Subgroups — C₃×#10615281 #14459122

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65889	C₂	1	1	yes	maximal, characteristic
3	C₃×#65516	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#3967	C₂	1	2	yes	maximal, complemented
5	C₃×#65372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65370	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65337	C₂	1	2	yes	maximal, complemented
8	C₃×#65332	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×#688	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65309	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615281	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
14	C₂×C₃×#711	—	2	1	no	—
15	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
18	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	—	2	1	no	—
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×#688	C₂²	1	1	yes	characteristic
23	C₂×C₃×#688	C₂²	1	2	yes	—
24	C₃×#4076	C₂²	1	2	yes	—
25	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
26	C₂²×C₃×#168	C₂²	1	2	yes	—
27	C₃×#4043	—	2	1	no	—
28	C₃×#4032	—	2	2	no	—
29	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
30	C₃×#4015	C₂²	1	1	yes	characteristic
31	C₃×#3967	C₂²	1	2	yes	—
32	C₃×#3967	C₂²	1	1	yes	characteristic
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3967	C₂²	1	2	yes	—
35	C₃×#3967	C₂²	1	2	yes	—
36	C₃×C₂²⋊#168	C₂²	1	2	yes	—
37	C₃×#3941	C₂²	1	1	yes	characteristic
38	C₃×#3940	C₂²	1	2	yes	—
39	C₃×#3940	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3298	—	5	1	no	maximal, Hall
43	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
44	#65889	C₂×C₃	1	1	yes	characteristic
45	#65516	C₂×C₃	1	2	yes	complemented
46	C₂×#3967	C₂×C₃	1	2	yes	complemented
47	#65372	C₂×C₃	1	1	yes	characteristic, complemented
48	#65370	C₂×C₃	1	1	yes	characteristic, complemented
49	#65337	C₂×C₃	1	2	yes	complemented
50	#65332	C₂×C₃	1	2	yes	complemented
51	C₄×#688	C₂×C₃	1	1	yes	characteristic, complemented
52	#65309	C₂×C₃	1	1	yes	characteristic, complemented
53	D₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×Q₈	—	2	2	no	—
55	C₂×C₃×C₅×Q₈	—	2	4	no	—
56	C₂×C₃×C₅×Q₈	—	4	2	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
63	C₂²×C₃×Dic₅	—	2	2	no	—
64	C₃×#711	—	4	4	no	—
65	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	—	2	1	no	—
67	C₂×C₃×Dic₁₀	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
76	C₃×C₄²×C₅	—	2	1	no	—
77	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₃×#688	—	2	2	no	—
79	C₃×#688	—	4	2	no	—
80	C₃×#685	—	2	1	no	—
81	C₃×#685	—	2	2	no	—
82	C₃×C₄⋊Dic₅	—	2	1	no	—
83	C₃×C₄⋊Dic₅	—	2	2	no	—
84	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
85	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
86	C₂×C₃×#168	—	4	2	no	—
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	C₂×C₃×#168	C₂³	1	2	yes	—
89	C₂×C₃×#168	C₂³	1	1	yes	characteristic
90	C₃×D₄×Q₈	D₅	1	1	yes	characteristic, complemented
91	C₃×#547	—	5	1	no	—
92	C₃×#487	—	5	1	no	—
93	C₃×#483	—	5	2	no	—
94	C₃×#475	—	5	1	no	—
95	C₃×#465	—	5	2	no	—
96	C₃×#461	—	5	1	no	—
97	C₃×#448	—	5	2	no	—
98	C₃×C₄×SD₁₆	—	5	1	no	—
99	C₃×C₈×D₄	—	5	1	no	—
100	C₂×C₃×#103	—	5	2	no	—
101	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
102	C₂×#711	—	2	1	no	—
103	C₅×C₄⋊Q₈	—	2	1	no	—
