	—
203	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
204	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
205	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
206	C₂²×C₄×C₅	—	2	2	no	—
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
209	C₅×SD₁₆	—	2	2	no	—
210	C₅×SD₁₆	—	4	2	no	—
211	C₂×C₅×C₈	—	4	2	no	—
212	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
213	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
214	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
215	C₅×C₄⋊C₄	—	2	2	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	2	no	—
219	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
221	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
222	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
223	C₅×C₂²⋊C₄	—	2	2	no	—
224	C₅×C₂²⋊C₄	—	2	1	no	—
225	C₅×C₂²⋊C₄	—	2	2	no	—
226	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
229	#554	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	D₄²	C₂×C₃×C₅	1	1	yes	characteristic
231	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	#481	C₂×C₃×C₅	1	2	yes	complemented
233	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
234	#465	C₂×C₃×C₅	1	2	yes	complemented
235	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
236	#450	C₂×C₃×C₅	1	2	yes	complemented
237	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
239	C₂×#102	C₂×C₃×C₅	1	2	yes	complemented
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	2	2	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	—	4	2	no	—
247	C₂²×C₃×C₅	—	4	2	no	—
248	C₂²×C₃×C₅	—	8	8	no	—
249	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	—
250	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	—	2	1	no	—
253	C₃×C₄×C₅	—	4	1	no	—
254	C₃×C₄×C₅	—	4	1	no	—
255	C₃×C₄×C₅	—	4	1	no	—
256	C₃×C₄×C₅	—	4	2	no	—
257	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
258	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
259	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂⁴×C₃	—	2	2	no	—
261	C₂×C₃×Q₈	—	2	1	no	—
262	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₃×D₄	—	2	4	no	—
264	C₂×C₃×D₄	—	2	2	no	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	—	2	1	no	—
267	C₂×C₃×D₄	—	2	1	no	—
268	C₂×C₃×D₄	—	4	2	no	—
269	C₂×C₃×D₄	—	4	4	no	—
270	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
271	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
272	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
273	C₂²×C₃×C₄	—	2	2	no	—
274	C₂²×C₃×C₄	—	2	1	no	—
275	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
276	C₃×SD₁₆	—	2	2	no	—
277	C₃×SD₁₆	—	4	2	no	—
278	C₂×C₃×C₈	—	4	2	no	—
279	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
281	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
282	C₃×C₄⋊C₄	—	2	2	no	—
283	C₃×C₄⋊C₄	—	2	1	no	—
284	C₃×C₄⋊C₄	—	2	1	no	—
285	C₃×C₄⋊C₄	—	2	2	no	—
286	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
287	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
288	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
289	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
290	C₃×C₂²⋊C₄	—	2	2	no	—
291	C₃×C₂²⋊C₄	—	2	1	no	—
292	C₃×C₂²⋊C₄	—	2	2	no	—
293	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
294	C₃×C₄²	—	2	1	no	—
295	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	4	4	no	—
299	C₂³×C₅	—	4	4	no	—
300	C₂³×C₅	—	8	2	no	—
301	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
302	C₅×Q₈	—	2	1	no	—
303	C₅×Q₈	—	2	1	no	—
304	C₅×Q₈	—	8	1	no	—
305	C₅×D₄	—	2	2	no	—
306	C₅×D₄	—	2	1	no	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	4	4	no	—
