Subgroups — C₃×#92027 #13089231

Order 1440.

704 conjugacy classes of subgroups.

The subgroup lattice has 486 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×D₃×D₄	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	C₃×D₃×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#1203	C₂	1	2	yes	maximal, complemented
7	C₃×#6782	C₂	1	2	yes	maximal, complemented
8	C₃×D₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6771	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6769	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4144	—	3	1	no	maximal
13	#92027	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃×D₁₅	C₂²	1	2	yes	complemented
15	C₂²×C₃×C₅×D₃	C₂²	1	2	yes	complemented
16	C₂×C₃×D₃×D₅	C₂²	1	2	yes	complemented
17	C₃²×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₃×#1220	C₂²	1	2	yes	complemented
19	C₃×D₆₀	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₄×D₁₅	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#67	C₂²	1	2	yes	complemented
22	C₃×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₄×C₅×D₃	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	1	yes	characteristic, complemented
29	C₃×#1203	C₂²	1	2	yes	complemented
30	C₃×#1203	C₂²	1	2	yes	complemented
31	C₃×#1203	C₂²	1	1	yes	characteristic, complemented
32	C₃×#1203	C₂²	1	2	yes	complemented
33	C₃×#1202	C₂²	1	1	yes	characteristic, complemented
34	C₃×#1201	C₂²	1	1	yes	characteristic, complemented
35	C₃×#1200	C₂²	1	2	yes	complemented
36	C₃×D₃×Dic₅	C₂²	1	2	yes	complemented
37	C₃×#1009	—	5	1	no	maximal, Hall
38	C₂×C₃×C₅×D₄	—	3	1	no	—
39	D₄×D₁₅	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×C₃×C₂²⋊D₅	—	3	2	no	—
42	C₂×C₃×C₂²⋊D₅	—	3	2	no	—
43	C₃×#711	—	2	1	no	—
44	C₃×#711	—	3	2	no	—
45	C₃×#711	—	3	1	no	—
46	C₃×#711	D₃	1	1	yes	characteristic, complemented
47	C₃×#711	C₂×C₃	1	1	yes	characteristic, complemented
48	C₃×D₄×D₅	—	3	1	no	—
49	C₃×D₄×D₅	—	3	2	no	—
50	C₃×D₄×D₅	—	3	1	no	—
51	C₃×#709	—	3	1	no	—
52	C₃×#709	—	3	1	no	—
53	#6790	C₂×C₃	1	2	yes	complemented
54	D₃×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
55	C₂×#1203	C₂×C₃	1	2	yes	complemented
56	#6782	C₂×C₃	1	2	yes	complemented
57	D₅×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
