Subgroups — C₃×#10613368 #14437780

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66022	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66002	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65345	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65093	C₂	1	2	yes	maximal, complemented
7	C₃×#65081	C₂	1	2	yes	maximal, complemented
8	C₃×#65061	C₂	1	2	yes	maximal, complemented
9	C₃×#65049	C₂	1	2	yes	maximal, complemented
10	C₃×#64986	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613368	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	1	yes	characteristic
14	C₂×C₃×#711	C₂²	1	1	yes	characteristic
15	C₃×C₅×#125	C₂²	1	1	yes	characteristic
16	C₃×C₅×#124	C₂²	1	1	yes	characteristic
17	C₃×#4090	C₂²	1	1	yes	characteristic
18	C₃×#4086	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
20	C₃×#4042	—	2	2	no	—
21	C₃×#4038	C₂²	1	2	yes	—
22	C₃×#4034	C₂²	1	2	yes	—
23	C₃×#4033	—	2	2	no	—
24	C₃×#4030	—	2	2	no	—
25	C₃×#4027	—	2	2	no	—
26	C₃×#4021	C₂²	1	1	yes	characteristic
27	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
28	C₃×#4016	C₂²	1	1	yes	characteristic
29	C₃×C₅×#103	C₂²	1	2	yes	—
30	C₃×C₅×#102	C₂²	1	2	yes	—
31	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₃×#3967	C₂²	1	2	yes	—
33	C₃×#3964	C₂²	1	2	yes	—
34	C₃×#3953	C₂²	1	2	yes	—
35	C₃×#3948	C₂²	1	2	yes	—
36	C₃×C₈×Dic₅	C₂²	1	2	yes	—
37	C₃×#3942	C₂²	1	2	yes	—
38	C₃×#3941	C₂²	1	2	yes	—
39	C₃×C₄×#168	C₂²	1	1	yes	characteristic
40	C₃×#3131	—	5	1	no	maximal, Hall
41	#66022	C₂×C₃	1	1	yes	characteristic, complemented
42	#66002	C₂×C₃	1	1	yes	characteristic
43	C₅×#488	C₂×C₃	1	1	yes	characteristic, complemented
44	#65357	C₂×C₃	1	1	yes	characteristic, complemented
45	#65345	C₂×C₃	1	1	yes	characteristic, complemented
46	#65093	C₂×C₃	1	2	yes	complemented
47	#65081	C₂×C₃	1	2	yes	complemented
48	#65061	C₂×C₃	1	2	yes	complemented
49	#65049	C₂×C₃	1	2	yes	complemented
50	#64986	C₂×C₃	1	1	yes	characteristic, complemented
51	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
55	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
56	C₂²×C₃×Dic₅	—	2	1	no	—
57	C₃×#713	—	2	4	no	—
58	C₃×#711	—	2	4	no	—
59	C₂×C₃×D₂₀	—	2	1	no	—
60	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×D₅	—	2	1	no	—
62	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
63	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
64	C₂×C₃×Dic₁₀	—	2	2	no	—
65	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₃×#685	—	2	2	no	—
72	C₃×#685	—	2	2	no	—
73	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
74	C₃×#683	—	2	2	no	—
75	C₃×#683	—	2	2	no	—
76	C₃×#683	—	2	2	no	—
77	C₃×C₄×Dic₅	—	2	2	no	—
78	C₃×C₄×Dic₅	D₄	1	2	yes	—
79	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×#168	C₂³	1	2	yes	—
81	C₃×C₈×D₅	—	2	4	no	—
82	C₃×#533	—	5	1	no	—
83	C₃×#532	—	5	1	no	—
84	C₃×#488	—	5	1	no	—
85	C₃×#488	—	5	1	no	—
86	C₃×#488	—	5	1	no	—
