Subgroups — C₃×#92025 #13089229

Order 1440.

718 conjugacy classes of subgroups.

The subgroup lattice has 490 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×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₃×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
5	C₃×D₅×#67	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#1201	C₂	1	2	yes	maximal, complemented
7	C₃×#6780	C₂	1	2	yes	maximal, complemented
8	C₃×#6777	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6772	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6771	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6765	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4144	—	3	1	no	maximal
13	#92025	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃×C₅×D₃	C₂²	1	2	yes	complemented
15	C₂²×C₃²×D₅	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	C₂×C₃×Dic₁₅	C₂²	1	2	yes	complemented
20	C₃×C₄×D₁₅	C₂²	1	1	yes	characteristic, complemented
21	C₃×Dic₃₀	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×#67	C₂²	1	2	yes	complemented
23	C₃×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₄×C₅×D₃	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, complemented
28	C₃×#1204	C₂²	1	1	yes	characteristic, complemented
29	C₃×#1203	C₂²	1	1	yes	characteristic, complemented
30	C₃×#1202	C₂²	1	1	yes	characteristic, complemented
31	C₃×#1201	C₂²	1	2	yes	complemented
32	C₃×#1201	C₂²	1	1	yes	characteristic, complemented
33	C₃×#1201	C₂²	1	2	yes	complemented
34	C₃×#1201	C₂²	1	2	yes	complemented
35	C₃×D₃×Dic₅	C₂²	1	2	yes	complemented
36	C₃×D₅×Dic₃	C₂²	1	2	yes	complemented
37	C₃×#1004	—	5	1	no	maximal, Hall
38	C₂×C₃×C₅×D₄	—	3	1	no	—
39	#6819	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	—	3	1	no	—
44	C₃×#711	—	3	2	no	—
45	C₃×#711	—	3	1	no	—
46	C₃×D₄×D₅	—	2	1	no	—
47	C₃×D₄×D₅	—	3	2	no	—
48	C₃×D₄×D₅	—	3	1	no	—
49	C₃×D₄×D₅	D₃	1	1	yes	characteristic, complemented
50	C₃×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
51	C₃×#709	—	3	1	no	—
52	C₃×#709	—	3	1	no	—
53	D₃×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
54	D₅×#67	C₂×C₃	1	2	yes	complemented
55	C₂×#1201	C₂×C₃	1	2	yes	complemented
56	#6780	C₂×C₃	1	2	yes	complemented
