Subgroups — C₃×#10617267 #14419601

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65958	C₂	1	1	yes	maximal, characteristic
2	C₃×#65788	C₂	1	2	yes	maximal, complemented
3	C₃×#65754	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4002	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65706	C₂	1	2	yes	maximal, complemented
6	C₃×#65704	C₂	1	2	yes	maximal, complemented
7	C₃×#65701	C₂	1	2	yes	maximal, complemented
8	C₃×#65693	C₂	1	2	yes	maximal, complemented
9	C₃×#65692	C₂	1	2	yes	maximal, complemented
10	#10617267	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×#170	C₂²	1	2	yes	—
12	C₂×C₃×#700	C₂²	1	2	yes	—
13	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
14	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
15	C₃×#4093	C₄	1	1	yes	characteristic
16	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
17	C₃×#4076	C₄	1	1	yes	characteristic
18	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
19	C₃×#4044	C₄	1	2	yes	—
20	C₃×#4039	C₂²	1	1	yes	characteristic
21	C₃×#4038	C₂²	1	2	yes	—
22	C₃×#4036	C₄	1	1	yes	characteristic
23	C₃×#4032	C₄	1	2	yes	—
24	C₃×#4027	C₂²	1	2	yes	—
25	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
26	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
27	C₃×#4004	C₂²	1	2	yes	—
28	C₃×#4004	C₂²	1	2	yes	—
29	C₃×#4003	C₂²	1	2	yes	—
30	C₃×#4003	C₂²	1	2	yes	—
31	C₃×#4002	C₂²	1	2	yes	—
32	C₃×#4002	C₂²	1	1	yes	characteristic
33	C₃×#4002	C₂²	1	2	yes	—
34	C₃×#4002	C₂²	1	1	yes	characteristic
35	C₃×C₄⋊#170	C₂²	1	2	yes	—
36	C₃×C₄×#170	C₂²	1	2	yes	—
37	C₃×C₄×#170	C₂²	1	2	yes	—
38	C₃×#2968	—	5	1	no	maximal, Hall
39	#65958	C₂×C₃	1	1	yes	characteristic
40	#65788	C₂×C₃	1	2	yes	complemented
41	#65754	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×#4002	C₂×C₃	1	1	yes	characteristic, complemented
43	#65706	C₂×C₃	1	2	yes	complemented
44	#65704	C₂×C₃	1	2	yes	complemented
45	#65701	C₂×C₃	1	2	yes	complemented
46	#65693	C₂×C₃	1	2	yes	complemented
47	#65692	C₂×C₃	1	2	yes	complemented
48	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
51	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
53	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
54	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
55	C₂×C₃×#170	—	2	4	no	—
56	C₂×C₃×#170	C₂³	1	2	yes	—
57	C₂×C₃×#170	C₂³	1	2	yes	—
58	C₂×C₃×#170	C₂³	1	2	yes	—
59	C₂×C₃×#170	C₂³	1	2	yes	—
60	C₃×#700	—	2	4	no	—
61	C₃×D₅⋊C₈	—	2	4	no	—
62	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×#685	C₂×C₄	1	2	yes	—
66	C₃×#685	C₂×C₄	1	2	yes	—
67	C₃×#685	C₂×C₄	1	2	yes	—
68	C₃×#685	C₂×C₄	1	2	yes	—
69	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
70	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
72	C₃×#683	C₂×C₄	1	2	yes	—
73	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₃×C₄×Dic₅	C₂³	1	2	yes	—
76	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
