Subgroups — C₃×#92024 #13089228

Order 1440.

696 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#711	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6790	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#1200	C₂	1	2	yes	maximal, complemented
6	C₃×#6782	C₂	1	2	yes	maximal, complemented
7	C₃×#6779	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×D₃×D₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6773	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₁₅⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6769	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₅×#41	—	3	1	no	maximal
13	#92024	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃×D₁₅	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	C₃×D₆₀	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₄×D₁₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#67	C₂²	1	2	yes	complemented
21	C₂×C₃×C₅×Dic₃	C₂²	1	2	yes	complemented
22	C₃×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
24	C₃²×C₂²⋊D₅	C₂²	1	2	yes	complemented
25	C₂×C₃²×Dic₅	C₂²	1	2	yes	complemented
26	C₃²×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₃²×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
28	C₃×#1204	C₂²	1	2	yes	complemented
29	C₃×#1203	C₂²	1	2	yes	complemented
30	C₃×#1202	C₂²	1	2	yes	complemented
31	C₃×#1200	C₂²	1	2	yes	—
32	C₃×#1200	C₂²	1	1	yes	characteristic
33	C₃×#1200	C₂²	1	2	yes	complemented
34	C₃×#1200	C₂²	1	2	yes	complemented
35	C₃×D₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
36	C₃×D₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₃×D₃×#41	—	5	1	no	maximal, Hall
38	C₃×C₅×#41	—	3	1	no	—
39	D₄×D₁₅	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	—	2	1	no	—
44	C₃×#711	—	3	2	no	—
45	C₃×#711	D₃	1	1	yes	characteristic, complemented
46	C₃×#711	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×D₄×D₅	—	3	1	no	—
48	C₃×D₄×D₅	—	3	2	no	—
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	#6790	C₂×C₃	1	2	yes	complemented
54	C₂×#1200	C₂×C₃	1	2	yes	complemented
55	#6782	C₂×C₃	1	2	yes	complemented
56	#6779	C₂×C₃	1	2	yes	complemented
57	C₄×D₃×D₅	C₂×C₃	1	1	yes	characteristic, complemented
58	#6773	C₂×C₃	1	1	yes	characteristic, complemented
59	D₁₅⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
60	#6769	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂²×C₃²×C₅	C₂³	1	2	yes	—
62	C₂×C₃×D₁₅	—	2	4	no	—