57	#6777	C₂×C₃	1	1	yes	characteristic, complemented
58	#6772	C₂×C₃	1	1	yes	characteristic, complemented
59	#6771	C₂×C₃	1	1	yes	characteristic, complemented
60	#6765	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	—	4	2	no	—
64	C₂×C₃×C₅×D₃	C₂³	1	2	yes	—
65	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
66	C₂×C₃²×D₅	—	4	2	no	—
67	C₂×C₃²×D₅	C₂³	1	2	yes	—
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	2	yes	—
72	C₃×Dic₁₅	C₂³	1	1	yes	characteristic
73	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
74	C₃²×Dic₅	C₂³	1	1	yes	characteristic
75	#4144	—	3	1	no	Hall
76	C₂×C₃²×D₄	—	5	1	no	—
77	C₂×C₃×#67	—	5	2	no	—
78	C₂×C₃×#67	—	5	2	no	—
79	C₃×#237	—	5	1	no	—
80	C₃×#237	—	5	2	no	—
81	C₃×#237	—	5	1	no	—
82	C₃×D₃×D₄	—	5	2	no	—
83	C₃×D₃×D₄	—	5	1	no	—
84	C₃×D₃×D₄	D₅	1	1	yes	characteristic, complemented
85	C₃×#235	—	5	1	no	—
86	C₃×#235	—	5	1	no	—
87	C₂³×C₃×C₅	—	3	2	no	—
88	C₂²×C₅×D₃	C₂²×C₃	1	2	yes	complemented
89	C₂²×C₃×D₅	—	2	2	no	—
90	C₂²×C₃×D₅	—	3	2	no	—
91	C₂²×C₃×D₅	C₂×D₃	1	2	yes	complemented
92	C₂²×C₃×D₅	C₂²×C₃	1	2	yes	complemented
93	C₂×D₃×D₅	C₂²×C₃	1	2	yes	complemented
94	C₃×C₅×D₄	—	2	1	no	—
95	C₃×C₅×D₄	—	3	2	no	—
96	C₃×C₅×D₄	—	3	1	no	—
97	C₃×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
98	C₃×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₂×C₃×C₄×C₅	—	3	1	no	—
100	#1220	C₂²×C₃	1	2	yes	complemented
101	C₂×Dic₁₅	C₂²×C₃	1	2	yes	complemented
102	C₄×D₁₅	C₂²×C₃	1	1	yes	characteristic, complemented
103	Dic₃₀	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₅×#67	C₂²×C₃	1	2	yes	complemented
105	C₅×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₄×C₅×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₃×C₂²⋊D₅	—	2	2	no	—
108	C₃×C₂²⋊D₅	—	3	2	no	—
109	C₃×C₂²⋊D₅	—	3	2	no	—
110	C₃×C₂²⋊D₅	—	3	1	no	—
111	C₃×C₂²⋊D₅	—	3	2	no	—
112	C₃×C₂²⋊D₅	—	3	2	no	—
113	C₃×C₂²⋊D₅	—	3	1	no	—
114	C₃×C₂²⋊D₅	C₂×D₃	1	2	yes	complemented
115	C₃×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
116	C₂×C₃×Dic₅	—	3	2	no	—
117	C₂×C₃×Dic₅	—	3	2	no	—
118	C₃×D₂₀	—	2	1	no	—
119	C₃×D₂₀	—	3	1	no	—
120	C₃×D₂₀	C₂×D₃	1	1	yes	characteristic, complemented
121	C₃×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₃×C₄×D₅	—	2	1	no	—
