Subgroups — C₃×#10615398 #14471586

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65913	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65372	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65346	C₂	1	2	yes	maximal
6	C₃×#65345	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×#688	C₂	1	2	yes	maximal, complemented
8	C₃×Q₈×#168	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65311	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×#686	C₂	1	1	yes	maximal, characteristic
11	C₃×#65297	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615398	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#126	—	2	2	no	—
15	C₃×C₅×#124	C₂²	1	2	yes	—
16	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
17	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	—	2	1	no	—
21	C₃×#4092	—	2	1	no	—
22	C₂×C₃×#688	C₂²	1	2	yes	—
23	C₂×C₃×#686	C₂²	1	1	yes	characteristic
24	C₃×#4042	—	2	2	no	—
25	C₃×D₅×C₄⋊C₄	—	2	1	no	—
26	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
27	C₃×C₄×D₂₀	C₂²	1	2	yes	—
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	2	yes	—
32	C₃×#3967	C₂²	1	2	yes	—
33	C₃×#3964	C₂²	1	2	yes	—
34	C₃×#3964	C₂²	1	1	yes	characteristic
35	C₃×#3941	C₂²	1	1	yes	characteristic
36	C₃×#3940	C₂²	1	2	yes	—
37	C₃×#3939	C₂²	1	1	yes	characteristic
38	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
39	C₃×C₄⋊#168	C₂²	1	2	yes	—
40	C₃×C₄×#168	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	2	yes	—
42	C₃×#3360	—	5	1	no	maximal, Hall
43	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
44	#65913	C₂×C₃	1	1	yes	characteristic, complemented
45	#65372	C₂×C₃	1	1	yes	characteristic, complemented
46	#65370	C₂×C₃	1	1	yes	characteristic, complemented
47	#65346	C₂×C₃	1	2	yes	—
48	#65345	C₂×C₃	1	2	yes	complemented
49	C₄×#688	C₂×C₃	1	2	yes	complemented
50	Q₈×#168	C₂×C₃	1	1	yes	characteristic, complemented
51	#65311	C₂×C₃	1	2	yes	complemented
52	C₄×#686	C₂×C₃	1	1	yes	characteristic
53	#65297	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	—	2	1	no	—
60	C₂×C₃×C₄×D₅	—	2	2	no	—
61	C₂×C₃×Dic₁₀	—	2	1	no	—
62	C₃×C₅×C₄⋊C₄	—	2	1	no	—
63	C₃×C₅×C₄⋊C₄	—	2	2	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	1	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₄²×C₅	—	2	2	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	2	yes	—
74	C₃×#688	—	2	4	no	—
75	C₃×#686	—	2	2	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	1	yes	characteristic
80	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
81	C₃×#683	—	2	2	no	—
82	C₃×#683	—	2	2	no	—
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	2	yes	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₃×#556	D₅	1	1	yes	characteristic, complemented
87	C₃×#554	—	5	1	no	—
88	C₃×#488	—	5	2	no	—
89	C₃×#487	—	5	1	no	—
90	C₃×#479	—	5	2	no	—
91	C₃×#476	—	5	1	no	—
92	C₃×#463	—	5	2	no	—
93	C₃×#461	—	5	1	no	—
94	C₃×C₈×Q₈	—	5	1	no	—
95	C₃×C₄×SD₁₆	—	5	2	no	—
96	C₃×C₄×D₈	—	5	1	no	—