63	C₂×C₃×D₁₅	C₂³	1	2	yes	—
64	C₂×C₃×D₁₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
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×C₅×Dic₃	C₂³	1	1	yes	characteristic
71	C₃×C₅×Dic₃	C₂³	1	2	yes	—
72	C₃²×Dic₅	C₂³	1	1	yes	characteristic
73	C₃²×Dic₅	C₂³	1	2	yes	—
74	D₅×#41	—	3	1	no	Hall
75	C₃²×#41	—	5	1	no	—
76	C₃×#239	—	5	1	no	—
77	C₃×D₃×Q₈	—	5	1	no	—
78	C₃×#237	—	5	2	no	—
79	C₃×#237	D₅	1	1	yes	characteristic, complemented
80	C₃×D₃×D₄	—	5	1	no	—
81	C₃×D₃×D₄	—	5	2	no	—
82	C₃×#235	—	5	2	no	—
83	C₃×#235	—	5	1	no	—
84	C₂×C₃×C₄×D₃	—	5	2	no	—
85	C₂×C₃×C₄×D₃	—	5	1	no	—
86	C₂²×D₁₅	C₂²×C₃	1	2	yes	—
87	C₂²×C₃×D₅	—	3	2	no	—
88	C₂²×C₃×D₅	—	3	1	no	—
89	C₂×D₃×D₅	C₂²×C₃	1	1	yes	characteristic
90	C₃×C₅×Q₈	—	3	1	no	—
91	C₃×C₅×D₄	—	2	1	no	—
92	C₃×C₅×D₄	—	3	2	no	—
93	C₃×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
94	C₃×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₂×C₃×C₄×C₅	—	3	2	no	—
96	C₂×C₃×C₄×C₅	—	3	1	no	—
97	#1220	C₂²×C₃	1	2	yes	complemented
98	D₆₀	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₄×D₁₅	C₂²×C₃	1	1	yes	characteristic
100	C₅×#67	C₂²×C₃	1	2	yes	complemented
101	C₂×C₅×Dic₃	C₂²×C₃	1	2	yes	complemented
102	C₄×C₅×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
103	C₅×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₃×C₂²⋊D₅	—	2	2	no	—
105	C₃×C₂²⋊D₅	—	3	2	no	—
106	C₃×C₂²⋊D₅	—	3	2	no	—
107	C₃×C₂²⋊D₅	C₂×D₃	1	2	yes	complemented
108	C₃×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
109	C₂×C₃×Dic₅	—	2	2	no	—
110	C₂×C₃×Dic₅	—	3	1	no	—
111	C₂×C₃×Dic₅	C₂×D₃	1	2	yes	complemented
112	C₂×C₃×Dic₅	C₂²×C₃	1	2	yes	complemented
113	C₃×D₂₀	—	3	2	no	—
114	C₃×D₂₀	—	3	1	no	—
115	C₃×C₄×D₅	—	2	1	no	—
116	C₃×C₄×D₅	—	3	1	no	—
117	C₃×C₄×D₅	—	3	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	C₂×D₃	1	1	yes	characteristic, complemented
123	C₃×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₃×Dic₁₀	—	2	1	no	—
125	C₃×Dic₁₀	—	3	2	no	—
126	C₃×Dic₁₀	C₂×D₃	1	1	yes	characteristic, complemented
127	C₃×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
128	#1204	C₂²×C₃	1	2	yes	complemented
129	#1203	C₂²×C₃	1	2	yes	complemented
130	#1202	C₂²×C₃	1	2	yes	complemented
131	#1200	C₂²×C₃	1	2	yes	—
132	#1200	C₂²×C₃	1	1	yes	characteristic
133	#1200	C₂²×C₃	1	2	yes	complemented
134	#1200	C₂²×C₃	1	2	yes	complemented
135	D₃×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
136	D₅×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₂×C₃×#41	—	15	1	no	—
