Subgroups — C₃×#10614279 #14417423

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#688	C₂	1	1	yes	maximal, characteristic
3	C₃×#65855	C₂	1	1	yes	maximal, characteristic
4	C₃×#65514	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65315	C₂	1	4	yes	maximal, complemented
6	C₃×C₄×#688	C₂	1	4	yes	maximal, complemented
7	C₃×#65290	C₂	1	1	yes	maximal, characteristic
8	C₃×#65287	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65286	C₂	1	1	yes	maximal, characteristic, complemented
10	#10614279	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₅×Q₈	—	2	2	no	—
14	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
15	C₃×C₅×#117	—	2	2	no	—
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	C₂²	1	1	yes	characteristic
18	C₂×C₃×#688	C₄	1	8	yes	complemented
19	C₂×C₃×#688	C₂²	1	2	yes	—
20	C₂×C₃×#688	C₂²	1	2	yes	—
21	C₃×#4072	C₂²	1	1	yes	characteristic
22	C₂×C₃×#681	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
24	C₃×#4039	—	2	2	no	—
25	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
26	C₃×C₄×D₂₀	C₂²	1	4	yes	—
27	C₃×#3967	C₂²	1	4	yes	complemented
28	C₃×#3941	C₂²	1	4	yes	—
29	C₃×#3940	C₂²	1	2	yes	complemented
30	C₃×#3939	C₂²	1	2	yes	complemented
31	C₃×#3935	C₂²	1	2	yes	complemented
32	C₃×C₄×#168	C₂²	1	2	yes	complemented
33	C₃×#2949	—	5	1	no	maximal, Hall
34	C₅×#519	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂²×#688	C₂×C₃	1	1	yes	characteristic
36	#65855	C₂×C₃	1	1	yes	characteristic
37	#65514	C₂×C₃	1	1	yes	characteristic, complemented
38	#65315	C₂×C₃	1	4	yes	complemented
39	C₄×#688	C₂×C₃	1	4	yes	complemented
40	#65290	C₂×C₃	1	1	yes	characteristic
41	#65287	C₂×C₃	1	1	yes	characteristic, complemented
42	#65286	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂³×C₃×D₅	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	1	no	—
45	C₂×C₃×C₅×Q₈	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
47	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	—	2	1	no	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂×C₃×D₂₀	—	2	1	no	—
51	C₂×C₃×D₂₀	—	2	2	no	—
52	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
53	C₂×C₃×D₂₀	C₂³	1	2	yes	—
54	C₂×C₃×C₄×D₅	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
59	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	—	2	1	no	—
62	C₃×C₄²×C₅	C₂³	1	2	yes	—
63	C₃×C₂²⋊Dic₅	—	2	1	no	—
64	C₃×#688	C₂×C₄	1	8	yes	complemented
65	C₃×#688	C₂×C₄	1	8	yes	complemented
66	C₃×#685	—	2	4	no	—
67	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
68	C₃×C₄×Dic₅	—	2	1	no	—
69	C₃×#681	—	2	2	no	—
70	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
71	C₂×C₃×#168	C₂³	1	2	yes	—
72	C₂×C₃×#168	C₂³	1	1	yes	characteristic
73	C₂×C₃×#168	C₂³	1	1	yes	characteristic
74	C₂²×C₃×SD₁₆	—	5	1	no	—
75	C₃×#519	D₅	1	1	yes	characteristic, complemented
76	C₃×#518	—	5	1	no	—
77	C₃×#440	—	5	4	no	—
78	C₃×C₄×SD₁₆	—	5	4	no	—
79	C₃×#427	—	5	1	no	—
80	C₃×#419	—	5	1	no	—
81	C₃×#418	—	5	1	no	—