97	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₅×#126	—	2	2	no	—
99	C₅×#124	C₂²×C₃	1	2	yes	—
100	C₅×C₂²⋊Q₈	—	2	1	no	—
101	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
102	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
104	C₅×#117	—	2	1	no	—
105	#4092	—	2	1	no	—
106	C₂×#688	C₂²×C₃	1	2	yes	—
107	C₂×#686	C₂²×C₃	1	1	yes	characteristic
108	#4042	—	2	2	no	—
109	D₅×C₄⋊C₄	—	2	1	no	—
110	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
111	C₄×D₂₀	C₂²×C₃	1	2	yes	—
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	2	yes	—
116	#3967	C₂²×C₃	1	2	yes	—
117	#3964	C₂²×C₃	1	2	yes	—
118	#3964	C₂²×C₃	1	1	yes	characteristic
119	#3941	C₂²×C₃	1	1	yes	characteristic
120	#3940	C₂²×C₃	1	2	yes	—
121	#3939	C₂²×C₃	1	1	yes	characteristic
122	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
123	C₄⋊#168	C₂²×C₃	1	2	yes	—
124	C₄×#168	C₂²×C₃	1	1	yes	characteristic
125	C₄×#168	C₂²×C₃	1	2	yes	—
126	#3360	—	5	1	no	Sylow
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₂²×C₃×D₅	—	2	1	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×Q₈	—	2	2	no	—
132	C₃×C₅×D₄	—	2	1	no	—
133	C₃×C₅×D₄	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	4	2	no	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₂×C₃×Dic₅	—	2	1	no	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₃×D₂₀	—	2	1	no	—
145	C₃×D₂₀	#41	1	2	yes	—
146	C₃×C₄×D₅	—	4	2	no	—
147	C₃×C₄×D₅	—	8	2	no	—
148	C₃×Dic₁₀	—	8	1	no	—
149	C₃×#168	—	2	1	no	—
150	C₃×#168	—	2	2	no	—
151	C₃×#168	—	2	1	no	—
152	C₂×C₃×SD₁₆	—	5	2	no	—
153	C₂×C₃×D₈	—	5	1	no	—
154	C₃×C₄⋊Q₈	—	5	1	no	—
155	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
156	C₃×#126	—	2	2	no	—
157	C₃×#125	—	5	2	no	—
158	C₃×#124	C₂×D₅	1	2	yes	—
159	C₃×C₂²⋊Q₈	—	2	1	no	—
160	C₃×C₂²⋊Q₈	—	10	1	no	—
161	C₃×C₂²⋊Q₈	—	10	2	no	—
162	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
163	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
164	C₃×C₄×D₄	—	5	1	no	—
165	C₃×C₄×D₄	—	5	2	no	—
166	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
167	C₃×#117	—	2	1	no	—
168	C₂×C₃×C₄⋊C₄	—	10	1	no	—
169	C₃×#107	—	5	1	no	—
170	C₃×#106	—	5	2	no	—
171	C₃×C₄⋊C₈	—	5	1	no	—
172	C₃×C₄⋊C₈	—	5	2	no	—
173	C₃×#103	—	5	2	no	—
174	C₃×#103	—	5	2	no	—
175	C₃×#103	—	5	2	no	—
176	C₃×#102	—	5	1	no	—
177	C₃×#102	—	5	2	no	—
178	C₃×#102	—	5	1	no	—
179	C₃×C₄×C₈	—	5	1	no	—
180	C₃×C₄×C₈	—	5	2	no	—
181	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
182	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
183	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₄×D₅	—	2	1	no	—
187	C₂×C₄×D₅	—	2	2	no	—
188	C₂×Dic₁₀	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
193	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
194	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₅×C₂²⋊C₄	—	2	1	no	—
197	C₅×C₂²⋊C₄	—	2	2	no	—
198	C₄²×C₅	—	2	2	no	—
199	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
200	C₄²×C₅	C₂³×C₃	1	2	yes	—
201	#688	—	2	4	no	—
202	#686	—	2	2	no	—
203	#685	—	2	1	no	—
