Subgroups — C₃×#10617334 #14419597

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×#66025	C₂	1	1	yes	maximal, characteristic
2	C₃×#65707	C₂	1	2	yes	maximal, complemented
3	C₃×#65706	C₂	1	2	yes	maximal, complemented
4	C₃×#65704	C₂	1	2	yes	maximal, complemented
5	C₃×#65704	C₂	1	2	yes	maximal, complemented
6	C₃×#65702	C₂	1	2	yes	maximal, complemented
7	C₃×#65701	C₂	1	2	yes	maximal, complemented
8	C₃×#65678	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65676	C₂	1	1	yes	maximal, characteristic, complemented
10	#10617334	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×#700	C₂²	1	2	yes	—
12	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
13	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
14	C₃×C₅×#125	C₄	1	1	yes	characteristic
15	C₃×#4044	C₄	1	2	yes	—
16	C₃×#4043	C₄	1	1	yes	characteristic
17	C₃×#4041	C₄	1	1	yes	characteristic
18	C₃×#4040	C₄	1	2	yes	—
19	C₃×#4039	C₂²	1	2	yes	—
20	C₃×#4039	C₂²	1	1	yes	characteristic
21	C₃×#4038	C₂²	1	2	yes	—
22	C₃×#4033	C₂²	1	1	yes	characteristic
23	C₃×#4021	C₄	1	1	yes	characteristic
24	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
25	C₃×#4004	C₂²	1	2	yes	—
26	C₃×#4004	C₂²	1	2	yes	—
27	C₃×#4003	C₂²	1	1	yes	characteristic
28	C₃×#4003	C₂²	1	1	yes	characteristic
29	C₃×#4003	C₂²	1	2	yes	—
30	C₃×#4003	C₂²	1	2	yes	—
31	C₃×#4002	C₂²	1	1	yes	characteristic
32	C₃×#4002	C₂²	1	2	yes	—
33	C₃×#4002	C₂²	1	1	yes	characteristic
34	C₃×#4002	C₂²	1	2	yes	—
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	#66025	C₂×C₃	1	1	yes	characteristic
40	#65707	C₂×C₃	1	2	yes	complemented
41	#65706	C₂×C₃	1	2	yes	complemented
42	#65704	C₂×C₃	1	2	yes	complemented
43	#65704	C₂×C₃	1	2	yes	complemented
44	#65702	C₂×C₃	1	2	yes	complemented
45	#65701	C₂×C₃	1	2	yes	complemented
46	#65678	C₂×C₃	1	1	yes	characteristic, complemented
47	#65676	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
49	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
54	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×#170	C₂³	1	2	yes	—
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	C₃×#700	—	2	4	no	—
60	C₃×D₅⋊C₈	—	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×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
67	C₃×#685	C₂×C₄	1	2	yes	—
68	C₃×#685	C₂×C₄	1	2	yes	—
69	C₃×#685	C₂×C₄	1	2	yes	—
70	C₃×#685	C₂×C₄	1	2	yes	—
71	C₃×#685	C₂×C₄	1	2	yes	—
72	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
73	C₃×#683	C₂×C₄	1	2	yes	—
74	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
76	C₃×C₄×Dic₅	C₂³	1	2	yes	—
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	C₂×#700	C₂²×C₃	1	2	yes	—
88	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
89	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
90	C₅×#125	C₃×C₄	1	1	yes	characteristic
91	#4044	C₃×C₄	1	2	yes	—
92	#4043	C₃×C₄	1	1	yes	characteristic
93	#4041	C₃×C₄	1	1	yes	characteristic
94	#4040	C₃×C₄	1	2	yes	—
95	#4039	C₂²×C₃	1	2	yes	—
96	#4039	C₂²×C₃	1	1	yes	characteristic
97	#4038	C₂²×C₃	1	2	yes	—
98	#4033	C₂²×C₃	1	1	yes	characteristic
99	#4021	C₃×C₄	1	1	yes	characteristic
100	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
101	#4004	C₂²×C₃	1	2	yes	—
102	#4004	C₂²×C₃	1	2	yes	—
103	#4003	C₂²×C₃	1	1	yes	characteristic
104	#4003	C₂²×C₃	1	1	yes	characteristic
105	#4003	C₂²×C₃	1	2	yes	—
106	#4003	C₂²×C₃	1	2	yes	—
107	#4002	C₂²×C₃	1	1	yes	characteristic
108	#4002	C₂²×C₃	1	2	yes	—
109	#4002	C₂²×C₃	1	1	yes	characteristic
110	#4002	C₂²×C₃	1	2	yes	—
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	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
116	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
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×Dic₅	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
125	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
126	C₃×D₂₀	—	2	4	no	—
127	C₃×D₂₀	—	4	1	no	—
128	C₃×C₄×D₅	—	2	2	no	—
129	C₃×C₄×D₅	—	2	2	no	—
130	C₃×C₄×D₅	—	2	2	no	—
131	C₃×C₄×D₅	—	2	2	no	—
132	C₃×C₄×D₅	—	4	1	no	—
133	C₃×Dic₁₀	—	4	1	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	AGL(1,𝔽₅)	1	1	yes	characteristic
143	C₃×#124	—	5	1	no	—
144	C₃×#123	—	5	2	no	—
145	C₃×C₂²⋊Q₈	—	5	1	no	—
146	C₃×#121	—	5	1	no	—
147	C₃×C₄×Q₈	—	5	1	no	—
148	C₃×C₄×D₄	—	5	2	no	—
149	C₃×C₄×D₄	—	5	1	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	1	no	—
156	C₃×C₂²⋊C₈	—	5	1	no	—
157	C₃×C₂²⋊C₈	—	5	2	no	—
158	C₃×C₂²⋊C₈	—	5	2	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×D₂₀	C₂×C₃×C₄	1	2	yes	—
166	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
169	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
171	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
172	C₂×#170	C₂³×C₃	1	2	yes	—
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	#700	—	2	4	no	—
177	D₅⋊C₈	—	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×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
182	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
183	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
184	#685	C₂×C₃×C₄	1	2	yes	—
185	#685	C₂×C₃×C₄	1	2	yes	—
186	#685	C₂×C₃×C₄	1	2	yes	—
187	#685	C₂×C₃×C₄	1	2	yes	—
188	#685	C₂×C₃×C₄	1	2	yes	—
189	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
190	#683	C₂×C₃×C₄	1	2	yes	—
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	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₃×D₅	—	2	1	no	—