138	D₃×#41	—	5	1	no	—
139	C₂×C₃²×C₅	—	2	2	no	—
140	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
141	C₃×D₁₅	—	2	2	no	—
142	C₃×D₁₅	#41	1	2	yes	complemented
143	C₃×C₅×D₃	—	2	1	no	—
144	C₃²×D₅	—	2	1	no	—
145	C₅×#41	—	3	1	no	—
146	#713	—	3	1	no	—
147	Q₈×D₅	—	3	1	no	—
148	#711	—	3	2	no	—
149	#711	C₃×D₃	1	1	yes	characteristic, complemented
150	D₄×D₅	—	3	1	no	—
151	D₄×D₅	—	3	2	no	—
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	C₂²×C₃×D₃	—	5	2	no	—
157	C₂²×C₃×D₃	—	5	1	no	—
158	C₃²×Q₈	—	5	1	no	—
159	C₃²×D₄	—	5	2	no	—
160	C₃²×D₄	C₂×D₅	1	1	yes	characteristic, complemented
161	C₂×C₃²×C₄	—	5	2	no	—
162	C₂×C₃²×C₄	—	5	1	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	1	no	—
167	C₂×C₃×Dic₃	C₂×D₅	1	2	yes	complemented
168	C₃×D₁₂	—	5	2	no	—
169	C₃×D₁₂	—	5	1	no	—
170	C₃×C₄×D₃	—	5	1	no	—
171	C₃×C₄×D₃	—	5	1	no	—
172	C₃×C₄×D₃	—	5	1	no	—
173	C₃×C₄×D₃	—	5	2	no	—
174	C₃×C₄×D₃	—	5	2	no	—
175	C₃×C₄×D₃	—	5	2	no	—
176	C₃×C₄×D₃	C₂×D₅	1	1	yes	characteristic, complemented
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	—	2	4	no	—
184	C₂×D₁₅	C₂³×C₃	1	2	yes	—
185	C₂×D₁₅	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₅×D₃	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₃×D₅	—	2	1	no	—
188	C₂×C₃×D₅	—	3	1	no	—
189	C₂×C₃×D₅	—	3	2	no	—
190	C₂×C₃×D₅	—	6	2	no	—
191	C₂×C₃×D₅	—	6	4	no	—
192	C₂×C₃×D₅	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₃×D₅	C₂³×C₃	1	1	yes	characteristic
194	D₃×D₅	—	2	2	no	—
195	C₃×C₄×C₅	—	2	1	no	—
196	C₃×C₄×C₅	—	3	2	no	—
197	C₃×C₄×C₅	—	3	1	no	—
198	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
199	C₃×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
200	Dic₁₅	C₂³×C₃	1	1	yes	characteristic
201	C₃×Dic₅	—	2	2	no	—
202	C₃×Dic₅	—	2	1	no	—
203	C₃×Dic₅	—	3	1	no	—
204	C₃×Dic₅	C₂²×D₃	1	2	yes	—
205	C₃×Dic₅	C₂²×D₃	1	1	yes	characteristic
206	C₃×Dic₅	C₂³×C₃	1	1	yes	characteristic
207	C₃×Dic₅	C₂³×C₃	1	2	yes	—
208	C₅×Dic₃	C₂³×C₃	1	1	yes	characteristic
209	C₅×Dic₃	C₂³×C₃	1	2	yes	—
210	C₃×#41	—	3	1	no	—
211	C₃×#41	—	5	1	no	—
212	C₃×#41	—	5	1	no	—
213	C₃×#41	—	10	1	no	—
214	C₃×#41	—	15	2	no	—
215	C₃×#41	—	15	1	no	—
216	C₃×#41	—	15	2	no	—
217	C₃×#41	—	15	1	no	—
218	C₂×C₃×Q₈	—	15	1	no	—
219	C₂×C₃×D₄	—	15	2	no	—
220	C₂×C₃×D₄	—	15	1	no	—
221	C₂²×C₃×C₄	—	15	2	no	—
222	C₂²×C₃×C₄	—	15	1	no	—
223	#239	—	5	1	no	—
224	D₃×Q₈	—	5	1	no	—
225	#237	—	5	2	no	—