82	C₃×#405	—	5	1	no	—
83	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
85	C₄×C₅×Q₈	—	2	2	no	—
86	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	complemented
87	C₅×#117	—	2	2	no	—
88	C₅×#117	C₂²×C₃	1	1	yes	characteristic
89	C₅×#117	C₂²×C₃	1	1	yes	characteristic
90	C₂×#688	C₃×C₄	1	8	yes	complemented
91	C₂×#688	C₂²×C₃	1	2	yes	—
92	C₂×#688	C₂²×C₃	1	2	yes	—
93	#4072	C₂²×C₃	1	1	yes	characteristic
94	C₂×#681	C₂²×C₃	1	1	yes	characteristic
95	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
96	#4039	—	2	2	no	—
97	D₅×C₂²⋊C₄	—	2	2	no	—
98	C₄×D₂₀	C₂²×C₃	1	4	yes	—
99	#3967	C₂²×C₃	1	4	yes	complemented
100	#3941	C₂²×C₃	1	4	yes	—
101	#3940	C₂²×C₃	1	2	yes	complemented
102	#3939	C₂²×C₃	1	2	yes	complemented
103	#3935	C₂²×C₃	1	2	yes	complemented
104	C₄×#168	C₂²×C₃	1	2	yes	complemented
105	#2949	—	5	1	no	Sylow
106	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₃×D₅	—	2	2	no	—
108	C₂²×C₃×D₅	—	2	4	no	—
109	C₂²×C₃×D₅	—	8	2	no	—
110	C₃×C₅×Q₈	—	2	4	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	#41	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₃×D₂₀	—	2	4	no	—
123	C₃×D₂₀	—	2	2	no	—
124	C₃×D₂₀	C₂²×C₄	1	4	yes	—
125	C₃×C₄×D₅	—	8	4	no	—
126	C₃×#168	—	2	2	no	—
127	C₃×#168	C₂²×C₄	1	2	yes	—
128	C₃×#168	C₂²×C₄	1	2	yes	—
129	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
130	C₂²×C₃×D₄	—	5	1	no	—
131	C₂×C₃×SD₁₆	—	5	8	no	—
132	C₂×C₃×SD₁₆	—	5	2	no	—
133	C₂×C₃×SD₁₆	—	5	2	no	—
134	C₂×C₃×M₁₆	—	5	1	no	—
135	C₂²×C₃×C₈	—	5	1	no	—
136	C₃×C₄×Q₈	—	2	2	no	—
137	C₃×C₄×Q₈	C₂×D₅	1	4	yes	complemented
138	C₃×C₄×D₄	—	5	4	no	—
139	C₃×C₄×D₄	—	10	2	no	—
140	C₃×#117	—	2	2	no	—
141	C₃×#117	—	5	1	no	—
142	C₃×#117	C₂×D₅	1	1	yes	characteristic
143	C₃×#117	C₂×D₅	1	1	yes	characteristic
144	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
145	C₃×#107	—	5	2	no	—
146	C₃×#106	—	5	2	no	—
147	C₃×#103	—	5	4	no	—
148	C₃×#102	—	5	4	no	—
149	C₃×#97	—	5	2	no	—
150	C₃×C₄×C₈	—	5	2	no	—
151	C₂³×D₅	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	2	no	—
154	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
155	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₂×D₂₀	—	2	1	no	—
159	C₂×D₂₀	—	2	2	no	—
160	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
161	C₂×D₂₀	C₂³×C₃	1	2	yes	—
162	C₂×C₄×D₅	—	2	4	no	—
163	C₅×C₄⋊C₄	—	2	4	no	—
164	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
165	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
166	C₅×C₂²⋊C₄	—	2	1	no	—
167	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
168	C₄²×C₅	—	2	4	no	—
169	C₄²×C₅	—	2	1	no	—
170	C₄²×C₅	C₂³×C₃	1	2	yes	—
171	C₂²⋊Dic₅	—	2	1	no	—
172	#688	C₂×C₃×C₄	1	8	yes	complemented
173	#688	C₂×C₃×C₄	1	8	yes	complemented
174	#685	—	2	4	no	—
175	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
176	C₄×Dic₅	—	2	1	no	—
177	#681	—	2	2	no	—
178	C₂×#168	C₂×C₃×C₄	1	4	yes	complemented
179	C₂×#168	C₂³×C₃	1	2	yes	—
180	C₂×#168	C₂³×C₃	1	1	yes	characteristic