104	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₅×C₂²⋊Q₈	—	2	2	no	—
106	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
107	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
108	C₄×C₅×D₄	—	2	1	no	—
109	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
110	C₂×#688	C₂²×C₃	1	1	yes	characteristic
111	C₂×#688	C₂²×C₃	1	2	yes	—
112	#4076	C₂²×C₃	1	2	yes	—
113	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
114	C₂²×#168	C₂²×C₃	1	2	yes	—
115	#4043	—	2	1	no	—
116	#4032	—	2	2	no	—
117	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
118	#4015	C₂²×C₃	1	1	yes	characteristic
119	#3967	C₂²×C₃	1	2	yes	—
120	#3967	C₂²×C₃	1	1	yes	characteristic
121	#3967	C₂²×C₃	1	2	yes	—
122	#3967	C₂²×C₃	1	2	yes	—
123	#3967	C₂²×C₃	1	2	yes	—
124	C₂²⋊#168	C₂²×C₃	1	2	yes	—
125	#3941	C₂²×C₃	1	1	yes	characteristic
126	#3940	C₂²×C₃	1	2	yes	—
127	#3940	C₂²×C₃	1	1	yes	characteristic
128	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
129	C₄×#168	C₂²×C₃	1	1	yes	characteristic
130	#3298	—	5	1	no	Sylow
131	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
132	C₂²×C₃×D₅	—	2	1	no	—
133	C₃×C₅×Q₈	—	2	1	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×Q₈	—	4	4	no	—
137	C₃×C₅×Q₈	#41	1	2	yes	complemented
138	C₃×C₅×D₄	SD₁₆	1	4	yes	complemented
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	4	4	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₃×C₂²⋊D₅	—	4	4	no	—
150	C₂×C₃×Dic₅	—	2	2	no	—
151	C₂×C₃×Dic₅	—	2	1	no	—
152	C₂×C₃×Dic₅	—	4	4	no	—
153	C₃×D₂₀	—	2	1	no	—
154	C₃×D₂₀	—	2	1	no	—
155	C₃×C₄×D₅	—	4	2	no	—
156	C₃×Dic₁₀	—	4	2	no	—
157	C₃×#168	—	2	1	no	—
158	C₃×#168	—	2	1	no	—
159	C₃×#168	—	2	2	no	—
160	C₂×C₃×#41	—	10	1	no	—
161	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
162	C₂×C₃×SD₁₆	—	5	1	no	—
163	C₂×C₃×SD₁₆	—	5	2	no	—
164	C₂²×C₃×C₈	—	5	2	no	—
165	C₃×C₄⋊Q₈	—	2	1	no	—
166	C₃×C₄⋊Q₈	—	5	1	no	—
167	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
168	C₃×#123	—	10	2	no	—
169	C₃×C₂²⋊Q₈	—	2	2	no	—
170	C₃×C₂²⋊Q₈	—	10	1	no	—
171	C₃×C₂²⋊Q₈	C₂×D₅	1	2	yes	—
172	C₃×#121	—	5	2	no	—
173	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
174	C₃×C₄×D₄	—	2	1	no	—
175	C₃×C₄×D₄	—	5	1	no	—
176	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	—	5	2	no	—
178	C₃×#106	—	5	1	no	—
179	C₃×#106	—	5	2	no	—
180	C₃×C₄⋊C₈	—	5	1	no	—
181	C₃×#103	—	5	1	no	—
182	C₃×#103	—	5	2	no	—
183	C₃×#103	—	5	2	no	—
184	C₃×#103	—	5	2	no	—
185	C₃×#103	—	5	2	no	—
186	C₃×#102	—	5	1	no	—
187	C₃×C₂²⋊C₈	—	5	2	no	—
188	C₃×C₄×C₈	—	5	1	no	—
189	C₂×C₅×Q₈	—	2	2	no	—
190	C₂×C₅×Q₈	—	2	4	no	—
191	C₂×C₅×Q₈	—	4	2	no	—
192	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
193	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
197	C₂×C₂²⋊D₅	—	2	2	no	—
198	C₂²×Dic₅	—	2	2	no	—
199	#711	—	4	4	no	—
200	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₄×D₅	—	2	1	no	—
202	C₂×Dic₁₀	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	2	no	—
207	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
208	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
209	C₅×C₂²⋊C₄	—	2	2	no	—
210	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
211	C₄²×C₅	—	2	1	no	—
212	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
213	#688	—	2	2	no	—
214	#688	—	4	2	no	—
215	#685	—	2	1	no	—
216	#685	—	2	2	no	—
217	C₄⋊Dic₅	—	2	1	no	—