123	C₃×C₄×D₅	—	3	2	no	—
124	C₃×C₄×D₅	—	3	1	no	—
125	C₃×C₄×D₅	C₂×D₃	1	1	yes	characteristic, complemented
126	C₃×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₃×Dic₁₀	—	3	1	no	—
128	C₃×Dic₁₀	—	3	1	no	—
129	#1204	C₂²×C₃	1	1	yes	characteristic, complemented
130	#1203	C₂²×C₃	1	1	yes	characteristic, complemented
131	#1202	C₂²×C₃	1	1	yes	characteristic, complemented
132	#1201	C₂²×C₃	1	2	yes	complemented
133	#1201	C₂²×C₃	1	1	yes	characteristic, complemented
134	#1201	C₂²×C₃	1	2	yes	complemented
135	#1201	C₂²×C₃	1	2	yes	complemented
136	D₃×Dic₅	C₂²×C₃	1	2	yes	complemented
137	D₅×Dic₃	C₂²×C₃	1	2	yes	complemented
138	C₃×H(5,𝔽₂)	—	15	1	no	—
139	#1004	—	5	1	no	—
140	C₂×C₃²×C₅	—	2	2	no	—
141	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
142	C₃×D₁₅	—	2	1	no	—
143	C₃×C₅×D₃	—	2	2	no	—
144	C₃×C₅×D₃	—	2	1	no	—
145	C₃²×D₅	—	2	1	no	—
146	C₃²×D₅	—	2	2	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	1	no	—
151	#711	—	3	2	no	—
152	#711	—	3	1	no	—
153	D₄×D₅	—	3	2	no	—
154	D₄×D₅	—	3	1	no	—
155	D₄×D₅	C₃×D₃	1	1	yes	characteristic, complemented
156	#709	—	3	1	no	—
157	#709	—	3	1	no	—
158	C₂³×C₃²	—	5	2	no	—
159	C₂²×C₃×D₃	—	5	2	no	—
160	C₂²×C₃×D₃	C₂×D₅	1	2	yes	complemented
161	C₃²×D₄	—	5	2	no	—
162	C₃²×D₄	—	5	1	no	—
163	C₃²×D₄	C₂×D₅	1	1	yes	characteristic, complemented
164	C₂×C₃²×C₄	—	5	1	no	—
165	C₃×#67	—	5	2	no	—
166	C₃×#67	—	5	2	no	—
167	C₃×#67	—	5	1	no	—
168	C₃×#67	—	5	2	no	—
169	C₃×#67	—	5	2	no	—
170	C₃×#67	—	5	1	no	—
171	C₃×#67	C₂×D₅	1	2	yes	complemented
172	C₂×C₃×Dic₃	—	5	2	no	—
173	C₂×C₃×Dic₃	—	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	C₂×D₅	1	1	yes	characteristic, complemented
179	C₃×Dic₆	—	5	1	no	—
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	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₅×D₃	—	4	2	no	—
189	C₂×C₅×D₃	C₂³×C₃	1	2	yes	—
190	C₂×C₅×D₃	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₃×D₅	—	2	1	no	—
192	C₂×C₃×D₅	—	2	2	no	—
193	C₂×C₃×D₅	—	3	1	no	—
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	4	2	no	—
196	C₂×C₃×D₅	—	4	4	no	—
197	C₂×C₃×D₅	—	12	2	no	—
198	C₂×C₃×D₅	C₂²×D₃	1	2	yes	—
199	C₂×C₃×D₅	C₂²×D₃	1	1	yes	characteristic
200	C₂×C₃×D₅	C₂³×C₃	1	2	yes	—