181	C₂×#168	C₂³×C₃	1	1	yes	characteristic
182	C₂²×SD₁₆	—	5	1	no	—
183	#519	C₃×D₅	1	1	yes	characteristic, complemented
184	#518	—	5	1	no	—
185	#440	—	5	4	no	—
186	C₄×SD₁₆	—	5	4	no	—
187	#427	—	5	1	no	—
188	#419	—	5	1	no	—
189	#418	—	5	1	no	—
190	#405	—	5	1	no	—
191	C₂²×C₃×C₅	—	2	2	no	—
192	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
193	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₃×D₅	—	2	4	no	—
195	C₂×C₃×D₅	—	4	4	no	—
196	C₂×C₃×D₅	—	8	4	no	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	2	4	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
201	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
202	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
203	C₃×Dic₅	—	4	2	no	—
204	C₂⁴×C₃	—	10	1	no	—
205	C₂×C₃×Q₈	—	2	2	no	—
206	C₂×C₃×Q₈	—	2	1	no	—
207	C₂×C₃×Q₈	C₄×D₅	1	4	yes	complemented
208	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
209	C₂×C₃×D₄	—	5	4	no	—
210	C₂×C₃×D₄	—	5	2	no	—
211	C₂×C₃×D₄	—	10	2	no	—
212	C₂×C₃×D₄	—	10	1	no	—
213	C₂²×C₃×C₄	—	2	1	no	—
214	C₂²×C₃×C₄	—	10	4	no	—
215	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
216	C₃×SD₁₆	—	5	8	no	—
217	C₃×SD₁₆	—	5	8	no	—
218	C₃×M₁₆	—	10	2	no	—
219	C₂×C₃×C₈	—	5	4	no	—
220	C₂×C₃×C₈	—	5	1	no	—
221	C₂×C₃×C₈	—	5	1	no	—
222	C₂×C₃×C₈	—	5	2	no	—
223	C₃×C₄⋊C₄	—	2	4	no	—
224	C₃×C₄⋊C₄	—	5	2	no	—
225	C₃×C₄⋊C₄	C₂²⋊D₅	1	2	yes	—
226	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
227	C₃×C₂²⋊C₄	—	2	1	no	—
228	C₃×C₂²⋊C₄	—	10	1	no	—
229	C₃×C₂²⋊C₄	—	10	4	no	—
230	C₃×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
231	C₃×C₄²	—	2	4	no	—
232	C₃×C₄²	—	2	1	no	—
233	C₃×C₄²	—	10	1	no	—
234	C₃×C₄²	C₂²×D₅	1	2	yes	—
235	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂²×D₅	—	2	2	no	—
237	C₂²×D₅	—	2	4	no	—
238	C₂²×D₅	—	8	2	no	—
239	C₅×Q₈	—	2	4	no	—
240	C₅×Q₈	—	2	2	no	—
241	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
242	C₂×C₄×C₅	—	2	4	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
247	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₃×#41	1	2	yes	—
249	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
250	C₂×Dic₅	—	2	2	no	—
251	D₂₀	—	2	4	no	—
252	D₂₀	—	2	2	no	—
253	D₂₀	C₂²×C₃×C₄	1	4	yes	—
254	C₄×D₅	—	8	4	no	—
255	#168	—	2	2	no	—
256	#168	C₂²×C₃×C₄	1	2	yes	—
257	#168	C₂²×C₃×C₄	1	2	yes	—
258	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
259	C₂²×D₄	—	5	1	no	—
260	C₂×SD₁₆	—	5	8	no	—
261	C₂×SD₁₆	—	5	2	no	—
262	C₂×SD₁₆	—	5	2	no	—
263	C₂×M₁₆	—	5	1	no	—
264	C₂²×C₈	—	5	1	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	C₂×C₃×D₅	1	4	yes	complemented
267	C₄×D₄	—	5	4	no	—
268	C₄×D₄	—	10	2	no	—
269	#117	—	2	2	no	—
270	#117	—	5	1	no	—
271	#117	C₂×C₃×D₅	1	1	yes	characteristic
272	#117	C₂×C₃×D₅	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	—	10	2	no	—
274	#107	—	5	2	no	—
275	#106	—	5	2	no	—
276	#103	—	5	4	no	—
277	#102	—	5	4	no	—
278	#97	—	5	2	no	—
279	C₄×C₈	—	5	2	no	—
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂×C₃×C₅	#577	1	2	yes	—