226	#237	C₃×D₅	1	1	yes	characteristic, complemented
227	D₃×D₄	—	5	1	no	—
228	D₃×D₄	—	5	2	no	—
229	#235	—	5	2	no	—
230	#235	—	5	1	no	—
231	C₂×C₄×D₃	—	5	2	no	—
232	C₂×C₄×D₃	—	5	1	no	—
233	C₃²×C₅	C₂×#41	1	1	yes	characteristic, complemented, Hall
234	C₂²×D₅	—	3	2	no	—
235	C₂²×D₅	—	3	1	no	—
236	C₅×Q₈	—	3	1	no	—
237	C₅×D₄	—	3	2	no	—
238	C₅×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
239	C₂×C₄×C₅	—	3	2	no	—
240	C₂×C₄×C₅	—	3	1	no	—
241	C₂²⋊D₅	—	3	2	no	—
242	C₂²⋊D₅	—	3	2	no	—
243	C₂²⋊D₅	C₂×C₃×D₃	1	2	yes	complemented
244	C₂×Dic₅	—	3	1	no	—
245	C₂×Dic₅	C₂×C₃×D₃	1	2	yes	complemented
246	D₂₀	—	3	2	no	—
247	D₂₀	—	3	1	no	—
248	C₄×D₅	—	3	1	no	—
249	C₄×D₅	—	3	1	no	—
250	C₄×D₅	—	3	1	no	—
251	C₄×D₅	—	3	2	no	—
252	C₄×D₅	—	3	2	no	—
253	C₄×D₅	—	3	2	no	—
254	C₄×D₅	C₂×C₃×D₃	1	1	yes	characteristic, complemented
255	Dic₁₀	—	3	2	no	—
256	Dic₁₀	C₂×C₃×D₃	1	1	yes	characteristic, complemented
257	C₂²×C₃²	—	5	1	no	—
258	C₂²×C₃²	C₂²×D₅	1	2	yes	—
259	C₂×C₃×D₃	—	5	1	no	—
260	C₂×C₃×D₃	—	5	2	no	—
261	C₂×C₃×D₃	—	10	2	no	—
262	C₂×C₃×D₃	—	10	4	no	—
263	C₂×C₃×D₃	C₂²×D₅	1	1	yes	characteristic
264	C₃²×C₄	—	5	2	no	—
265	C₃²×C₄	—	5	1	no	—
266	C₃²×C₄	C₂²×D₅	1	1	yes	characteristic
267	C₃×Dic₃	—	5	1	no	—
268	C₃×Dic₃	C₂²×D₅	1	2	yes	—
269	C₃×Dic₃	C₂²×D₅	1	1	yes	characteristic
270	C₂×#41	—	15	1	no	Sylow
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	—	2	2	no	—
273	C₂×C₃×C₅	—	2	1	no	—
274	C₂×C₃×C₅	—	4	2	no	—
275	C₂×C₃×C₅	—	6	1	no	—
276	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂⁴×C₃	1	1	yes	characteristic
278	D₁₅	—	2	2	no	—
279	D₁₅	C₃×#41	1	2	yes	complemented
280	C₃×D₅	—	2	1	no	—
281	C₃×D₅	—	2	1	no	—
282	C₃×D₅	—	3	2	no	—
283	C₃×D₅	—	4	1	no	—
284	C₃×D₅	—	6	2	no	—
285	C₅×D₃	—	2	1	no	—
286	C₂³×C₃	—	15	1	no	—
287	C₂³×C₃	—	15	2	no	—
288	C₂²×D₃	—	5	2	no	—
289	C₂²×D₃	—	5	1	no	—
290	C₃×Q₈	—	3	1	no	—
291	C₃×Q₈	—	5	1	no	—
292	C₃×Q₈	—	5	1	no	—
293	C₃×Q₈	—	10	1	no	—
294	C₃×Q₈	—	15	2	no	—
295	C₃×D₄	—	2	1	no	—
296	C₃×D₄	—	3	2	no	—
297	C₃×D₄	—	5	2	no	—
298	C₃×D₄	—	5	2	no	—
299	C₃×D₄	—	10	2	no	—
300	C₃×D₄	—	15	2	no	—
301	C₃×D₄	—	15	2	no	—
302	C₃×D₄	—	15	2	no	—
303	C₃×D₄	—	15	1	no	—
304	C₃×D₄	D₃×D₅	1	1	yes	characteristic, complemented
305	C₃×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
306	C₂×C₃×C₄	—	3	2	no	—
307	C₂×C₃×C₄	—	3	1	no	—
308	C₂×C₃×C₄	—	5	2	no	—
309	C₂×C₃×C₄	—	5	2	no	—
310	C₂×C₃×C₄	—	5	1	no	—
311	C₂×C₃×C₄	—	5	1	no	—
312	C₂×C₃×C₄	—	10	1	no	—