309	C₅×D₄	—	4	4	no	—
310	C₅×D₄	—	4	2	no	—
311	C₅×D₄	—	8	1	no	—
312	C₅×D₄	C₃×SD₁₆	1	4	yes	complemented
313	C₅×D₄	C₃×#41	1	2	yes	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	4	2	no	—
321	C₂×C₄×C₅	—	8	2	no	—
322	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
324	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	2	1	no	—
328	C₅×C₈	—	2	2	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
331	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
332	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
333	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	complemented
334	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
335	#127	C₂²×C₃×C₅	1	1	yes	characteristic
336	#125	—	2	1	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
339	#121	—	2	1	no	—
340	#121	C₂²×C₃×C₅	1	2	yes	—
341	#120	—	2	2	no	—
342	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
345	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
347	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
348	#106	C₂²×C₃×C₅	1	2	yes	complemented
349	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
350	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
351	#102	C₂²×C₃×C₅	1	1	yes	characteristic
352	#102	C₂²×C₃×C₅	1	2	yes	—
353	#102	C₂²×C₃×C₅	1	2	yes	complemented
354	#102	C₂²×C₃×C₅	1	2	yes	complemented
355	#102	C₂²×C₃×C₅	1	2	yes	complemented
356	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
357	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
358	C₂×C₃×C₅	—	2	4	no	—
359	C₂×C₃×C₅	—	4	2	no	—
360	C₂×C₃×C₅	—	8	2	no	—
361	C₂×C₃×C₅	#546	1	1	yes	characteristic
362	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
363	C₂×C₃×C₅	#576	1	1	yes	characteristic
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	2	2	no	—
366	C₂³×C₃	—	4	4	no	—
367	C₂³×C₃	—	4	4	no	—
368	C₂³×C₃	—	8	2	no	—
369	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
370	C₃×Q₈	—	2	1	no	—
371	C₃×Q₈	—	2	1	no	—
372	C₃×Q₈	—	8	1	no	—
373	C₃×D₄	—	2	2	no	—
374	C₃×D₄	—	2	1	no	—
375	C₃×D₄	—	2	2	no	—
376	C₃×D₄	—	4	4	no	—
377	C₃×D₄	—	4	4	no	—
378	C₃×D₄	—	4	2	no	—
379	C₃×D₄	—	8	1	no	—
380	C₃×D₄	C₅×SD₁₆	1	4	yes	complemented
381	C₃×D₄	C₅×#41	1	2	yes	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	4	2	no	—
389	C₂×C₃×C₄	—	8	2	no	—
390	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
392	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
394	C₃×C₈	—	2	1	no	—
395	C₃×C₈	—	2	1	no	—
396	C₃×C₈	—	2	2	no	—
397	C₂²×C₅	—	2	2	no	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	—	4	2	no	—
403	C₂²×C₅	—	4	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	8	8	no	—
406	C₂²×C₅	C₂×C₃×SD₁₆	1	4	yes	—
407	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	4	1	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	2	no	—
413	C₄×C₅	—	4	1	no	—
414	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
415	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
416	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂⁴	—	2	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	—	4	4	no	—
427	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
428	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
429	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
433	SD₁₆	—	2	2	no	—
434	SD₁₆	—	4	2	no	—
435	C₂×C₈	—	4	2	no	—
436	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
437	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
438	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
444	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