283	C₃×D₅	—	4	4	no	—
284	C₂³×C₃	—	10	2	no	—
285	C₂³×C₃	—	10	4	no	—
286	C₂³×C₃	—	40	2	no	—
287	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
288	C₃×Q₈	—	2	2	no	—
289	C₃×Q₈	—	2	4	no	—
290	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
291	C₃×D₄	—	5	4	no	—
292	C₃×D₄	—	10	2	no	—
293	C₃×D₄	—	10	4	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	10	2	no	—
298	C₂×C₃×C₄	—	40	4	no	—
299	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
300	C₂×C₃×C₄	#709	1	2	yes	—
301	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
302	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
304	C₃×C₈	—	5	2	no	—
305	C₃×C₈	—	5	2	no	—
306	C₃×C₈	—	10	2	no	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
309	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
310	C₂×D₅	—	2	4	no	—
311	C₂×D₅	—	4	4	no	—
312	C₂×D₅	—	8	4	no	—
313	C₄×C₅	—	2	4	no	—
314	C₄×C₅	—	2	4	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
317	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
318	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
319	Dic₅	—	4	2	no	—
320	C₂⁴	—	10	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	C₃×C₄×D₅	1	4	yes	complemented
324	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
325	C₂×D₄	—	5	4	no	—
326	C₂×D₄	—	5	2	no	—
327	C₂×D₄	—	10	2	no	—
328	C₂×D₄	—	10	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	10	4	no	—
331	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
332	SD₁₆	—	5	8	no	—
333	SD₁₆	—	5	8	no	—
334	M₁₆	—	10	2	no	—
335	C₂×C₈	—	5	4	no	—
336	C₂×C₈	—	5	1	no	—
337	C₂×C₈	—	5	1	no	—
338	C₂×C₈	—	5	2	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	5	2	no	—
341	C₄⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
342	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	10	1	no	—
345	C₂²⋊C₄	—	10	4	no	—
346	C₂²⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	10	1	no	—
350	C₄²	C₂²×C₃×D₅	1	2	yes	—
351	C₃×C₅	#2949	1	1	yes	characteristic, complemented, Hall
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	10	4	no	—
354	C₂²×C₃	—	20	4	no	—
355	C₂²×C₃	—	40	4	no	—
356	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
357	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	4	2	no	—
361	C₃×C₄	—	20	2	no	—
362	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
363	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
364	C₃×C₄	C₂×#709	1	1	yes	characteristic
365	C₂×C₅	—	2	2	no	—
366	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
367	C₂×C₅	C₃×#577	1	2	yes	—
368	D₅	—	4	4	no	—
369	C₂³	—	10	2	no	—
370	C₂³	—	10	4	no	—
371	C₂³	—	40	2	no	—
372	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
373	Q₈	—	2	2	no	—
374	Q₈	—	2	4	no	—
375	Q₈	C₂×C₃×C₄×D₅	1	4	yes	—
376	D₄	—	5	4	no	—
377	D₄	—	10	2	no	—
378	D₄	—	10	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	10	2	no	—
383	C₂×C₄	—	40	4	no	—
384	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
