Subgroups — C₃×#10612790 #14430229

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66062	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65296	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65149	C₂	1	2	yes	maximal, complemented
7	C₃×#65146	C₂	1	2	yes	maximal, complemented
8	C₃×#65140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65061	C₂	1	2	yes	maximal
11	C₃×#65052	C₂	1	2	yes	maximal, complemented
12	#10612790	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#711	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×#4092	—	2	1	no	—
17	C₃×Q₈×Dic₅	—	2	1	no	—
18	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
20	C₂×C₃×C₄×Dic₅	—	2	1	no	—
21	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
22	C₃×#4043	—	2	1	no	—
23	C₃×#4038	C₂²	1	1	yes	characteristic
24	C₃×#4038	C₂²	1	2	yes	—
25	C₃×#4036	C₂²	1	2	yes	—
26	C₃×#4033	—	2	1	no	—
27	C₃×#4033	C₂²	1	1	yes	characteristic
28	C₃×#4027	—	2	1	no	—
29	C₃×#4023	—	2	1	no	—
30	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
31	C₃×#4015	C₂²	1	1	yes	characteristic
32	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
33	C₃×C₅×#106	C₂²	1	2	yes	—
34	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₃×#3964	C₂²	1	2	yes	—
37	C₃×#3949	C₂²	1	2	yes	—
38	C₃×#3948	C₂²	1	2	yes	—
39	C₃×#3946	C₂²	1	2	yes	—
40	C₃×#3942	C₂²	1	2	yes	—
41	C₃×#3939	C₂²	1	2	yes	—
42	C₃×#3939	C₂²	1	2	yes	—
43	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
44	C₃×#3076	—	5	1	no	maximal, Hall
45	#66062	C₂×C₃	1	1	yes	characteristic, complemented
46	C₄×#711	C₂×C₃	1	1	yes	characteristic
47	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
48	#65380	C₂×C₃	1	1	yes	characteristic, complemented
49	#65296	C₂×C₃	1	1	yes	characteristic, complemented
50	#65149	C₂×C₃	1	2	yes	complemented
51	#65146	C₂×C₃	1	2	yes	complemented
52	#65140	C₂×C₃	1	1	yes	characteristic, complemented
53	D₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
54	#65061	C₂×C₃	1	2	yes	—
55	#65052	C₂×C₃	1	2	yes	complemented
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	—	2	1	no	—
59	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
60	C₂²×C₃×Dic₅	—	2	1	no	—
61	C₂²×C₃×Dic₅	—	2	1	no	—
62	C₃×#711	—	2	2	no	—
63	C₃×#711	Q₈	1	4	yes	complemented
64	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₁₀	—	2	1	no	—
68	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₃×C₂²⋊Dic₅	—	2	1	no	—
76	C₃×#685	—	2	2	no	—
77	C₃×#685	—	2	1	no	—
78	C₃×C₄⋊Dic₅	—	2	1	no	—
79	C₃×C₄⋊Dic₅	—	2	2	no	—
80	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
81	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
82	C₃×#683	—	2	1	no	—
83	C₃×#683	—	2	2	no	—
84	C₃×#683	—	2	1	no	—
85	C₃×C₄×Dic₅	—	2	1	no	—
86	C₃×C₄×Dic₅	—	2	2	no	—
87	C₃×C₄×Dic₅	—	2	1	no	—
88	C₃×C₄×Dic₅	—	2	1	no	—