77	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
78	C₃×#529	—	5	1	no	—
79	C₃×#446	—	5	2	no	—
80	C₃×#435	—	5	2	no	—
81	C₃×#435	—	5	2	no	—
82	C₃×C₈×D₄	—	5	2	no	—
83	C₃×#433	—	5	2	no	—
84	C₃×#431	—	5	1	no	—
85	C₃×#405	—	5	2	no	—
86	C₂×C₃×#97	—	5	1	no	—
87	C₂²×#170	C₂²×C₃	1	2	yes	—
88	C₂×#700	C₂²×C₃	1	2	yes	—
89	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
90	C₅×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
91	#4093	C₃×C₄	1	1	yes	characteristic
92	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
93	#4076	C₃×C₄	1	1	yes	characteristic
94	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
95	#4044	C₃×C₄	1	2	yes	—
96	#4039	C₂²×C₃	1	1	yes	characteristic
97	#4038	C₂²×C₃	1	2	yes	—
98	#4036	C₃×C₄	1	1	yes	characteristic
99	#4032	C₃×C₄	1	2	yes	—
100	#4027	C₂²×C₃	1	2	yes	—
101	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
102	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
103	#4004	C₂²×C₃	1	2	yes	—
104	#4004	C₂²×C₃	1	2	yes	—
105	#4003	C₂²×C₃	1	2	yes	—
106	#4003	C₂²×C₃	1	2	yes	—
107	#4002	C₂²×C₃	1	2	yes	—
108	#4002	C₂²×C₃	1	1	yes	characteristic
109	#4002	C₂²×C₃	1	2	yes	—
110	#4002	C₂²×C₃	1	1	yes	characteristic
111	C₄⋊#170	C₂²×C₃	1	2	yes	—
112	C₄×#170	C₂²×C₃	1	2	yes	—
113	C₄×#170	C₂²×C₃	1	2	yes	—
114	#2968	—	5	1	no	Sylow
115	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
117	C₃×C₅×Q₈	—	4	1	no	—
118	C₂×C₃×C₄×C₅	—	4	1	no	—
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
123	C₃×C₂²⋊D₅	—	2	4	no	—
124	C₂×C₃×Dic₅	—	2	2	no	—
125	C₂×C₃×Dic₅	—	2	2	no	—
126	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
131	C₃×D₂₀	—	4	1	no	—
132	C₃×C₄×D₅	—	2	2	no	—
133	C₃×C₄×D₅	—	2	2	no	—
134	C₃×#170	—	2	2	no	—
135	C₃×#170	—	2	2	no	—
136	C₃×#170	—	2	2	no	—
137	C₃×#170	#41	1	4	yes	—
138	C₂×C₃×M₁₆	—	5	2	no	—
139	C₂²×C₃×C₈	—	5	2	no	—
140	C₂²×C₃×C₈	—	5	2	no	—
141	C₃×#126	—	5	2	no	—
142	C₃×#125	—	5	1	no	—
143	C₃×#124	—	5	1	no	—
144	C₃×#123	—	5	2	no	—
145	C₃×C₂²⋊Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
146	C₃×#121	—	5	1	no	—
147	C₃×C₄×Q₈	—	5	1	no	—
148	C₃×C₄×D₄	—	5	1	no	—
149	C₃×C₄×D₄	—	5	2	no	—
150	C₃×#117	—	5	2	no	—
151	C₂×C₃×C₄²	—	5	1	no	—
152	C₃×C₄⋊C₈	—	5	2	no	—
153	C₃×C₄⋊C₈	—	5	2	no	—
154	C₃×C₄⋊C₈	—	5	2	no	—
155	C₃×C₂²⋊C₈	—	5	2	no	—
156	C₃×C₂²⋊C₈	—	5	2	no	—
157	C₃×C₂²⋊C₈	—	5	1	no	—
158	C₃×C₂²⋊C₈	—	5	1	no	—
159	C₃×#97	—	5	1	no	—
160	C₃×#97	—	5	1	no	—
161	C₃×#97	—	5	2	no	—
162	C₃×#97	—	5	2	no	—
163	C₃×C₄×C₈	—	5	2	no	—
164	C₃×C₄×C₈	—	5	2	no	—
165	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
168	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
169	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
170	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
171	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
172	C₂×#170	—	2	4	no	—
173	C₂×#170	C₂³×C₃	1	2	yes	—
174	C₂×#170	C₂³×C₃	1	2	yes	—
175	C₂×#170	C₂³×C₃	1	2	yes	—
