Subgroups — C₃×C₅×#3204 #14276238

Order 1920.

804 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#537	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#483	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#481	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3204	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
19	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₃×C₅×#121	—	2	2	no	—
22	C₃×C₅×#121	—	2	2	no	—
23	C₃×C₅×#121	—	2	2	no	—
24	C₃×C₅×#121	C₂²	1	2	yes	—
25	C₃×C₅×#121	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
27	C₃×C₅×#106	C₂²	1	2	yes	—
28	C₃×C₅×#106	C₂²	1	1	yes	characteristic
29	C₃×C₅×#106	C₂²	1	1	yes	characteristic
30	C₃×C₅×#103	C₂²	1	2	yes	—
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₅×#102	C₂²	1	2	yes	—
33	C₃×C₅×#102	C₂²	1	2	yes	—
34	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₃×#3204	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#537	C₂×C₃	1	2	yes	complemented
38	C₅×#483	C₂×C₃	1	2	yes	complemented
39	C₅×#481	C₂×C₃	1	2	yes	complemented
40	C₅×#470	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#469	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#465	C₂×C₃	1	2	yes	complemented
43	C₅×#452	C₂×C₃	1	2	yes	complemented
44	C₅×#449	C₂×C₃	1	2	yes	complemented
45	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×C₅×#41	—	4	1	no	—
47	C₃×C₅×#41	—	4	1	no	—
48	C₃×C₅×#41	—	4	2	no	—
49	C₃×C₅×#41	—	4	2	no	—
50	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
51	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	—	2	2	no	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	—	2	2	no	—
59	C₂²×C₃×C₄×C₅	—	2	2	no	—
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₃×C₅×Q₁₆	—	4	1	no	—
63	C₃×C₅×SD₁₆	—	4	2	no	—
64	C₃×C₅×D₈	—	4	1	no	—
65	C₃×C₅×M₁₆	—	4	1	no	—
66	C₂×C₃×C₅×C₈	—	4	1	no	—
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
74	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×#537	C₂×C₅	1	2	yes	complemented
80	C₃×#483	C₂×C₅	1	2	yes	complemented
81	C₃×#481	C₂×C₅	1	2	yes	complemented
82	C₃×#470	C₂×C₅	1	1	yes	characteristic, complemented
83	C₃×#469	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#465	C₂×C₅	1	2	yes	complemented
85	C₃×#452	C₂×C₅	1	2	yes	complemented
86	C₃×#449	C₂×C₅	1	2	yes	complemented
87	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
89	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
92	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
95	C₅×C₂²⋊Q₈	—	2	2	no	—
96	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
97	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
98	C₅×#121	—	2	2	no	—
99	C₅×#121	—	2	2	no	—
100	C₅×#121	—	2	2	no	—
101	C₅×#121	C₂²×C₃	1	2	yes	—
102	C₅×#121	C₂²×C₃	1	2	yes	—
103	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
104	C₅×#106	C₂²×C₃	1	2	yes	—
105	C₅×#106	C₂²×C₃	1	1	yes	characteristic
106	C₅×#106	C₂²×C₃	1	1	yes	characteristic
107	C₅×#103	C₂²×C₃	1	2	yes	—
108	C₅×#103	C₂²×C₃	1	2	yes	—
109	C₅×#102	C₂²×C₃	1	2	yes	—
110	C₅×#102	C₂²×C₃	1	2	yes	—
111	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
112	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
113	#3204	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
117	C₃×C₅×Q₈	—	2	2	no	—
118	C₃×C₅×Q₈	—	2	2	no	—
119	C₃×C₅×Q₈	—	4	1	no	—
120	C₃×C₅×D₄	—	2	2	no	—
121	C₃×C₅×D₄	—	2	2	no	—
122	C₃×C₅×D₄	—	4	2	no	—
123	C₃×C₅×D₄	—	4	1	no	—
124	C₃×C₅×D₄	—	4	4	no	—
125	C₃×C₅×D₄	—	8	2	no	—
126	C₃×C₅×D₄	—	8	2	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	—	2	1	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	4	4	no	—
135	C₂×C₃×C₄×C₅	—	8	2	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₃×C₅×C₈	—	2	2	no	—