313	C₂×C₃×C₄	—	10	2	no	—
314	C₂×C₃×C₄	—	15	1	no	—
315	C₂×C₃×C₄	—	15	2	no	—
316	C₂×C₃×C₄	—	15	2	no	—
317	C₂×C₃×C₄	—	15	2	no	—
318	C₂×C₃×C₄	—	15	1	no	—
319	C₂×C₃×C₄	—	15	1	no	—
320	C₂×C₃×C₄	—	15	1	no	—
321	#67	—	5	2	no	—
322	#67	—	5	2	no	—
323	#67	C₂×C₃×D₅	1	2	yes	complemented
324	C₂×Dic₃	—	5	1	no	—
325	C₂×Dic₃	C₂×C₃×D₅	1	2	yes	complemented
326	D₁₂	—	5	2	no	—
327	D₁₂	—	5	1	no	—
328	C₄×D₃	—	5	1	no	—
329	C₄×D₃	—	5	1	no	—
330	C₄×D₃	—	5	1	no	—
331	C₄×D₃	—	5	2	no	—
332	C₄×D₃	—	5	2	no	—
333	C₄×D₃	—	5	2	no	—
334	C₄×D₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented
335	Dic₆	—	5	2	no	—
336	Dic₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
337	C₂²×C₅	—	3	1	no	—
338	C₂²×C₅	C₂²×C₃×D₃	1	2	yes	—
339	C₂×D₅	—	3	1	no	—
340	C₂×D₅	—	3	2	no	—
341	C₂×D₅	—	6	2	no	—
342	C₂×D₅	—	6	4	no	—
343	C₂×D₅	C₂²×C₃×D₃	1	1	yes	characteristic
344	C₄×C₅	—	3	2	no	—
345	C₄×C₅	—	3	1	no	—
346	C₄×C₅	C₂²×C₃×D₃	1	1	yes	characteristic
347	Dic₅	—	3	1	no	—
348	Dic₅	C₂²×C₃×D₃	1	2	yes	—
349	Dic₅	C₂²×C₃×D₃	1	1	yes	characteristic
350	C₂×C₃²	—	2	2	no	—
351	C₂×C₃²	—	10	1	no	—
352	C₂×C₃²	C₂³×D₅	1	1	yes	characteristic
353	C₃×D₃	—	2	1	no	—
354	C₃×D₃	—	5	2	no	—
355	C₃×D₃	—	10	2	no	—
356	#41	—	3	1	no	—
357	#41	—	5	1	no	—
358	#41	—	15	2	no	—
359	#41	—	15	1	no	—
360	#41	—	15	2	no	—
361	#41	—	15	1	no	—
362	C₂×Q₈	—	15	1	no	—
363	C₂×D₄	—	15	2	no	—
364	C₂×D₄	—	15	1	no	—
365	C₂²×C₄	—	15	2	no	—
366	C₂²×C₄	—	15	1	no	—
367	C₃×C₅	—	2	1	no	—
368	C₃×C₅	D₃×#41	1	1	yes	characteristic, complemented
369	C₃×C₅	C₂×C₃×#41	1	1	yes	characteristic, complemented
370	C₂²×C₃	—	2	2	no	—
371	C₂²×C₃	—	3	1	no	—
372	C₂²×C₃	—	5	1	no	—
373	C₂²×C₃	—	5	1	no	—
374	C₂²×C₃	—	10	1	no	—
375	C₂²×C₃	—	15	1	no	—
376	C₂²×C₃	—	15	2	no	—
377	C₂²×C₃	—	30	4	no	—
378	C₂²×C₃	—	30	2	no	—
379	C₂²×C₃	C₂×D₃×D₅	1	2	yes	—
380	C₂²×C₃	C₂²×C₃×D₅	1	2	yes	—
381	C₂×D₃	—	5	1	no	—
382	C₂×D₃	—	5	2	no	—
383	C₂×D₃	—	10	2	no	—
384	C₂×D₃	—	10	4	no	—
385	C₂×D₃	C₂²×C₃×D₅	1	1	yes	characteristic
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	3	1	no	—
388	C₃×C₄	—	3	2	no	—
389	C₃×C₄	—	5	1	no	—
390	C₃×C₄	—	5	2	no	—
391	C₃×C₄	—	5	2	no	—
392	C₃×C₄	—	5	1	no	—
393	C₃×C₄	—	10	1	no	—
394	C₃×C₄	—	10	2	no	—
395	C₃×C₄	—	15	1	no	—
396	C₃×C₄	C₂×D₃×D₅	1	1	yes	characteristic
397	C₃×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
398	Dic₃	—	5	1	no	—
399	Dic₃	C₂²×C₃×D₅	1	2	yes	—
400	Dic₃	C₂²×C₃×D₅	1	1	yes	characteristic
401	C₂×C₅	—	2	2	no	—
