Subgroups — C₃×#10615444 #14471745

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65913	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65361	C₂	1	1	yes	maximal, characteristic
4	C₃×#65359	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65346	C₂	1	2	yes	maximal, complemented
6	C₃×#65345	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×#688	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×Q₈×#168	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65310	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×#686	C₂	1	2	yes	maximal, complemented
11	C₃×#65298	C₂	1	2	yes	maximal, complemented
12	#10615444	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×#127	C₂²	1	1	yes	characteristic
14	C₃×C₅×#124	—	2	1	no	—
15	C₃×C₅×#124	C₂²	1	2	yes	—
16	C₃×C₅×#123	—	2	2	no	—
17	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	—	2	1	no	—
20	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
21	C₃×#4092	—	2	1	no	—
22	C₂×C₃×#688	C₂²	1	1	yes	characteristic
23	C₂×C₃×#686	C₂²	1	2	yes	—
24	C₃×#4042	—	2	2	no	—
25	C₃×D₅×C₄⋊C₄	—	2	1	no	—
26	C₃×C₄×D₂₀	C₂²	1	2	yes	—
27	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
28	C₃×#4016	C₂²	1	2	yes	—
29	C₃×#4015	C₂²	1	1	yes	characteristic
30	C₃×#3967	C₂²	1	2	yes	—
31	C₃×#3967	C₂²	1	1	yes	characteristic
32	C₃×#3964	C₂²	1	2	yes	—
33	C₃×#3964	C₂²	1	2	yes	—
34	C₃×#3964	C₂²	1	2	yes	—
35	C₃×#3941	C₂²	1	1	yes	characteristic
36	C₃×#3940	C₂²	1	1	yes	characteristic
37	C₃×#3939	C₂²	1	2	yes	—
38	C₃×C₄⋊#168	C₂²	1	2	yes	—
39	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
40	C₃×C₄×#168	C₂²	1	2	yes	—
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3361	—	5	1	no	maximal, Hall
43	C₅×#559	C₂×C₃	1	1	yes	characteristic, complemented
44	#65913	C₂×C₃	1	1	yes	characteristic, complemented
45	#65361	C₂×C₃	1	1	yes	characteristic
46	#65359	C₂×C₃	1	1	yes	characteristic, complemented
47	#65346	C₂×C₃	1	2	yes	complemented
48	#65345	C₂×C₃	1	2	yes	complemented
49	C₄×#688	C₂×C₃	1	1	yes	characteristic, complemented
50	Q₈×#168	C₂×C₃	1	1	yes	characteristic, complemented
51	#65310	C₂×C₃	1	1	yes	characteristic, complemented
52	C₄×#686	C₂×C₃	1	2	yes	complemented
53	#65298	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	—	2	1	no	—
57	C₂×C₃×C₅×D₄	—	2	1	no	—
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	—	2	2	no	—
60	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×D₅	—	2	1	no	—
62	C₂×C₃×C₄×D₅	—	2	2	no	—
63	C₂×C₃×Dic₁₀	—	2	1	no	—
64	C₃×C₅×C₄⋊C₄	—	2	1	no	—
65	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₄²×C₅	—	2	1	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	2	yes	—
74	C₃×#688	—	2	2	no	—
75	C₃×#686	—	2	4	no	—
76	C₃×#685	—	2	2	no	—
77	C₃×#685	—	2	1	no	—
78	C₃×C₄⋊Dic₅	—	2	1	no	—
79	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
80	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
81	C₃×#683	—	2	2	no	—
82	C₃×#683	—	2	2	no	—
83	C₂×C₃×#168	C₂³	1	2	yes	—
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₃×#559	D₅	1	1	yes	characteristic, complemented
87	C₃×#554	—	5	1	no	—
88	C₃×#488	—	5	2	no	—
89	C₃×#486	—	5	1	no	—
90	C₃×#478	—	5	2	no	—