445	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
446	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
451	C₄²	—	2	1	no	—
452	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
453	C₃×C₅	#3295	1	1	yes	characteristic, direct product factor, Hall
454	C₂²×C₃	—	2	2	no	—
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	2	2	no	—
457	C₂²×C₃	—	4	1	no	—
458	C₂²×C₃	—	4	1	no	—
459	C₂²×C₃	—	4	2	no	—
460	C₂²×C₃	—	4	2	no	—
461	C₂²×C₃	—	4	2	no	—
462	C₂²×C₃	—	8	8	no	—
463	C₂²×C₃	C₂×C₅×SD₁₆	1	4	yes	—
464	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
465	C₃×C₄	—	2	2	no	—
466	C₃×C₄	—	2	1	no	—
467	C₃×C₄	—	4	1	no	—
468	C₃×C₄	—	4	1	no	—
469	C₃×C₄	—	4	1	no	—
470	C₃×C₄	—	4	2	no	—
471	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
472	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
473	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂×C₅	—	2	4	no	—
475	C₂×C₅	—	4	2	no	—
476	C₂×C₅	—	8	2	no	—
477	C₂×C₅	C₃×#546	1	1	yes	characteristic
478	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
479	C₂×C₅	C₃×#576	1	1	yes	characteristic
480	C₂³	—	2	1	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	4	4	no	—
483	C₂³	—	4	4	no	—
484	C₂³	—	8	2	no	—
485	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	8	1	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	1	no	—
491	D₄	—	2	2	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	2	no	—
495	D₄	—	8	1	no	—
496	D₄	C₃×C₅×SD₁₆	1	4	yes	complemented
497	D₄	C₃×C₅×#41	1	2	yes	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
507	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
508	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
509	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	2	2	no	—
513	C₂×C₃	—	2	4	no	—
514	C₂×C₃	—	4	2	no	—
515	C₂×C₃	—	8	2	no	—
516	C₂×C₃	C₅×#546	1	1	yes	characteristic
517	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
518	C₂×C₃	C₅×#576	1	1	yes	characteristic
519	C₅	C₃×#3295	1	1	yes	characteristic, direct product factor, Sylow
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	8	8	no	—
529	C₂²	C₂×C₃×C₅×SD₁₆	1	4	yes	—
530	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
531	C₄	—	2	2	no	—
532	C₄	—	2	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	2	no	—
537	C₄	C₂×C₃×C₅×SD₁₆	1	2	yes	—
538	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
539	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
540	C₃	C₅×#3295	1	1	yes	characteristic, direct product factor, Sylow
541	C₂	—	2	4	no	—
542	C₂	—	4	2	no	—
543	C₂	—	8	2	no	—
544	C₂	C₃×C₅×#546	1	1	yes	characteristic
545	C₂	C₂²×C₃×C₅×SD₁₆	1	1	yes	characteristic
546	C₂	C₃×C₅×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×D₄²	C₂
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. C₃×C₅×#554	C₂	semidirect
3. C₃×C₅×#486	C₂	semidirect
4. C₃×C₅×#481	C₂	semidirect
5. C₃×C₅×#476	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#460	C₂	semidirect
8. C₃×C₅×#450	C₂	semidirect
9. C₃×C₄×C₅×SD₁₆	C₂	semidirect
10. C₃×C₅×C₈×D₄	C₂	semidirect
11. C₂×C₃×C₅×#102	C₂	semidirect
12. C₅×#3295	C₃	direct (N × H)
16. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
17. C₂²×C₃×C₅×C₈	C₂²	semidirect
18. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
22. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
26. C₃×C₄×C₅×Q₈	C₂²	semidirect
30. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
31. C₃×C₅×#106	C₂²	semidirect
32. C₃×C₅×#106	C₂²	semidirect
33. C₃×C₅×C₄⋊C₈	C₂²	semidirect
34. C₃×C₅×#103	C₂²	semidirect
37. C₃×C₅×#102	C₂²	semidirect
