Subgroups — C₃×D₅×#237 #13089226

Order 1440.

710 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6819	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×#67	C₂	1	2	yes	maximal, complemented
5	C₃×#6780	C₂	1	2	yes	maximal, complemented
6	C₃×#6779	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×D₅×Dic₃	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×D₃×D₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6766	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6765	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₅×#41	—	3	1	no	maximal
13	D₅×#237	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃²×D₅	C₂²	1	2	yes	—
15	C₂×C₃×D₃×D₅	C₂²	1	1	yes	characteristic
16	C₃²×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₃×#1220	C₂²	1	2	yes	complemented
18	C₂×C₃×Dic₁₅	C₂²	1	2	yes	complemented
19	C₃×C₄×D₁₅	C₂²	1	1	yes	characteristic, complemented
20	C₃×Dic₃₀	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#67	C₂²	1	2	yes	complemented
22	C₂×C₃×C₅×Dic₃	C₂²	1	2	yes	complemented
23	C₃×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
25	C₃²×C₂²⋊D₅	C₂²	1	2	yes	complemented
26	C₃²×D₂₀	C₂²	1	1	yes	characteristic, complemented
27	C₃²×C₄×D₅	C₂²	1	1	yes	characteristic
28	C₃×#1204	C₂²	1	2	yes	complemented
29	C₃×#1202	C₂²	1	2	yes	complemented
30	C₃×#1201	C₂²	1	2	yes	complemented
31	C₃×#1200	C₂²	1	1	yes	characteristic, complemented
32	C₃×D₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
33	C₃×D₅×Dic₃	C₂²	1	2	yes	—
34	C₃×D₅×Dic₃	C₂²	1	1	yes	characteristic
35	C₃×D₅×Dic₃	C₂²	1	2	yes	complemented
36	C₃×D₅×Dic₃	C₂²	1	2	yes	complemented
37	C₂×C₃×#237	—	5	1	no	maximal, Hall
38	C₃×C₅×#41	—	3	1	no	—
39	#6819	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#237	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×#713	—	3	1	no	—
42	C₃×Q₈×D₅	—	3	1	no	—
43	C₃×#711	—	3	1	no	—
44	C₃×#711	—	3	2	no	—
45	C₃×D₄×D₅	—	2	1	no	—
46	C₃×D₄×D₅	—	3	2	no	—
47	C₃×D₄×D₅	D₃	1	1	yes	characteristic, complemented
48	C₃×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
49	C₃×#709	—	3	2	no	—
50	C₃×#709	—	3	1	no	—
51	C₂×C₃×C₄×D₅	—	3	2	no	—
52	C₂×C₃×C₄×D₅	—	3	1	no	—
53	D₅×#67	C₂×C₃	1	2	yes	complemented
54	#6780	C₂×C₃	1	2	yes	complemented
