Subgroups — C₃×#10611451 #14417529

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#65906	C₂	1	2	yes	maximal
3	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Q₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65319	C₂	1	2	yes	maximal, complemented
6	C₃×#65169	C₂	1	1	yes	maximal, characteristic
7	C₃×#65162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65091	C₂	1	2	yes	maximal
9	C₃×#65078	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64978	C₂	1	1	yes	maximal, characteristic
12	#10611451	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×#689	C₂²	1	2	yes	—
18	C₃×D₅×Q₁₆	C₄	1	8	yes	complemented
19	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
20	C₂×C₃×#676	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
22	C₃×#4038	—	2	2	no	—
23	C₃×#4038	C₂²	1	2	yes	—
24	C₃×#4033	—	2	2	no	—
25	C₃×#4033	C₂²	1	2	yes	—
26	C₃×#4018	—	2	2	no	—
27	C₃×#4018	C₂²	1	1	yes	characteristic
28	C₃×C₄×Dic₁₀	—	2	2	no	—
29	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3950	C₂²	1	1	yes	characteristic
35	C₃×#3948	C₂²	1	2	yes	—
36	C₃×#3947	C₂²	1	1	yes	characteristic
37	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
38	C₃×#3942	C₂²	1	2	yes	—
39	C₃×#3940	C₂²	1	2	yes	—
40	C₃×#3935	C₂²	1	1	yes	characteristic
41	C₃×#2950	—	5	1	no	maximal, Hall
42	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic
43	#65906	C₂×C₃	1	2	yes	—
44	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
45	Q₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
46	#65319	C₂×C₃	1	2	yes	complemented
47	#65169	C₂×C₃	1	1	yes	characteristic
48	#65162	C₂×C₃	1	1	yes	characteristic, complemented
49	#65091	C₂×C₃	1	2	yes	—
50	#65078	C₂×C₃	1	2	yes	complemented
51	C₄×Dic₂₀	C₂×C₃	1	1	yes	characteristic, complemented
52	#64978	C₂×C₃	1	1	yes	characteristic
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₃×Q₈×D₅	—	2	4	no	—
55	C₃×Q₈×D₅	C₂×C₄	1	8	yes	—
56	C₂×C₃×C₄×D₅	—	2	2	no	—
57	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×Dic₁₀	—	2	2	no	—
59	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
60	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₄²×C₅	—	2	2	no	—
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×#689	C₂×C₄	1	8	yes	—
68	C₃×#685	—	2	2	no	—
69	C₃×#685	D₄	1	1	yes	characteristic
70	C₃×#685	D₄	1	1	yes	characteristic
71	C₃×C₄⋊Dic₅	—	2	2	no	—
72	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
73	C₃×#683	—	2	2	no	—
74	C₃×#683	—	2	2	no	—
75	C₃×#683	D₄	1	1	yes	characteristic
76	C₃×#683	D₄	1	1	yes	characteristic
77	C₃×C₄×Dic₅	—	2	2	no	—
78	C₃×C₄×Dic₅	—	2	2	no	—
79	C₃×C₄×Dic₅	—	2	2	no	—
80	C₃×C₄×Dic₅	—	2	2	no	—
81	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₃×Dic₂₀	C₂×C₄	1	4	yes	—
85	C₃×#676	—	2	2	no	—
86	C₃×C₈×D₅	C₂×C₄	1	4	yes	—
87	C₂²×C₃×Q₁₆	—	5	1	no	—
88	C₃×#519	—	5	2	no	—
89	C₃×#441	—	5	2	no	—
90	C₃×#441	—	5	2	no	—
91	C₃×C₄×Q₁₆	—	5	1	no	—
92	C₃×C₄×Q₁₆	—	5	1	no	—
93	C₃×C₄×Q₁₆	—	5	1	no	—
94	C₃×C₄×Q₁₆	D₅	1	1	yes	characteristic, complemented