176	C₂×#170	C₂³×C₃	1	2	yes	—
177	#700	—	2	4	no	—
178	D₅⋊C₈	—	2	4	no	—
179	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
180	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
181	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
182	#685	C₂×C₃×C₄	1	2	yes	—
183	#685	C₂×C₃×C₄	1	2	yes	—
184	#685	C₂×C₃×C₄	1	2	yes	—
185	#685	C₂×C₃×C₄	1	2	yes	—
186	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
187	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
188	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
189	#683	C₂×C₃×C₄	1	2	yes	—
190	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
191	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
192	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
193	C₄×Dic₅	C₂³×C₃	1	2	yes	—
194	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
195	#529	—	5	1	no	—
196	#446	—	5	2	no	—
197	#435	—	5	2	no	—
198	#435	—	5	2	no	—
199	C₈×D₄	—	5	2	no	—
200	#433	—	5	2	no	—
201	#431	—	5	1	no	—
202	#405	—	5	2	no	—
203	C₂×#97	—	5	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	#131	1	2	yes	—
207	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₃×D₅	—	2	2	no	—
209	C₂×C₃×D₅	—	2	2	no	—
210	C₂×C₃×D₅	—	2	2	no	—
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	—	2	1	no	—
213	C₃×C₄×C₅	—	2	1	no	—
214	C₃×C₄×C₅	—	2	2	no	—
215	C₃×Dic₅	—	2	1	no	—
216	C₃×Dic₅	—	2	1	no	—
217	C₃×Dic₅	—	2	1	no	—
218	C₃×Dic₅	—	2	2	no	—
219	C₃×Dic₅	C₂×#41	1	2	yes	—
220	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
221	C₂×C₃×D₄	—	5	2	no	—
222	C₂×C₃×D₄	—	5	1	no	—
223	C₂²×C₃×C₄	—	5	1	no	—
224	C₂²×C₃×C₄	—	5	1	no	—
225	C₂²×C₃×C₄	—	5	2	no	—
226	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
227	C₃×M₁₆	—	10	4	no	—
228	C₂×C₃×C₈	—	5	2	no	—
229	C₂×C₃×C₈	—	5	2	no	—
230	C₂×C₃×C₈	—	5	2	no	—
231	C₂×C₃×C₈	—	5	2	no	—
232	C₂×C₃×C₈	—	10	4	no	—
233	C₂×C₃×C₈	—	10	4	no	—
234	C₃×C₄⋊C₄	—	5	2	no	—
235	C₃×C₄⋊C₄	—	5	2	no	—
236	C₃×C₄⋊C₄	—	5	1	no	—
237	C₃×C₄⋊C₄	—	5	2	no	—
238	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
239	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
240	C₃×C₂²⋊C₄	—	5	2	no	—
241	C₃×C₂²⋊C₄	—	5	2	no	—
242	C₃×C₂²⋊C₄	—	5	2	no	—
243	C₃×C₂²⋊C₄	—	5	2	no	—
244	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
245	C₃×C₄²	—	5	1	no	—
246	C₃×C₄²	—	5	1	no	—
247	C₃×C₄²	—	5	1	no	—
248	C₃×C₄²	—	5	2	no	—
249	C₃×C₄²	—	5	1	no	—
250	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
251	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
252	C₅×Q₈	—	4	1	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
257	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
258	C₂²⋊D₅	—	2	4	no	—
259	C₂×Dic₅	—	2	2	no	—
260	C₂×Dic₅	—	2	2	no	—
261	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
262	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
263	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