55	#6779	C₂×C₃	1	2	yes	complemented
56	C₂×D₅×Dic₃	C₂×C₃	1	2	yes	complemented
57	C₄×D₃×D₅	C₂×C₃	1	1	yes	characteristic, complemented
58	#6766	C₂×C₃	1	1	yes	characteristic, complemented
59	#6765	C₂×C₃	1	1	yes	characteristic, complemented
60	D₅×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂²×C₃²×C₅	C₂³	1	2	yes	—
62	C₂×C₃×D₁₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
64	C₂×C₃²×D₅	—	2	4	no	—
65	C₂×C₃²×D₅	C₂³	1	2	yes	—
66	C₂×C₃²×D₅	C₂³	1	1	yes	characteristic
67	C₃×D₃×D₅	—	2	2	no	—
68	C₃²×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₃×Dic₁₅	C₂³	1	1	yes	characteristic
70	C₃×Dic₁₅	C₂³	1	2	yes	—
71	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₃×C₅×Dic₃	C₂³	1	2	yes	—
73	C₃²×Dic₅	C₂³	1	1	yes	characteristic
74	D₅×#41	—	3	1	no	Hall
75	C₂×C₃²×D₄	—	5	1	no	—
76	C₂×C₃×#67	—	5	2	no	—
77	C₂²×C₃×Dic₃	—	5	2	no	—
78	C₃×#237	—	5	1	no	—
79	C₃×#237	—	5	2	no	—
80	C₃×#237	—	5	2	no	—
81	C₃×#237	—	5	1	no	—
82	C₃×#237	—	5	1	no	—
83	C₃×#237	D₅	1	1	yes	characteristic, direct product factor
84	C₂×C₃×C₄×D₃	—	5	1	no	—
85	C₂×C₃×Dic₆	—	5	1	no	—
86	C₂²×C₃×D₅	—	2	2	no	—
87	C₂²×C₃×D₅	—	3	1	no	—
88	C₂²×C₃×D₅	C₂×D₃	1	2	yes	—
89	C₂²×C₃×D₅	C₂²×C₃	1	2	yes	—
90	C₂×D₃×D₅	C₂²×C₃	1	1	yes	characteristic
91	C₃×C₅×Q₈	—	3	1	no	—
92	C₃×C₅×D₄	—	2	1	no	—
93	C₃×C₅×D₄	—	3	2	no	—
94	C₃×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
95	C₃×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
96	C₂×C₃×C₄×C₅	—	3	2	no	—
97	C₂×C₃×C₄×C₅	—	3	1	no	—
98	#1220	C₂²×C₃	1	2	yes	complemented
99	C₂×Dic₁₅	C₂²×C₃	1	2	yes	complemented
100	C₄×D₁₅	C₂²×C₃	1	1	yes	characteristic, complemented
101	Dic₃₀	C₂²×C₃	1	1	yes	characteristic, complemented
102	C₅×#67	C₂²×C₃	1	2	yes	complemented
103	C₂×C₅×Dic₃	C₂²×C₃	1	2	yes	complemented
104	C₄×C₅×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₅×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₃×C₂²⋊D₅	—	2	2	no	—
107	C₃×C₂²⋊D₅	—	3	2	no	—
108	C₃×C₂²⋊D₅	—	3	2	no	—
109	C₃×C₂²⋊D₅	C₂×D₃	1	2	yes	complemented
110	C₃×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
111	C₂×C₃×Dic₅	—	3	2	no	—
112	C₂×C₃×Dic₅	—	3	1	no	—
113	C₃×D₂₀	—	2	1	no	—
114	C₃×D₂₀	—	3	2	no	—
115	C₃×D₂₀	C₂×D₃	1	1	yes	characteristic, complemented
116	C₃×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₃×C₄×D₅	—	2	1	no	—