89	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
90	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
91	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	C₃×C₈×D₅	—	2	4	no	—
94	C₃×#533	—	5	1	no	—
95	C₃×C₄×#41	—	5	1	no	—
96	C₃×#479	—	5	2	no	—
97	C₃×#478	—	5	2	no	—
98	C₃×#477	—	5	1	no	—
99	C₃×#476	D₅	1	1	yes	characteristic, complemented
100	C₃×#475	—	5	1	no	—
101	C₃×#474	—	5	1	no	—
102	C₃×#427	—	5	2	no	—
103	C₂×C₃×C₄⋊C₈	—	5	1	no	—
104	C₃×#416	—	5	2	no	—
105	C₂×#711	C₂²×C₃	1	1	yes	characteristic
106	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
108	#4092	—	2	1	no	—
109	Q₈×Dic₅	—	2	1	no	—
110	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
111	C₄×C₂²⋊D₅	—	2	1	no	—
112	C₂×C₄×Dic₅	—	2	1	no	—
113	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
114	#4043	—	2	1	no	—
115	#4038	C₂²×C₃	1	2	yes	—
116	#4038	C₂²×C₃	1	1	yes	characteristic
117	#4036	C₂²×C₃	1	2	yes	—
118	#4033	—	2	1	no	—
119	#4033	C₂²×C₃	1	1	yes	characteristic
120	#4027	—	2	1	no	—
121	#4023	—	2	1	no	—
122	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
123	#4015	C₂²×C₃	1	1	yes	characteristic
124	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
125	C₅×#106	C₂²×C₃	1	2	yes	—
126	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
127	C₅×#102	C₂²×C₃	1	2	yes	—
128	#3964	C₂²×C₃	1	2	yes	—
129	#3949	C₂²×C₃	1	2	yes	—
130	#3948	C₂²×C₃	1	2	yes	—
131	#3946	C₂²×C₃	1	2	yes	—
132	#3942	C₂²×C₃	1	2	yes	—
133	#3939	C₂²×C₃	1	2	yes	—
134	#3939	C₂²×C₃	1	2	yes	—
135	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
136	#3076	—	5	1	no	Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
139	C₃×C₅×Q₈	—	4	2	no	—
140	C₃×C₅×D₄	—	2	1	no	—
141	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	4	2	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₃×C₂²⋊D₅	—	2	4	no	—
149	C₂×C₃×Dic₅	—	2	1	no	—
150	C₂×C₃×Dic₅	—	2	4	no	—
151	C₂×C₃×Dic₅	—	2	1	no	—
152	C₂×C₃×Dic₅	—	2	2	no	—
153	C₂×C₃×Dic₅	—	4	2	no	—
154	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
157	C₃×C₄×D₅	—	2	2	no	—
158	C₃×C₄×D₅	—	4	1	no	—
159	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
160	C₃×C₄×D₅	#41	1	2	yes	—
161	C₃×Dic₁₀	—	2	1	no	—
162	C₃×Dic₁₀	—	4	2	no	—
163	C₃×Dic₁₀	C₂×Q₈	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×#168	—	2	2	no	—
166	C₂×C₃×#41	—	5	1	no	—
167	C₂²×C₃×C₈	—	5	2	no	—
168	C₃×C₄⋊Q₈	—	5	1	no	—
169	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
170	C₃×#125	—	5	2	no	—
171	C₃×C₂²⋊Q₈	—	10	1	no	—
172	C₃×C₂²⋊Q₈	—	10	1	no	—
173	C₃×C₄×Q₈	—	5	1	no	—
174	C₃×C₄×Q₈	—	5	1	no	—
175	C₃×C₄×Q₈	—	10	1	no	—
176	C₃×C₄×Q₈	—	10	1	no	—
177	C₃×C₄×D₄	—	5	1	no	—
178	C₃×C₄×D₄	—	10	1	no	—
179	C₃×C₄×D₄	—	10	1	no	—
180	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
181	C₃×#117	—	5	2	no	—
182	C₃×#117	—	5	1	no	—
183	C₃×#117	—	10	1	no	—
184	C₂×C₃×C₄²	—	5	1	no	—