201	C₂×C₃×D₅	C₂³×C₃	1	1	yes	characteristic
202	D₃×D₅	—	4	2	no	—
203	C₃×C₄×C₅	—	2	1	no	—
204	C₃×C₄×C₅	—	3	1	no	—
205	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
206	C₃×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
207	Dic₁₅	C₂³×C₃	1	2	yes	—
208	Dic₁₅	C₂³×C₃	1	1	yes	characteristic
209	C₃×Dic₅	—	2	1	no	—
210	C₃×Dic₅	—	3	2	no	—
211	C₃×Dic₅	—	3	1	no	—
212	C₃×Dic₅	C₂²×D₃	1	1	yes	characteristic
213	C₃×Dic₅	C₂³×C₃	1	1	yes	characteristic
214	C₅×Dic₃	C₂³×C₃	1	1	yes	characteristic
215	C₃×#41	—	15	1	no	—
216	C₃×#41	—	15	1	no	—
217	C₃×#41	—	15	1	no	—
218	C₃×#41	—	15	2	no	—
219	C₃×#41	—	15	1	no	—
220	C₂×C₃×D₄	—	3	1	no	—
221	C₂×C₃×D₄	—	5	1	no	—
222	C₂×C₃×D₄	—	5	1	no	—
223	C₂×C₃×D₄	—	10	1	no	—
224	C₂×C₃×D₄	—	15	1	no	—
225	C₂×C₃×D₄	—	15	2	no	—
226	C₂×C₃×D₄	—	15	2	no	—
227	C₂×C₃×D₄	—	15	2	no	—
228	C₂×#67	—	5	2	no	—
229	C₂×#67	—	5	2	no	—
230	#237	—	5	1	no	—
231	#237	—	5	2	no	—
232	#237	—	5	1	no	—
233	D₃×D₄	—	5	2	no	—
234	D₃×D₄	—	5	1	no	—
235	D₃×D₄	C₃×D₅	1	1	yes	characteristic, complemented
236	#235	—	5	1	no	—
237	#235	—	5	1	no	—
238	C₃²×C₅	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
239	C₂³×C₅	—	3	2	no	—
240	C₂²×D₅	—	3	2	no	—
241	C₂²×D₅	C₂×C₃×D₃	1	2	yes	complemented
242	C₅×D₄	—	3	2	no	—
243	C₅×D₄	—	3	1	no	—
244	C₅×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
245	C₂×C₄×C₅	—	3	1	no	—
246	C₂²⋊D₅	—	3	2	no	—
247	C₂²⋊D₅	—	3	2	no	—
248	C₂²⋊D₅	—	3	1	no	—
249	C₂²⋊D₅	—	3	2	no	—
250	C₂²⋊D₅	—	3	2	no	—
251	C₂²⋊D₅	—	3	1	no	—
252	C₂²⋊D₅	C₂×C₃×D₃	1	2	yes	complemented
253	C₂×Dic₅	—	3	2	no	—
254	C₂×Dic₅	—	3	2	no	—
255	D₂₀	—	3	1	no	—
256	D₂₀	C₂×C₃×D₃	1	1	yes	characteristic, complemented
257	C₄×D₅	—	3	2	no	—
258	C₄×D₅	—	3	1	no	—
259	C₄×D₅	C₂×C₃×D₃	1	1	yes	characteristic, complemented
260	Dic₁₀	—	3	1	no	—
261	Dic₁₀	—	3	1	no	—
262	C₂²×C₃²	—	5	2	no	—
263	C₂²×C₃²	—	5	1	no	—
264	C₂²×C₃²	—	20	2	no	—
265	C₂²×C₃²	C₂²×D₅	1	2	yes	—
266	C₂×C₃×D₃	—	4	2	no	—
267	C₂×C₃×D₃	—	5	1	no	—
268	C₂×C₃×D₃	—	20	2	no	—
269	C₂×C₃×D₃	C₂²×D₅	1	2	yes	—
270	C₂×C₃×D₃	C₂²×D₅	1	1	yes	characteristic
271	C₃²×C₄	—	5	1	no	—
272	C₃²×C₄	C₂²×D₅	1	1	yes	characteristic
273	C₃×Dic₃	—	5	2	no	—
274	C₃×Dic₃	—	5	1	no	—
275	C₃×Dic₃	C₂²×D₅	1	1	yes	characteristic
