Subgroups — C₃×#10610678 #14417411

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×#66146	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×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65420	C₂	1	1	yes	maximal, characteristic
6	C₃×#65411	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65287	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65106	C₂	1	4	yes	maximal, complemented
9	C₃×#65077	C₂	1	4	yes	maximal, complemented
10	#10610678	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	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₃×Q₈×Dic₅	—	2	2	no	—
16	C₃×Q₈×Dic₅	C₂²	1	4	yes	complemented
17	C₂×C₃×#688	C₄	1	8	yes	complemented
18	C₂×C₃×#688	C₂²	1	2	yes	—
19	C₂×C₃×#688	C₂²	1	2	yes	—
20	C₃×#4072	—	2	2	no	—
21	C₃×#4072	C₂²	1	1	yes	characteristic
22	C₃×#4072	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
24	C₃×#4039	C₂²	1	4	yes	—
25	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
26	C₃×C₄×D₂₀	—	2	2	no	—
27	C₃×C₅×#103	C₂²	1	4	yes	complemented
28	C₃×#3953	C₂²	1	4	yes	—
29	C₃×#3947	C₂²	1	2	yes	complemented
30	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
31	C₃×#3940	C₂²	1	2	yes	complemented
32	C₃×#3939	C₂²	1	2	yes	complemented
33	C₃×#2949	—	5	1	no	maximal, Hall
34	#66146	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	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
38	#65420	C₂×C₃	1	1	yes	characteristic
39	#65411	C₂×C₃	1	1	yes	characteristic, complemented
40	#65287	C₂×C₃	1	1	yes	characteristic, complemented
41	#65106	C₂×C₃	1	4	yes	complemented
42	#65077	C₂×C₃	1	4	yes	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×M₁₆	—	2	2	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
59	C₃×C₄²×C₅	—	2	1	no	—
60	C₃×C₂²⋊Dic₅	—	2	1	no	—
61	C₃×C₂²⋊Dic₅	D₄	1	2	yes	—
62	C₃×#688	C₂×C₄	1	8	yes	complemented
63	C₃×#688	C₂×C₄	1	8	yes	complemented
64	C₃×#685	—	2	4	no	—
65	C₃×C₄⋊Dic₅	—	2	4	no	—
66	C₃×C₄⋊Dic₅	D₄	1	2	yes	—
67	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
68	C₃×C₄×Dic₅	—	2	1	no	—
69	C₃×C₄×Dic₅	—	2	4	no	—
70	C₃×C₄×Dic₅	C₂³	1	2	yes	—
71	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
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	—	5	1	no	—
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	D₅	1	1	yes	characteristic, complemented
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	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
86	C₅×#117	C₂²×C₃	1	1	yes	characteristic
87	Q₈×Dic₅	—	2	2	no	—
88	Q₈×Dic₅	C₂²×C₃	1	4	yes	complemented
89	C₂×#688	C₃×C₄	1	8	yes	complemented
90	C₂×#688	C₂²×C₃	1	2	yes	—
91	C₂×#688	C₂²×C₃	1	2	yes	—
92	#4072	—	2	2	no	—
93	#4072	C₂²×C₃	1	1	yes	characteristic
94	#4072	C₂²×C₃	1	1	yes	characteristic
95	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
96	#4039	C₂²×C₃	1	4	yes	—
97	D₅×C₂²⋊C₄	—	2	2	no	—
98	C₄×D₂₀	—	2	2	no	—
99	C₅×#103	C₂²×C₃	1	4	yes	complemented
100	#3953	C₂²×C₃	1	4	yes	—
101	#3947	C₂²×C₃	1	2	yes	complemented
102	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
103	#3940	C₂²×C₃	1	2	yes	complemented
104	#3939	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	1	yes	characteristic
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
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×C₅×C₈	—	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	C₂×D₅	1	1	yes	characteristic
135	C₂²×C₃×C₈	—	5	1	no	—
136	C₃×C₄×Q₈	—	5	4	no	—
137	C₃×C₄×Q₈	—	10	2	no	—
138	C₃×C₄×D₄	—	5	4	no	—
139	C₃×C₄×D₄	—	10	2	no	—
140	C₃×#117	—	5	1	no	—
141	C₃×#117	—	5	1	no	—
142	C₃×#117	—	10	2	no	—
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	C₂×D₅	1	4	yes	complemented
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×M₁₆	—	2	2	no	—
164	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
165	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
166	C₅×C₂²⋊C₄	—	2	1	no	—
167	C₄²×C₅	—	2	1	no	—
168	C₂²⋊Dic₅	—	2	1	no	—
169	C₂²⋊Dic₅	C₃×D₄	1	2	yes	—
170	#688	C₂×C₃×C₄	1	8	yes	complemented
171	#688	C₂×C₃×C₄	1	8	yes	complemented
172	#685	—	2	4	no	—
173	C₄⋊Dic₅	—	2	4	no	—
174	C₄⋊Dic₅	C₃×D₄	1	2	yes	—
175	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
176	C₄×Dic₅	—	2	1	no	—
177	C₄×Dic₅	—	2	4	no	—
178	C₄×Dic₅	C₂³×C₃	1	2	yes	—
179	C₂×#168	C₂×C₃×C₄	1	4	yes	complemented
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	—	5	1	no	—
184	#518	—	5	1	no	—
185	#440	—	5	4	no	—
186	C₄×SD₁₆	—	5	4	no	—
187	#427	—	5	1	no	—
188	#419	C₃×D₅	1	1	yes	characteristic, complemented