95	C₃×#427	—	5	1	no	—
96	C₃×#419	—	5	2	no	—
97	C₃×#405	—	5	1	no	—
98	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
99	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
100	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
101	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
102	C₂×#689	C₂²×C₃	1	2	yes	—
103	D₅×Q₁₆	C₃×C₄	1	8	yes	complemented
104	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
105	C₂×#676	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
107	#4038	—	2	2	no	—
108	#4038	C₂²×C₃	1	2	yes	—
109	#4033	—	2	2	no	—
110	#4033	C₂²×C₃	1	2	yes	—
111	#4018	—	2	2	no	—
112	#4018	C₂²×C₃	1	1	yes	characteristic
113	C₄×Dic₁₀	—	2	2	no	—
114	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
115	C₅×#107	C₂²×C₃	1	1	yes	characteristic
116	C₅×#103	C₂²×C₃	1	2	yes	—
117	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
118	#3967	C₂²×C₃	1	2	yes	—
119	#3950	C₂²×C₃	1	1	yes	characteristic
120	#3948	C₂²×C₃	1	2	yes	—
121	#3947	C₂²×C₃	1	1	yes	characteristic
122	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
123	#3942	C₂²×C₃	1	2	yes	—
124	#3940	C₂²×C₃	1	2	yes	—
125	#3935	C₂²×C₃	1	1	yes	characteristic
126	#2950	—	5	1	no	Sylow
127	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×C₃×Dic₅	—	2	2	no	—
136	C₂×C₃×Dic₅	—	2	2	no	—
137	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
140	C₃×C₄×D₅	—	2	8	no	—
141	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
142	C₃×C₄×D₅	#41	1	2	yes	—
143	C₃×Dic₁₀	—	2	2	no	—
144	C₃×Dic₁₀	—	2	8	no	—
145	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
146	C₃×C₅×C₈	—	2	1	no	—
147	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
148	C₃×#168	—	2	1	no	—
149	C₃×#168	C₂²×C₄	1	2	yes	—
150	C₂²×C₃×Q₈	—	5	2	no	—
151	C₂×C₃×Q₁₆	—	5	2	no	—
152	C₂×C₃×Q₁₆	—	5	8	no	—
153	C₂×C₃×Q₁₆	—	5	1	no	—
154	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
155	C₂×C₃×M₁₆	—	5	1	no	—
156	C₂²×C₃×C₈	—	5	1	no	—
157	C₃×C₄×Q₈	—	5	2	no	—
158	C₃×C₄×Q₈	—	5	2	no	—
159	C₃×C₄×Q₈	—	5	2	no	—
160	C₃×C₄×Q₈	—	10	2	no	—
161	C₃×C₄×Q₈	—	10	2	no	—
162	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
163	C₃×#117	—	5	1	no	—
164	C₃×#117	—	5	2	no	—
165	C₃×#117	—	10	2	no	—
166	C₃×#117	—	10	2	no	—
167	C₃×#107	—	5	1	no	—
168	C₃×#107	C₂×D₅	1	1	yes	characteristic
169	C₃×#106	—	5	2	no	—
170	C₃×#103	—	5	2	no	—
171	C₃×#103	—	5	2	no	—
172	C₃×#103	—	5	2	no	—
173	C₃×#103	C₂×D₅	1	2	yes	—
174	C₃×#97	—	5	1	no	—
175	C₃×#97	—	5	1	no	—
176	C₃×C₄×C₈	—	5	1	no	—
177	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
178	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
179	Q₈×D₅	—	2	4	no	—
180	Q₈×D₅	C₂×C₃×C₄	1	8	yes	—
181	C₂×C₄×D₅	—	2	2	no	—
182	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
183	C₂×Dic₁₀	—	2	2	no	—
184	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
185	C₅×Q₁₆	C₂×C₃×C₄	1	4	yes	—
186	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
188	C₅×C₄⋊C₄	—	2	2	no	—
189	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