185	C₂×C₃×C₄²	—	10	1	no	—
186	C₃×#107	—	5	2	no	—
187	C₃×#107	—	5	2	no	—
188	C₃×#106	—	5	2	no	—
189	C₃×#106	C₂×D₅	1	2	yes	—
190	C₃×C₄⋊C₈	—	5	2	no	—
191	C₃×C₄⋊C₈	—	5	1	no	—
192	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
193	C₃×#103	—	5	2	no	—
194	C₃×#103	—	5	2	no	—
195	C₃×#102	—	5	2	no	—
196	C₃×#102	C₂×D₅	1	2	yes	—
197	C₂×C₅×Q₈	—	2	1	no	—
198	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂×C₂²⋊D₅	—	2	1	no	—
201	C₂²×Dic₅	—	2	1	no	—
202	C₂²×Dic₅	—	2	1	no	—
203	#711	—	2	2	no	—
204	#711	C₃×Q₈	1	4	yes	complemented
205	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
206	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
207	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
208	C₂×Dic₁₀	—	2	1	no	—
209	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
213	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
214	C₅×C₂²⋊C₄	—	2	1	no	—
215	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
216	C₂²⋊Dic₅	—	2	1	no	—
217	#685	—	2	1	no	—
218	#685	—	2	2	no	—
219	C₄⋊Dic₅	—	2	1	no	—
220	C₄⋊Dic₅	—	2	2	no	—
221	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
222	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
223	#683	—	2	1	no	—
224	#683	—	2	1	no	—
225	#683	—	2	2	no	—
226	C₄×Dic₅	—	2	1	no	—
227	C₄×Dic₅	—	2	1	no	—
228	C₄×Dic₅	—	2	1	no	—
229	C₄×Dic₅	—	2	2	no	—
230	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
231	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
232	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
233	C₂×#168	C₂³×C₃	1	2	yes	—
234	C₈×D₅	—	2	4	no	—
235	#533	—	5	1	no	—
236	C₄×#41	—	5	1	no	—
237	#479	—	5	2	no	—
238	#478	—	5	2	no	—
239	#477	—	5	1	no	—
240	#476	C₃×D₅	1	1	yes	characteristic, complemented
241	#475	—	5	1	no	—
242	#474	—	5	1	no	—
243	#427	—	5	2	no	—
244	C₂×C₄⋊C₈	—	5	1	no	—
245	#416	—	5	2	no	—
246	C₂²×C₃×C₅	—	2	2	no	—
247	C₂²×C₃×C₅	—	4	1	no	—
248	C₂²×C₃×C₅	—	4	1	no	—
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₃×D₅	—	2	1	no	—
251	C₂×C₃×D₅	—	2	1	no	—
252	C₂×C₃×D₅	C₂²⋊Q₈	1	2	yes	—
253	C₃×C₄×C₅	—	2	1	no	—
254	C₃×C₄×C₅	—	4	1	no	—
255	C₃×C₄×C₅	—	4	2	no	—
256	C₃×C₄×C₅	#135	1	2	yes	—
257	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
258	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
259	C₃×Dic₅	—	2	2	no	—
260	C₃×Dic₅	—	2	1	no	—
261	C₃×Dic₅	—	2	1	no	—
262	C₃×Dic₅	—	4	2	no	—
263	C₃×Dic₅	—	4	1	no	—
264	C₃×Dic₅	C₂²⋊Q₈	1	2	yes	—
265	C₃×#41	—	5	4	no	—
266	C₃×#41	—	10	2	no	—
267	C₂×C₃×Q₈	—	2	1	no	—
268	C₂×C₃×Q₈	—	5	1	no	—
269	C₂×C₃×Q₈	—	10	1	no	—
270	C₂×C₃×D₄	—	10	1	no	—
271	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	—	2	1	no	—
273	C₂²×C₃×C₄	—	5	1	no	—
274	C₂²×C₃×C₄	—	5	1	no	—
275	C₂²×C₃×C₄	—	5	1	no	—
276	C₂²×C₃×C₄	—	10	1	no	—
277	C₂²×C₃×C₄	—	10	1	no	—
278	C₂×C₃×C₈	—	5	2	no	—
279	C₂×C₃×C₈	—	10	4	no	—