276	H(5,𝔽₂)	—	15	1	no	Sylow
277	C₂×C₃×C₅	—	2	2	no	—
278	C₂×C₃×C₅	—	2	2	no	—
279	C₂×C₃×C₅	—	2	1	no	—
280	C₂×C₃×C₅	—	4	2	no	—
281	C₂×C₃×C₅	—	6	2	no	—
282	C₂×C₃×C₅	—	6	1	no	—
283	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
284	C₂×C₃×C₅	C₂⁴×C₃	1	1	yes	characteristic
285	D₁₅	—	2	1	no	—
286	C₃×D₅	—	2	2	no	—
287	C₃×D₅	—	2	1	no	—
288	C₃×D₅	—	2	2	no	—
289	C₃×D₅	—	2	2	no	—
290	C₃×D₅	—	2	1	no	—
291	C₃×D₅	—	4	2	no	—
292	C₃×D₅	—	6	1	no	—
293	C₅×D₃	—	2	2	no	—
294	C₅×D₃	—	2	1	no	—
295	C₂³×C₃	—	3	2	no	—
296	C₂³×C₃	—	5	2	no	—
297	C₂³×C₃	—	5	2	no	—
298	C₂³×C₃	—	10	2	no	—
299	C₂³×C₃	—	15	2	no	—
300	C₂²×D₃	—	5	2	no	—
301	C₂²×D₃	C₂×C₃×D₅	1	2	yes	complemented
302	C₃×Q₈	—	15	1	no	—
303	C₃×Q₈	—	15	1	no	—
304	C₃×D₄	—	2	1	no	—
305	C₃×D₄	—	3	2	no	—
306	C₃×D₄	—	3	1	no	—
307	C₃×D₄	—	5	2	no	—
308	C₃×D₄	—	5	2	no	—
309	C₃×D₄	—	5	1	no	—
310	C₃×D₄	—	5	1	no	—
311	C₃×D₄	—	10	1	no	—
312	C₃×D₄	—	10	2	no	—
313	C₃×D₄	—	15	1	no	—
314	C₃×D₄	—	15	1	no	—
315	C₃×D₄	—	15	1	no	—
316	C₃×D₄	—	15	2	no	—
317	C₃×D₄	—	15	2	no	—
318	C₃×D₄	—	15	2	no	—
319	C₃×D₄	—	15	2	no	—
320	C₃×D₄	D₃×D₅	1	1	yes	characteristic, complemented
321	C₃×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
322	C₂×C₃×C₄	—	3	1	no	—
323	C₂×C₃×C₄	—	5	1	no	—
324	C₂×C₃×C₄	—	5	1	no	—
325	C₂×C₃×C₄	—	10	1	no	—
326	C₂×C₃×C₄	—	15	2	no	—
327	C₂×C₃×C₄	—	15	2	no	—
328	C₂×C₃×C₄	—	15	2	no	—
329	C₂×C₃×C₄	—	15	1	no	—
330	#67	—	5	2	no	—
331	#67	—	5	2	no	—
332	#67	—	5	1	no	—
333	#67	—	5	2	no	—
334	#67	—	5	2	no	—
335	#67	—	5	1	no	—
336	#67	C₂×C₃×D₅	1	2	yes	complemented
337	C₂×Dic₃	—	5	2	no	—
338	C₂×Dic₃	—	5	2	no	—
339	D₁₂	—	5	1	no	—
340	D₁₂	C₂×C₃×D₅	1	1	yes	characteristic, complemented
341	C₄×D₃	—	5	2	no	—
342	C₄×D₃	—	5	1	no	—
343	C₄×D₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented
344	Dic₆	—	5	1	no	—
345	Dic₆	—	5	1	no	—
346	C₂²×C₅	—	3	2	no	—
347	C₂²×C₅	—	3	1	no	—
348	C₂²×C₅	—	12	2	no	—
349	C₂²×C₅	C₂²×C₃×D₃	1	2	yes	—
350	C₂×D₅	—	3	1	no	—
351	C₂×D₅	—	4	2	no	—
352	C₂×D₅	—	12	2	no	—
353	C₂×D₅	C₂²×C₃×D₃	1	2	yes	—
354	C₂×D₅	C₂²×C₃×D₃	1	1	yes	characteristic
355	C₄×C₅	—	3	1	no	—
356	C₄×C₅	C₂²×C₃×D₃	1	1	yes	characteristic
357	Dic₅	—	3	2	no	—
358	Dic₅	—	3	1	no	—
359	Dic₅	C₂²×C₃×D₃	1	1	yes	characteristic