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	—	4	2	no	—
199	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
200	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
201	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
202	C₃×Dic₅	—	2	4	no	—
203	C₃×Dic₅	—	4	2	no	—
204	C₂⁴×C₃	—	10	1	no	—
205	C₂×C₃×Q₈	—	2	1	no	—
206	C₂×C₃×Q₈	—	2	2	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	1	no	—
212	C₂×C₃×D₄	—	10	2	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	—	2	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	C₂²×D₅	1	2	yes	—
223	C₃×C₄⋊C₄	—	5	2	no	—
224	C₃×C₄⋊C₄	—	5	2	no	—
225	C₃×C₄⋊C₄	—	10	4	no	—
226	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
227	C₃×C₂²⋊C₄	—	2	1	no	—
228	C₃×C₂²⋊C₄	—	5	2	no	—
229	C₃×C₂²⋊C₄	—	10	4	no	—
230	C₃×C₂²⋊C₄	—	10	1	no	—
231	C₃×C₄²	—	2	1	no	—
232	C₃×C₄²	—	5	2	no	—
233	C₃×C₄²	—	10	4	no	—
234	C₃×C₄²	—	10	1	no	—
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	1	yes	characteristic
247	C₂×C₄×C₅	C₃×#41	1	2	yes	—
248	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
249	C₂×Dic₅	—	2	2	no	—
250	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
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	C₅×C₈	—	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	C₂×C₃×D₅	1	1	yes	characteristic
264	C₂²×C₈	—	5	1	no	—
265	C₄×Q₈	—	5	4	no	—
266	C₄×Q₈	—	10	2	no	—
267	C₄×D₄	—	5	4	no	—
268	C₄×D₄	—	10	2	no	—
269	#117	—	5	1	no	—
270	#117	—	5	1	no	—
271	#117	—	10	2	no	—
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	C₂×C₃×D₅	1	4	yes	complemented
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	D₄×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	—	5	4	no	—
298	C₂×C₃×C₄	—	10	2	no	—
299	C₂×C₃×C₄	—	40	4	no	—
300	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
301	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
302	C₂×C₃×C₄	#711	1	2	yes	—
303	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
304	C₃×C₈	—	2	2	no	—
305	C₃×C₈	—	5	2	no	—
306	C₃×C₈	—	5	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	—	4	2	no	—
315	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
316	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
317	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
318	Dic₅	—	2	4	no	—
319	Dic₅	—	4	2	no	—
320	C₂⁴	—	10	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	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	1	no	—
328	C₂×D₄	—	10	2	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	—	2	2	no	—
335	C₂×C₈	—	5	4	no	—
336	C₂×C₈	—	5	1	no	—
337	C₂×C₈	—	5	1	no	—
338	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
339	C₄⋊C₄	—	5	2	no	—
340	C₄⋊C₄	—	5	2	no	—
341	C₄⋊C₄	—	10	4	no	—
342	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	5	2	no	—
345	C₂²⋊C₄	—	10	4	no	—
346	C₂²⋊C₄	—	10	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	5	2	no	—
349	C₄²	—	10	4	no	—
350	C₄²	—	10	1	no	—
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	#4027	1	2	yes	—
357	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	4	2	no	—
360	C₃×C₄	—	10	4	no	—
361	C₃×C₄	—	20	2	no	—
362	C₃×C₄	#4027	1	2	yes	—
363	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
364	C₃×C₄	C₂×#711	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	C₃×D₄×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	—	5	4	no	—
383	C₂×C₄	—	10	2	no	—
384	C₂×C₄	—	40	4	no	—
385	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
386	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
387	C₂×C₄	C₃×#711	1	2	yes	—
388	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	5	2	no	—
391	C₈	—	5	2	no	—
392	C₂×C₃	—	2	2	no	—
393	C₂×C₃	—	20	4	no	—
394	C₂×C₃	C₂×#4027	1	1	yes	characteristic
395	C₂×C₃	#66112	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×#4027	1	2	yes	—
402	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
403	C₄	—	2	4	no	—
404	C₄	—	4	2	no	—
405	C₄	—	10	4	no	—
406	C₄	—	20	2	no	—
407	C₄	C₃×#4027	1	2	yes	—
408	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
409	C₄	C₂×C₃×#711	1	1	yes	characteristic
410	C₃	#10610678	1	1	yes	characteristic, direct product factor, Sylow
411	C₂	—	2	2	no	—
412	C₂	—	20	4	no	—
413	C₂	C₂×C₃×#4027	1	1	yes	characteristic
414	C₂	C₃×#66112	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#419	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#419	D₅
hypocenter	C₅	C₃×#2949
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#419