204	#685	—	2	2	no	—
205	C₄⋊Dic₅	—	2	1	no	—
206	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
207	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
208	#683	—	2	2	no	—
209	#683	—	2	2	no	—
210	C₂×#168	C₂³×C₃	1	1	yes	characteristic
211	C₂×#168	C₂³×C₃	1	1	yes	characteristic
212	C₂×#168	C₂³×C₃	1	2	yes	—
213	#556	C₃×D₅	1	1	yes	characteristic, complemented
214	#554	—	5	1	no	—
215	#488	—	5	2	no	—
216	#487	—	5	1	no	—
217	#479	—	5	2	no	—
218	#476	—	5	1	no	—
219	#463	—	5	2	no	—
220	#461	—	5	1	no	—
221	C₈×Q₈	—	5	1	no	—
222	C₄×SD₁₆	—	5	2	no	—
223	C₄×D₈	—	5	1	no	—
224	C₂²×C₃×C₅	—	4	1	no	—
225	C₂²×C₃×C₅	—	4	1	no	—
226	C₂²×C₃×C₅	—	4	1	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₃×D₅	—	2	2	no	—
229	C₂×C₃×D₅	—	4	1	no	—
230	C₂×C₃×D₅	—	4	1	no	—
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	2	1	no	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	—	4	2	no	—
235	C₃×C₄×C₅	—	4	1	no	—
236	C₃×C₄×C₅	#135	1	2	yes	—
237	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
239	C₃×Dic₅	—	4	1	no	—
240	C₃×Dic₅	—	4	2	no	—
241	C₂×C₃×Q₈	—	10	1	no	—
242	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
243	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
244	C₂×C₃×D₄	—	5	1	no	—
245	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	—	2	1	no	—
247	C₂²×C₃×C₄	—	10	1	no	—
248	C₂²×C₃×C₄	—	10	2	no	—
249	C₃×SD₁₆	—	10	4	no	—
250	C₃×D₈	—	10	2	no	—
251	C₂×C₃×C₈	—	5	1	no	—
252	C₂×C₃×C₈	—	5	2	no	—
253	C₂×C₃×C₈	—	5	1	no	—
254	C₃×C₄⋊C₄	—	2	1	no	—
255	C₃×C₄⋊C₄	—	2	2	no	—
256	C₃×C₄⋊C₄	—	2	1	no	—
257	C₃×C₄⋊C₄	—	5	2	no	—
258	C₃×C₄⋊C₄	—	5	1	no	—
259	C₃×C₄⋊C₄	—	10	2	no	—
260	C₃×C₄⋊C₄	—	10	2	no	—
261	C₃×C₄⋊C₄	—	10	1	no	—
262	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
263	C₃×C₄⋊C₄	C₂²⋊D₅	1	2	yes	—
264	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
265	C₃×C₂²⋊C₄	—	2	2	no	—
266	C₃×C₂²⋊C₄	—	2	1	no	—
267	C₃×C₂²⋊C₄	—	2	2	no	—
268	C₃×C₂²⋊C₄	—	10	1	no	—
269	C₃×C₂²⋊C₄	—	10	2	no	—
270	C₃×C₄²	—	2	2	no	—
271	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
272	C₃×C₄²	C₂²×D₅	1	2	yes	—
273	C₂³×C₅	—	2	1	no	—
274	C₂²×D₅	—	2	1	no	—
275	C₅×Q₈	—	2	2	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	2	2	no	—
278	C₅×D₄	—	2	1	no	—
279	C₅×D₄	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	4	2	no	—
283	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
284	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
285	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
288	C₂×Dic₅	—	2	1	no	—
289	C₂×Dic₅	—	2	2	no	—
290	D₂₀	—	2	1	no	—
291	D₂₀	C₃×#41	1	2	yes	—
292	C₄×D₅	—	4	2	no	—
293	C₄×D₅	—	8	2	no	—
294	Dic₁₀	—	8	1	no	—
295	#168	—	2	1	no	—
296	#168	—	2	2	no	—
297	#168	—	2	1	no	—
298	C₂×SD₁₆	—	5	2	no	—
299	C₂×D₈	—	5	1	no	—
300	C₄⋊Q₈	—	5	1	no	—
301	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
302	#126	—	2	2	no	—
303	#125	—	5	2	no	—
304	#124	C₂×C₃×D₅	1	2	yes	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	10	1	no	—
307	C₂²⋊Q₈	—	10	2	no	—