118	C₃×C₄×D₅	—	3	1	no	—
119	C₃×C₄×D₅	—	3	2	no	—
120	C₃×C₄×D₅	—	3	2	no	—
121	C₃×C₄×D₅	—	3	2	no	—
122	C₃×C₄×D₅	—	3	1	no	—
123	C₃×C₄×D₅	—	3	1	no	—
124	C₃×C₄×D₅	C₂×D₃	1	1	yes	characteristic
125	C₃×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
126	C₃×Dic₁₀	—	3	1	no	—
127	C₃×Dic₁₀	—	3	2	no	—
128	#1204	C₂²×C₃	1	2	yes	complemented
129	#1202	C₂²×C₃	1	2	yes	complemented
130	#1201	C₂²×C₃	1	2	yes	complemented
131	#1200	C₂²×C₃	1	1	yes	characteristic, complemented
132	D₃×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
133	D₅×Dic₃	C₂²×C₃	1	2	yes	—
134	D₅×Dic₃	C₂²×C₃	1	1	yes	characteristic
135	D₅×Dic₃	C₂²×C₃	1	2	yes	complemented
136	D₅×Dic₃	C₂²×C₃	1	2	yes	complemented
137	C₂×C₃×#41	—	15	1	no	—
138	C₂×#237	—	5	1	no	—
139	C₂×C₃²×C₅	—	2	2	no	—
140	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
141	C₃×D₁₅	—	2	1	no	—
142	C₃×C₅×D₃	—	2	1	no	—
143	C₃²×D₅	—	2	2	no	—
144	C₃²×D₅	#41	1	2	yes	complemented
145	C₅×#41	—	3	1	no	—
146	#713	—	3	1	no	—
147	Q₈×D₅	—	3	1	no	—
148	#711	—	3	1	no	—
149	#711	—	3	2	no	—
150	D₄×D₅	—	3	2	no	—
151	D₄×D₅	C₃×D₃	1	1	yes	characteristic, complemented
152	#709	—	3	2	no	—
153	#709	—	3	1	no	—
154	C₂×C₄×D₅	—	3	2	no	—
155	C₂×C₄×D₅	—	3	1	no	—
156	C₂³×C₃²	—	5	2	no	—
157	C₂²×C₃×D₃	—	5	1	no	—
158	C₃²×D₄	—	5	2	no	—
159	C₃²×D₄	—	5	1	no	—
160	C₃²×D₄	C₂×D₅	1	1	yes	characteristic, complemented
161	C₂×C₃²×C₄	—	5	1	no	—
162	C₃×#67	—	5	2	no	—
163	C₃×#67	—	5	2	no	—
164	C₃×#67	—	5	2	no	—
165	C₃×#67	C₂×D₅	1	2	yes	complemented
166	C₂×C₃×Dic₃	—	5	2	no	—
167	C₂×C₃×Dic₃	—	5	2	no	—
168	C₂×C₃×Dic₃	—	5	1	no	—
169	C₂×C₃×Dic₃	—	5	2	no	—
170	C₂×C₃×Dic₃	—	5	2	no	—
171	C₂×C₃×Dic₃	C₂×D₅	1	2	yes	complemented
172	C₃×C₄×D₃	—	5	1	no	—
173	C₃×C₄×D₃	—	5	1	no	—
174	C₃×C₄×D₃	—	5	1	no	—
175	C₃×C₄×D₃	C₂×D₅	1	1	yes	characteristic, complemented
176	C₃×Dic₆	—	5	1	no	—
177	C₃×Dic₆	—	5	2	no	—
178	C₃×Dic₆	C₂×D₅	1	1	yes	characteristic, complemented
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	3	1	no	—
181	C₂²×C₃×C₅	C₂²×D₃	1	2	yes	—
182	C₂²×C₃×C₅	C₂³×C₃	1	2	yes	—
183	C₂×D₁₅	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₅×D₃	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₃×D₅	—	2	4	no	—
186	C₂×C₃×D₅	—	2	4	no	—