58	#6771	C₂×C₃	1	1	yes	characteristic, complemented
59	#6769	C₂×C₃	1	1	yes	characteristic, complemented
60	#6768	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂²×C₃²×C₅	C₂³	1	2	yes	—
62	C₂×C₃×D₁₅	—	4	2	no	—
63	C₂×C₃×D₁₅	C₂³	1	2	yes	—
64	C₂×C₃×D₁₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×D₃	—	4	2	no	—
66	C₂×C₃×C₅×D₃	C₂³	1	2	yes	—
67	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
68	C₂×C₃²×D₅	C₂³	1	1	yes	characteristic
69	C₃×D₃×D₅	—	4	2	no	—
70	C₃²×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₃×Dic₁₅	C₂³	1	1	yes	characteristic
72	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
73	C₃²×Dic₅	C₂³	1	2	yes	—
74	C₃²×Dic₅	C₂³	1	1	yes	characteristic
75	#4144	—	3	1	no	Hall
76	C₃²×#41	—	5	1	no	—
77	C₃×#239	—	5	1	no	—
78	C₃×#239	—	5	1	no	—
79	C₃×D₃×D₄	—	5	2	no	—
80	C₃×D₃×D₄	—	5	1	no	—
81	C₃×D₃×D₄	—	5	2	no	—
82	C₃×D₃×D₄	D₅	1	1	yes	characteristic, complemented
83	C₃×#235	—	5	2	no	—
84	C₃×#235	—	5	1	no	—
85	C₂×C₃×D₁₂	—	5	2	no	—
86	C₂×C₃×D₁₂	—	5	1	no	—
87	C₂³×C₃×C₅	—	3	2	no	—
88	C₂²×D₁₅	C₂²×C₃	1	2	yes	complemented
89	C₂²×C₅×D₃	C₂²×C₃	1	2	yes	complemented
90	C₂²×C₃×D₅	—	3	2	no	—
91	C₂²×C₃×D₅	—	3	2	no	—
92	C₂×D₃×D₅	C₂²×C₃	1	2	yes	complemented
93	C₃×C₅×D₄	—	2	1	no	—
94	C₃×C₅×D₄	—	3	2	no	—
95	C₃×C₅×D₄	—	3	1	no	—
96	C₃×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
97	C₃×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₂×C₃×C₄×C₅	—	3	1	no	—
99	#1220	C₂²×C₃	1	2	yes	complemented
100	D₆₀	C₂²×C₃	1	1	yes	characteristic, complemented
101	C₄×D₁₅	C₂²×C₃	1	1	yes	characteristic, complemented
102	C₅×#67	C₂²×C₃	1	2	yes	complemented
103	C₅×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₄×C₅×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₃×C₂²⋊D₅	—	2	2	no	—
106	C₃×C₂²⋊D₅	—	3	2	no	—
107	C₃×C₂²⋊D₅	—	3	1	no	—
108	C₃×C₂²⋊D₅	—	3	1	no	—
109	C₃×C₂²⋊D₅	—	3	2	no	—
110	C₃×C₂²⋊D₅	—	3	2	no	—
111	C₃×C₂²⋊D₅	—	3	2	no	—
112	C₃×C₂²⋊D₅	C₂×D₃	1	2	yes	complemented
113	C₃×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
114	C₂×C₃×Dic₅	—	2	2	no	—
115	C₂×C₃×Dic₅	—	3	2	no	—
116	C₂×C₃×Dic₅	C₂×D₃	1	2	yes	complemented
117	C₂×C₃×Dic₅	C₂²×C₃	1	2	yes	complemented
118	C₃×D₂₀	—	3	1	no	—
119	C₃×D₂₀	—	3	1	no	—
120	C₃×C₄×D₅	—	2	1	no	—