206	C₂×C₃×D₅	—	2	1	no	—
207	C₂×C₃×D₅	—	2	2	no	—
208	C₂×C₃×D₅	—	2	2	no	—
209	C₂×C₃×D₅	—	2	2	no	—
210	C₂×C₃×D₅	#131	1	2	yes	—
211	C₃×C₄×C₅	—	2	1	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	2	1	no	—
214	C₃×C₄×C₅	—	2	2	no	—
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×Dic₅	—	2	1	no	—
217	C₃×Dic₅	—	2	2	no	—
218	C₃×Dic₅	—	2	1	no	—
219	C₃×Dic₅	C₂×#41	1	2	yes	—
220	C₂×C₃×Q₈	—	5	1	no	—
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	2	no	—
225	C₂²×C₃×C₄	—	5	1	no	—
226	C₂²×C₃×C₄	—	5	1	no	—
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	C₂×AGL(1,𝔽₅)	1	2	yes	—
237	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
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	—	5	2	no	—
245	C₃×C₄²	—	5	1	no	—
246	C₃×C₄²	—	5	1	no	—
247	C₃×C₄²	—	5	2	no	—
248	C₃×C₄²	—	5	1	no	—
249	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
250	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
251	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
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×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
258	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
259	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
260	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
261	D₂₀	—	2	4	no	—
262	D₂₀	—	4	1	no	—
263	C₄×D₅	—	2	2	no	—
264	C₄×D₅	—	2	2	no	—
265	C₄×D₅	—	2	2	no	—
266	C₄×D₅	—	2	2	no	—
267	C₄×D₅	—	4	1	no	—
268	Dic₁₀	—	4	1	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	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
278	#124	—	5	1	no	—
279	#123	—	5	2	no	—
280	C₂²⋊Q₈	—	5	1	no	—
281	#121	—	5	1	no	—
282	C₄×Q₈	—	5	1	no	—
283	C₄×D₄	—	5	2	no	—
284	C₄×D₄	—	5	1	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	1	no	—
291	C₂²⋊C₈	—	5	1	no	—
292	C₂²⋊C₈	—	5	2	no	—
293	C₂²⋊C₈	—	5	2	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	C₄×#41	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
302	C₂×C₃×C₅	#568	1	1	yes	characteristic
303	C₃×D₅	—	2	2	no	—
304	C₃×D₅	—	4	2	no	—
305	C₂³×C₃	—	5	1	no	—
306	C₂³×C₃	—	5	2	no	—
307	C₃×Q₈	—	20	1	no	—
308	C₃×D₄	—	10	4	no	—
309	C₃×D₄	—	20	1	no	—
310	C₂×C₃×C₄	—	5	1	no	—
311	C₂×C₃×C₄	—	5	1	no	—
312	C₂×C₃×C₄	—	5	1	no	—
313	C₂×C₃×C₄	—	5	2	no	—
314	C₂×C₃×C₄	—	10	2	no	—
315	C₂×C₃×C₄	—	10	2	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	20	1	no	—
319	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
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	C₂³×C₃×C₄	1	1	yes	characteristic
329	C₂×D₅	—	2	1	no	—
330	C₂×D₅	—	2	1	no	—
331	C₂×D₅	—	2	2	no	—
332	C₂×D₅	—	2	2	no	—
333	C₂×D₅	—	2	2	no	—
334	C₂×D₅	C₃×#131	1	2	yes	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	2	2	no	—
337	C₄×C₅	—	2	1	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	2	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	—	5	1	no	—
345	C₂×D₄	—	5	2	no	—
346	C₂×D₄	—	5	1	no	—
347	C₂²×C₄	—	5	1	no	—
348	C₂²×C₄	—	5	2	no	—
349	C₂²×C₄	—	5	1	no	—
350	C₂²×C₄	—	5	1	no	—
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	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
361	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
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	—	5	2	no	—
369	C₄²	—	5	1	no	—
370	C₄²	—	5	2	no	—
371	C₄²	—	5	1	no	—
372	C₄²	—	5	1	no	—
373	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₃×C₅	#2968	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	5	2	no	—
376	C₂²×C₃	—	10	1	no	—
377	C₂²×C₃	—	10	1	no	—
378	C₂²×C₃	—	10	2	no	—
379	C₂²×C₃	—	10	2	no	—
380	C₂²×C₃	—	10	2	no	—
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	1	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	5	2	no	—
388	C₃×C₄	—	10	1	no	—
389	C₃×C₄	—	10	2	no	—
390	C₃×C₄	—	10	1	no	—
391	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
392	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
393	C₂×C₅	C₃×#568	1	1	yes	characteristic
394	D₅	—	2	2	no	—
395	D₅	—	4	2	no	—
396	C₂³	—	5	1	no	—
397	C₂³	—	5	2	no	—
398	Q₈	—	20	1	no	—
399	D₄	—	10	4	no	—
400	D₄	—	20	1	no	—
401	C₂×C₄	—	5	1	no	—
402	C₂×C₄	—	5	1	no	—
403	C₂×C₄	—	5	1	no	—
404	C₂×C₄	—	5	2	no	—
405	C₂×C₄	—	10	2	no	—
406	C₂×C₄	—	10	2	no	—
407	C₂×C₄	—	10	2	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	—	20	1	no	—
410	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
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	—	10	2	no	—
420	C₂×C₃	—	20	2	no	—
421	C₂×C₃	#66260	1	1	yes	characteristic
422	C₂×C₃	D₅⋊#131	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	—	5	2	no	—
426	C₂²	—	10	1	no	—
427	C₂²	—	10	1	no	—
428	C₂²	—	10	2	no	—
429	C₂²	—	10	2	no	—
430	C₂²	—	10	2	no	—
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	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	5	2	no	—
438	C₄	—	10	1	no	—
439	C₄	—	10	2	no	—
440	C₄	—	10	1	no	—
441	C₃	#10617334	1	1	yes	characteristic, direct product factor, Sylow
442	C₂	—	10	2	no	—
443	C₂	—	20	2	no	—
444	C₂	C₃×#66260	1	1	yes	characteristic
445	C₂	C₃×D₅⋊#131	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×#125	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#4041	C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#125	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2968
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#125