187	C₂×C₃×D₅	—	2	1	no	—
188	C₂×C₃×D₅	—	2	2	no	—
189	C₂×C₃×D₅	—	3	1	no	—
190	C₂×C₃×D₅	—	4	4	no	—
191	C₂×C₃×D₅	—	6	2	no	—
192	C₂×C₃×D₅	C₂²×D₃	1	2	yes	—
193	C₂×C₃×D₅	C₂²×D₃	1	1	yes	characteristic
194	C₂×C₃×D₅	C₂³×C₃	1	2	yes	—
195	C₂×C₃×D₅	C₂³×C₃	1	1	yes	characteristic
196	D₃×D₅	—	2	2	no	—
197	C₃×C₄×C₅	—	2	1	no	—
198	C₃×C₄×C₅	—	3	2	no	—
199	C₃×C₄×C₅	—	3	1	no	—
200	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
201	C₃×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
202	Dic₁₅	C₂³×C₃	1	1	yes	characteristic
203	Dic₁₅	C₂³×C₃	1	2	yes	—
204	C₃×Dic₅	—	2	1	no	—
205	C₃×Dic₅	—	3	2	no	—
206	C₃×Dic₅	—	3	1	no	—
207	C₃×Dic₅	C₂²×D₃	1	1	yes	characteristic
208	C₃×Dic₅	C₂³×C₃	1	1	yes	characteristic
209	C₅×Dic₃	C₂³×C₃	1	1	yes	characteristic
210	C₅×Dic₃	C₂³×C₃	1	2	yes	—
211	C₃×#41	—	3	1	no	—
212	C₃×#41	—	15	2	no	—
213	C₃×#41	—	15	1	no	—
214	C₃×#41	—	15	2	no	—
215	C₃×#41	—	15	1	no	—
216	C₃×#41	—	15	1	no	—
217	C₂×C₃×Q₈	—	15	1	no	—
218	C₂×C₃×D₄	—	5	1	no	—
219	C₂×C₃×D₄	—	5	1	no	—
220	C₂×C₃×D₄	—	10	1	no	—
221	C₂×C₃×D₄	—	15	2	no	—
222	C₂²×C₃×C₄	—	15	1	no	—
223	C₂²×C₃×C₄	—	15	2	no	—
224	C₂×#67	—	5	2	no	—
225	C₂²×Dic₃	—	5	2	no	—
226	#237	—	5	1	no	—
227	#237	—	5	2	no	—
228	#237	—	5	2	no	—
229	#237	—	5	1	no	—
230	#237	—	5	1	no	—
231	#237	C₃×D₅	1	1	yes	characteristic, direct product factor
232	C₂×C₄×D₃	—	5	1	no	—
233	C₂×Dic₆	—	5	1	no	—
234	C₃²×C₅	C₂×#41	1	1	yes	characteristic, complemented, Hall
235	C₂²×D₅	—	3	1	no	—
236	C₂²×D₅	C₂×C₃×D₃	1	2	yes	—
237	C₅×Q₈	—	3	1	no	—
238	C₅×D₄	—	3	2	no	—
239	C₅×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
240	C₂×C₄×C₅	—	3	2	no	—
241	C₂×C₄×C₅	—	3	1	no	—
242	C₂²⋊D₅	—	3	2	no	—
243	C₂²⋊D₅	—	3	2	no	—
244	C₂²⋊D₅	C₂×C₃×D₃	1	2	yes	complemented
245	C₂×Dic₅	—	3	2	no	—
246	C₂×Dic₅	—	3	1	no	—
247	D₂₀	—	3	2	no	—
248	D₂₀	C₂×C₃×D₃	1	1	yes	characteristic, complemented
249	C₄×D₅	—	3	1	no	—
250	C₄×D₅	—	3	2	no	—
251	C₄×D₅	—	3	2	no	—
252	C₄×D₅	—	3	2	no	—
253	C₄×D₅	—	3	1	no	—
254	C₄×D₅	—	3	1	no	—
255	C₄×D₅	C₂×C₃×D₃	1	1	yes	characteristic
256	Dic₁₀	—	3	1	no	—
257	Dic₁₀	—	3	2	no	—
258	C₂²×C₃²	—	5	1	no	—
259	C₂²×C₃²	—	5	2	no	—
260	C₂²×C₃²	—	10	4	no	—
261	C₂²×C₃²	C₂²×D₅	1	2	yes	—
262	C₂×C₃×D₃	—	5	1	no	—
263	C₂×C₃×D₃	—	10	2	no	—
264	C₂×C₃×D₃	C₂²×D₅	1	1	yes	characteristic