280	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
281	C₃×C₄⋊C₄	—	2	1	no	—
282	C₃×C₄⋊C₄	—	5	2	no	—
283	C₃×C₄⋊C₄	—	5	1	no	—
284	C₃×C₄⋊C₄	—	10	1	no	—
285	C₃×C₄⋊C₄	—	10	2	no	—
286	C₃×C₄⋊C₄	—	10	2	no	—
287	C₃×C₄⋊C₄	—	10	1	no	—
288	C₃×C₄⋊C₄	—	10	1	no	—
289	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
290	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
291	C₃×C₂²⋊C₄	—	2	1	no	—
292	C₃×C₂²⋊C₄	—	10	1	no	—
293	C₃×C₂²⋊C₄	—	10	2	no	—
294	C₃×C₂²⋊C₄	—	10	1	no	—
295	C₃×C₄²	—	5	1	no	—
296	C₃×C₄²	—	5	1	no	—
297	C₃×C₄²	—	5	1	no	—
298	C₃×C₄²	—	10	1	no	—
299	C₃×C₄²	—	10	1	no	—
300	C₃×C₄²	—	10	2	no	—
301	C₃×C₄²	—	10	1	no	—
302	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
303	C₂³×C₅	—	2	1	no	—
304	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
305	C₅×Q₈	—	4	2	no	—
306	C₅×D₄	—	2	1	no	—
307	C₅×D₄	C₂×C₃×Q₈	1	2	yes	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	4	2	no	—
311	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
314	C₂²⋊D₅	—	2	4	no	—
315	C₂×Dic₅	—	2	1	no	—
316	C₂×Dic₅	—	2	4	no	—
317	C₂×Dic₅	—	2	1	no	—
318	C₂×Dic₅	—	2	2	no	—
319	C₂×Dic₅	—	4	2	no	—
320	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
321	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
322	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
323	C₄×D₅	—	2	2	no	—
324	C₄×D₅	—	4	1	no	—
325	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
326	C₄×D₅	C₃×#41	1	2	yes	—
327	Dic₁₀	—	2	1	no	—
328	Dic₁₀	—	4	2	no	—
329	Dic₁₀	C₂×C₃×Q₈	1	2	yes	—
330	C₅×C₈	—	2	2	no	—
331	#168	—	2	2	no	—
332	C₂×#41	—	5	1	no	—
333	C₂²×C₈	—	5	2	no	—
334	C₄⋊Q₈	—	5	1	no	—
335	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
336	#125	—	5	2	no	—
337	C₂²⋊Q₈	—	10	1	no	—
338	C₂²⋊Q₈	—	10	1	no	—
339	C₄×Q₈	—	5	1	no	—
340	C₄×Q₈	—	5	1	no	—
341	C₄×Q₈	—	10	1	no	—
342	C₄×Q₈	—	10	1	no	—
343	C₄×D₄	—	5	1	no	—
344	C₄×D₄	—	10	1	no	—
345	C₄×D₄	—	10	1	no	—
346	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
347	#117	—	5	1	no	—
348	#117	—	5	2	no	—
349	#117	—	10	1	no	—
350	C₂×C₄²	—	5	1	no	—
351	C₂×C₄²	—	10	1	no	—
352	#107	—	5	2	no	—
353	#107	—	5	2	no	—
354	#106	—	5	2	no	—
355	#106	C₂×C₃×D₅	1	2	yes	—
356	C₄⋊C₈	—	5	2	no	—
357	C₄⋊C₈	—	5	1	no	—
358	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
359	#103	—	5	2	no	—
360	#103	—	5	2	no	—
361	#102	—	5	2	no	—
362	#102	C₂×C₃×D₅	1	2	yes	—
363	C₂×C₃×C₅	—	4	2	no	—
364	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
366	C₂×C₃×C₅	#575	1	1	yes	characteristic
367	C₃×D₅	—	2	2	no	—
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	—	5	1	no	—
370	C₃×Q₈	—	4	2	no	—
371	C₃×Q₈	—	5	2	no	—
372	C₃×Q₈	—	10	1	no	—
373	C₃×Q₈	—	20	2	no	—
374	C₃×D₄	—	2	1	no	—
375	C₃×D₄	—	10	4	no	—
376	C₃×D₄	Q₈×D₅	1	2	yes	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	4	2	no	—
380	C₂×C₃×C₄	—	5	1	no	—