308	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
309	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
310	C₄×D₄	—	5	1	no	—
311	C₄×D₄	—	5	2	no	—
312	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
313	#117	—	2	1	no	—
314	C₂×C₄⋊C₄	—	10	1	no	—
315	#107	—	5	1	no	—
316	#106	—	5	2	no	—
317	C₄⋊C₈	—	5	1	no	—
318	C₄⋊C₈	—	5	2	no	—
319	#103	—	5	2	no	—
320	#103	—	5	2	no	—
321	#103	—	5	2	no	—
322	#102	—	5	1	no	—
323	#102	—	5	2	no	—
324	#102	—	5	1	no	—
325	C₄×C₈	—	5	1	no	—
326	C₄×C₈	—	5	2	no	—
327	C₂×C₃×C₅	—	8	1	no	—
328	C₂×C₃×C₅	#548	1	1	yes	characteristic
329	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
330	C₂×C₃×C₅	#577	1	1	yes	characteristic
331	C₃×D₅	—	4	2	no	—
332	C₂³×C₃	—	2	1	no	—
333	C₂³×C₃	—	10	1	no	—
334	C₃×Q₈	—	2	2	no	—
335	C₃×Q₈	—	2	2	no	—
336	C₃×Q₈	—	2	2	no	—
337	C₃×Q₈	—	40	1	no	—
338	C₃×D₄	—	2	1	no	—
339	C₃×D₄	—	2	1	no	—
340	C₃×D₄	—	5	2	no	—
341	C₃×D₄	—	10	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	4	2	no	—
345	C₂×C₃×C₄	—	10	1	no	—
346	C₂×C₃×C₄	—	10	2	no	—
347	C₂×C₃×C₄	—	20	2	no	—
348	C₂×C₃×C₄	—	40	2	no	—
349	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
350	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
351	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
354	C₃×C₈	—	10	1	no	—
355	C₃×C₈	—	10	2	no	—
356	C₃×C₈	—	10	1	no	—
357	C₂²×C₅	—	4	1	no	—
358	C₂²×C₅	—	4	1	no	—
359	C₂²×C₅	—	4	1	no	—
360	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
361	C₂×D₅	—	2	2	no	—
362	C₂×D₅	—	4	1	no	—
363	C₂×D₅	—	4	1	no	—
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	—	2	1	no	—
366	C₄×C₅	—	2	2	no	—
367	C₄×C₅	—	4	1	no	—
368	C₄×C₅	—	4	2	no	—
369	C₄×C₅	C₃×#135	1	2	yes	—
370	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
371	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
372	Dic₅	—	4	1	no	—
373	Dic₅	—	4	2	no	—
374	C₂×Q₈	—	10	1	no	—
375	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
376	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
377	C₂×D₄	—	5	1	no	—
378	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	10	1	no	—
381	C₂²×C₄	—	10	2	no	—
382	SD₁₆	—	10	4	no	—
383	D₈	—	10	2	no	—
384	C₂×C₈	—	5	1	no	—
385	C₂×C₈	—	5	2	no	—
386	C₂×C₈	—	5	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	5	2	no	—
391	C₄⋊C₄	—	5	1	no	—
392	C₄⋊C₄	—	10	2	no	—
393	C₄⋊C₄	—	10	1	no	—
394	C₄⋊C₄	—	10	2	no	—
395	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
396	C₄⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
397	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	10	1	no	—
402	C₂²⋊C₄	—	10	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
405	C₄²	C₂²×C₃×D₅	1	2	yes	—
406	C₃×C₅	#3360	1	1	yes	characteristic, complemented, Hall
407	C₂²×C₃	—	4	1	no	—
408	C₂²×C₃	—	4	1	no	—
409	C₂²×C₃	—	4	1	no	—
410	C₂²×C₃	—	10	2	no	—
411	C₂²×C₃	—	20	1	no	—
412	C₂²×C₃	—	20	1	no	—
413	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	4	1	no	—
418	C₃×C₄	—	4	2	no	—
419	C₃×C₄	—	20	1	no	—
420	C₃×C₄	—	20	2	no	—
421	C₃×C₄	#4096	1	2	yes	—