121	C₃×C₄×D₅	—	3	1	no	—
122	C₃×C₄×D₅	—	3	2	no	—
123	C₃×C₄×D₅	C₂×D₃	1	1	yes	characteristic, complemented
124	C₃×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₃×Dic₁₀	—	2	1	no	—
126	C₃×Dic₁₀	—	3	1	no	—
127	C₃×Dic₁₀	C₂×D₃	1	1	yes	characteristic, complemented
128	C₃×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
129	#1204	C₂²×C₃	1	1	yes	characteristic, complemented
130	#1203	C₂²×C₃	1	2	yes	complemented
131	#1203	C₂²×C₃	1	2	yes	complemented
132	#1203	C₂²×C₃	1	1	yes	characteristic, complemented
133	#1203	C₂²×C₃	1	2	yes	complemented
134	#1202	C₂²×C₃	1	1	yes	characteristic, complemented
135	#1201	C₂²×C₃	1	1	yes	characteristic, complemented
136	#1200	C₂²×C₃	1	2	yes	complemented
137	D₃×Dic₅	C₂²×C₃	1	2	yes	complemented
138	C₃×H(5,𝔽₂)	—	15	1	no	—
139	#1009	—	5	1	no	—
140	C₂×C₃²×C₅	—	2	2	no	—
141	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
142	C₃×D₁₅	—	2	2	no	—
143	C₃×D₁₅	—	2	1	no	—
144	C₃×C₅×D₃	—	2	2	no	—
145	C₃×C₅×D₃	—	2	1	no	—
146	C₃²×D₅	—	2	1	no	—
147	C₂×C₅×D₄	—	3	1	no	—
148	C₂×C₂²⋊D₅	—	3	2	no	—
149	C₂×C₂²⋊D₅	—	3	2	no	—
150	#711	—	3	2	no	—
151	#711	—	3	1	no	—
152	#711	C₃×D₃	1	1	yes	characteristic, complemented
153	D₄×D₅	—	3	1	no	—
154	D₄×D₅	—	3	2	no	—
155	D₄×D₅	—	3	1	no	—
156	#709	—	3	1	no	—
157	#709	—	3	1	no	—
158	C₂²×C₃×D₃	—	5	2	no	—
159	C₂²×C₃×D₃	—	5	2	no	—
160	C₂²×C₃×D₃	C₂×D₅	1	2	yes	complemented
161	C₃²×Q₈	—	5	1	no	—
162	C₃²×D₄	—	5	2	no	—
163	C₃²×D₄	C₂×D₅	1	1	yes	characteristic, complemented
164	C₂×C₃²×C₄	—	5	2	no	—
165	C₂×C₃²×C₄	—	5	1	no	—
166	C₃×#67	—	5	2	no	—
167	C₃×#67	—	5	1	no	—
168	C₃×#67	—	5	1	no	—
169	C₃×#67	C₂×D₅	1	2	yes	complemented
170	C₃×D₁₂	—	5	2	no	—
171	C₃×D₁₂	—	5	1	no	—
172	C₃×D₁₂	—	5	2	no	—
173	C₃×D₁₂	—	5	2	no	—
174	C₃×D₁₂	—	5	1	no	—
175	C₃×D₁₂	C₂×D₅	1	1	yes	characteristic, complemented
176	C₃×C₄×D₃	—	5	2	no	—
177	C₃×C₄×D₃	—	5	1	no	—
178	C₃×C₄×D₃	—	5	2	no	—
179	C₃×C₄×D₃	C₂×D₅	1	1	yes	characteristic, complemented
180	C₃×Dic₆	—	5	1	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	3	2	no	—
183	C₂²×C₃×C₅	—	3	1	no	—
184	C₂²×C₃×C₅	—	12	2	no	—
185	C₂²×C₃×C₅	C₂²×D₃	1	2	yes	—
186	C₂²×C₃×C₅	C₂³×C₃	1	2	yes	—
187	C₂×D₁₅	—	4	2	no	—
188	C₂×D₁₅	C₂³×C₃	1	2	yes	—
189	C₂×D₁₅	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₅×D₃	—	4	2	no	—