402	C₂×C₅	—	6	1	no	—
403	C₂×C₅	C₂³×C₃×D₃	1	1	yes	characteristic
404	D₅	—	2	1	no	—
405	D₅	—	3	2	no	—
406	D₅	—	6	2	no	—
407	C₃²	D₅×#41	1	1	yes	characteristic, complemented, Sylow
408	C₂³	—	15	1	no	—
409	C₂³	—	15	2	no	—
410	Q₈	—	3	1	no	—
411	Q₈	—	5	1	no	—
412	Q₈	—	15	2	no	—
413	D₄	—	3	2	no	—
414	D₄	—	5	2	no	—
415	D₄	—	15	2	no	—
416	D₄	—	15	2	no	—
417	D₄	—	15	2	no	—
418	D₄	—	15	1	no	—
419	D₄	C₃×D₃×D₅	1	1	yes	characteristic, complemented
420	C₂×C₄	—	3	2	no	—
421	C₂×C₄	—	3	1	no	—
422	C₂×C₄	—	5	2	no	—
423	C₂×C₄	—	5	1	no	—
424	C₂×C₄	—	15	1	no	—
425	C₂×C₄	—	15	2	no	—
426	C₂×C₄	—	15	2	no	—
427	C₂×C₄	—	15	2	no	—
428	C₂×C₄	—	15	1	no	—
429	C₂×C₄	—	15	1	no	—
430	C₂×C₄	—	15	1	no	—
431	C₂×C₃	—	2	2	no	—
432	C₂×C₃	—	2	2	no	—
433	C₂×C₃	—	2	1	no	—
434	C₂×C₃	—	4	2	no	—
435	C₂×C₃	—	6	1	no	—
436	C₂×C₃	—	10	1	no	—
437	C₂×C₃	—	10	1	no	—
438	C₂×C₃	—	15	2	no	—
439	C₂×C₃	—	20	1	no	—
440	C₂×C₃	—	30	2	no	—
441	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
442	C₂×C₃	C₂³×C₃×D₅	1	1	yes	characteristic
443	D₃	—	2	1	no	—
444	D₃	—	5	2	no	—
445	D₃	—	10	2	no	—
446	C₅	C₃×D₃×#41	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	3	1	no	—
448	C₂²	—	5	1	no	—
449	C₂²	—	15	1	no	—
450	C₂²	—	15	2	no	—
451	C₂²	—	30	4	no	—
452	C₂²	—	30	2	no	—
453	C₂²	C₂×C₃×D₃×D₅	1	2	yes	—
454	C₄	—	3	1	no	—
455	C₄	—	3	2	no	—
456	C₄	—	5	1	no	—
457	C₄	—	5	2	no	—
458	C₄	—	15	1	no	—
459	C₄	C₂×C₃×D₃×D₅	1	1	yes	characteristic
460	C₃	—	2	1	no	—
461	C₃	#92024	1	1	yes	characteristic, direct product factor
462	C₃	C₃×D₅×#41	1	1	yes	characteristic, complemented
463	C₂	—	2	2	no	—
464	C₂	—	6	1	no	—
465	C₂	—	10	1	no	—
466	C₂	—	15	2	no	—
467	C₂	—	30	2	no	—
468	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×D₄×D₁₅	C₂	semidirect
2. C₃×C₅×#237	C₂	semidirect
3. C₃²×#711	C₂	semidirect
4. C₃×#6790	C₂	semidirect
5. C₂×C₃×#1200	C₂	semidirect
6. C₃×#6782	C₂	semidirect
7. C₃×#6779	C₂	semidirect
8. C₃×C₄×D₃×D₅	C₂	semidirect
9. C₃×#6773	C₂	semidirect
10. C₃×D₁₅⋊Q₈	C₂	semidirect
11. C₃×#6769	C₂	semidirect
13. #92024	C₃	direct (N × H)
16. C₃²×C₅×D₄	C₂²	semidirect
17. C₃×#1220	C₂²	semidirect
18. C₃×D₆₀	C₂²	semidirect
20. C₃×C₅×#67	C₂²	semidirect
21. C₂×C₃×C₅×Dic₃	C₂²	semidirect
22. C₃×C₄×C₅×D₃	C₂²	semidirect
23. C₃×C₅×Dic₆	C₂²	semidirect
24. C₃²×C₂²⋊D₅	C₂²	semidirect
25. C₂×C₃²×Dic₅	C₂²	semidirect
26. C₃²×C₄×D₅	C₂²	semidirect
27. C₃²×Dic₁₀	C₂²	semidirect
28. C₃×#1204	C₂²	semidirect