87	C₃×#488	D₅	1	1	yes	characteristic, complemented
88	C₃×#487	—	5	2	no	—
89	C₃×#486	—	5	2	no	—
90	C₃×#416	—	5	2	no	—
91	C₃×#416	—	5	2	no	—
92	C₂×C₃×C₄×C₈	—	5	1	no	—
93	C₂×#713	C₂²×C₃	1	1	yes	characteristic
94	C₂×#711	C₂²×C₃	1	1	yes	characteristic
95	C₅×#125	C₂²×C₃	1	1	yes	characteristic
96	C₅×#124	C₂²×C₃	1	1	yes	characteristic
97	#4090	C₂²×C₃	1	1	yes	characteristic
98	#4086	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
100	#4042	—	2	2	no	—
101	#4038	C₂²×C₃	1	2	yes	—
102	#4034	C₂²×C₃	1	2	yes	—
103	#4033	—	2	2	no	—
104	#4030	—	2	2	no	—
105	#4027	—	2	2	no	—
106	#4021	C₂²×C₃	1	1	yes	characteristic
107	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
108	#4016	C₂²×C₃	1	1	yes	characteristic
109	C₅×#103	C₂²×C₃	1	2	yes	—
110	C₅×#102	C₂²×C₃	1	2	yes	—
111	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
112	#3967	C₂²×C₃	1	2	yes	—
113	#3964	C₂²×C₃	1	2	yes	—
114	#3953	C₂²×C₃	1	2	yes	—
115	#3948	C₂²×C₃	1	2	yes	—
116	C₈×Dic₅	C₂²×C₃	1	2	yes	—
117	#3942	C₂²×C₃	1	2	yes	—
118	#3941	C₂²×C₃	1	2	yes	—
119	C₄×#168	C₂²×C₃	1	1	yes	characteristic
120	#3131	—	5	1	no	Sylow
121	C₂³×C₃×C₅	—	2	1	no	—
122	C₂²×C₃×D₅	—	2	1	no	—
123	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
124	C₃×C₅×Q₈	—	2	2	no	—
125	C₃×C₅×D₄	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
130	C₃×C₂²⋊D₅	—	4	2	no	—
131	C₃×C₂²⋊D₅	—	4	4	no	—
132	C₂×C₃×Dic₅	—	2	2	no	—
133	C₂×C₃×Dic₅	—	2	1	no	—
134	C₂×C₃×Dic₅	—	4	2	no	—
135	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
137	C₃×D₂₀	—	2	2	no	—
138	C₃×D₂₀	—	4	2	no	—
139	C₃×C₄×D₅	—	2	4	no	—
140	C₃×C₄×D₅	—	4	2	no	—
141	C₃×C₄×D₅	#41	1	4	yes	—
142	C₃×Dic₁₀	—	2	2	no	—
143	C₃×Dic₁₀	—	4	4	no	—
144	C₃×C₅×C₈	—	2	2	no	—
145	C₃×#168	—	2	2	no	—
146	C₂×C₃×#41	—	5	1	no	—
147	C₂×C₃×#41	—	5	1	no	—
148	C₂²×C₃×C₈	—	5	2	no	—
149	C₃×C₄⋊Q₈	—	5	2	no	—
150	C₃×C₄⋊Q₈	—	5	1	no	—
151	C₃×#127	—	5	1	no	—
152	C₃×#125	—	5	1	no	—
153	C₃×#125	C₂×D₅	1	1	yes	characteristic
154	C₃×#124	—	5	1	no	—
155	C₃×#124	C₂×D₅	1	1	yes	characteristic
156	C₃×C₂²⋊Q₈	—	10	2	no	—
157	C₃×#121	—	10	2	no	—
158	C₃×C₄×Q₈	—	10	2	no	—
159	C₃×C₄×D₄	—	10	2	no	—
160	C₃×#117	—	5	2	no	—
161	C₂×C₃×C₄²	—	5	1	no	—
162	C₃×#103	—	5	2	no	—
163	C₃×#103	—	5	2	no	—
164	C₃×#103	—	5	2	no	—
165	C₃×#103	C₂×D₅	1	2	yes	—
166	C₃×#102	—	5	2	no	—
167	C₃×#102	—	5	2	no	—
168	C₃×#102	—	5	2	no	—
169	C₃×#102	C₂×D₅	1	2	yes	—
170	C₃×C₄×C₈	—	5	2	no	—
171	C₃×C₄×C₈	—	5	1	no	—
172	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
173	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₂²⋊D₅	—	2	1	no	—
176	C₂×C₂²⋊D₅	—	2	2	no	—
177	C₂²×Dic₅	—	2	1	no	—
178	#713	—	2	4	no	—
179	#711	—	2	4	no	—
180	C₂×D₂₀	—	2	1	no	—
181	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₄×D₅	—	2	1	no	—
183	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
184	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
185	C₂×Dic₁₀	—	2	2	no	—