191	C₂×C₅×D₃	C₂³×C₃	1	2	yes	—
192	C₂×C₅×D₃	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₃×D₅	—	2	1	no	—
194	C₂×C₃×D₅	—	3	2	no	—
195	C₂×C₃×D₅	—	3	1	no	—
196	C₂×C₃×D₅	—	12	2	no	—
197	C₂×C₃×D₅	—	12	2	no	—
198	C₂×C₃×D₅	C₂²×D₃	1	1	yes	characteristic
199	C₂×C₃×D₅	C₂³×C₃	1	1	yes	characteristic
200	D₃×D₅	—	4	2	no	—
201	C₃×C₄×C₅	—	2	1	no	—
202	C₃×C₄×C₅	—	3	1	no	—
203	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
204	C₃×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	Dic₁₅	C₂³×C₃	1	1	yes	characteristic
206	C₃×Dic₅	—	2	2	no	—
207	C₃×Dic₅	—	2	1	no	—
208	C₃×Dic₅	—	3	1	no	—
209	C₃×Dic₅	C₂²×D₃	1	1	yes	characteristic
210	C₃×Dic₅	C₂²×D₃	1	2	yes	—
211	C₃×Dic₅	C₂³×C₃	1	2	yes	—
212	C₃×Dic₅	C₂³×C₃	1	1	yes	characteristic
213	C₅×Dic₃	C₂³×C₃	1	1	yes	characteristic
214	C₃×#41	—	5	1	no	—
215	C₃×#41	—	5	1	no	—
216	C₃×#41	—	10	1	no	—
217	C₃×#41	—	15	1	no	—
218	C₃×#41	—	15	1	no	—
219	C₃×#41	—	15	2	no	—
220	C₃×#41	—	15	1	no	—
221	C₂×C₃×D₄	—	3	1	no	—
222	C₂×C₃×D₄	—	15	1	no	—
223	C₂×C₃×D₄	—	15	2	no	—
224	C₂×C₃×D₄	—	15	2	no	—
225	C₂×C₃×D₄	—	15	2	no	—
226	C₂×C₃×D₄	—	15	1	no	—
227	#239	—	5	1	no	—
228	#239	—	5	1	no	—
229	D₃×D₄	—	5	2	no	—
230	D₃×D₄	—	5	1	no	—
231	D₃×D₄	—	5	2	no	—
232	D₃×D₄	C₃×D₅	1	1	yes	characteristic, complemented
233	#235	—	5	2	no	—
234	#235	—	5	1	no	—
235	C₂×D₁₂	—	5	2	no	—
236	C₂×D₁₂	—	5	1	no	—
237	C₃²×C₅	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
238	C₂³×C₅	—	3	2	no	—
239	C₂²×D₅	—	3	2	no	—
240	C₂²×D₅	—	3	2	no	—
241	C₅×D₄	—	3	2	no	—
242	C₅×D₄	—	3	1	no	—
243	C₅×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
244	C₂×C₄×C₅	—	3	1	no	—
245	C₂²⋊D₅	—	3	2	no	—
246	C₂²⋊D₅	—	3	1	no	—
247	C₂²⋊D₅	—	3	1	no	—
248	C₂²⋊D₅	—	3	2	no	—
249	C₂²⋊D₅	—	3	2	no	—
250	C₂²⋊D₅	—	3	2	no	—
251	C₂²⋊D₅	C₂×C₃×D₃	1	2	yes	complemented
252	C₂×Dic₅	—	3	2	no	—
253	C₂×Dic₅	C₂×C₃×D₃	1	2	yes	complemented
254	D₂₀	—	3	1	no	—
255	D₂₀	—	3	1	no	—
256	C₄×D₅	—	3	1	no	—
257	C₄×D₅	—	3	2	no	—
258	C₄×D₅	C₂×C₃×D₃	1	1	yes	characteristic, complemented
259	Dic₁₀	—	3	1	no	—
260	Dic₁₀	C₂×C₃×D₃	1	1	yes	characteristic, complemented
261	C₂²×C₃²	—	5	1	no	—
262	C₂²×C₃²	C₂²×D₅	1	2	yes	—
263	C₂×C₃×D₃	—	4	2	no	—
264	C₂×C₃×D₃	—	5	2	no	—
265	C₂×C₃×D₃	—	5	1	no	—