218	C₄⋊Dic₅	—	2	2	no	—
219	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
220	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
221	C₂×#168	—	4	2	no	—
222	C₂×#168	C₂³×C₃	1	1	yes	characteristic
223	C₂×#168	C₂³×C₃	1	1	yes	characteristic
224	C₂×#168	C₂³×C₃	1	2	yes	—
225	D₄×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
226	#547	—	5	1	no	—
227	#487	—	5	1	no	—
228	#483	—	5	2	no	—
229	#475	—	5	1	no	—
230	#465	—	5	2	no	—
231	#461	—	5	1	no	—
232	#448	—	5	2	no	—
233	C₄×SD₁₆	—	5	1	no	—
234	C₈×D₄	—	5	1	no	—
235	C₂×#103	—	5	2	no	—
236	C₂²×C₃×C₅	—	2	2	no	—
237	C₂²×C₃×C₅	—	2	2	no	—
238	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	—
239	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₃×D₅	—	4	1	no	—
241	C₂×C₃×D₅	—	4	1	no	—
242	C₂×C₃×D₅	—	4	1	no	—
243	C₃×C₄×C₅	—	2	2	no	—
244	C₃×C₄×C₅	—	2	2	no	—
245	C₃×C₄×C₅	—	2	1	no	—
246	C₃×C₄×C₅	—	4	2	no	—
247	C₃×C₄×C₅	—	4	1	no	—
248	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
249	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
251	C₃×Dic₅	—	4	2	no	—
252	C₃×Dic₅	—	4	1	no	—
253	C₃×#41	—	20	4	no	—
254	C₂×C₃×Q₈	—	2	2	no	—
255	C₂×C₃×Q₈	—	2	4	no	—
256	C₂×C₃×Q₈	—	4	2	no	—
257	C₂×C₃×Q₈	—	10	1	no	—
258	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
259	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
260	C₂×C₃×D₄	—	5	1	no	—
261	C₂×C₃×D₄	—	10	2	no	—
262	C₂×C₃×D₄	C₂²⋊D₅	1	1	yes	characteristic
263	C₂²×C₃×C₄	—	2	2	no	—
264	C₂²×C₃×C₄	—	10	2	no	—
265	C₂²×C₃×C₄	—	10	1	no	—
266	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
267	C₃×SD₁₆	—	10	2	no	—
268	C₃×SD₁₆	—	20	2	no	—
269	C₂×C₃×C₈	—	5	1	no	—
270	C₂×C₃×C₈	—	5	1	no	—
271	C₂×C₃×C₈	—	5	2	no	—
272	C₂×C₃×C₈	—	20	2	no	—
273	C₃×C₄⋊C₄	—	2	1	no	—
274	C₃×C₄⋊C₄	—	2	1	no	—
275	C₃×C₄⋊C₄	—	2	1	no	—
276	C₃×C₄⋊C₄	—	2	2	no	—
277	C₃×C₄⋊C₄	—	5	1	no	—
278	C₃×C₄⋊C₄	—	5	2	no	—
279	C₃×C₄⋊C₄	—	10	2	no	—
280	C₃×C₄⋊C₄	—	10	1	no	—
281	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
282	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
283	C₃×C₂²⋊C₄	—	2	2	no	—
284	C₃×C₂²⋊C₄	—	10	1	no	—
285	C₃×C₂²⋊C₄	—	10	2	no	—
286	C₃×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
287	C₃×C₄²	—	2	1	no	—
288	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
289	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
290	C₂²×D₅	—	2	1	no	—
291	C₅×Q₈	—	2	1	no	—
292	C₅×Q₈	—	2	2	no	—
293	C₅×Q₈	—	2	2	no	—
294	C₅×Q₈	—	4	4	no	—
295	C₅×Q₈	C₃×#41	1	2	yes	complemented
296	C₅×D₄	C₃×SD₁₆	1	4	yes	complemented
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	4	4	no	—
303	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
305	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
307	C₂²⋊D₅	—	4	4	no	—
308	C₂×Dic₅	—	2	2	no	—
309	C₂×Dic₅	—	2	1	no	—
310	C₂×Dic₅	—	4	4	no	—
311	D₂₀	—	2	1	no	—
312	D₂₀	—	2	1	no	—
313	C₄×D₅	—	4	2	no	—
314	Dic₁₀	—	4	2	no	—
315	#168	—	2	1	no	—
316	#168	—	2	1	no	—
317	#168	—	2	2	no	—
318	C₂×#41	—	10	1	no	—
319	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
320	C₂×SD₁₆	—	5	1	no	—
321	C₂×SD₁₆	—	5	2	no	—
322	C₂²×C₈	—	5	2	no	—
323	C₄⋊Q₈	—	2	1	no	—
324	C₄⋊Q₈	—	5	1	no	—
325	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
326	#123	—	10	2	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	—	10	1	no	—
329	C₂²⋊Q₈	C₂×C₃×D₅	1	2	yes	—