265	C₃²×C₄	—	5	1	no	—
266	C₃²×C₄	C₂²×D₅	1	1	yes	characteristic
267	C₃×Dic₃	—	5	2	no	—
268	C₃×Dic₃	—	5	1	no	—
269	C₃×Dic₃	C₂²×D₅	1	2	yes	—
270	C₃×Dic₃	C₂²×D₅	1	1	yes	characteristic
271	C₂×#41	—	15	1	no	Sylow
272	C₂×C₃×C₅	—	2	2	no	—
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	—	2	1	no	—
275	C₂×C₃×C₅	—	4	2	no	—
276	C₂×C₃×C₅	—	6	1	no	—
277	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
278	C₂×C₃×C₅	C₂⁴×C₃	1	1	yes	characteristic
279	D₁₅	—	2	1	no	—
280	C₃×D₅	—	2	2	no	—
281	C₃×D₅	—	2	2	no	—
282	C₃×D₅	—	2	2	no	—
283	C₃×D₅	—	4	2	no	—
284	C₃×D₅	—	6	1	no	—
285	C₃×D₅	#237	1	2	yes	direct product factor
286	C₃×D₅	C₃×#41	1	2	yes	complemented
287	C₅×D₃	—	2	1	no	—
288	C₂³×C₃	—	5	2	no	—
289	C₂³×C₃	—	5	2	no	—
290	C₂³×C₃	—	10	2	no	—
291	C₂³×C₃	—	15	1	no	—
292	C₂²×D₃	—	5	1	no	—
293	C₃×Q₈	—	3	1	no	—
294	C₃×Q₈	—	15	2	no	—
295	C₃×Q₈	—	15	1	no	—
296	C₃×D₄	—	2	1	no	—
297	C₃×D₄	—	3	2	no	—
298	C₃×D₄	—	5	2	no	—
299	C₃×D₄	—	5	2	no	—
300	C₃×D₄	—	5	1	no	—
301	C₃×D₄	—	5	1	no	—
302	C₃×D₄	—	10	1	no	—
303	C₃×D₄	—	10	2	no	—
304	C₃×D₄	—	15	2	no	—
305	C₃×D₄	—	15	2	no	—
306	C₃×D₄	—	15	2	no	—
307	C₃×D₄	D₃×D₅	1	1	yes	characteristic, complemented
308	C₃×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
309	C₂×C₃×C₄	—	3	2	no	—
310	C₂×C₃×C₄	—	3	1	no	—
311	C₂×C₃×C₄	—	5	1	no	—
312	C₂×C₃×C₄	—	5	1	no	—
313	C₂×C₃×C₄	—	10	1	no	—
314	C₂×C₃×C₄	—	15	1	no	—
315	C₂×C₃×C₄	—	15	1	no	—
316	C₂×C₃×C₄	—	15	2	no	—
317	C₂×C₃×C₄	—	15	2	no	—
318	C₂×C₃×C₄	—	15	2	no	—
319	C₂×C₃×C₄	—	15	1	no	—
320	C₂×C₃×C₄	—	15	2	no	—
321	C₂×C₃×C₄	—	15	1	no	—
322	#67	—	5	2	no	—
323	#67	—	5	2	no	—
324	#67	—	5	2	no	—
325	#67	C₂×C₃×D₅	1	2	yes	complemented
326	C₂×Dic₃	—	5	2	no	—
327	C₂×Dic₃	—	5	2	no	—
328	C₂×Dic₃	—	5	1	no	—
329	C₂×Dic₃	—	5	2	no	—
330	C₂×Dic₃	—	5	2	no	—
331	C₂×Dic₃	C₂×C₃×D₅	1	2	yes	complemented
332	C₄×D₃	—	5	1	no	—
333	C₄×D₃	—	5	1	no	—
334	C₄×D₃	—	5	1	no	—
335	C₄×D₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented
336	Dic₆	—	5	1	no	—
337	Dic₆	—	5	2	no	—
338	Dic₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
339	C₂²×C₅	—	3	1	no	—
340	C₂²×C₅	C₂²×C₃×D₃	1	2	yes	—
341	C₂×D₅	—	2	4	no	—
342	C₂×D₅	—	3	1	no	—
343	C₂×D₅	—	6	2	no	—
344	C₂×D₅	C₂²×C₃×D₃	1	2	yes	—
345	C₂×D₅	C₂²×C₃×D₃	1	1	yes	characteristic