266	C₂×C₃×D₃	—	20	2	no	—
267	C₂×C₃×D₃	—	20	2	no	—
268	C₂×C₃×D₃	C₂²×D₅	1	2	yes	—
269	C₂×C₃×D₃	C₂²×D₅	1	1	yes	characteristic
270	C₃²×C₄	—	5	1	no	—
271	C₃²×C₄	—	5	2	no	—
272	C₃²×C₄	C₂²×D₅	1	1	yes	characteristic
273	C₃×Dic₃	—	5	1	no	—
274	C₃×Dic₃	C₂²×D₅	1	1	yes	characteristic
275	H(5,𝔽₂)	—	15	1	no	Sylow
276	C₂×C₃×C₅	—	2	2	no	—
277	C₂×C₃×C₅	—	2	2	no	—
278	C₂×C₃×C₅	—	2	1	no	—
279	C₂×C₃×C₅	—	4	2	no	—
280	C₂×C₃×C₅	—	6	2	no	—
281	C₂×C₃×C₅	—	6	1	no	—
282	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
283	C₂×C₃×C₅	C₂⁴×C₃	1	1	yes	characteristic
284	D₁₅	—	2	2	no	—
285	D₁₅	—	2	1	no	—
286	C₃×D₅	—	2	1	no	—
287	C₃×D₅	—	2	1	no	—
288	C₃×D₅	—	4	1	no	—
289	C₃×D₅	—	6	2	no	—
290	C₃×D₅	—	6	1	no	—
291	C₅×D₃	—	2	2	no	—
292	C₅×D₃	—	2	1	no	—
293	C₂³×C₃	—	3	2	no	—
294	C₂³×C₃	—	15	2	no	—
295	C₂³×C₃	—	15	2	no	—
296	C₂²×D₃	—	5	2	no	—
297	C₂²×D₃	—	5	2	no	—
298	C₂²×D₃	C₂×C₃×D₅	1	2	yes	complemented
299	C₃×Q₈	—	5	1	no	—
300	C₃×Q₈	—	5	1	no	—
301	C₃×Q₈	—	10	1	no	—
302	C₃×Q₈	—	15	1	no	—
303	C₃×D₄	—	2	1	no	—
304	C₃×D₄	—	3	2	no	—
305	C₃×D₄	—	3	1	no	—
306	C₃×D₄	—	5	2	no	—
307	C₃×D₄	—	5	2	no	—
308	C₃×D₄	—	10	2	no	—
309	C₃×D₄	—	15	1	no	—
310	C₃×D₄	—	15	1	no	—
311	C₃×D₄	—	15	2	no	—
312	C₃×D₄	—	15	2	no	—
313	C₃×D₄	—	15	2	no	—
314	C₃×D₄	—	15	1	no	—
315	C₃×D₄	—	15	2	no	—
316	C₃×D₄	—	15	1	no	—
317	C₃×D₄	D₃×D₅	1	1	yes	characteristic, complemented
318	C₃×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
319	C₂×C₃×C₄	—	3	1	no	—
320	C₂×C₃×C₄	—	5	2	no	—
321	C₂×C₃×C₄	—	5	2	no	—
322	C₂×C₃×C₄	—	5	1	no	—
323	C₂×C₃×C₄	—	5	1	no	—
324	C₂×C₃×C₄	—	10	1	no	—
325	C₂×C₃×C₄	—	10	2	no	—
326	C₂×C₃×C₄	—	15	2	no	—
327	C₂×C₃×C₄	—	15	2	no	—
328	C₂×C₃×C₄	—	15	1	no	—
329	#67	—	5	2	no	—
330	#67	—	5	1	no	—
331	#67	—	5	1	no	—
332	#67	C₂×C₃×D₅	1	2	yes	complemented
333	D₁₂	—	5	2	no	—
334	D₁₂	—	5	1	no	—
335	D₁₂	—	5	2	no	—
336	D₁₂	—	5	2	no	—
337	D₁₂	—	5	1	no	—
338	D₁₂	C₂×C₃×D₅	1	1	yes	characteristic, complemented
339	C₄×D₃	—	5	2	no	—
340	C₄×D₃	—	5	1	no	—
341	C₄×D₃	—	5	2	no	—
342	C₄×D₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented
343	Dic₆	—	5	1	no	—
344	C₂²×C₅	—	3	2	no	—
345	C₂²×C₅	—	3	1	no	—
346	C₂²×C₅	—	12	2	no	—
347	C₂²×C₅	C₂²×C₃×D₃	1	2	yes	—
348	C₂×D₅	—	3	2	no	—
349	C₂×D₅	—	3	1	no	—