186	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
188	C₅×C₄⋊C₄	—	2	2	no	—
189	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
190	C₅×C₂²⋊C₄	—	2	2	no	—
191	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
192	#685	—	2	2	no	—
193	#685	—	2	2	no	—
194	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
195	#683	—	2	2	no	—
196	#683	—	2	2	no	—
197	#683	—	2	2	no	—
198	C₄×Dic₅	—	2	2	no	—
199	C₄×Dic₅	C₃×D₄	1	2	yes	—
200	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
201	C₂×#168	C₂³×C₃	1	2	yes	—
202	C₈×D₅	—	2	4	no	—
203	#533	—	5	1	no	—
204	#532	—	5	1	no	—
205	#488	—	5	1	no	—
206	#488	—	5	1	no	—
207	#488	—	5	1	no	—
208	#488	C₃×D₅	1	1	yes	characteristic, complemented
209	#487	—	5	2	no	—
210	#486	—	5	2	no	—
211	#416	—	5	2	no	—
212	#416	—	5	2	no	—
213	C₂×C₄×C₈	—	5	1	no	—
214	C₂²×C₃×C₅	—	4	1	no	—
215	C₂²×C₃×C₅	—	4	2	no	—
216	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₃×D₅	—	2	2	no	—
218	C₂×C₃×D₅	—	4	1	no	—
219	C₂×C₃×D₅	—	4	2	no	—
220	C₂×C₃×D₅	#124	1	2	yes	—
221	C₃×C₄×C₅	—	2	2	no	—
222	C₃×C₄×C₅	—	4	1	no	—
223	C₃×C₄×C₅	—	4	2	no	—
224	C₃×C₄×C₅	C₂×#41	1	2	yes	—
225	C₃×Dic₅	—	4	1	no	—
226	C₃×Dic₅	—	4	2	no	—
227	C₃×Dic₅	#124	1	2	yes	—
228	C₃×Dic₅	#135	1	4	yes	—
229	C₃×#41	—	10	4	no	—
230	C₃×#41	—	10	4	no	—
231	C₂×C₃×Q₈	—	5	1	no	—
232	C₂×C₃×Q₈	—	10	2	no	—
233	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
234	C₂×C₃×D₄	—	5	1	no	—
235	C₂×C₃×D₄	—	10	1	no	—
236	C₂×C₃×D₄	—	10	2	no	—
237	C₂×C₃×D₄	—	10	1	no	—
238	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	—	5	1	no	—
240	C₂²×C₃×C₄	—	5	2	no	—
241	C₂²×C₃×C₄	—	10	1	no	—
242	C₂²×C₃×C₄	—	10	1	no	—
243	C₂×C₃×C₈	—	5	2	no	—
244	C₂×C₃×C₈	—	10	4	no	—
245	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
246	C₃×C₄⋊C₄	—	2	2	no	—
247	C₃×C₄⋊C₄	—	5	2	no	—
248	C₃×C₄⋊C₄	—	10	2	no	—
249	C₃×C₄⋊C₄	—	10	2	no	—
250	C₃×C₄⋊C₄	—	10	2	no	—
251	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
252	C₃×C₂²⋊C₄	—	2	2	no	—
253	C₃×C₂²⋊C₄	—	10	2	no	—
254	C₃×C₂²⋊C₄	—	10	2	no	—
255	C₃×C₄²	—	5	2	no	—
256	C₃×C₄²	—	5	1	no	—
257	C₃×C₄²	—	10	2	no	—
258	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
259	C₂³×C₅	—	2	1	no	—
260	C₂²×D₅	—	2	1	no	—
261	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
262	C₅×Q₈	—	2	2	no	—
263	C₅×D₄	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
267	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
268	C₂²⋊D₅	—	4	2	no	—
269	C₂²⋊D₅	—	4	4	no	—
270	C₂×Dic₅	—	2	2	no	—
271	C₂×Dic₅	—	2	1	no	—
272	C₂×Dic₅	—	4	2	no	—
273	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
274	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
275	D₂₀	—	2	2	no	—
276	D₂₀	—	4	2	no	—
277	C₄×D₅	—	2	4	no	—
278	C₄×D₅	—	4	2	no	—
279	C₄×D₅	C₃×#41	1	4	yes	—
280	Dic₁₀	—	2	2	no	—
281	Dic₁₀	—	4	4	no	—
282	C₅×C₈	—	2	2	no	—
283	#168	—	2	2	no	—
284	C₂×#41	—	5	1	no	—
285	C₂×#41	—	5	1	no	—
286	C₂²×C₈	—	5	2	no	—
287	C₄⋊Q₈	—	5	2	no	—