346	C₄×C₅	—	3	2	no	—
347	C₄×C₅	—	3	1	no	—
348	C₄×C₅	C₂²×C₃×D₃	1	1	yes	characteristic
349	Dic₅	—	3	2	no	—
350	Dic₅	—	3	1	no	—
351	Dic₅	C₂²×C₃×D₃	1	1	yes	characteristic
352	C₂×C₃²	—	2	2	no	—
353	C₂×C₃²	—	5	2	no	—
354	C₂×C₃²	—	10	2	no	—
355	C₂×C₃²	C₂³×D₅	1	1	yes	characteristic
356	C₃×D₃	—	2	1	no	—
357	C₃×D₃	—	10	1	no	—
358	#41	—	3	1	no	—
359	#41	—	15	2	no	—
360	#41	—	15	1	no	—
361	#41	—	15	2	no	—
362	#41	—	15	1	no	—
363	#41	—	15	1	no	—
364	C₂×Q₈	—	15	1	no	—
365	C₂×D₄	—	5	1	no	—
366	C₂×D₄	—	15	2	no	—
367	C₂²×C₄	—	15	1	no	—
368	C₂²×C₄	—	15	2	no	—
369	C₃×C₅	—	2	1	no	—
370	C₃×C₅	C₂×#237	1	1	yes	characteristic, complemented
371	C₃×C₅	C₂×C₃×#41	1	1	yes	characteristic, complemented
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	3	1	no	—
374	C₂²×C₃	—	5	1	no	—
375	C₂²×C₃	—	5	1	no	—
376	C₂²×C₃	—	5	2	no	—
377	C₂²×C₃	—	5	2	no	—
378	C₂²×C₃	—	10	1	no	—
379	C₂²×C₃	—	10	2	no	—
380	C₂²×C₃	—	10	4	no	—
381	C₂²×C₃	—	10	4	no	—
382	C₂²×C₃	—	15	1	no	—
383	C₂²×C₃	—	20	4	no	—
384	C₂²×C₃	—	30	2	no	—
385	C₂²×C₃	C₂×D₃×D₅	1	2	yes	—
386	C₂²×C₃	C₂²×C₃×D₅	1	2	yes	—
387	C₂×D₃	—	5	1	no	—
388	C₂×D₃	—	10	2	no	—
389	C₂×D₃	C₂²×C₃×D₅	1	1	yes	characteristic
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	3	1	no	—
392	C₃×C₄	—	3	2	no	—
393	C₃×C₄	—	5	1	no	—
394	C₃×C₄	—	5	1	no	—
395	C₃×C₄	—	10	1	no	—
396	C₃×C₄	—	15	1	no	—
397	C₃×C₄	—	15	2	no	—
398	C₃×C₄	C₂×D₃×D₅	1	1	yes	characteristic
399	C₃×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
400	Dic₃	—	5	2	no	—
401	Dic₃	—	5	1	no	—
402	Dic₃	C₂²×C₃×D₅	1	2	yes	—
403	Dic₃	C₂²×C₃×D₅	1	1	yes	characteristic
404	C₂×C₅	—	2	2	no	—
405	C₂×C₅	—	6	1	no	—
406	C₂×C₅	C₂³×C₃×D₃	1	1	yes	characteristic
407	D₅	—	2	2	no	—
408	D₅	—	6	1	no	—
409	D₅	C₃×#237	1	2	yes	direct product factor
410	C₃²	D₅×#41	1	1	yes	characteristic, complemented, Sylow
411	C₂³	—	5	2	no	—
412	C₂³	—	15	1	no	—
413	Q₈	—	3	1	no	—
414	Q₈	—	15	2	no	—
415	Q₈	—	15	1	no	—
416	D₄	—	3	2	no	—
417	D₄	—	5	2	no	—
418	D₄	—	5	1	no	—
419	D₄	—	15	2	no	—
420	D₄	—	15	2	no	—
421	D₄	—	15	2	no	—
422	D₄	C₃×D₃×D₅	1	1	yes	characteristic, complemented
423	C₂×C₄	—	3	2	no	—
424	C₂×C₄	—	3	1	no	—
425	C₂×C₄	—	5	1	no	—
426	C₂×C₄	—	15	1	no	—
427	C₂×C₄	—	15	1	no	—
428	C₂×C₄	—	15	2	no	—