91	C₃×#477	—	5	1	no	—
92	C₃×#463	—	5	2	no	—
93	C₃×#459	—	5	1	no	—
94	C₃×C₈×Q₈	—	5	1	no	—
95	C₃×C₄×SD₁₆	—	5	1	no	—
96	C₃×C₄×D₈	—	5	2	no	—
97	C₅×#127	C₂²×C₃	1	1	yes	characteristic
98	C₅×#124	—	2	1	no	—
99	C₅×#124	C₂²×C₃	1	2	yes	—
100	C₅×#123	—	2	2	no	—
101	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
102	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₄×C₅×D₄	—	2	1	no	—
104	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
105	#4092	—	2	1	no	—
106	C₂×#688	C₂²×C₃	1	1	yes	characteristic
107	C₂×#686	C₂²×C₃	1	2	yes	—
108	#4042	—	2	2	no	—
109	D₅×C₄⋊C₄	—	2	1	no	—
110	C₄×D₂₀	C₂²×C₃	1	2	yes	—
111	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
112	#4016	C₂²×C₃	1	2	yes	—
113	#4015	C₂²×C₃	1	1	yes	characteristic
114	#3967	C₂²×C₃	1	2	yes	—
115	#3967	C₂²×C₃	1	1	yes	characteristic
116	#3964	C₂²×C₃	1	2	yes	—
117	#3964	C₂²×C₃	1	2	yes	—
118	#3964	C₂²×C₃	1	2	yes	—
119	#3941	C₂²×C₃	1	1	yes	characteristic
120	#3940	C₂²×C₃	1	1	yes	characteristic
121	#3939	C₂²×C₃	1	2	yes	—
122	C₄⋊#168	C₂²×C₃	1	2	yes	—
123	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
124	C₄×#168	C₂²×C₃	1	2	yes	—
125	C₄×#168	C₂²×C₃	1	1	yes	characteristic
126	#3361	—	5	1	no	Sylow
127	C₂³×C₃×C₅	—	2	2	no	—
128	C₂²×C₃×D₅	—	2	1	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	2	1	no	—
131	C₃×C₅×Q₈	—	2	1	no	—
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	—	2	2	no	—
134	C₃×C₅×D₄	—	4	2	no	—
135	C₃×C₅×D₄	—	8	1	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	8	2	no	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
144	C₂×C₃×Dic₅	—	2	1	no	—
145	C₂×C₃×Dic₅	—	2	2	no	—
146	C₃×D₂₀	—	2	1	no	—
147	C₃×D₂₀	#41	1	2	yes	—
148	C₃×C₄×D₅	—	4	2	no	—
149	C₃×C₄×D₅	—	8	2	no	—
150	C₃×Dic₁₀	—	8	1	no	—
151	C₃×#168	—	2	2	no	—
152	C₃×#168	—	2	1	no	—
153	C₃×#168	—	2	1	no	—
154	C₂×C₃×SD₁₆	—	5	1	no	—
155	C₂×C₃×D₈	—	5	2	no	—
156	C₃×C₄⋊Q₈	—	5	1	no	—
157	C₃×#127	C₂×D₅	1	1	yes	characteristic
158	C₃×#125	—	5	2	no	—
159	C₃×#124	—	2	1	no	—
160	C₃×#124	C₂×D₅	1	2	yes	—
161	C₃×#123	—	2	2	no	—
162	C₃×C₂²⋊Q₈	—	10	1	no	—
163	C₃×C₂²⋊Q₈	—	10	2	no	—
164	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
165	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
166	C₃×C₄×D₄	—	2	1	no	—
167	C₃×C₄×D₄	—	5	2	no	—
168	C₃×C₄×D₄	—	5	1	no	—
169	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	—	10	1	no	—
171	C₃×#107	—	5	2	no	—
172	C₃×#106	—	5	1	no	—
173	C₃×C₄⋊C₈	—	5	1	no	—
174	C₃×C₄⋊C₈	—	5	2	no	—
175	C₃×#103	—	5	1	no	—
176	C₃×#103	—	5	2	no	—
177	C₃×#102	—	5	2	no	—
178	C₃×#102	—	5	2	no	—
179	C₃×#102	—	5	2	no	—
180	C₃×#102	—	5	1	no	—
181	C₃×C₄×C₈	—	5	2	no	—
182	C₃×C₄×C₈	—	5	1	no	—
183	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
184	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	—	2	1	no	—
187	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
188	C₂²×C₄×C₅	—	2	2	no	—
189	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₄×D₅	—	2	1	no	—
191	C₂×C₄×D₅	—	2	2	no	—
192	C₂×Dic₁₀	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
195	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
196	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