360	C₂×C₃²	—	2	2	no	—
361	C₂×C₃²	—	10	1	no	—
362	C₂×C₃²	—	10	2	no	—
363	C₂×C₃²	C₂³×D₅	1	1	yes	characteristic
364	C₃×D₃	—	2	1	no	—
365	C₃×D₃	—	2	2	no	—
366	C₃×D₃	—	10	1	no	—
367	#41	—	15	1	no	—
368	#41	—	15	1	no	—
369	#41	—	15	1	no	—
370	#41	—	15	2	no	—
371	#41	—	15	1	no	—
372	C₂×D₄	—	3	1	no	—
373	C₂×D₄	—	5	1	no	—
374	C₂×D₄	—	15	1	no	—
375	C₂×D₄	—	15	2	no	—
376	C₂×D₄	—	15	2	no	—
377	C₂×D₄	—	15	2	no	—
378	C₃×C₅	—	2	1	no	—
379	C₃×C₅	#1004	1	1	yes	characteristic, complemented
380	C₃×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	3	1	no	—
383	C₂²×C₃	—	3	2	no	—
384	C₂²×C₃	—	5	1	no	—
385	C₂²×C₃	—	5	2	no	—
386	C₂²×C₃	—	5	2	no	—
387	C₂²×C₃	—	5	1	no	—
388	C₂²×C₃	—	10	1	no	—
389	C₂²×C₃	—	10	2	no	—
390	C₂²×C₃	—	12	2	no	—
391	C₂²×C₃	—	15	1	no	—
392	C₂²×C₃	—	20	2	no	—
393	C₂²×C₃	—	20	2	no	—
394	C₂²×C₃	—	20	4	no	—
395	C₂²×C₃	—	60	2	no	—
396	C₂²×C₃	C₂×D₃×D₅	1	2	yes	—
397	C₂²×C₃	C₂²×C₃×D₅	1	2	yes	—
398	C₂×D₃	—	4	2	no	—
399	C₂×D₃	—	5	1	no	—
400	C₂×D₃	—	20	2	no	—
401	C₂×D₃	C₂²×C₃×D₅	1	2	yes	—
402	C₂×D₃	C₂²×C₃×D₅	1	1	yes	characteristic
403	C₃×C₄	—	2	1	no	—
404	C₃×C₄	—	3	1	no	—
405	C₃×C₄	—	5	1	no	—
406	C₃×C₄	—	5	1	no	—
407	C₃×C₄	—	10	1	no	—
408	C₃×C₄	—	15	2	no	—
409	C₃×C₄	—	15	1	no	—
410	C₃×C₄	C₂×D₃×D₅	1	1	yes	characteristic
411	C₃×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
412	Dic₃	—	5	2	no	—
413	Dic₃	—	5	1	no	—
414	Dic₃	C₂²×C₃×D₅	1	1	yes	characteristic
415	C₂×C₅	—	2	2	no	—
416	C₂×C₅	—	6	2	no	—
417	C₂×C₅	—	6	1	no	—
418	C₂×C₅	C₂³×C₃×D₃	1	1	yes	characteristic
419	D₅	—	2	1	no	—
420	D₅	—	2	2	no	—
421	D₅	—	6	1	no	—
422	C₃²	#4144	1	1	yes	characteristic, complemented, Sylow
423	C₂³	—	3	2	no	—
424	C₂³	—	5	2	no	—
425	C₂³	—	15	2	no	—
426	Q₈	—	15	1	no	—
427	Q₈	—	15	1	no	—
428	D₄	—	3	2	no	—
429	D₄	—	3	1	no	—
430	D₄	—	5	2	no	—
431	D₄	—	5	1	no	—
432	D₄	—	15	1	no	—
433	D₄	—	15	1	no	—
434	D₄	—	15	1	no	—
435	D₄	—	15	2	no	—
436	D₄	—	15	2	no	—
437	D₄	—	15	2	no	—
438	D₄	—	15	2	no	—
439	D₄	C₃×D₃×D₅	1	1	yes	characteristic, complemented
440	C₂×C₄	—	3	1	no	—
441	C₂×C₄	—	5	1	no	—
442	C₂×C₄	—	15	2	no	—
443	C₂×C₄	—	15	2	no	—
444	C₂×C₄	—	15	2	no	—
445	C₂×C₄	—	15	1	no	—
446	C₂×C₃	—	2	2	no	—
447	C₂×C₃	—	2	2	no	—
448	C₂×C₃	—	2	1	no	—