381	C₂×C₃×C₄	—	5	2	no	—
382	C₂×C₃×C₄	—	5	2	no	—
383	C₂×C₃×C₄	—	5	1	no	—
384	C₂×C₃×C₄	—	5	1	no	—
385	C₂×C₃×C₄	—	10	4	no	—
386	C₂×C₃×C₄	—	10	1	no	—
387	C₂×C₃×C₄	—	10	2	no	—
388	C₂×C₃×C₄	—	10	1	no	—
389	C₂×C₃×C₄	—	10	2	no	—
390	C₂×C₃×C₄	—	20	1	no	—
391	C₂×C₃×C₄	—	20	2	no	—
392	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
393	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
395	C₃×C₈	—	2	2	no	—
396	C₃×C₈	—	10	2	no	—
397	C₂²×C₅	—	2	2	no	—
398	C₂²×C₅	—	4	1	no	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
401	C₂×D₅	—	2	1	no	—
402	C₂×D₅	—	2	1	no	—
403	C₂×D₅	C₃×C₂²⋊Q₈	1	2	yes	—
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	—	4	2	no	—
407	C₄×C₅	C₃×#135	1	2	yes	—
408	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
409	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
410	Dic₅	—	2	1	no	—
411	Dic₅	—	2	1	no	—
412	Dic₅	—	2	2	no	—
413	Dic₅	—	4	2	no	—
414	Dic₅	—	4	1	no	—
415	Dic₅	C₃×C₂²⋊Q₈	1	2	yes	—
416	#41	—	5	4	no	—
417	#41	—	10	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	5	1	no	—
420	C₂×Q₈	—	10	1	no	—
421	C₂×D₄	—	10	1	no	—
422	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	5	1	no	—
425	C₂²×C₄	—	5	1	no	—
426	C₂²×C₄	—	5	1	no	—
427	C₂²×C₄	—	10	1	no	—
428	C₂²×C₄	—	10	1	no	—
429	C₂×C₈	—	5	2	no	—
430	C₂×C₈	—	10	4	no	—
431	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	5	2	no	—
434	C₄⋊C₄	—	5	1	no	—
435	C₄⋊C₄	—	10	1	no	—
436	C₄⋊C₄	—	10	2	no	—
437	C₄⋊C₄	—	10	2	no	—
438	C₄⋊C₄	—	10	1	no	—
439	C₄⋊C₄	—	10	1	no	—
440	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
441	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	10	1	no	—
444	C₂²⋊C₄	—	10	2	no	—
445	C₂²⋊C₄	—	10	1	no	—
446	C₄²	—	5	1	no	—
447	C₄²	—	5	1	no	—
448	C₄²	—	5	1	no	—
449	C₄²	—	10	1	no	—
450	C₄²	—	10	1	no	—
451	C₄²	—	10	2	no	—
452	C₄²	—	10	1	no	—
453	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
454	C₃×C₅	#3076	1	1	yes	characteristic, complemented, Hall
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	4	1	no	—
457	C₂²×C₃	—	4	1	no	—
458	C₂²×C₃	—	5	2	no	—
459	C₂²×C₃	—	10	1	no	—
460	C₂²×C₃	—	10	1	no	—
461	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	4	1	no	—
464	C₃×C₄	—	4	2	no	—
465	C₃×C₄	—	5	2	no	—
466	C₃×C₄	—	10	1	no	—
467	C₃×C₄	—	10	1	no	—
468	C₃×C₄	—	10	2	no	—
469	C₃×C₄	—	20	2	no	—
470	C₃×C₄	—	20	1	no	—
471	C₃×C₄	#4062	1	2	yes	—
472	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
473	C₃×C₄	D₅×#41	1	1	yes	characteristic
474	C₂×C₅	—	4	2	no	—
475	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
476	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
477	C₂×C₅	C₃×#575	1	1	yes	characteristic
478	D₅	—	2	2	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	5	1	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	5	2	no	—
483	Q₈	—	10	1	no	—
484	Q₈	—	20	2	no	—