197	C₅×C₂²⋊C₄	—	2	2	no	—
198	C₅×C₂²⋊C₄	—	2	2	no	—
199	C₅×C₂²⋊C₄	—	2	2	no	—
200	C₄²×C₅	—	2	1	no	—
201	C₄²×C₅	C₂³×C₃	1	2	yes	—
202	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
203	#688	—	2	2	no	—
204	#686	—	2	4	no	—
205	#685	—	2	1	no	—
206	#685	—	2	2	no	—
207	C₄⋊Dic₅	—	2	1	no	—
208	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
209	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
210	#683	—	2	2	no	—
211	#683	—	2	2	no	—
212	C₂×#168	C₂³×C₃	1	1	yes	characteristic
213	C₂×#168	C₂³×C₃	1	2	yes	—
214	C₂×#168	C₂³×C₃	1	1	yes	characteristic
215	#559	C₃×D₅	1	1	yes	characteristic, complemented
216	#554	—	5	1	no	—
217	#488	—	5	2	no	—
218	#486	—	5	1	no	—
219	#478	—	5	2	no	—
220	#477	—	5	1	no	—
221	#463	—	5	2	no	—
222	#459	—	5	1	no	—
223	C₈×Q₈	—	5	1	no	—
224	C₄×SD₁₆	—	5	1	no	—
225	C₄×D₈	—	5	2	no	—
226	C₂²×C₃×C₅	—	4	2	no	—
227	C₂²×C₃×C₅	—	4	2	no	—
228	C₂²×C₃×C₅	—	4	2	no	—
229	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₃×D₅	—	2	2	no	—
231	C₂×C₃×D₅	—	4	1	no	—
232	C₂×C₃×D₅	—	4	1	no	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	2	no	—
236	C₃×C₄×C₅	—	4	1	no	—
237	C₃×C₄×C₅	—	4	1	no	—
238	C₃×C₄×C₅	#135	1	2	yes	—
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
241	C₃×Dic₅	—	4	1	no	—
242	C₃×Dic₅	—	4	2	no	—
243	C₂×C₃×Q₈	—	10	1	no	—
244	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
245	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
246	C₂×C₃×D₄	—	2	1	no	—
247	C₂×C₃×D₄	—	2	1	no	—
248	C₂×C₃×D₄	—	5	1	no	—
249	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
250	C₂²×C₃×C₄	—	2	2	no	—
251	C₂²×C₃×C₄	—	10	1	no	—
252	C₂²×C₃×C₄	—	10	2	no	—
253	C₃×SD₁₆	—	10	2	no	—
254	C₃×D₈	—	10	4	no	—
255	C₂×C₃×C₈	—	5	1	no	—
256	C₂×C₃×C₈	—	5	1	no	—
257	C₂×C₃×C₈	—	5	2	no	—
258	C₃×C₄⋊C₄	—	2	1	no	—
259	C₃×C₄⋊C₄	—	5	1	no	—
260	C₃×C₄⋊C₄	—	5	2	no	—
261	C₃×C₄⋊C₄	—	10	2	no	—
262	C₃×C₄⋊C₄	—	10	2	no	—
263	C₃×C₄⋊C₄	—	10	1	no	—
264	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
265	C₃×C₄⋊C₄	C₂²⋊D₅	1	2	yes	—
266	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
267	C₃×C₂²⋊C₄	—	2	2	no	—
268	C₃×C₂²⋊C₄	—	2	2	no	—
269	C₃×C₂²⋊C₄	—	2	2	no	—
270	C₃×C₂²⋊C₄	—	10	1	no	—
271	C₃×C₂²⋊C₄	—	10	2	no	—
272	C₃×C₄²	—	2	1	no	—
273	C₃×C₄²	C₂²×D₅	1	2	yes	—
274	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
275	C₂³×C₅	—	2	2	no	—
276	C₂²×D₅	—	2	1	no	—
277	C₅×Q₈	—	2	2	no	—
278	C₅×Q₈	—	2	1	no	—
279	C₅×Q₈	—	2	1	no	—
280	C₅×D₄	—	2	2	no	—
281	C₅×D₄	—	2	2	no	—
282	C₅×D₄	—	4	2	no	—
283	C₅×D₄	—	8	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	8	2	no	—
287	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
288	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
289	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
292	C₂×Dic₅	—	2	1	no	—
293	C₂×Dic₅	—	2	2	no	—
294	D₂₀	—	2	1	no	—
295	D₂₀	C₃×#41	1	2	yes	—
296	C₄×D₅	—	4	2	no	—
297	C₄×D₅	—	8	2	no	—
298	Dic₁₀	—	8	1	no	—
299	#168	—	2	2	no	—
300	#168	—	2	1	no	—
301	#168	—	2	1	no	—
302	C₂×SD₁₆	—	5	1	no	—
303	C₂×D₈	—	5	2	no	—
304	C₄⋊Q₈	—	5	1	no	—
305	#127	C₂×C₃×D₅	1	1	yes	characteristic
306	#125	—	5	2	no	—
307	#124	—	2	1	no	—
308	#124	C₂×C₃×D₅	1	2	yes	—
