Subgroups — C₃×#10617373 #14415857

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	C₂×C₃×#4133	C₂	1	2	yes	maximal, complemented
2	C₃×#66059	C₂	1	1	yes	maximal, characteristic
3	C₃×#65787	C₂	1	2	yes	maximal, complemented
4	C₃×#65705	C₂	1	2	yes	maximal, complemented
5	C₃×#65704	C₂	1	4	yes	maximal, complemented
6	C₃×#65702	C₂	1	2	yes	maximal, complemented
7	C₃×D₅⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#700	C₂	1	1	yes	maximal, characteristic, complemented
9	#10617373	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#713	C₂²	1	2	yes	—
11	C₃×#4133	—	2	8	no	—
12	C₂×C₃×#700	C₂²	1	1	yes	characteristic
13	C₂×C₃×#700	C₂²	1	4	yes	—
14	C₂×C₃×#700	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
16	C₂×C₃×D₅⋊C₈	C₂²	1	4	yes	—
17	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
18	C₃×#4093	C₄	1	2	yes	—
19	C₃×#4041	C₄	1	2	yes	—
20	C₃×#4041	C₄	1	2	yes	—
21	C₃×#4039	C₂²	1	2	yes	—
22	C₃×#4039	C₂²	1	2	yes	—
23	C₃×#4020	C₄	1	1	yes	characteristic
24	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
25	C₃×#4004	C₂²	1	2	yes	—
26	C₃×#4003	C₂²	1	4	yes	—
27	C₃×#4003	C₂²	1	4	yes	—
28	C₃×#4002	C₂²	1	2	yes	—
29	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
30	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
31	C₃×C₄×#170	C₂²	1	2	yes	—
32	C₃×#2935	—	5	1	no	maximal, Hall
33	C₂×#4133	C₂×C₃	1	2	yes	complemented
34	#66059	C₂×C₃	1	1	yes	characteristic
35	#65787	C₂×C₃	1	2	yes	complemented
36	#65705	C₂×C₃	1	2	yes	complemented
37	#65704	C₂×C₃	1	4	yes	complemented
38	#65702	C₂×C₃	1	2	yes	complemented
39	D₅⋊(C₄⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
40	C₄×#700	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
42	C₃×#713	—	2	4	no	—
43	C₃×#713	—	2	4	no	—
44	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
45	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
46	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
47	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
51	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×#170	C₂³	1	2	yes	—
53	C₂×C₃×#170	C₂³	1	2	yes	—
54	C₂×C₃×#170	C₂³	1	2	yes	—
55	C₂×C₃×#170	C₂³	1	2	yes	—
56	C₃×#700	—	2	2	no	—
57	C₃×#700	—	2	8	no	—
58	C₃×#700	D₄	1	4	yes	complemented
59	C₃×D₅⋊C₈	—	2	4	no	—
60	C₃×D₅⋊C₈	—	2	8	no	—
61	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
64	C₃×#685	C₂×C₄	1	4	yes	—
65	C₃×#685	C₂×C₄	1	4	yes	—
66	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
67	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
68	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×#131	—	5	2	no	—
70	C₃×#532	—	5	1	no	—
71	C₃×#436	—	5	2	no	—
72	C₃×#435	—	5	4	no	—
73	C₃×C₈×D₄	—	5	2	no	—
74	C₂×C₃×C₄⋊C₈	—	5	1	no	—
75	C₃×#408	—	5	2	no	—
76	C₃×C₄×M₁₆	—	5	1	no	—
77	C₂×#713	C₂²×C₃	1	2	yes	—
78	#4133	—	2	8	no	—
79	C₂×#700	C₂²×C₃	1	1	yes	characteristic
80	C₂×#700	C₂²×C₃	1	4	yes	—
81	C₂×#700	C₂²×C₃	1	1	yes	characteristic
82	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
83	C₂×D₅⋊C₈	C₂²×C₃	1	4	yes	—
84	C₅×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic
85	#4093	C₃×C₄	1	2	yes	—
86	#4041	C₃×C₄	1	2	yes	—
87	#4041	C₃×C₄	1	2	yes	—
88	#4039	C₂²×C₃	1	2	yes	—
89	#4039	C₂²×C₃	1	2	yes	—
90	#4020	C₃×C₄	1	1	yes	characteristic
91	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
92	#4004	C₂²×C₃	1	2	yes	—
93	#4003	C₂²×C₃	1	4	yes	—
94	#4003	C₂²×C₃	1	4	yes	—
95	#4002	C₂²×C₃	1	2	yes	—
96	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
97	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