429	C₂×C₄	—	15	2	no	—
430	C₂×C₄	—	15	2	no	—
431	C₂×C₄	—	15	1	no	—
432	C₂×C₄	—	15	2	no	—
433	C₂×C₄	—	15	1	no	—
434	C₂×C₃	—	2	2	no	—
435	C₂×C₃	—	2	2	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	4	2	no	—
438	C₂×C₃	—	5	2	no	—
439	C₂×C₃	—	5	2	no	—
440	C₂×C₃	—	6	1	no	—
441	C₂×C₃	—	10	2	no	—
442	C₂×C₃	—	10	2	no	—
443	C₂×C₃	—	10	2	no	—
444	C₂×C₃	—	20	2	no	—
445	C₂×C₃	—	30	1	no	—
446	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
447	C₂×C₃	C₂³×C₃×D₅	1	1	yes	characteristic
448	D₃	—	2	1	no	—
449	D₃	—	10	1	no	—
450	C₅	C₂×C₃×#237	1	1	yes	characteristic, complemented, Sylow
451	C₂²	—	3	1	no	—
452	C₂²	—	5	1	no	—
453	C₂²	—	5	2	no	—
454	C₂²	—	10	4	no	—
455	C₂²	—	15	1	no	—
456	C₂²	—	30	2	no	—
457	C₂²	C₂×C₃×D₃×D₅	1	2	yes	—
458	C₄	—	3	1	no	—
459	C₄	—	3	2	no	—
460	C₄	—	5	1	no	—
461	C₄	—	15	1	no	—
462	C₄	—	15	2	no	—
463	C₄	C₂×C₃×D₃×D₅	1	1	yes	characteristic
464	C₃	—	2	1	no	—
465	C₃	D₅×#237	1	1	yes	characteristic, direct product factor
466	C₃	C₃×D₅×#41	1	1	yes	characteristic, complemented
467	C₂	—	2	2	no	—
468	C₂	—	5	2	no	—
469	C₂	—	6	1	no	—
470	C₂	—	10	2	no	—
471	C₂	—	30	1	no	—
472	C₂	C₂²×C₃×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₃×D₅
commutator, cosocle	C₂×C₃×C₅	C₂⁴×C₃
Frattini	C₂	C₂²×C₃×D₃×D₅
Fitting	C₃²×C₅×D₄	C₂²
socle	C₂×C₃²×C₅	C₂⁴
hypercenter	C₃×D₄	D₃×D₅
hypocenter	C₃×C₅	C₂×C₃×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×#6819	C₂	semidirect
2. C₃×C₅×#237	C₂	semidirect
3. C₃²×D₄×D₅	C₂	semidirect
4. C₃×D₅×#67	C₂	semidirect
5. C₃×#6780	C₂	semidirect
6. C₃×#6779	C₂	semidirect
7. C₂×C₃×D₅×Dic₃	C₂	semidirect
8. C₃×C₄×D₃×D₅	C₂	semidirect
9. C₃×#6766	C₂	semidirect
10. C₃×#6765	C₂	semidirect
11. C₃×D₅×Dic₆	C₂	semidirect
13. D₅×#237	C₃	direct (N × H)
16. C₃²×C₅×D₄	C₂²	semidirect
17. C₃×#1220	C₂²	semidirect
18. C₂×C₃×Dic₁₅	C₂²	semidirect
19. C₃×C₄×D₁₅	C₂²	semidirect
20. C₃×Dic₃₀	C₂²	semidirect
21. C₃×C₅×#67	C₂²	semidirect
22. C₂×C₃×C₅×Dic₃	C₂²	semidirect
23. C₃×C₄×C₅×D₃	C₂²	semidirect
24. C₃×C₅×Dic₆	C₂²	semidirect
25. C₃²×C₂²⋊D₅	C₂²	semidirect
26. C₃²×D₂₀	C₂²	semidirect
28. C₃×#1204	C₂²	semidirect
29. C₃×#1202	C₂²	semidirect
30. C₃×#1201	C₂²	semidirect
31. C₃×#1200	C₂²	semidirect
32. C₃×D₃×Dic₅	C₂²	semidirect
35. C₃×D₅×Dic₃	C₂²	semidirect