309	#123	—	2	2	no	—
310	C₂²⋊Q₈	—	10	1	no	—
311	C₂²⋊Q₈	—	10	2	no	—
312	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
313	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	5	2	no	—
316	C₄×D₄	—	5	1	no	—
317	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
318	C₂×C₄⋊C₄	—	10	1	no	—
319	#107	—	5	2	no	—
320	#106	—	5	1	no	—
321	C₄⋊C₈	—	5	1	no	—
322	C₄⋊C₈	—	5	2	no	—
323	#103	—	5	1	no	—
324	#103	—	5	2	no	—
325	#102	—	5	2	no	—
326	#102	—	5	2	no	—
327	#102	—	5	2	no	—
328	#102	—	5	1	no	—
329	C₄×C₈	—	5	2	no	—
330	C₄×C₈	—	5	1	no	—
331	C₂×C₃×C₅	—	8	2	no	—
332	C₂×C₃×C₅	#548	1	1	yes	characteristic
333	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
334	C₂×C₃×C₅	#576	1	1	yes	characteristic
335	C₃×D₅	—	4	2	no	—
336	C₂³×C₃	—	2	2	no	—
337	C₂³×C₃	—	10	1	no	—
338	C₃×Q₈	—	2	2	no	—
339	C₃×Q₈	—	2	1	no	—
340	C₃×Q₈	—	2	1	no	—
341	C₃×Q₈	—	40	1	no	—
342	C₃×D₄	—	2	2	no	—
343	C₃×D₄	—	2	2	no	—
344	C₃×D₄	—	4	2	no	—
345	C₃×D₄	—	5	2	no	—
346	C₃×D₄	—	8	1	no	—
347	C₃×D₄	—	10	1	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	8	2	no	—
351	C₂×C₃×C₄	—	10	1	no	—
352	C₂×C₃×C₄	—	10	2	no	—
353	C₂×C₃×C₄	—	20	2	no	—
354	C₂×C₃×C₄	—	40	2	no	—
355	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
356	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
357	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
360	C₃×C₈	—	10	2	no	—
361	C₃×C₈	—	10	1	no	—
362	C₃×C₈	—	10	1	no	—
363	C₂²×C₅	—	4	2	no	—
364	C₂²×C₅	—	4	2	no	—
365	C₂²×C₅	—	4	2	no	—
366	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
367	C₂×D₅	—	2	2	no	—
368	C₂×D₅	—	4	1	no	—
369	C₂×D₅	—	4	1	no	—
370	C₄×C₅	—	2	2	no	—
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	2	2	no	—
373	C₄×C₅	—	4	1	no	—
374	C₄×C₅	—	4	1	no	—
375	C₄×C₅	C₃×#135	1	2	yes	—
376	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
377	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
378	Dic₅	—	4	1	no	—
379	Dic₅	—	4	2	no	—
380	C₂×Q₈	—	10	1	no	—
381	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
382	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	5	1	no	—
386	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	10	1	no	—
389	C₂²×C₄	—	10	2	no	—
390	SD₁₆	—	10	2	no	—
391	D₈	—	10	4	no	—
392	C₂×C₈	—	5	1	no	—
393	C₂×C₈	—	5	1	no	—
394	C₂×C₈	—	5	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	5	1	no	—
397	C₄⋊C₄	—	5	2	no	—
398	C₄⋊C₄	—	10	2	no	—
399	C₄⋊C₄	—	10	1	no	—
400	C₄⋊C₄	—	10	2	no	—
401	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
402	C₄⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
403	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	10	1	no	—
408	C₂²⋊C₄	—	10	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	C₂²×C₃×D₅	1	2	yes	—
411	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
412	C₃×C₅	#3361	1	1	yes	characteristic, complemented, Hall
413	C₂²×C₃	—	4	2	no	—
414	C₂²×C₃	—	4	2	no	—
415	C₂²×C₃	—	4	2	no	—
416	C₂²×C₃	—	10	2	no	—
417	C₂²×C₃	—	20	1	no	—
418	C₂²×C₃	—	20	1	no	—
419	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
420	C₃×C₄	—	2	2	no	—
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	4	1	no	—
424	C₃×C₄	—	4	1	no	—