38. C₃×C₅×#102	C₂²	semidirect
39. C₃×C₅×#102	C₂²	semidirect
40. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
41. C₃×C₄×C₅×C₈	C₂²	semidirect
42. C₃×#3295	C₅	direct (N × H)
43. C₅×#554	C₂×C₃	semidirect
45. C₅×#486	C₂×C₃	semidirect
46. C₅×#481	C₂×C₃	semidirect
47. C₅×#476	C₂×C₃	semidirect
48. C₅×#465	C₂×C₃	semidirect
49. C₅×#460	C₂×C₃	semidirect
50. C₅×#450	C₂×C₃	semidirect
51. C₄×C₅×SD₁₆	C₂×C₃	semidirect
52. C₅×C₈×D₄	C₂×C₃	semidirect
53. C₂×C₅×#102	C₂×C₃	semidirect
90. C₃×#554	C₂×C₅	semidirect
92. C₃×#486	C₂×C₅	semidirect
93. C₃×#481	C₂×C₅	semidirect
94. C₃×#476	C₂×C₅	semidirect
95. C₃×#465	C₂×C₅	semidirect
96. C₃×#460	C₂×C₅	semidirect
97. C₃×#450	C₂×C₅	semidirect
98. C₃×C₄×SD₁₆	C₂×C₅	semidirect
99. C₃×C₈×D₄	C₂×C₅	semidirect
100. C₂×C₃×#102	C₂×C₅	semidirect
104. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
105. C₂²×C₅×C₈	C₂²×C₃	semidirect
106. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
110. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
114. C₄×C₅×Q₈	C₂²×C₃	semidirect
118. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
119. C₅×#106	C₂²×C₃	semidirect
120. C₅×#106	C₂²×C₃	semidirect
121. C₅×C₄⋊C₈	C₂²×C₃	semidirect
122. C₅×#103	C₂²×C₃	semidirect
125. C₅×#102	C₂²×C₃	semidirect
126. C₅×#102	C₂²×C₃	semidirect
127. C₅×#102	C₂²×C₃	semidirect
128. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
129. C₄×C₅×C₈	C₂²×C₃	semidirect
130. #3295	C₃×C₅	direct (N × H)
147. C₃×C₅×D₄	SD₁₆	semidirect
167. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
168. C₂²×C₃×C₈	C₂²×C₅	semidirect
169. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
173. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
177. C₃×C₄×Q₈	C₂²×C₅	semidirect
181. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
182. C₃×#106	C₂²×C₅	semidirect
183. C₃×#106	C₂²×C₅	semidirect
184. C₃×C₄⋊C₈	C₂²×C₅	semidirect
185. C₃×#103	C₂²×C₅	semidirect
188. C₃×#102	C₂²×C₅	semidirect
189. C₃×#102	C₂²×C₅	semidirect
190. C₃×#102	C₂²×C₅	semidirect
191. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
192. C₃×C₄×C₈	C₂²×C₅	semidirect
229. #554	C₂×C₃×C₅	semidirect
231. #486	C₂×C₃×C₅	semidirect
232. #481	C₂×C₃×C₅	semidirect
233. #476	C₂×C₃×C₅	semidirect
234. #465	C₂×C₃×C₅	semidirect
235. #460	C₂×C₃×C₅	semidirect
236. #450	C₂×C₃×C₅	semidirect
237. C₄×SD₁₆	C₂×C₃×C₅	semidirect
238. C₈×D₄	C₂×C₃×C₅	semidirect
239. C₂×#102	C₂×C₃×C₅	semidirect
312. C₅×D₄	C₃×SD₁₆	semidirect
332. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
333. C₂²×C₈	C₂²×C₃×C₅	semidirect
334. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
338. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
342. C₄×Q₈	C₂²×C₃×C₅	semidirect
346. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
347. #106	C₂²×C₃×C₅	semidirect
348. #106	C₂²×C₃×C₅	semidirect
349. C₄⋊C₈	C₂²×C₃×C₅	semidirect
350. #103	C₂²×C₃×C₅	semidirect
353. #102	C₂²×C₃×C₅	semidirect
354. #102	C₂²×C₃×C₅	semidirect
355. #102	C₂²×C₃×C₅	semidirect
356. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
357. C₄×C₈	C₂²×C₃×C₅	semidirect
380. C₃×D₄	C₅×SD₁₆	semidirect
453. C₃×C₅	#3295	direct (N × H)
496. D₄	C₃×C₅×SD₁₆	semidirect
519. C₅	C₃×#3295	direct (N × H)
540. C₃	C₅×#3295	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×#554	2
C₃×C₅×D₄²	2
C₃×C₅×#486	2
C₃×C₅×#481	2
C₃×C₅×#476	2
C₃×C₅×#465	2
C₃×C₅×#460	2
C₃×C₅×#450	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×C₈×D₄	2
C₂×C₃×C₅×#102	2
C₅×#3295	3
C₃×#3295	5

Subgroups — C3×C5×#3295 #14276329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3295 #14276329