449	C₂×C₃	—	4	2	no	—
450	C₂×C₃	—	6	1	no	—
451	C₂×C₃	—	6	2	no	—
452	C₂×C₃	—	10	2	no	—
453	C₂×C₃	—	10	1	no	—
454	C₂×C₃	—	10	2	no	—
455	C₂×C₃	—	10	2	no	—
456	C₂×C₃	—	10	1	no	—
457	C₂×C₃	—	20	2	no	—
458	C₂×C₃	—	30	1	no	—
459	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
460	C₂×C₃	C₂³×C₃×D₅	1	1	yes	characteristic
461	D₃	—	2	1	no	—
462	D₃	—	2	2	no	—
463	D₃	—	10	1	no	—
464	C₅	C₃×#1004	1	1	yes	characteristic, complemented, Sylow
465	C₂²	—	3	1	no	—
466	C₂²	—	3	2	no	—
467	C₂²	—	5	1	no	—
468	C₂²	—	5	2	no	—
469	C₂²	—	12	2	no	—
470	C₂²	—	15	1	no	—
471	C₂²	—	20	2	no	—
472	C₂²	—	60	2	no	—
473	C₂²	C₂×C₃×D₃×D₅	1	2	yes	—
474	C₄	—	3	1	no	—
475	C₄	—	5	1	no	—
476	C₄	—	15	2	no	—
477	C₄	—	15	1	no	—
478	C₄	C₂×C₃×D₃×D₅	1	1	yes	characteristic
479	C₃	—	2	1	no	—
480	C₃	#92025	1	1	yes	characteristic, direct product factor
481	C₃	C₃×#4144	1	1	yes	characteristic, complemented
482	C₂	—	2	2	no	—
483	C₂	—	6	1	no	—
484	C₂	—	6	2	no	—
485	C₂	—	10	1	no	—
486	C₂	—	10	2	no	—
487	C₂	—	30	1	no	—
488	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×#6819	C₂	semidirect
2. C₃×C₅×D₃×D₄	C₂	semidirect
3. C₃²×D₄×D₅	C₂	semidirect
4. C₃×D₃×C₂²⋊D₅	C₂	semidirect
5. C₃×D₅×#67	C₂	semidirect
6. C₂×C₃×#1201	C₂	semidirect
7. C₃×#6780	C₂	semidirect
8. C₃×#6777	C₂	semidirect
9. C₃×#6772	C₂	semidirect
10. C₃×#6771	C₂	semidirect
11. C₃×#6765	C₂	semidirect
13. #92025	C₃	direct (N × H)
14. C₂²×C₃×C₅×D₃	C₂²	semidirect
15. C₂²×C₃²×D₅	C₂²	semidirect
16. C₂×C₃×D₃×D₅	C₂²	semidirect
17. C₃²×C₅×D₄	C₂²	semidirect
18. C₃×#1220	C₂²	semidirect
19. C₂×C₃×Dic₁₅	C₂²	semidirect
20. C₃×C₄×D₁₅	C₂²	semidirect
21. C₃×Dic₃₀	C₂²	semidirect
22. C₃×C₅×#67	C₂²	semidirect
23. C₃×C₅×D₁₂	C₂²	semidirect
24. C₃×C₄×C₅×D₃	C₂²	semidirect
25. C₃²×C₂²⋊D₅	C₂²	semidirect
26. C₃²×D₂₀	C₂²	semidirect
27. C₃²×C₄×D₅	C₂²	semidirect
28. C₃×#1204	C₂²	semidirect
29. C₃×#1203	C₂²	semidirect
30. C₃×#1202	C₂²	semidirect
31. C₃×#1201	C₂²	semidirect
32. C₃×#1201	C₂²	semidirect
33. C₃×#1201	C₂²	semidirect
34. C₃×#1201	C₂²	semidirect
35. C₃×D₃×Dic₅	C₂²	semidirect
36. C₃×D₅×Dic₃	C₂²	semidirect
39. #6819	C₂×C₃	semidirect
40. C₅×D₃×D₄	C₂×C₃	semidirect
49. C₃×D₄×D₅	D₃	semidirect
50. C₃×D₄×D₅	C₂×C₃	semidirect
53. D₃×C₂²⋊D₅	C₂×C₃	semidirect