190	C₄²×C₅	—	2	2	no	—
191	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
192	#689	C₂×C₃×C₄	1	8	yes	—
193	#685	—	2	2	no	—
194	#685	C₃×D₄	1	1	yes	characteristic
195	#685	C₃×D₄	1	1	yes	characteristic
196	C₄⋊Dic₅	—	2	2	no	—
197	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
198	#683	—	2	2	no	—
199	#683	—	2	2	no	—
200	#683	C₃×D₄	1	1	yes	characteristic
201	#683	C₃×D₄	1	1	yes	characteristic
202	C₄×Dic₅	—	2	2	no	—
203	C₄×Dic₅	—	2	2	no	—
204	C₄×Dic₅	—	2	2	no	—
205	C₄×Dic₅	—	2	2	no	—
206	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
207	C₂×#168	C₂³×C₃	1	1	yes	characteristic
208	C₂×#168	C₂³×C₃	1	1	yes	characteristic
209	Dic₂₀	C₂×C₃×C₄	1	4	yes	—
210	#676	—	2	2	no	—
211	C₈×D₅	C₂×C₃×C₄	1	4	yes	—
212	C₂²×Q₁₆	—	5	1	no	—
213	#519	—	5	2	no	—
214	#441	—	5	2	no	—
215	#441	—	5	2	no	—
216	C₄×Q₁₆	—	5	1	no	—
217	C₄×Q₁₆	—	5	1	no	—
218	C₄×Q₁₆	—	5	1	no	—
219	C₄×Q₁₆	C₃×D₅	1	1	yes	characteristic, complemented
220	#427	—	5	1	no	—
221	#419	—	5	2	no	—
222	#405	—	5	1	no	—
223	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₃×D₅	—	2	1	no	—
225	C₂×C₃×D₅	—	2	1	no	—
226	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
227	C₃×C₄×C₅	—	2	4	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	—	2	1	no	—
230	C₃×C₄×C₅	—	4	2	no	—
231	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₃×Dic₅	—	2	4	no	—
234	C₃×Dic₅	—	2	1	no	—
235	C₃×Dic₅	—	2	1	no	—
236	C₃×Dic₅	—	4	2	no	—
237	C₃×Dic₅	C₄×D₄	1	2	yes	—
238	C₂×C₃×Q₈	—	5	8	no	—
239	C₂×C₃×Q₈	—	5	2	no	—
240	C₂×C₃×Q₈	—	10	2	no	—
241	C₂×C₃×Q₈	—	10	4	no	—
242	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
243	C₂²×C₃×C₄	—	5	1	no	—
244	C₂²×C₃×C₄	—	10	2	no	—
245	C₃×Q₁₆	—	5	8	no	—
246	C₃×Q₁₆	—	5	4	no	—
247	C₃×Q₁₆	C₄×D₅	1	4	yes	—
248	C₃×M₁₆	—	10	2	no	—
249	C₂×C₃×C₈	—	5	1	no	—
250	C₂×C₃×C₈	—	5	4	no	—
251	C₂×C₃×C₈	—	5	1	no	—
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	—	2	2	no	—
255	C₃×C₄⋊C₄	—	5	1	no	—
256	C₃×C₄⋊C₄	—	5	1	no	—
257	C₃×C₄⋊C₄	—	5	2	no	—
258	C₃×C₄⋊C₄	—	10	2	no	—
259	C₃×C₄⋊C₄	—	10	2	no	—
260	C₃×C₄⋊C₄	—	10	2	no	—
261	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
262	C₃×C₂²⋊C₄	—	5	1	no	—
263	C₃×C₂²⋊C₄	—	5	1	no	—
264	C₃×C₂²⋊C₄	—	10	2	no	—
265	C₃×C₄²	—	2	2	no	—
266	C₃×C₄²	—	5	1	no	—
267	C₃×C₄²	—	10	2	no	—
268	C₃×C₄²	—	10	2	no	—
269	C₃×C₄²	—	10	2	no	—
270	C₃×C₄²	—	10	2	no	—
271	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
272	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
273	C₅×Q₈	—	2	2	no	—
274	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
280	C₂×Dic₅	—	2	2	no	—
281	C₂×Dic₅	—	2	2	no	—
282	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
285	C₄×D₅	—	2	8	no	—
286	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
287	C₄×D₅	C₃×#41	1	2	yes	—
288	Dic₁₀	—	2	2	no	—
289	Dic₁₀	—	2	8	no	—
290	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
291	C₅×C₈	—	2	1	no	—
292	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
293	#168	—	2	1	no	—