264	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
265	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
266	D₂₀	—	4	1	no	—
267	C₄×D₅	—	2	2	no	—
268	C₄×D₅	—	2	2	no	—
269	#170	—	2	2	no	—
270	#170	—	2	2	no	—
271	#170	—	2	2	no	—
272	#170	C₃×#41	1	4	yes	—
273	C₂×M₁₆	—	5	2	no	—
274	C₂²×C₈	—	5	2	no	—
275	C₂²×C₈	—	5	2	no	—
276	#126	—	5	2	no	—
277	#125	—	5	1	no	—
278	#124	—	5	1	no	—
279	#123	—	5	2	no	—
280	C₂²⋊Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
281	#121	—	5	1	no	—
282	C₄×Q₈	—	5	1	no	—
283	C₄×D₄	—	5	1	no	—
284	C₄×D₄	—	5	2	no	—
285	#117	—	5	2	no	—
286	C₂×C₄²	—	5	1	no	—
287	C₄⋊C₈	—	5	2	no	—
288	C₄⋊C₈	—	5	2	no	—
289	C₄⋊C₈	—	5	2	no	—
290	C₂²⋊C₈	—	5	2	no	—
291	C₂²⋊C₈	—	5	2	no	—
292	C₂²⋊C₈	—	5	1	no	—
293	C₂²⋊C₈	—	5	1	no	—
294	#97	—	5	1	no	—
295	#97	—	5	1	no	—
296	#97	—	5	2	no	—
297	#97	—	5	2	no	—
298	C₄×C₈	—	5	2	no	—
299	C₄×C₈	—	5	2	no	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
303	C₂×C₃×C₅	#568	1	1	yes	characteristic
304	C₃×D₅	—	4	2	no	—
305	C₂³×C₃	—	5	2	no	—
306	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
307	C₃×Q₈	—	4	1	no	—
308	C₃×D₄	—	10	4	no	—
309	C₃×D₄	—	20	1	no	—
310	C₂×C₃×C₄	—	4	1	no	—
311	C₂×C₃×C₄	—	5	1	no	—
312	C₂×C₃×C₄	—	5	1	no	—
313	C₂×C₃×C₄	—	5	1	no	—
314	C₂×C₃×C₄	—	5	1	no	—
315	C₂×C₃×C₄	—	5	2	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	10	2	no	—
319	C₂×C₃×C₄	—	10	2	no	—
320	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
323	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
324	C₃×C₈	—	5	4	no	—
325	C₃×C₈	—	10	2	no	—
326	C₃×C₈	—	10	2	no	—
327	C₃×C₈	—	10	2	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	C₃×#131	1	2	yes	—
331	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
332	C₂×D₅	—	2	2	no	—
333	C₂×D₅	—	2	2	no	—
334	C₂×D₅	—	2	2	no	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	—	2	2	no	—
339	Dic₅	—	2	1	no	—
340	Dic₅	—	2	1	no	—
341	Dic₅	—	2	2	no	—
342	Dic₅	—	2	1	no	—
343	Dic₅	C₂×C₃×#41	1	2	yes	—
344	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
345	C₂×D₄	—	5	2	no	—
346	C₂×D₄	—	5	1	no	—
347	C₂²×C₄	—	5	1	no	—
348	C₂²×C₄	—	5	1	no	—
349	C₂²×C₄	—	5	2	no	—
350	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
351	M₁₆	—	10	4	no	—
352	C₂×C₈	—	5	2	no	—
353	C₂×C₈	—	5	2	no	—
354	C₂×C₈	—	5	2	no	—
355	C₂×C₈	—	5	2	no	—
356	C₂×C₈	—	10	4	no	—
357	C₂×C₈	—	10	4	no	—
358	C₄⋊C₄	—	5	2	no	—
359	C₄⋊C₄	—	5	2	no	—
360	C₄⋊C₄	—	5	1	no	—
361	C₄⋊C₄	—	5	2	no	—
362	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
363	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₂²⋊C₄	—	5	2	no	—
365	C₂²⋊C₄	—	5	2	no	—
366	C₂²⋊C₄	—	5	2	no	—
367	C₂²⋊C₄	—	5	2	no	—
368	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
369	C₄²	—	5	1	no	—
370	C₄²	—	5	2	no	—
371	C₄²	—	5	1	no	—
372	C₄²	—	5	1	no	—
373	C₄²	—	5	1	no	—
374	C₃×C₅	#2968	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	—	10	2	no	—
378	C₂²×C₃	—	10	2	no	—