54. D₅×#67	C₂×C₃	semidirect
55. C₂×#1201	C₂×C₃	semidirect
56. #6780	C₂×C₃	semidirect
57. #6777	C₂×C₃	semidirect
58. #6772	C₂×C₃	semidirect
59. #6771	C₂×C₃	semidirect
60. #6765	C₂×C₃	semidirect
84. C₃×D₃×D₄	D₅	semidirect
88. C₂²×C₅×D₃	C₂²×C₃	semidirect
91. C₂²×C₃×D₅	C₂×D₃	semidirect
92. C₂²×C₃×D₅	C₂²×C₃	semidirect
93. C₂×D₃×D₅	C₂²×C₃	semidirect
97. C₃×C₅×D₄	C₂×D₃	semidirect
98. C₃×C₅×D₄	C₂²×C₃	semidirect
100. #1220	C₂²×C₃	semidirect
101. C₂×Dic₁₅	C₂²×C₃	semidirect
102. C₄×D₁₅	C₂²×C₃	semidirect
103. Dic₃₀	C₂²×C₃	semidirect
104. C₅×#67	C₂²×C₃	semidirect
105. C₅×D₁₂	C₂²×C₃	semidirect
106. C₄×C₅×D₃	C₂²×C₃	semidirect
114. C₃×C₂²⋊D₅	C₂×D₃	semidirect
115. C₃×C₂²⋊D₅	C₂²×C₃	semidirect
120. C₃×D₂₀	C₂×D₃	semidirect
121. C₃×D₂₀	C₂²×C₃	semidirect
125. C₃×C₄×D₅	C₂×D₃	semidirect
126. C₃×C₄×D₅	C₂²×C₃	semidirect
129. #1204	C₂²×C₃	semidirect
130. #1203	C₂²×C₃	semidirect
131. #1202	C₂²×C₃	semidirect
132. #1201	C₂²×C₃	semidirect
133. #1201	C₂²×C₃	semidirect
134. #1201	C₂²×C₃	semidirect
135. #1201	C₂²×C₃	semidirect
136. D₃×Dic₅	C₂²×C₃	semidirect
137. D₅×Dic₃	C₂²×C₃	semidirect
155. D₄×D₅	C₃×D₃	semidirect
160. C₂²×C₃×D₃	C₂×D₅	semidirect
163. C₃²×D₄	C₂×D₅	semidirect
171. C₃×#67	C₂×D₅	semidirect
175. C₃×D₁₂	C₂×D₅	semidirect
178. C₃×C₄×D₃	C₂×D₅	semidirect
235. D₃×D₄	C₃×D₅	semidirect
238. C₃²×C₅	H(5,𝔽₂)	semidirect
241. C₂²×D₅	C₂×C₃×D₃	semidirect
244. C₅×D₄	C₂×C₃×D₃	semidirect
252. C₂²⋊D₅	C₂×C₃×D₃	semidirect
256. D₂₀	C₂×C₃×D₃	semidirect
259. C₄×D₅	C₂×C₃×D₃	semidirect
301. C₂²×D₃	C₂×C₃×D₅	semidirect
320. C₃×D₄	D₃×D₅	semidirect
321. C₃×D₄	C₂×C₃×D₅	semidirect
336. #67	C₂×C₃×D₅	semidirect
340. D₁₂	C₂×C₃×D₅	semidirect
343. C₄×D₃	C₂×C₃×D₅	semidirect
379. C₃×C₅	#1004	semidirect
380. C₃×C₅	C₃×H(5,𝔽₂)	semidirect
422. C₃²	#4144	semidirect
439. D₄	C₃×D₃×D₅	semidirect
464. C₅	C₃×#1004	semidirect
480. C₃	#92025	direct (N × H)
481. 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×#6819	2
C₃×C₅×D₃×D₄	2
C₃²×D₄×D₅	2
C₃×D₃×C₂²⋊D₅	2
C₃×D₅×#67	2
C₂×C₃×#1201	2
C₃×#6780	2
C₃×#6777	2
C₃×#6772	2
C₃×#6771	2
C₃×#6765	2
C₃×#4144	3
#92025	3
C₃×#1004	5

Subgroups — C3×#92025 #13089229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#92025 #13089229