Complements

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

N	H ≅ G/N	type
2. C₃×#65707	C₂	semidirect
3. C₃×#65706	C₂	semidirect
4. C₃×#65704	C₂	semidirect
5. C₃×#65704	C₂	semidirect
6. C₃×#65702	C₂	semidirect
7. C₃×#65701	C₂	semidirect
8. C₃×#65678	C₂	semidirect
9. C₃×#65676	C₂	semidirect
10. #10617334	C₃	direct (N × H)
40. #65707	C₂×C₃	semidirect
41. #65706	C₂×C₃	semidirect
42. #65704	C₂×C₃	semidirect
43. #65704	C₂×C₃	semidirect
44. #65702	C₂×C₃	semidirect
45. #65701	C₂×C₃	semidirect
46. #65678	C₂×C₃	semidirect
47. #65676	C₂×C₃	semidirect
374. C₃×C₅	#2968	semidirect
424. C₅	C₃×#2968	semidirect
441. C₃	#10617334	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×#66025	2
C₃×#65707	2
C₃×#65706	2
C₃×#65704	2
C₃×#65702	2
C₃×#65701	2
C₃×#65678	2
C₃×#65676	2
#10617334	3
C₃×#2968	5

Subgroups — C3×#10617334 #14419597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617334 #14419597