385	C₂×C₄	C₃×#709	1	2	yes	—
386	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
387	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
388	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
389	C₈	—	5	2	no	—
390	C₈	—	5	2	no	—
391	C₈	—	10	2	no	—
392	C₂×C₃	—	2	2	no	—
393	C₂×C₃	—	20	4	no	—
394	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
395	C₂×C₃	#66171	1	2	yes	—
396	C₅	C₃×#2949	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	10	4	no	—
399	C₂²	—	20	4	no	—
400	C₂²	—	40	4	no	—
401	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
402	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
403	C₄	—	2	4	no	—
404	C₄	—	2	4	no	—
405	C₄	—	4	2	no	—
406	C₄	—	20	2	no	—
407	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
408	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
409	C₄	C₂×C₃×#709	1	1	yes	characteristic
410	C₃	#10614279	1	1	yes	characteristic, direct product factor, Sylow
411	C₂	—	2	2	no	—
412	C₂	—	20	4	no	—
413	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
414	C₂	C₃×#66171	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#519	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#519	D₅
hypocenter	C₅	C₃×#2949
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#519

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#519	C₂	semidirect
4. C₃×#65514	C₂	semidirect
5. C₃×#65315	C₂	semidirect
6. C₃×C₄×#688	C₂	semidirect
8. C₃×#65287	C₂	semidirect
9. C₃×#65286	C₂	semidirect
10. #10614279	C₃	direct (N × H)
14. C₃×C₄×C₅×Q₈	C₂²	semidirect
18. C₂×C₃×#688	C₄	semidirect
27. C₃×#3967	C₂²	semidirect
29. C₃×#3940	C₂²	semidirect
30. C₃×#3939	C₂²	semidirect
31. C₃×#3935	C₂²	semidirect
32. C₃×C₄×#168	C₂²	semidirect
34. C₅×#519	C₂×C₃	semidirect
37. #65514	C₂×C₃	semidirect
38. #65315	C₂×C₃	semidirect
39. C₄×#688	C₂×C₃	semidirect
41. #65287	C₂×C₃	semidirect
42. #65286	C₂×C₃	semidirect
46. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
64. C₃×#688	C₂×C₄	semidirect
65. C₃×#688	C₂×C₄	semidirect
70. C₂×C₃×#168	C₂×C₄	semidirect
75. C₃×#519	D₅	semidirect
86. C₄×C₅×Q₈	C₂²×C₃	semidirect
90. C₂×#688	C₃×C₄	semidirect
99. #3967	C₂²×C₃	semidirect
101. #3940	C₂²×C₃	semidirect
102. #3939	C₂²×C₃	semidirect
103. #3935	C₂²×C₃	semidirect
104. C₄×#168	C₂²×C₃	semidirect
137. C₃×C₄×Q₈	C₂×D₅	semidirect
154. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
172. #688	C₂×C₃×C₄	semidirect
173. #688	C₂×C₃×C₄	semidirect
178. C₂×#168	C₂×C₃×C₄	semidirect
183. #519	C₃×D₅	semidirect
207. C₂×C₃×Q₈	C₄×D₅	semidirect
266. C₄×Q₈	C₂×C₃×D₅	semidirect
323. C₂×Q₈	C₃×C₄×D₅	semidirect
351. C₃×C₅	#2949	semidirect
396. C₅	C₃×#2949	semidirect
410. C₃	#10614279	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×#519	2
C₂²×C₃×#688	2
C₃×#65855	2
C₃×#65514	2
C₃×#65315	2
C₃×C₄×#688	2
C₃×#65290	2
C₃×#65287	2
C₃×#65286	2
#10614279	3
C₃×#2949	5

Subgroups — C3×#10614279 #14417423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614279 #14417423