350	C₂×D₅	—	12	2	no	—
351	C₂×D₅	—	12	2	no	—
352	C₂×D₅	C₂²×C₃×D₃	1	1	yes	characteristic
353	C₄×C₅	—	3	1	no	—
354	C₄×C₅	C₂²×C₃×D₃	1	1	yes	characteristic
355	Dic₅	—	3	1	no	—
356	Dic₅	C₂²×C₃×D₃	1	1	yes	characteristic
357	Dic₅	C₂²×C₃×D₃	1	2	yes	—
358	C₂×C₃²	—	2	2	no	—
359	C₂×C₃²	—	10	1	no	—
360	C₂×C₃²	C₂³×D₅	1	1	yes	characteristic
361	C₃×D₃	—	2	1	no	—
362	C₃×D₃	—	2	2	no	—
363	C₃×D₃	—	10	2	no	—
364	C₃×D₃	—	10	1	no	—
365	#41	—	5	1	no	—
366	#41	—	15	1	no	—
367	#41	—	15	1	no	—
368	#41	—	15	2	no	—
369	#41	—	15	1	no	—
370	C₂×D₄	—	3	1	no	—
371	C₂×D₄	—	15	1	no	—
372	C₂×D₄	—	15	2	no	—
373	C₂×D₄	—	15	2	no	—
374	C₂×D₄	—	15	2	no	—
375	C₂×D₄	—	15	1	no	—
376	C₃×C₅	—	2	1	no	—
377	C₃×C₅	#1009	1	1	yes	characteristic, complemented
378	C₃×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	3	1	no	—
381	C₂²×C₃	—	3	2	no	—
382	C₂²×C₃	—	5	1	no	—
383	C₂²×C₃	—	5	1	no	—
384	C₂²×C₃	—	10	1	no	—
385	C₂²×C₃	—	12	2	no	—
386	C₂²×C₃	—	15	2	no	—
387	C₂²×C₃	—	15	1	no	—
388	C₂²×C₃	—	60	2	no	—
389	C₂²×C₃	—	60	2	no	—
390	C₂²×C₃	C₂×D₃×D₅	1	2	yes	—
391	C₂²×C₃	C₂²×C₃×D₅	1	2	yes	—
392	C₂×D₃	—	4	2	no	—
393	C₂×D₃	—	5	2	no	—
394	C₂×D₃	—	5	1	no	—
395	C₂×D₃	—	20	2	no	—
396	C₂×D₃	—	20	2	no	—
397	C₂×D₃	C₂²×C₃×D₅	1	2	yes	—
398	C₂×D₃	C₂²×C₃×D₅	1	1	yes	characteristic
399	C₃×C₄	—	2	1	no	—
400	C₃×C₄	—	3	1	no	—
401	C₃×C₄	—	5	1	no	—
402	C₃×C₄	—	5	2	no	—
403	C₃×C₄	—	5	1	no	—
404	C₃×C₄	—	5	2	no	—
405	C₃×C₄	—	10	1	no	—
406	C₃×C₄	—	10	2	no	—
407	C₃×C₄	—	15	1	no	—
408	C₃×C₄	C₂×D₃×D₅	1	1	yes	characteristic
409	C₃×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
410	Dic₃	—	5	1	no	—
411	Dic₃	C₂²×C₃×D₅	1	1	yes	characteristic
412	C₂×C₅	—	2	2	no	—
413	C₂×C₅	—	6	2	no	—
414	C₂×C₅	—	6	1	no	—
415	C₂×C₅	C₂³×C₃×D₃	1	1	yes	characteristic
416	D₅	—	2	1	no	—
417	D₅	—	6	2	no	—
418	D₅	—	6	1	no	—
419	C₃²	#4144	1	1	yes	characteristic, complemented, Sylow
420	C₂³	—	3	2	no	—
421	C₂³	—	15	2	no	—
422	C₂³	—	15	2	no	—
423	Q₈	—	5	1	no	—
424	Q₈	—	15	1	no	—
425	D₄	—	3	2	no	—
426	D₄	—	3	1	no	—
427	D₄	—	5	2	no	—
428	D₄	—	15	1	no	—
429	D₄	—	15	1	no	—
430	D₄	—	15	2	no	—
431	D₄	—	15	2	no	—
432	D₄	—	15	2	no	—
433	D₄	—	15	1	no	—
434	D₄	—	15	2	no	—
435	D₄	—	15	1	no	—
436	D₄	C₃×D₃×D₅	1	1	yes	characteristic, complemented
437	C₂×C₄	—	3	1	no	—