140	C₃×C₅×C₈	—	2	1	no	—
141	C₃×C₅×C₈	—	2	1	no	—
142	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
143	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
146	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
148	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
149	C₃×C₂²⋊Q₈	—	2	2	no	—
150	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
151	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
152	C₃×#121	—	2	2	no	—
153	C₃×#121	—	2	2	no	—
154	C₃×#121	—	2	2	no	—
155	C₃×#121	C₂²×C₅	1	2	yes	—
156	C₃×#121	C₂²×C₅	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
158	C₃×#106	C₂²×C₅	1	2	yes	—
159	C₃×#106	C₂²×C₅	1	1	yes	characteristic
160	C₃×#106	C₂²×C₅	1	1	yes	characteristic
161	C₃×#103	C₂²×C₅	1	2	yes	—
162	C₃×#103	C₂²×C₅	1	2	yes	—
163	C₃×#102	C₂²×C₅	1	2	yes	—
164	C₃×#102	C₂²×C₅	1	2	yes	—
165	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
166	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
167	C₅×#41	—	4	1	no	—
168	C₅×#41	—	4	1	no	—
169	C₅×#41	—	4	2	no	—
170	C₅×#41	—	4	2	no	—
171	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
172	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
173	C₂×C₅×D₄	—	2	2	no	—
174	C₂×C₅×D₄	—	2	2	no	—
175	C₂×C₅×D₄	—	2	2	no	—
176	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
177	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
178	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
179	C₂²×C₄×C₅	—	2	2	no	—
180	C₂²×C₄×C₅	—	2	2	no	—
181	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
182	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
183	C₅×Q₁₆	—	4	1	no	—
184	C₅×SD₁₆	—	4	2	no	—
185	C₅×D₈	—	4	1	no	—
186	C₅×M₁₆	—	4	1	no	—
187	C₂×C₅×C₈	—	4	1	no	—
188	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
189	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
195	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	2	2	no	—
198	C₅×C₂²⋊C₄	—	2	2	no	—
199	C₅×C₂²⋊C₄	—	2	2	no	—
200	#537	C₂×C₃×C₅	1	2	yes	complemented
201	#483	C₂×C₃×C₅	1	2	yes	complemented
202	#481	C₂×C₃×C₅	1	2	yes	complemented
203	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
204	#469	C₂×C₃×C₅	1	1	yes	characteristic, complemented
205	#465	C₂×C₃×C₅	1	2	yes	complemented
206	#452	C₂×C₃×C₅	1	2	yes	complemented
207	#449	C₂×C₃×C₅	1	2	yes	complemented
208	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	1	no	—
211	C₂²×C₃×C₅	—	2	2	no	—
212	C₂²×C₃×C₅	—	2	2	no	—
213	C₂²×C₃×C₅	—	2	2	no	—
214	C₂²×C₃×C₅	—	4	2	no	—
215	C₂²×C₃×C₅	—	4	2	no	—
216	C₂²×C₃×C₅	—	4	2	no	—
217	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₃×C₄×C₅	—	2	2	no	—
219	C₃×C₄×C₅	—	2	1	no	—
220	C₃×C₄×C₅	—	4	2	no	—
221	C₃×C₄×C₅	—	4	2	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
224	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
225	C₃×#41	—	4	1	no	—
226	C₃×#41	—	4	1	no	—
227	C₃×#41	—	4	2	no	—
228	C₃×#41	—	4	2	no	—
229	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
230	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
231	C₂×C₃×D₄	—	2	2	no	—
232	C₂×C₃×D₄	—	2	2	no	—
233	C₂×C₃×D₄	—	2	2	no	—
234	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
235	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
236	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
237	C₂²×C₃×C₄	—	2	2	no	—
238	C₂²×C₃×C₄	—	2	2	no	—
239	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
240	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
241	C₃×Q₁₆	—	4	1	no	—
242	C₃×SD₁₆	—	4	2	no	—
243	C₃×D₈	—	4	1	no	—
244	C₃×M₁₆	—	4	1	no	—
245	C₂×C₃×C₈	—	4	1	no	—
246	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
248	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
249	C₃×C₄⋊C₄	—	2	2	no	—