Complements

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

N	H ≅ G/N	type
1. C₃×#66146	C₂	semidirect
4. C₃×C₅×#419	C₂	semidirect
6. C₃×#65411	C₂	semidirect
7. C₃×#65287	C₂	semidirect
8. C₃×#65106	C₂	semidirect
9. C₃×#65077	C₂	semidirect
10. #10610678	C₃	direct (N × H)
16. C₃×Q₈×Dic₅	C₂²	semidirect
17. C₂×C₃×#688	C₄	semidirect
27. C₃×C₅×#103	C₂²	semidirect
29. C₃×#3947	C₂²	semidirect
30. C₃×C₈×Dic₅	C₂²	semidirect
31. C₃×#3940	C₂²	semidirect
32. C₃×#3939	C₂²	semidirect
34. #66146	C₂×C₃	semidirect
37. C₅×#419	C₂×C₃	semidirect
39. #65411	C₂×C₃	semidirect
40. #65287	C₂×C₃	semidirect
41. #65106	C₂×C₃	semidirect
42. #65077	C₂×C₃	semidirect
46. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
62. C₃×#688	C₂×C₄	semidirect
63. C₃×#688	C₂×C₄	semidirect
71. C₂×C₃×#168	C₂×C₄	semidirect
80. C₃×#419	D₅	semidirect
88. Q₈×Dic₅	C₂²×C₃	semidirect
89. C₂×#688	C₃×C₄	semidirect
99. C₅×#103	C₂²×C₃	semidirect
101. #3947	C₂²×C₃	semidirect
102. C₈×Dic₅	C₂²×C₃	semidirect
103. #3940	C₂²×C₃	semidirect
104. #3939	C₂²×C₃	semidirect
147. C₃×#103	C₂×D₅	semidirect
154. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
170. #688	C₂×C₃×C₄	semidirect
171. #688	C₂×C₃×C₄	semidirect
179. C₂×#168	C₂×C₃×C₄	semidirect
188. #419	C₃×D₅	semidirect
207. C₂×C₃×Q₈	C₄×D₅	semidirect
276. #103	C₂×C₃×D₅	semidirect
323. C₂×Q₈	C₃×C₄×D₅	semidirect
351. C₃×C₅	#2949	semidirect
396. C₅	C₃×#2949	semidirect
410. C₃	#10610678	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×#66146	2
C₂²×C₃×#688	2
C₃×#65855	2
C₃×C₅×#419	2
C₃×#65420	2
C₃×#65411	2
C₃×#65287	2
C₃×#65106	2
C₃×#65077	2
#10610678	3
C₃×#2949	5

Subgroups — C3×#10610678 #14417411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610678 #14417411