438	C₂×C₄	—	5	2	no	—
439	C₂×C₄	—	5	1	no	—
440	C₂×C₄	—	15	2	no	—
441	C₂×C₄	—	15	2	no	—
442	C₂×C₄	—	15	1	no	—
443	C₂×C₃	—	2	2	no	—
444	C₂×C₃	—	2	2	no	—
445	C₂×C₃	—	2	1	no	—
446	C₂×C₃	—	4	2	no	—
447	C₂×C₃	—	6	1	no	—
448	C₂×C₃	—	6	2	no	—
449	C₂×C₃	—	10	1	no	—
450	C₂×C₃	—	10	1	no	—
451	C₂×C₃	—	20	1	no	—
452	C₂×C₃	—	30	1	no	—
453	C₂×C₃	—	30	2	no	—
454	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
455	C₂×C₃	C₂³×C₃×D₅	1	1	yes	characteristic
456	D₃	—	2	1	no	—
457	D₃	—	2	2	no	—
458	D₃	—	10	2	no	—
459	D₃	—	10	1	no	—
460	C₅	C₃×#1009	1	1	yes	characteristic, complemented, Sylow
461	C₂²	—	3	1	no	—
462	C₂²	—	3	2	no	—
463	C₂²	—	5	1	no	—
464	C₂²	—	12	2	no	—
465	C₂²	—	15	2	no	—
466	C₂²	—	15	1	no	—
467	C₂²	—	60	2	no	—
468	C₂²	—	60	2	no	—
469	C₂²	C₂×C₃×D₃×D₅	1	2	yes	—
470	C₄	—	3	1	no	—
471	C₄	—	5	1	no	—
472	C₄	—	5	2	no	—
473	C₄	—	15	1	no	—
474	C₄	C₂×C₃×D₃×D₅	1	1	yes	characteristic
475	C₃	—	2	1	no	—
476	C₃	#92027	1	1	yes	characteristic, direct product factor
477	C₃	C₃×#4144	1	1	yes	characteristic, complemented
478	C₂	—	2	2	no	—
479	C₂	—	6	1	no	—
480	C₂	—	6	2	no	—
481	C₂	—	10	1	no	—
482	C₂	—	30	1	no	—
483	C₂	—	30	2	no	—
484	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	C₃×H(5,𝔽₂)
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×D₃×D₄	C₂	semidirect
3. C₃²×#711	C₂	semidirect
4. C₃×#6790	C₂	semidirect
5. C₃×D₃×C₂²⋊D₅	C₂	semidirect
6. C₂×C₃×#1203	C₂	semidirect
7. C₃×#6782	C₂	semidirect
8. C₃×D₅×D₁₂	C₂	semidirect
9. C₃×#6771	C₂	semidirect
10. C₃×#6769	C₂	semidirect
11. C₃×#6768	C₂	semidirect
13. #92027	C₃	direct (N × H)
14. C₂²×C₃×D₁₅	C₂²	semidirect
15. C₂²×C₃×C₅×D₃	C₂²	semidirect
16. C₂×C₃×D₃×D₅	C₂²	semidirect
17. C₃²×C₅×D₄	C₂²	semidirect
18. C₃×#1220	C₂²	semidirect
19. C₃×D₆₀	C₂²	semidirect
20. C₃×C₄×D₁₅	C₂²	semidirect
21. C₃×C₅×#67	C₂²	semidirect
22. C₃×C₅×D₁₂	C₂²	semidirect
23. C₃×C₄×C₅×D₃	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×#1203	C₂²	semidirect
31. C₃×#1203	C₂²	semidirect
32. C₃×#1203	C₂²	semidirect
33. C₃×#1202	C₂²	semidirect
34. C₃×#1201	C₂²	semidirect
35. C₃×#1200	C₂²	semidirect
36. C₃×D₃×Dic₅	C₂²	semidirect
39. D₄×D₁₅	C₂×C₃	semidirect
40. C₅×D₃×D₄	C₂×C₃	semidirect
46. C₃×#711	D₃	semidirect
47. C₃×#711	C₂×C₃	semidirect