288	C₄⋊Q₈	—	5	1	no	—
289	#127	—	5	1	no	—
290	#125	—	5	1	no	—
291	#125	C₂×C₃×D₅	1	1	yes	characteristic
292	#124	—	5	1	no	—
293	#124	C₂×C₃×D₅	1	1	yes	characteristic
294	C₂²⋊Q₈	—	10	2	no	—
295	#121	—	10	2	no	—
296	C₄×Q₈	—	10	2	no	—
297	C₄×D₄	—	10	2	no	—
298	#117	—	5	2	no	—
299	C₂×C₄²	—	5	1	no	—
300	#103	—	5	2	no	—
301	#103	—	5	2	no	—
302	#103	—	5	2	no	—
303	#103	C₂×C₃×D₅	1	2	yes	—
304	#102	—	5	2	no	—
305	#102	—	5	2	no	—
306	#102	—	5	2	no	—
307	#102	C₂×C₃×D₅	1	2	yes	—
308	C₄×C₈	—	5	2	no	—
309	C₄×C₈	—	5	1	no	—
310	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
311	C₂×C₃×C₅	—	8	1	no	—
312	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
313	C₂×C₃×C₅	C₂×#135	1	2	yes	—
314	C₃×D₅	—	2	2	no	—
315	C₃×D₅	—	8	1	no	—
316	C₂³×C₃	—	2	1	no	—
317	C₂³×C₃	—	5	1	no	—
318	C₂³×C₃	—	10	1	no	—
319	C₃×Q₈	—	2	2	no	—
320	C₃×Q₈	—	10	2	no	—
321	C₃×Q₈	—	20	4	no	—
322	C₃×D₄	—	2	2	no	—
323	C₃×D₄	—	10	2	no	—
324	C₃×D₄	—	20	2	no	—
325	C₃×D₄	—	20	4	no	—
326	C₃×D₄	—	20	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	5	1	no	—
330	C₂×C₃×C₄	—	5	2	no	—
331	C₂×C₃×C₄	—	5	4	no	—
332	C₂×C₃×C₄	—	10	4	no	—
333	C₂×C₃×C₄	—	10	2	no	—
334	C₂×C₃×C₄	—	10	1	no	—
335	C₂×C₃×C₄	—	20	2	no	—
336	C₂×C₃×C₄	—	20	2	no	—
337	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
338	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
339	C₃×C₈	—	2	2	no	—
340	C₃×C₈	—	10	2	no	—
341	C₂²×C₅	—	4	2	no	—
342	C₂²×C₅	—	4	1	no	—
343	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
344	C₂×D₅	—	2	2	no	—
345	C₂×D₅	—	4	2	no	—
346	C₂×D₅	—	4	1	no	—
347	C₂×D₅	C₃×#124	1	2	yes	—
348	C₄×C₅	—	2	2	no	—
349	C₄×C₅	—	4	2	no	—
350	C₄×C₅	—	4	1	no	—
351	C₄×C₅	C₂×C₃×#41	1	2	yes	—
352	Dic₅	—	4	2	no	—
353	Dic₅	—	4	1	no	—
354	Dic₅	C₃×#124	1	2	yes	—
355	Dic₅	C₃×#135	1	4	yes	—
356	#41	—	10	4	no	—
357	#41	—	10	4	no	—
358	C₂×Q₈	—	5	1	no	—
359	C₂×Q₈	—	10	2	no	—
360	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
361	C₂×D₄	—	5	1	no	—
362	C₂×D₄	—	10	1	no	—
363	C₂×D₄	—	10	2	no	—
364	C₂×D₄	—	10	1	no	—
365	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
366	C₂²×C₄	—	5	1	no	—
367	C₂²×C₄	—	5	2	no	—
368	C₂²×C₄	—	10	1	no	—
369	C₂²×C₄	—	10	1	no	—
370	C₂×C₈	—	5	2	no	—
371	C₂×C₈	—	10	4	no	—
372	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	5	2	no	—
375	C₄⋊C₄	—	10	2	no	—
376	C₄⋊C₄	—	10	2	no	—
377	C₄⋊C₄	—	10	2	no	—
378	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	10	2	no	—
381	C₂²⋊C₄	—	10	2	no	—
382	C₄²	—	5	2	no	—
383	C₄²	—	5	1	no	—
384	C₄²	—	10	2	no	—
385	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
386	C₃×C₅	#3131	1	1	yes	characteristic, complemented, Hall
387	C₂²×C₃	—	4	2	no	—
388	C₂²×C₃	—	4	1	no	—
389	C₂²×C₃	—	5	2	no	—
390	C₂²×C₃	—	10	2	no	—
391	C₂²×C₃	—	20	2	no	—
392	C₂²×C₃	—	20	1	no	—
393	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	4	2	no	—
396	C₃×C₄	—	4	1	no	—
397	C₃×C₄	—	5	4	no	—
398	C₃×C₄	—	5	2	no	—