379	C₂²×C₃	—	10	2	no	—
380	C₂²×C₃	#4133	1	2	yes	—
381	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	5	2	no	—
387	C₃×C₄	—	10	1	no	—
388	C₃×C₄	—	10	1	no	—
389	C₃×C₄	—	10	2	no	—
390	C₃×C₄	—	10	1	no	—
391	C₂×C₅	—	2	2	no	—
392	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
393	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
394	C₂×C₅	C₃×#568	1	1	yes	characteristic
395	D₅	—	4	2	no	—
396	C₂³	—	5	2	no	—
397	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
398	Q₈	—	4	1	no	—
399	D₄	—	10	4	no	—
400	D₄	—	20	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	5	1	no	—
403	C₂×C₄	—	5	1	no	—
404	C₂×C₄	—	5	1	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	5	2	no	—
407	C₂×C₄	—	10	2	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	—	10	2	no	—
410	C₂×C₄	—	10	2	no	—
411	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
414	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
415	C₈	—	5	4	no	—
416	C₈	—	10	2	no	—
417	C₈	—	10	2	no	—
418	C₈	—	10	2	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	20	2	no	—
421	C₂×C₃	#66256	1	1	yes	characteristic
422	C₂×C₃	C₂×#4133	1	1	yes	characteristic
423	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
424	C₅	C₃×#2968	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	10	2	no	—
428	C₂²	—	10	2	no	—
429	C₂²	—	10	2	no	—
430	C₂²	C₃×#4133	1	2	yes	—
431	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	5	2	no	—
437	C₄	—	10	1	no	—
438	C₄	—	10	1	no	—
439	C₄	—	10	2	no	—
440	C₄	—	10	1	no	—
441	C₃	#10617267	1	1	yes	characteristic, direct product factor, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	20	2	no	—
444	C₂	C₃×#66256	1	1	yes	characteristic
445	C₂	C₂×C₃×#4133	1	1	yes	characteristic
446	C₂	C₃×#41×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×C₂²⋊Q₈	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#4076	C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×C₂²⋊Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2968
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₃×#65788	C₂	semidirect
3. C₃×#65754	C₂	semidirect
4. C₂×C₃×#4002	C₂	semidirect
5. C₃×#65706	C₂	semidirect
6. C₃×#65704	C₂	semidirect
7. C₃×#65701	C₂	semidirect
8. C₃×#65693	C₂	semidirect
9. C₃×#65692	C₂	semidirect
10. #10617267	C₃	direct (N × H)
40. #65788	C₂×C₃	semidirect
41. #65754	C₂×C₃	semidirect
42. C₂×#4002	C₂×C₃	semidirect
43. #65706	C₂×C₃	semidirect
44. #65704	C₂×C₃	semidirect
45. #65701	C₂×C₃	semidirect
46. #65693	C₂×C₃	semidirect
47. #65692	C₂×C₃	semidirect
374. C₃×C₅	#2968	semidirect
424. C₅	C₃×#2968	semidirect
441. C₃	#10617267	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×#65958	2
C₃×#65788	2
C₃×#65754	2
C₂×C₃×#4002	2
C₃×#65706	2
C₃×#65704	2
C₃×#65701	2
C₃×#65693	2
C₃×#65692	2
#10617267	3
C₃×#2968	5

Subgroups — C3×#10617267 #14419601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617267 #14419601