485	D₄	—	2	1	no	—
486	D₄	—	10	4	no	—
487	D₄	C₃×Q₈×D₅	1	2	yes	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	5	1	no	—
492	C₂×C₄	—	5	2	no	—
493	C₂×C₄	—	5	2	no	—
494	C₂×C₄	—	5	1	no	—
495	C₂×C₄	—	5	1	no	—
496	C₂×C₄	—	10	4	no	—
497	C₂×C₄	—	10	1	no	—
498	C₂×C₄	—	10	2	no	—
499	C₂×C₄	—	10	1	no	—
500	C₂×C₄	—	10	2	no	—
501	C₂×C₄	—	20	1	no	—
502	C₂×C₄	—	20	2	no	—
503	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
504	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
505	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	10	2	no	—
508	C₂×C₃	—	4	2	no	—
509	C₂×C₃	—	10	2	no	—
510	C₂×C₃	D₅×C₂²⋊Q₈	1	1	yes	characteristic
511	C₂×C₃	C₂×#4062	1	1	yes	characteristic
512	C₂×C₃	#66107	1	1	yes	characteristic
513	C₅	C₃×#3076	1	1	yes	characteristic, complemented, Sylow
514	C₂²	—	2	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	5	2	no	—
518	C₂²	—	10	1	no	—
519	C₂²	—	10	1	no	—
520	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	1	no	—
524	C₄	—	5	2	no	—
525	C₄	—	10	1	no	—
526	C₄	—	10	2	no	—
527	C₄	—	10	1	no	—
528	C₄	—	20	1	no	—
529	C₄	—	20	2	no	—
530	C₄	C₃×#4062	1	2	yes	—
531	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
532	C₄	C₃×D₅×#41	1	1	yes	characteristic
533	C₃	#10612790	1	1	yes	characteristic, direct product factor, Sylow
534	C₂	—	4	2	no	—
535	C₂	—	10	2	no	—
536	C₂	C₃×D₅×C₂²⋊Q₈	1	1	yes	characteristic
537	C₂	C₂×C₃×#4062	1	1	yes	characteristic
538	C₂	C₃×#66107	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#476	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#711	C₂²
hypercenter	C₃×#476	D₅
hypocenter	C₅	C₃×#3076
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#476

Complements

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

N	H ≅ G/N	type
1. C₃×#66062	C₂	semidirect
3. C₃×C₅×#476	C₂	semidirect
4. C₃×#65380	C₂	semidirect
5. C₃×#65296	C₂	semidirect
6. C₃×#65149	C₂	semidirect
7. C₃×#65146	C₂	semidirect
8. C₃×#65140	C₂	semidirect
9. C₃×D₅×C₄⋊C₈	C₂	semidirect
11. C₃×#65052	C₂	semidirect
12. #10612790	C₃	direct (N × H)
45. #66062	C₂×C₃	semidirect
47. C₅×#476	C₂×C₃	semidirect
48. #65380	C₂×C₃	semidirect
49. #65296	C₂×C₃	semidirect
50. #65149	C₂×C₃	semidirect
51. #65146	C₂×C₃	semidirect
52. #65140	C₂×C₃	semidirect
53. D₅×C₄⋊C₈	C₂×C₃	semidirect
55. #65052	C₂×C₃	semidirect
63. C₃×#711	Q₈	semidirect
99. C₃×#476	D₅	semidirect
204. #711	C₃×Q₈	semidirect
240. #476	C₃×D₅	semidirect
454. C₃×C₅	#3076	semidirect
513. C₅	C₃×#3076	semidirect
533. C₃	#10612790	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×#66062	2
C₃×C₄×#711	2
C₃×C₅×#476	2
C₃×#65380	2
C₃×#65296	2
C₃×#65149	2
C₃×#65146	2
C₃×#65140	2
C₃×D₅×C₄⋊C₈	2
C₃×#65061	2
C₃×#65052	2
#10612790	3
C₃×#3076	5

Subgroups — C3×#10612790 #14430229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612790 #14430229