53. #6790	C₂×C₃	semidirect
54. D₃×C₂²⋊D₅	C₂×C₃	semidirect
55. C₂×#1203	C₂×C₃	semidirect
56. #6782	C₂×C₃	semidirect
57. D₅×D₁₂	C₂×C₃	semidirect
58. #6771	C₂×C₃	semidirect
59. #6769	C₂×C₃	semidirect
60. #6768	C₂×C₃	semidirect
82. C₃×D₃×D₄	D₅	semidirect
88. C₂²×D₁₅	C₂²×C₃	semidirect
89. C₂²×C₅×D₃	C₂²×C₃	semidirect
92. C₂×D₃×D₅	C₂²×C₃	semidirect
96. C₃×C₅×D₄	C₂×D₃	semidirect
97. C₃×C₅×D₄	C₂²×C₃	semidirect
99. #1220	C₂²×C₃	semidirect
100. D₆₀	C₂²×C₃	semidirect
101. C₄×D₁₅	C₂²×C₃	semidirect
102. C₅×#67	C₂²×C₃	semidirect
103. C₅×D₁₂	C₂²×C₃	semidirect
104. C₄×C₅×D₃	C₂²×C₃	semidirect
112. C₃×C₂²⋊D₅	C₂×D₃	semidirect
113. C₃×C₂²⋊D₅	C₂²×C₃	semidirect
116. C₂×C₃×Dic₅	C₂×D₃	semidirect
117. C₂×C₃×Dic₅	C₂²×C₃	semidirect
123. C₃×C₄×D₅	C₂×D₃	semidirect
124. C₃×C₄×D₅	C₂²×C₃	semidirect
127. C₃×Dic₁₀	C₂×D₃	semidirect
128. C₃×Dic₁₀	C₂²×C₃	semidirect
129. #1204	C₂²×C₃	semidirect
130. #1203	C₂²×C₃	semidirect
131. #1203	C₂²×C₃	semidirect
132. #1203	C₂²×C₃	semidirect
133. #1203	C₂²×C₃	semidirect
134. #1202	C₂²×C₃	semidirect
135. #1201	C₂²×C₃	semidirect
136. #1200	C₂²×C₃	semidirect
137. D₃×Dic₅	C₂²×C₃	semidirect
152. #711	C₃×D₃	semidirect
160. C₂²×C₃×D₃	C₂×D₅	semidirect
163. C₃²×D₄	C₂×D₅	semidirect
169. C₃×#67	C₂×D₅	semidirect
175. C₃×D₁₂	C₂×D₅	semidirect
179. C₃×C₄×D₃	C₂×D₅	semidirect
232. D₃×D₄	C₃×D₅	semidirect
237. C₃²×C₅	H(5,𝔽₂)	semidirect
243. C₅×D₄	C₂×C₃×D₃	semidirect
251. C₂²⋊D₅	C₂×C₃×D₃	semidirect
253. C₂×Dic₅	C₂×C₃×D₃	semidirect
258. C₄×D₅	C₂×C₃×D₃	semidirect
260. Dic₁₀	C₂×C₃×D₃	semidirect
298. C₂²×D₃	C₂×C₃×D₅	semidirect
317. C₃×D₄	D₃×D₅	semidirect
318. C₃×D₄	C₂×C₃×D₅	semidirect
332. #67	C₂×C₃×D₅	semidirect
338. D₁₂	C₂×C₃×D₅	semidirect
342. C₄×D₃	C₂×C₃×D₅	semidirect
377. C₃×C₅	#1009	semidirect
378. C₃×C₅	C₃×H(5,𝔽₂)	semidirect
419. C₃²	#4144	semidirect
436. D₄	C₃×D₃×D₅	semidirect
460. C₅	C₃×#1009	semidirect
476. C₃	#92027	direct (N × H)
477. C₃	C₃×#4144	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×D₃×D₄	2
C₃²×#711	2
C₃×#6790	2
C₃×D₃×C₂²⋊D₅	2
C₂×C₃×#1203	2
C₃×#6782	2
C₃×D₅×D₁₂	2
C₃×#6771	2
C₃×#6769	2
C₃×#6768	2
C₃×#4144	3
#92027	3
C₃×#1009	5

Subgroups — C3×#92027 #13089231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#92027 #13089231