330	#121	—	5	2	no	—
331	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	5	1	no	—
334	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
335	C₂×C₄⋊C₄	—	5	2	no	—
336	#106	—	5	1	no	—
337	#106	—	5	2	no	—
338	C₄⋊C₈	—	5	1	no	—
339	#103	—	5	1	no	—
340	#103	—	5	2	no	—
341	#103	—	5	2	no	—
342	#103	—	5	2	no	—
343	#103	—	5	2	no	—
344	#102	—	5	1	no	—
345	C₂²⋊C₈	—	5	2	no	—
346	C₄×C₈	—	5	1	no	—
347	C₂×C₃×C₅	—	2	4	no	—
348	C₂×C₃×C₅	#546	1	1	yes	characteristic
349	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
350	C₂×C₃×C₅	#578	1	1	yes	characteristic
351	C₃×D₅	—	8	1	no	—
352	C₂³×C₃	—	10	1	no	—
353	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
354	C₃×Q₈	—	2	1	no	—
355	C₃×Q₈	—	2	2	no	—
356	C₃×Q₈	—	2	2	no	—
357	C₃×Q₈	—	4	4	no	—
358	C₃×Q₈	—	20	2	no	—
359	C₃×Q₈	#711	1	2	yes	complemented
360	C₃×D₄	—	10	1	no	—
361	C₃×D₄	—	10	1	no	—
362	C₃×D₄	—	20	4	no	—
363	C₃×D₄	#688	1	4	yes	complemented
364	C₂×C₃×C₄	—	2	1	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	4	4	no	—
370	C₂×C₃×C₄	—	10	1	no	—
371	C₂×C₃×C₄	—	10	2	no	—
372	C₂×C₃×C₄	—	20	4	no	—
373	C₂×C₃×C₄	—	20	2	no	—
374	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
376	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
378	C₃×C₈	—	10	1	no	—
379	C₃×C₈	—	10	1	no	—
380	C₃×C₈	—	10	2	no	—
381	C₂²×C₅	—	2	2	no	—
382	C₂²×C₅	—	2	2	no	—
383	C₂²×C₅	C₂×C₃×SD₁₆	1	4	yes	—
384	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
385	C₂×D₅	—	4	1	no	—
386	C₂×D₅	—	4	1	no	—
387	C₂×D₅	—	4	1	no	—
388	C₄×C₅	—	2	1	no	—
389	C₄×C₅	—	2	2	no	—
390	C₄×C₅	—	2	2	no	—
391	C₄×C₅	—	4	1	no	—
392	C₄×C₅	—	4	2	no	—
393	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
394	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
395	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
396	Dic₅	—	4	2	no	—
397	Dic₅	—	4	1	no	—
398	#41	—	20	4	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	4	2	no	—
402	C₂×Q₈	—	10	1	no	—
403	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
404	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
405	C₂×D₄	—	5	1	no	—
406	C₂×D₄	—	10	2	no	—
407	C₂×D₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	10	2	no	—
410	C₂²×C₄	—	10	1	no	—
411	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
412	SD₁₆	—	10	2	no	—
413	SD₁₆	—	20	2	no	—
414	C₂×C₈	—	5	1	no	—
415	C₂×C₈	—	5	1	no	—
416	C₂×C₈	—	5	2	no	—
417	C₂×C₈	—	20	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	5	1	no	—
423	C₄⋊C₄	—	5	2	no	—
424	C₄⋊C₄	—	10	2	no	—
425	C₄⋊C₄	—	10	1	no	—
426	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
427	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	10	1	no	—
430	C₂²⋊C₄	—	10	2	no	—
431	C₂²⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
432	C₄²	—	2	1	no	—
433	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
434	C₃×C₅	#3298	1	1	yes	characteristic, complemented, Hall
435	C₂²×C₃	—	2	2	no	—
436	C₂²×C₃	—	2	2	no	—
437	C₂²×C₃	—	20	1	no	—
438	C₂²×C₃	—	20	1	no	—
439	C₂²×C₃	—	20	1	no	—
440	C₂²×C₃	C₂×#688	1	4	yes	—
441	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
442	C₃×C₄	—	2	2	no	—
443	C₃×C₄	—	2	2	no	—
444	C₃×C₄	—	2	1	no	—
445	C₃×C₄	—	4	2	no	—
446	C₃×C₄	—	4	1	no	—
447	C₃×C₄	—	20	1	no	—
448	C₃×C₄	—	20	2	no	—
449	C₃×C₄	C₂×#688	1	2	yes	—
450	C₃×C₄	C₂×#711	1	1	yes	characteristic