36. C₃×D₅×Dic₃	C₂²	semidirect
39. #6819	C₂×C₃	semidirect
40. C₅×#237	C₂×C₃	semidirect
47. C₃×D₄×D₅	D₃	semidirect
48. C₃×D₄×D₅	C₂×C₃	semidirect
53. D₅×#67	C₂×C₃	semidirect
54. #6780	C₂×C₃	semidirect
55. #6779	C₂×C₃	semidirect
56. C₂×D₅×Dic₃	C₂×C₃	semidirect
57. C₄×D₃×D₅	C₂×C₃	semidirect
58. #6766	C₂×C₃	semidirect
59. #6765	C₂×C₃	semidirect
60. D₅×Dic₆	C₂×C₃	semidirect
83. C₃×#237	D₅	direct (N × H)
94. C₃×C₅×D₄	C₂×D₃	semidirect
95. C₃×C₅×D₄	C₂²×C₃	semidirect
98. #1220	C₂²×C₃	semidirect
99. C₂×Dic₁₅	C₂²×C₃	semidirect
100. C₄×D₁₅	C₂²×C₃	semidirect
101. Dic₃₀	C₂²×C₃	semidirect
102. C₅×#67	C₂²×C₃	semidirect
103. C₂×C₅×Dic₃	C₂²×C₃	semidirect
104. C₄×C₅×D₃	C₂²×C₃	semidirect
105. C₅×Dic₆	C₂²×C₃	semidirect
109. C₃×C₂²⋊D₅	C₂×D₃	semidirect
110. C₃×C₂²⋊D₅	C₂²×C₃	semidirect
115. C₃×D₂₀	C₂×D₃	semidirect
116. C₃×D₂₀	C₂²×C₃	semidirect
128. #1204	C₂²×C₃	semidirect
129. #1202	C₂²×C₃	semidirect
130. #1201	C₂²×C₃	semidirect
131. #1200	C₂²×C₃	semidirect
132. D₃×Dic₅	C₂²×C₃	semidirect
135. D₅×Dic₃	C₂²×C₃	semidirect
136. D₅×Dic₃	C₂²×C₃	semidirect
144. C₃²×D₅	#41	semidirect
151. D₄×D₅	C₃×D₃	semidirect
160. C₃²×D₄	C₂×D₅	semidirect
165. C₃×#67	C₂×D₅	semidirect
171. C₂×C₃×Dic₃	C₂×D₅	semidirect
175. C₃×C₄×D₃	C₂×D₅	semidirect
178. C₃×Dic₆	C₂×D₅	semidirect
231. #237	C₃×D₅	direct (N × H)
234. C₃²×C₅	C₂×#41	semidirect
239. C₅×D₄	C₂×C₃×D₃	semidirect
244. C₂²⋊D₅	C₂×C₃×D₃	semidirect
248. D₂₀	C₂×C₃×D₃	semidirect
285. C₃×D₅	#237	direct (N × H)
286. C₃×D₅	C₃×#41	semidirect
307. C₃×D₄	D₃×D₅	semidirect
308. C₃×D₄	C₂×C₃×D₅	semidirect
325. #67	C₂×C₃×D₅	semidirect
331. C₂×Dic₃	C₂×C₃×D₅	semidirect
335. C₄×D₃	C₂×C₃×D₅	semidirect
338. Dic₆	C₂×C₃×D₅	semidirect
370. C₃×C₅	C₂×#237	semidirect
371. C₃×C₅	C₂×C₃×#41	semidirect
409. D₅	C₃×#237	direct (N × H)
410. C₃²	D₅×#41	semidirect
422. D₄	C₃×D₃×D₅	semidirect
450. C₅	C₂×C₃×#237	semidirect
465. C₃	D₅×#237	direct (N × H)
466. C₃	C₃×D₅×#41	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6819	2
C₃×C₅×#237	2
C₃²×D₄×D₅	2
C₃×D₅×#67	2
C₃×#6780	2
C₃×#6779	2
C₂×C₃×D₅×Dic₃	2
C₃×C₄×D₃×D₅	2
C₃×#6766	2
C₃×#6765	2
C₃×D₅×Dic₆	2
C₃×D₅×#41	3
D₅×#237	3
C₂×C₃×#237	5

Subgroups — C3×D5×#237 #13089226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#237 #13089226