29. C₃×#1203	C₂²	semidirect
30. C₃×#1202	C₂²	semidirect
33. C₃×#1200	C₂²	semidirect
34. C₃×#1200	C₂²	semidirect
35. C₃×D₃×Dic₅	C₂²	semidirect
36. C₃×D₅×Dic₃	C₂²	semidirect
39. D₄×D₁₅	C₂×C₃	semidirect
40. C₅×#237	C₂×C₃	semidirect
45. C₃×#711	D₃	semidirect
46. C₃×#711	C₂×C₃	semidirect
53. #6790	C₂×C₃	semidirect
54. C₂×#1200	C₂×C₃	semidirect
55. #6782	C₂×C₃	semidirect
56. #6779	C₂×C₃	semidirect
57. C₄×D₃×D₅	C₂×C₃	semidirect
58. #6773	C₂×C₃	semidirect
59. D₁₅⋊Q₈	C₂×C₃	semidirect
60. #6769	C₂×C₃	semidirect
79. C₃×#237	D₅	semidirect
93. C₃×C₅×D₄	C₂×D₃	semidirect
94. C₃×C₅×D₄	C₂²×C₃	semidirect
97. #1220	C₂²×C₃	semidirect
98. D₆₀	C₂²×C₃	semidirect
100. C₅×#67	C₂²×C₃	semidirect
101. C₂×C₅×Dic₃	C₂²×C₃	semidirect
102. C₄×C₅×D₃	C₂²×C₃	semidirect
103. C₅×Dic₆	C₂²×C₃	semidirect
107. C₃×C₂²⋊D₅	C₂×D₃	semidirect
108. C₃×C₂²⋊D₅	C₂²×C₃	semidirect
111. C₂×C₃×Dic₅	C₂×D₃	semidirect
112. C₂×C₃×Dic₅	C₂²×C₃	semidirect
122. C₃×C₄×D₅	C₂×D₃	semidirect
123. C₃×C₄×D₅	C₂²×C₃	semidirect
126. C₃×Dic₁₀	C₂×D₃	semidirect
127. C₃×Dic₁₀	C₂²×C₃	semidirect
128. #1204	C₂²×C₃	semidirect
129. #1203	C₂²×C₃	semidirect
130. #1202	C₂²×C₃	semidirect
133. #1200	C₂²×C₃	semidirect
134. #1200	C₂²×C₃	semidirect
135. D₃×Dic₅	C₂²×C₃	semidirect
136. D₅×Dic₃	C₂²×C₃	semidirect
142. C₃×D₁₅	#41	semidirect
149. #711	C₃×D₃	semidirect
160. C₃²×D₄	C₂×D₅	semidirect
165. C₃×#67	C₂×D₅	semidirect
167. C₂×C₃×Dic₃	C₂×D₅	semidirect
176. C₃×C₄×D₃	C₂×D₅	semidirect
178. C₃×Dic₆	C₂×D₅	semidirect
226. #237	C₃×D₅	semidirect
233. C₃²×C₅	C₂×#41	semidirect
238. C₅×D₄	C₂×C₃×D₃	semidirect
243. C₂²⋊D₅	C₂×C₃×D₃	semidirect
245. C₂×Dic₅	C₂×C₃×D₃	semidirect
254. C₄×D₅	C₂×C₃×D₃	semidirect
256. Dic₁₀	C₂×C₃×D₃	semidirect
279. D₁₅	C₃×#41	semidirect
304. C₃×D₄	D₃×D₅	semidirect
305. C₃×D₄	C₂×C₃×D₅	semidirect
323. #67	C₂×C₃×D₅	semidirect
325. C₂×Dic₃	C₂×C₃×D₅	semidirect
334. C₄×D₃	C₂×C₃×D₅	semidirect
336. Dic₆	C₂×C₃×D₅	semidirect
368. C₃×C₅	D₃×#41	semidirect
369. C₃×C₅	C₂×C₃×#41	semidirect
407. C₃²	D₅×#41	semidirect
419. D₄	C₃×D₃×D₅	semidirect
446. C₅	C₃×D₃×#41	semidirect
461. C₃	#92024	direct (N × H)
462. 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×D₄×D₁₅	2
C₃×C₅×#237	2
C₃²×#711	2
C₃×#6790	2
C₂×C₃×#1200	2
C₃×#6782	2
C₃×#6779	2
C₃×C₄×D₃×D₅	2
C₃×#6773	2
C₃×D₁₅⋊Q₈	2
C₃×#6769	2
C₃×D₅×#41	3
#92024	3
C₃×D₃×#41	5

Subgroups — C3×#92024 #13089228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#92024 #13089228