294	#168	C₂²×C₃×C₄	1	2	yes	—
295	C₂²×Q₈	—	5	2	no	—
296	C₂×Q₁₆	—	5	2	no	—
297	C₂×Q₁₆	—	5	8	no	—
298	C₂×Q₁₆	—	5	1	no	—
299	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
300	C₂×M₁₆	—	5	1	no	—
301	C₂²×C₈	—	5	1	no	—
302	C₄×Q₈	—	5	2	no	—
303	C₄×Q₈	—	5	2	no	—
304	C₄×Q₈	—	5	2	no	—
305	C₄×Q₈	—	10	2	no	—
306	C₄×Q₈	—	10	2	no	—
307	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
308	#117	—	5	1	no	—
309	#117	—	5	2	no	—
310	#117	—	10	2	no	—
311	#117	—	10	2	no	—
312	#107	—	5	1	no	—
313	#107	C₂×C₃×D₅	1	1	yes	characteristic
314	#106	—	5	2	no	—
315	#103	—	5	2	no	—
316	#103	—	5	2	no	—
317	#103	—	5	2	no	—
318	#103	C₂×C₃×D₅	1	2	yes	—
319	#97	—	5	1	no	—
320	#97	—	5	1	no	—
321	C₄×C₈	—	5	1	no	—
322	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
324	C₂×C₃×C₅	#578	1	1	yes	characteristic
325	C₂×C₃×C₅	#578	1	1	yes	characteristic
326	C₃×D₅	—	2	2	no	—
327	C₂³×C₃	—	5	1	no	—
328	C₃×Q₈	—	2	2	no	—
329	C₃×Q₈	—	5	4	no	—
330	C₃×Q₈	—	10	8	no	—
331	C₃×Q₈	—	10	2	no	—
332	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	5	1	no	—
336	C₂×C₃×C₄	—	5	2	no	—
337	C₂×C₃×C₄	—	5	2	no	—
338	C₂×C₃×C₄	—	5	1	no	—
339	C₂×C₃×C₄	—	5	1	no	—
340	C₂×C₃×C₄	—	10	8	no	—
341	C₂×C₃×C₄	—	10	2	no	—
342	C₂×C₃×C₄	—	10	2	no	—
343	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
344	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
346	C₃×C₈	—	2	1	no	—
347	C₃×C₈	—	5	2	no	—
348	C₃×C₈	—	10	1	no	—
349	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
350	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
351	C₂×D₅	—	2	1	no	—
352	C₂×D₅	—	2	1	no	—
353	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	2	4	no	—
357	C₄×C₅	—	4	2	no	—
358	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
359	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
360	Dic₅	—	2	1	no	—
361	Dic₅	—	2	1	no	—
362	Dic₅	—	2	4	no	—
363	Dic₅	—	4	2	no	—
364	Dic₅	C₃×C₄×D₄	1	2	yes	—
365	C₂×Q₈	—	5	8	no	—
366	C₂×Q₈	—	5	2	no	—
367	C₂×Q₈	—	10	2	no	—
368	C₂×Q₈	—	10	4	no	—
369	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
370	C₂²×C₄	—	5	1	no	—
371	C₂²×C₄	—	10	2	no	—
372	Q₁₆	—	5	8	no	—
373	Q₁₆	—	5	4	no	—
374	Q₁₆	C₃×C₄×D₅	1	4	yes	—
375	M₁₆	—	10	2	no	—
376	C₂×C₈	—	5	1	no	—
377	C₂×C₈	—	5	4	no	—
378	C₂×C₈	—	5	1	no	—
379	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
380	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	5	1	no	—
383	C₄⋊C₄	—	5	1	no	—
384	C₄⋊C₄	—	5	2	no	—
385	C₄⋊C₄	—	10	2	no	—
386	C₄⋊C₄	—	10	2	no	—
387	C₄⋊C₄	—	10	2	no	—
388	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
389	C₂²⋊C₄	—	5	1	no	—
390	C₂²⋊C₄	—	5	1	no	—
391	C₂²⋊C₄	—	10	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	5	1	no	—
394	C₄²	—	10	2	no	—
395	C₄²	—	10	2	no	—
396	C₄²	—	10	2	no	—
397	C₄²	—	10	2	no	—
398	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
399	C₃×C₅	#2950	1	1	yes	characteristic, complemented, Hall
400	C₂²×C₃	—	5	2	no	—
401	C₂²×C₃	—	10	1	no	—
402	C₂²×C₃	—	10	1	no	—