250	C₃×C₄⋊C₄	—	2	2	no	—
251	C₃×C₄⋊C₄	—	2	2	no	—
252	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
253	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
254	C₃×C₂²⋊C₄	—	2	2	no	—
255	C₃×C₂²⋊C₄	—	2	2	no	—
256	C₃×C₂²⋊C₄	—	2	2	no	—
257	C₃×C₂²⋊C₄	—	2	2	no	—
258	C₂³×C₅	—	2	2	no	—
259	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
260	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
261	C₅×Q₈	—	2	2	no	—
262	C₅×Q₈	—	2	2	no	—
263	C₅×Q₈	—	4	1	no	—
264	C₅×D₄	—	2	2	no	—
265	C₅×D₄	—	2	2	no	—
266	C₅×D₄	—	4	2	no	—
267	C₅×D₄	—	4	1	no	—
268	C₅×D₄	—	4	4	no	—
269	C₅×D₄	—	8	2	no	—
270	C₅×D₄	—	8	2	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	4	4	no	—
279	C₂×C₄×C₅	—	8	2	no	—
280	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
282	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
283	C₅×C₈	—	2	2	no	—
284	C₅×C₈	—	2	1	no	—
285	C₅×C₈	—	2	1	no	—
286	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
287	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
288	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
289	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
290	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
291	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
292	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
293	C₂²⋊Q₈	—	2	2	no	—
294	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
295	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
296	#121	—	2	2	no	—
297	#121	—	2	2	no	—
298	#121	—	2	2	no	—
299	#121	C₂²×C₃×C₅	1	2	yes	—
300	#121	C₂²×C₃×C₅	1	2	yes	—
301	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
302	#106	C₂²×C₃×C₅	1	2	yes	—
303	#106	C₂²×C₃×C₅	1	1	yes	characteristic
304	#106	C₂²×C₃×C₅	1	1	yes	characteristic
305	#103	C₂²×C₃×C₅	1	2	yes	—
306	#103	C₂²×C₃×C₅	1	2	yes	—
307	#102	C₂²×C₃×C₅	1	2	yes	—
308	#102	C₂²×C₃×C₅	1	2	yes	—
309	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
310	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
311	C₂×C₃×C₅	—	4	2	no	—
312	C₂×C₃×C₅	—	4	1	no	—
313	C₂×C₃×C₅	—	8	2	no	—
314	C₂×C₃×C₅	#534	1	1	yes	characteristic
315	C₂×C₃×C₅	#577	1	2	yes	—
316	C₂³×C₃	—	2	2	no	—
317	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
319	C₃×Q₈	—	2	2	no	—
320	C₃×Q₈	—	2	2	no	—
321	C₃×Q₈	—	4	1	no	—
322	C₃×D₄	—	2	2	no	—
323	C₃×D₄	—	2	2	no	—
324	C₃×D₄	—	4	2	no	—
325	C₃×D₄	—	4	1	no	—
326	C₃×D₄	—	4	4	no	—
327	C₃×D₄	—	8	2	no	—
328	C₃×D₄	—	8	2	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	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	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	4	4	no	—
337	C₂×C₃×C₄	—	8	2	no	—
338	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
340	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
341	C₃×C₈	—	2	2	no	—
342	C₃×C₈	—	2	1	no	—
343	C₃×C₈	—	2	1	no	—
344	C₂²×C₅	—	2	2	no	—
345	C₂²×C₅	—	2	2	no	—
346	C₂²×C₅	—	2	2	no	—
347	C₂²×C₅	—	2	2	no	—
348	C₂²×C₅	—	2	1	no	—
349	C₂²×C₅	—	4	2	no	—
350	C₂²×C₅	—	4	2	no	—
351	C₂²×C₅	—	4	2	no	—
352	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
353	C₄×C₅	—	2	2	no	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	4	2	no	—
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	—	4	2	no	—
358	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
359	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
360	#41	—	4	1	no	—
361	#41	—	4	1	no	—
362	#41	—	4	2	no	—
363	#41	—	4	2	no	—
364	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
365	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
370	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
371	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
375	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