422	C₃×C₄	D₅×#41	1	1	yes	characteristic
423	C₃×C₄	#4150	1	1	yes	characteristic
424	C₂×C₅	—	8	1	no	—
425	C₂×C₅	C₃×#548	1	1	yes	characteristic
426	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
427	C₂×C₅	C₃×#577	1	1	yes	characteristic
428	D₅	—	4	2	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	10	1	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	40	1	no	—
435	D₄	—	2	1	no	—
436	D₄	—	2	1	no	—
437	D₄	—	5	2	no	—
438	D₄	—	10	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	10	1	no	—
443	C₂×C₄	—	10	2	no	—
444	C₂×C₄	—	20	2	no	—
445	C₂×C₄	—	40	2	no	—
446	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
447	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
448	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
449	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
450	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
451	C₈	—	10	1	no	—
452	C₈	—	10	2	no	—
453	C₈	—	10	1	no	—
454	C₂×C₃	—	8	1	no	—
455	C₂×C₃	—	20	2	no	—
456	C₂×C₃	C₂×#4096	1	1	yes	characteristic
457	C₂×C₃	#66165	1	1	yes	characteristic
458	C₂×C₃	#66171	1	1	yes	characteristic
459	C₅	C₃×#3360	1	1	yes	characteristic, complemented, Sylow
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	10	2	no	—
464	C₂²	—	20	1	no	—
465	C₂²	—	20	1	no	—
466	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	20	1	no	—
473	C₄	—	20	2	no	—
474	C₄	C₃×#4096	1	2	yes	—
475	C₄	C₃×D₅×#41	1	1	yes	characteristic
476	C₄	C₃×#4150	1	1	yes	characteristic
477	C₃	#10615398	1	1	yes	characteristic, direct product factor, Sylow
478	C₂	—	8	1	no	—
479	C₂	—	20	2	no	—
480	C₂	C₂×C₃×#4096	1	1	yes	characteristic
481	C₂	C₃×#66165	1	1	yes	characteristic
482	C₂	C₃×#66171	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×#556	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#686	C₂²
hypercenter	C₃×#556	D₅
hypocenter	C₅	C₃×#3360
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈ ◁ C₃×#556

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#556	C₂	semidirect
2. C₃×#65913	C₂	semidirect
3. C₃×#65372	C₂	semidirect
4. C₃×#65370	C₂	semidirect
6. C₃×#65345	C₂	semidirect
7. C₃×C₄×#688	C₂	semidirect
8. C₃×Q₈×#168	C₂	semidirect
9. C₃×#65311	C₂	semidirect
11. C₃×#65297	C₂	semidirect
12. #10615398	C₃	direct (N × H)
43. C₅×#556	C₂×C₃	semidirect
44. #65913	C₂×C₃	semidirect
45. #65372	C₂×C₃	semidirect
46. #65370	C₂×C₃	semidirect
48. #65345	C₂×C₃	semidirect
49. C₄×#688	C₂×C₃	semidirect
50. Q₈×#168	C₂×C₃	semidirect
51. #65311	C₂×C₃	semidirect
53. #65297	C₂×C₃	semidirect
86. C₃×#556	D₅	semidirect
213. #556	C₃×D₅	semidirect
406. C₃×C₅	#3360	semidirect
459. C₅	C₃×#3360	semidirect
477. C₃	#10615398	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×#556	2
C₃×#65913	2
C₃×#65372	2
C₃×#65370	2
C₃×#65346	2
C₃×#65345	2
C₃×C₄×#688	2
C₃×Q₈×#168	2
C₃×#65311	2
C₃×C₄×#686	2
C₃×#65297	2
#10615398	3
C₃×#3360	5

Subgroups — C3×#10615398 #14471586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615398 #14471586