403	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	2	1	no	—
406	C₃×C₄	—	2	4	no	—
407	C₃×C₄	—	4	2	no	—
408	C₃×C₄	—	5	2	no	—
409	C₃×C₄	—	10	1	no	—
410	C₃×C₄	—	10	1	no	—
411	C₃×C₄	—	10	4	no	—
412	C₃×C₄	—	20	2	no	—
413	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
414	C₃×C₄	D₅×#41	1	1	yes	characteristic
415	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
416	C₂×C₅	C₃×#578	1	1	yes	characteristic
417	C₂×C₅	C₃×#578	1	1	yes	characteristic
418	D₅	—	2	2	no	—
419	C₂³	—	5	1	no	—
420	Q₈	—	2	2	no	—
421	Q₈	—	5	4	no	—
422	Q₈	—	10	8	no	—
423	Q₈	—	10	2	no	—
424	Q₈	C₂×C₃×C₄×D₅	1	4	yes	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	5	1	no	—
428	C₂×C₄	—	5	2	no	—
429	C₂×C₄	—	5	2	no	—
430	C₂×C₄	—	5	1	no	—
431	C₂×C₄	—	5	1	no	—
432	C₂×C₄	—	10	8	no	—
433	C₂×C₄	—	10	2	no	—
434	C₂×C₄	—	10	2	no	—
435	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
436	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
437	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
438	C₈	—	2	1	no	—
439	C₈	—	5	2	no	—
440	C₈	—	10	1	no	—
441	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
442	C₂×C₃	—	10	2	no	—
443	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
444	C₂×C₃	#66100	1	1	yes	characteristic
445	C₂×C₃	#66105	1	1	yes	characteristic
446	C₅	C₃×#2950	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	5	2	no	—
448	C₂²	—	10	1	no	—
449	C₂²	—	10	1	no	—
450	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	4	no	—
454	C₄	—	4	2	no	—
455	C₄	—	5	2	no	—
456	C₄	—	10	1	no	—
457	C₄	—	10	1	no	—
458	C₄	—	10	4	no	—
459	C₄	—	20	2	no	—
460	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
461	C₄	C₃×D₅×#41	1	1	yes	characteristic
462	C₃	#10611451	1	1	yes	characteristic, direct product factor, Sylow
463	C₂	—	10	2	no	—
464	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
465	C₂	C₃×#66100	1	1	yes	characteristic
466	C₂	C₃×#66105	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×D₅	C₂×D₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×Q₁₆	D₅
hypocenter	C₅	C₃×#2950
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×C₅×Q₁₆	C₂	semidirect
4. C₃×Q₁₆×Dic₅	C₂	semidirect
5. C₃×#65319	C₂	semidirect
7. C₃×#65162	C₂	semidirect
9. C₃×#65078	C₂	semidirect
10. C₃×C₄×Dic₂₀	C₂	semidirect
12. #10611451	C₃	direct (N × H)
18. C₃×D₅×Q₁₆	C₄	semidirect
44. C₄×C₅×Q₁₆	C₂×C₃	semidirect
45. Q₁₆×Dic₅	C₂×C₃	semidirect
46. #65319	C₂×C₃	semidirect
48. #65162	C₂×C₃	semidirect
50. #65078	C₂×C₃	semidirect
51. C₄×Dic₂₀	C₂×C₃	semidirect
94. C₃×C₄×Q₁₆	D₅	semidirect
103. D₅×Q₁₆	C₃×C₄	semidirect
219. C₄×Q₁₆	C₃×D₅	semidirect
399. C₃×C₅	#2950	semidirect
446. C₅	C₃×#2950	semidirect
462. C₃	#10611451	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×D₅×Q₁₆	2
C₃×#65906	2
C₃×C₄×C₅×Q₁₆	2
C₃×Q₁₆×Dic₅	2
C₃×#65319	2
C₃×#65169	2
C₃×#65162	2
C₃×#65091	2
C₃×#65078	2
C₃×C₄×Dic₂₀	2
C₃×#64978	2
#10611451	3
C₃×#2950	5

Subgroups — C3×#10611451 #14417529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611451 #14417529