399	C₃×C₄	—	20	2	no	—
400	C₃×C₄	—	20	1	no	—
401	C₃×C₄	D₅×#41	1	2	yes	—
402	C₂×C₅	—	8	1	no	—
403	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
404	C₂×C₅	C₂×C₃×#135	1	2	yes	—
405	D₅	—	2	2	no	—
406	D₅	—	8	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	5	1	no	—
409	C₂³	—	10	1	no	—
410	Q₈	—	2	2	no	—
411	Q₈	—	10	2	no	—
412	Q₈	—	20	4	no	—
413	D₄	—	2	2	no	—
414	D₄	—	10	2	no	—
415	D₄	—	20	2	no	—
416	D₄	—	20	4	no	—
417	D₄	—	20	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	5	1	no	—
421	C₂×C₄	—	5	2	no	—
422	C₂×C₄	—	5	4	no	—
423	C₂×C₄	—	10	4	no	—
424	C₂×C₄	—	10	2	no	—
425	C₂×C₄	—	10	1	no	—
426	C₂×C₄	—	20	2	no	—
427	C₂×C₄	—	20	2	no	—
428	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
429	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	10	2	no	—
432	C₂×C₃	—	8	1	no	—
433	C₂×C₃	—	10	2	no	—
434	C₂×C₃	—	40	1	no	—
435	C₂×C₃	D₅×#124	1	1	yes	characteristic
436	C₂×C₃	D₅×#135	1	2	yes	—
437	C₅	C₃×#3131	1	1	yes	characteristic, complemented, Sylow
438	C₂²	—	4	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	5	2	no	—
441	C₂²	—	10	2	no	—
442	C₂²	—	20	2	no	—
443	C₂²	—	20	1	no	—
444	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	1	no	—
448	C₄	—	5	4	no	—
449	C₄	—	5	2	no	—
450	C₄	—	20	2	no	—
451	C₄	—	20	1	no	—
452	C₄	C₃×D₅×#41	1	2	yes	—
453	C₃	#10613368	1	1	yes	characteristic, direct product factor, Sylow
454	C₂	—	8	1	no	—
455	C₂	—	10	2	no	—
456	C₂	—	40	1	no	—
457	C₂	C₃×D₅×#124	1	1	yes	characteristic
458	C₂	C₃×D₅×#135	1	2	yes	—

	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×#488	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#66002	C₂
hypercenter	C₃×#488	D₅
hypocenter	C₅	C₃×#3131
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#488

Complements

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

N	H ≅ G/N	type
1. C₃×#66022	C₂	semidirect
3. C₃×C₅×#488	C₂	semidirect
4. C₃×#65357	C₂	semidirect
5. C₃×#65345	C₂	semidirect
6. C₃×#65093	C₂	semidirect
7. C₃×#65081	C₂	semidirect
8. C₃×#65061	C₂	semidirect
9. C₃×#65049	C₂	semidirect
10. C₃×#64986	C₂	semidirect
11. C₃×C₄×C₈×D₅	C₂	semidirect
12. #10613368	C₃	direct (N × H)
41. #66022	C₂×C₃	semidirect
43. C₅×#488	C₂×C₃	semidirect
44. #65357	C₂×C₃	semidirect
45. #65345	C₂×C₃	semidirect
46. #65093	C₂×C₃	semidirect
47. #65081	C₂×C₃	semidirect
48. #65061	C₂×C₃	semidirect
49. #65049	C₂×C₃	semidirect
50. #64986	C₂×C₃	semidirect
51. C₄×C₈×D₅	C₂×C₃	semidirect
87. C₃×#488	D₅	semidirect
208. #488	C₃×D₅	semidirect
386. C₃×C₅	#3131	semidirect
437. C₅	C₃×#3131	semidirect
453. C₃	#10613368	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×#66022	2
C₃×#66002	2
C₃×C₅×#488	2
C₃×#65357	2
C₃×#65345	2
C₃×#65093	2
C₃×#65081	2
C₃×#65061	2
C₃×#65049	2
C₃×#64986	2
C₃×C₄×C₈×D₅	2
#10613368	3
C₃×#3131	5

Subgroups — C3×#10613368 #14437780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613368 #14437780