376	Q₁₆	—	4	1	no	—
377	SD₁₆	—	4	2	no	—
378	D₈	—	4	1	no	—
379	M₁₆	—	4	1	no	—
380	C₂×C₈	—	4	1	no	—
381	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
382	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
383	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
388	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₃×C₅	#3204	1	1	yes	characteristic, direct product factor, Hall
394	C₂²×C₃	—	2	2	no	—
395	C₂²×C₃	—	2	1	no	—
396	C₂²×C₃	—	2	2	no	—
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	2	2	no	—
399	C₂²×C₃	—	4	2	no	—
400	C₂²×C₃	—	4	2	no	—
401	C₂²×C₃	—	4	2	no	—
402	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	4	2	no	—
406	C₃×C₄	—	4	2	no	—
407	C₃×C₄	—	4	2	no	—
408	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
409	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
410	C₂×C₅	—	4	2	no	—
411	C₂×C₅	—	4	1	no	—
412	C₂×C₅	—	8	2	no	—
413	C₂×C₅	C₃×#534	1	1	yes	characteristic
414	C₂×C₅	C₃×#577	1	2	yes	—
415	C₂³	—	2	2	no	—
416	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
417	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	4	1	no	—
421	D₄	—	2	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	4	no	—
426	D₄	—	8	2	no	—
427	D₄	—	8	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	8	2	no	—
437	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
438	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
439	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₂×C₃	—	4	2	no	—
444	C₂×C₃	—	4	1	no	—
445	C₂×C₃	—	8	2	no	—
446	C₂×C₃	C₅×#534	1	1	yes	characteristic
447	C₂×C₃	C₅×#577	1	2	yes	—
448	C₅	C₃×#3204	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	2	2	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	2	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
464	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
465	C₃	C₅×#3204	1	1	yes	characteristic, direct product factor, Sylow
466	C₂	—	4	2	no	—
467	C₂	—	4	1	no	—
468	C₂	—	8	2	no	—
469	C₂	C₃×C₅×#534	1	1	yes	characteristic
470	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
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#537	C₂	semidirect
2. C₃×C₅×#483	C₂	semidirect
3. C₃×C₅×#481	C₂	semidirect
4. C₃×C₅×#470	C₂	semidirect
5. C₃×C₅×#469	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#452	C₂	semidirect
8. C₃×C₅×#449	C₂	semidirect
9. C₃×C₅×#408	C₂	semidirect
10. C₅×#3204	C₃	direct (N × H)
36. C₃×#3204	C₅	direct (N × H)
37. C₅×#537	C₂×C₃	semidirect
38. C₅×#483	C₂×C₃	semidirect
39. C₅×#481	C₂×C₃	semidirect
40. C₅×#470	C₂×C₃	semidirect
41. C₅×#469	C₂×C₃	semidirect
42. C₅×#465	C₂×C₃	semidirect
43. C₅×#452	C₂×C₃	semidirect
44. C₅×#449	C₂×C₃	semidirect
45. C₅×#408	C₂×C₃	semidirect
79. C₃×#537	C₂×C₅	semidirect
80. C₃×#483	C₂×C₅	semidirect
81. C₃×#481	C₂×C₅	semidirect
82. C₃×#470	C₂×C₅	semidirect
83. C₃×#469	C₂×C₅	semidirect
84. C₃×#465	C₂×C₅	semidirect
85. C₃×#452	C₂×C₅	semidirect
86. C₃×#449	C₂×C₅	semidirect
87. C₃×#408	C₂×C₅	semidirect
113. #3204	C₃×C₅	direct (N × H)
200. #537	C₂×C₃×C₅	semidirect
201. #483	C₂×C₃×C₅	semidirect
202. #481	C₂×C₃×C₅	semidirect
203. #470	C₂×C₃×C₅	semidirect
204. #469	C₂×C₃×C₅	semidirect
205. #465	C₂×C₃×C₅	semidirect
206. #452	C₂×C₃×C₅	semidirect
207. #449	C₂×C₃×C₅	semidirect
208. #408	C₂×C₃×C₅	semidirect
393. C₃×C₅	#3204	direct (N × H)
448. C₅	C₃×#3204	direct (N × H)
465. C₃	C₅×#3204	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×#537	2
C₃×C₅×#483	2
C₃×C₅×#481	2
C₃×C₅×#470	2
C₃×C₅×#469	2
C₃×C₅×#465	2
C₃×C₅×#452	2
C₃×C₅×#449	2
C₃×C₅×#408	2
C₅×#3204	3
C₃×#3204	5

Subgroups — C3×C5×#3204 #14276238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3204 #14276238