425	C₃×C₄	—	20	1	no	—
426	C₃×C₄	—	20	2	no	—
427	C₃×C₄	#4096	1	2	yes	—
428	C₃×C₄	D₅×#41	1	1	yes	characteristic
429	C₃×C₄	#4150	1	1	yes	characteristic
430	C₂×C₅	—	8	2	no	—
431	C₂×C₅	C₃×#548	1	1	yes	characteristic
432	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
433	C₂×C₅	C₃×#576	1	1	yes	characteristic
434	D₅	—	4	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	10	1	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	1	no	—
439	Q₈	—	2	1	no	—
440	Q₈	—	40	1	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	5	2	no	—
445	D₄	—	8	1	no	—
446	D₄	—	10	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	8	2	no	—
450	C₂×C₄	—	10	1	no	—
451	C₂×C₄	—	10	2	no	—
452	C₂×C₄	—	20	2	no	—
453	C₂×C₄	—	40	2	no	—
454	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
455	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
456	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
457	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
458	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
459	C₈	—	10	2	no	—
460	C₈	—	10	1	no	—
461	C₈	—	10	1	no	—
462	C₂×C₃	—	8	2	no	—
463	C₂×C₃	—	20	2	no	—
464	C₂×C₃	C₂×#4096	1	1	yes	characteristic
465	C₂×C₃	#66165	1	1	yes	characteristic
466	C₂×C₃	#66169	1	1	yes	characteristic
467	C₅	C₃×#3361	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	10	2	no	—
472	C₂²	—	20	1	no	—
473	C₂²	—	20	1	no	—
474	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	20	1	no	—
481	C₄	—	20	2	no	—
482	C₄	C₃×#4096	1	2	yes	—
483	C₄	C₃×D₅×#41	1	1	yes	characteristic
484	C₄	C₃×#4150	1	1	yes	characteristic
485	C₃	#10615444	1	1	yes	characteristic, direct product factor, Sylow
486	C₂	—	8	2	no	—
487	C₂	—	20	2	no	—
488	C₂	C₂×C₃×#4096	1	1	yes	characteristic
489	C₂	C₃×#66165	1	1	yes	characteristic
490	C₂	C₃×#66169	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#559	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#65361	C₂
hypercenter	C₃×#559	D₅
hypocenter	C₅	C₃×#3361
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈ ◁ C₃×#559

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#559	C₂	semidirect
2. C₃×#65913	C₂	semidirect
4. C₃×#65359	C₂	semidirect
5. C₃×#65346	C₂	semidirect
6. C₃×#65345	C₂	semidirect
7. C₃×C₄×#688	C₂	semidirect
8. C₃×Q₈×#168	C₂	semidirect
9. C₃×#65310	C₂	semidirect
10. C₃×C₄×#686	C₂	semidirect
11. C₃×#65298	C₂	semidirect
12. #10615444	C₃	direct (N × H)
43. C₅×#559	C₂×C₃	semidirect
44. #65913	C₂×C₃	semidirect
46. #65359	C₂×C₃	semidirect
47. #65346	C₂×C₃	semidirect
48. #65345	C₂×C₃	semidirect
49. C₄×#688	C₂×C₃	semidirect
50. Q₈×#168	C₂×C₃	semidirect
51. #65310	C₂×C₃	semidirect
52. C₄×#686	C₂×C₃	semidirect
53. #65298	C₂×C₃	semidirect
86. C₃×#559	D₅	semidirect
215. #559	C₃×D₅	semidirect
412. C₃×C₅	#3361	semidirect
467. C₅	C₃×#3361	semidirect
485. C₃	#10615444	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×C₅×#559	2
C₃×#65913	2
C₃×#65361	2
C₃×#65359	2
C₃×#65346	2
C₃×#65345	2
C₃×C₄×#688	2
C₃×Q₈×#168	2
C₃×#65310	2
C₃×C₄×#686	2
C₃×#65298	2
#10615444	3
C₃×#3361	5

Subgroups — C3×#10615444 #14471745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615444 #14471745