451	C₃×C₄	#4144	1	1	yes	characteristic
452	C₂×C₅	—	2	4	no	—
453	C₂×C₅	C₃×#546	1	1	yes	characteristic
454	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
455	C₂×C₅	C₃×#578	1	1	yes	characteristic
456	D₅	—	8	1	no	—
457	C₂³	—	10	1	no	—
458	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	4	4	no	—
463	Q₈	—	20	2	no	—
464	Q₈	C₃×#711	1	2	yes	complemented
465	D₄	—	10	1	no	—
466	D₄	—	10	1	no	—
467	D₄	—	20	4	no	—
468	D₄	C₃×#688	1	4	yes	complemented
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	10	1	no	—
476	C₂×C₄	—	10	2	no	—
477	C₂×C₄	—	20	4	no	—
478	C₂×C₄	—	20	2	no	—
479	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
480	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
481	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
482	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
483	C₈	—	10	1	no	—
484	C₈	—	10	1	no	—
485	C₈	—	10	2	no	—
486	C₂×C₃	—	2	4	no	—
487	C₂×C₃	—	40	1	no	—
488	C₂×C₃	#66140	1	1	yes	characteristic
489	C₂×C₃	C₂²×#688	1	1	yes	characteristic
490	C₂×C₃	#66172	1	1	yes	characteristic
491	C₅	C₃×#3298	1	1	yes	characteristic, complemented, Sylow
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	20	1	no	—
495	C₂²	—	20	1	no	—
496	C₂²	—	20	1	no	—
497	C₂²	C₂×C₃×#688	1	4	yes	—
498	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	1	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	20	1	no	—
505	C₄	—	20	2	no	—
506	C₄	C₂×C₃×#688	1	2	yes	—
507	C₄	C₂×C₃×#711	1	1	yes	characteristic
508	C₄	C₃×#4144	1	1	yes	characteristic
509	C₃	#10615281	1	1	yes	characteristic, direct product factor, Sylow
510	C₂	—	2	4	no	—
511	C₂	—	40	1	no	—
512	C₂	C₃×#66140	1	1	yes	characteristic
513	C₂	C₂²×C₃×#688	1	1	yes	characteristic
514	C₂	C₃×#66172	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×D₄×Q₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#65889	C₂
hypercenter	C₃×D₄×Q₈	D₅
hypocenter	C₅	C₃×#3298
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄ ◁ C₃×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₄×Q₈	C₂	semidirect
3. C₃×#65516	C₂	semidirect
4. C₂×C₃×#3967	C₂	semidirect
5. C₃×#65372	C₂	semidirect
6. C₃×#65370	C₂	semidirect
7. C₃×#65337	C₂	semidirect
8. C₃×#65332	C₂	semidirect
9. C₃×C₄×#688	C₂	semidirect
10. C₃×#65309	C₂	semidirect
11. C₃×D₄×#168	C₂	semidirect
12. #10615281	C₃	direct (N × H)
43. C₅×D₄×Q₈	C₂×C₃	semidirect
45. #65516	C₂×C₃	semidirect
46. C₂×#3967	C₂×C₃	semidirect
47. #65372	C₂×C₃	semidirect
48. #65370	C₂×C₃	semidirect
49. #65337	C₂×C₃	semidirect
50. #65332	C₂×C₃	semidirect
51. C₄×#688	C₂×C₃	semidirect
52. #65309	C₂×C₃	semidirect
53. D₄×#168	C₂×C₃	semidirect
90. C₃×D₄×Q₈	D₅	semidirect
137. C₃×C₅×Q₈	#41	semidirect
138. C₃×C₅×D₄	SD₁₆	semidirect
225. D₄×Q₈	C₃×D₅	semidirect
295. C₅×Q₈	C₃×#41	semidirect
296. C₅×D₄	C₃×SD₁₆	semidirect
359. C₃×Q₈	#711	semidirect
363. C₃×D₄	#688	semidirect
434. C₃×C₅	#3298	semidirect
464. Q₈	C₃×#711	semidirect
468. D₄	C₃×#688	semidirect
491. C₅	C₃×#3298	semidirect
509. C₃	#10615281	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×D₄×Q₈	2
C₃×#65889	2
C₃×#65516	2
C₂×C₃×#3967	2
C₃×#65372	2
C₃×#65370	2
C₃×#65337	2
C₃×#65332	2
C₃×C₄×#688	2
C₃×#65309	2
C₃×D₄×#168	2
#10615281	3
C₃×#3298	5

Subgroups — C3×#10615281 #14459122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615281 #14459122