98	C₄×#170	C₂²×C₃	1	2	yes	—
99	#2935	—	5	1	no	Sylow
100	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
101	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
102	C₃×C₅×Q₈	—	2	4	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
110	C₃×D₂₀	—	2	8	no	—
111	C₃×D₂₀	—	2	4	no	—
112	C₃×D₂₀	—	2	4	no	—
113	C₃×D₂₀	—	4	2	no	—
114	C₃×C₄×D₅	—	2	2	no	—
115	C₃×C₄×D₅	—	2	4	no	—
116	C₃×C₄×D₅	—	2	4	no	—
117	C₃×C₄×D₅	—	4	1	no	—
118	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
119	C₃×C₄×D₅	#41	1	2	yes	—
120	C₃×#170	—	2	2	no	—
121	C₃×#170	—	2	2	no	—
122	C₃×#170	—	2	2	no	—
123	C₃×#170	C₂×D₄	1	4	yes	—
124	C₂×C₃×#41	—	5	2	no	—
125	C₃×#131	—	10	8	no	—
126	C₂×C₃×M₁₆	—	5	1	no	—
127	C₂×C₃×M₁₆	—	5	4	no	—
128	C₂×C₃×M₁₆	—	5	1	no	—
129	C₂²×C₃×C₈	—	5	2	no	—
130	C₂²×C₃×C₈	—	5	4	no	—
131	C₃×C₄⋊Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
132	C₃×#127	—	5	1	no	—
133	C₃×#124	—	5	2	no	—
134	C₃×#121	—	5	2	no	—
135	C₃×#121	—	5	2	no	—
136	C₃×C₄×D₄	—	5	2	no	—
137	C₃×C₄×D₄	—	5	2	no	—
138	C₂×C₃×C₄²	—	5	1	no	—
139	C₃×C₄⋊C₈	—	5	1	no	—
140	C₃×C₄⋊C₈	—	5	1	no	—
141	C₃×C₄⋊C₈	—	5	2	no	—
142	C₃×C₂²⋊C₈	—	5	4	no	—
143	C₃×C₂²⋊C₈	—	5	4	no	—
144	C₃×#97	—	5	2	no	—
145	C₃×C₄×C₈	—	5	2	no	—
146	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
147	#713	—	2	4	no	—
148	#713	—	2	4	no	—
149	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
150	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
151	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
152	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
153	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
156	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
157	C₂×#170	C₂³×C₃	1	2	yes	—
158	C₂×#170	C₂³×C₃	1	2	yes	—
159	C₂×#170	C₂³×C₃	1	2	yes	—
160	C₂×#170	C₂³×C₃	1	2	yes	—
161	#700	—	2	2	no	—
162	#700	—	2	8	no	—
163	#700	C₃×D₄	1	4	yes	complemented
164	D₅⋊C₈	—	2	4	no	—
165	D₅⋊C₈	—	2	8	no	—
166	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
167	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
168	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
169	#685	C₂×C₃×C₄	1	4	yes	—
170	#685	C₂×C₃×C₄	1	4	yes	—
171	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
172	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
173	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
174	C₂×#131	—	5	2	no	—
175	#532	—	5	1	no	—
176	#436	—	5	2	no	—
177	#435	—	5	4	no	—
178	C₈×D₄	—	5	2	no	—
179	C₂×C₄⋊C₈	—	5	1	no	—
180	#408	—	5	2	no	—
181	C₄×M₁₆	—	5	1	no	—
182	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₃×D₅	—	2	1	no	—
184	C₂×C₃×D₅	—	2	1	no	—
185	C₂×C₃×D₅	—	2	4	no	—
186	C₂×C₃×D₅	—	2	4	no	—
187	C₂×C₃×D₅	—	2	4	no	—
188	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
189	C₃×C₄×C₅	—	2	4	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
192	C₃×C₄×C₅	#131	1	2	yes	complemented
193	C₃×Dic₅	—	2	1	no	—
194	C₃×Dic₅	—	2	1	no	—
195	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
196	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
197	C₃×#41	—	10	4	no	—
198	C₃×#41	—	10	4	no	—
199	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
200	C₂×C₃×D₄	—	5	2	no	—
201	C₂×C₃×D₄	—	5	4	no	—
202	C₂×C₃×D₄	—	5	2	no	—
203	C₂×C₃×D₄	—	5	2	no	—
204	C₂²×C₃×C₄	—	5	1	no	—
205	C₂²×C₃×C₄	—	5	4	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	5	1	no	—
208	C₃×M₁₆	—	5	4	no	—
209	C₃×M₁₆	—	10	8	no	—
210	C₃×M₁₆	—	10	2	no	—
211	C₂×C₃×C₈	—	5	2	no	—
212	C₂×C₃×C₈	—	5	2	no	—
213	C₂×C₃×C₈	—	5	2	no	—
214	C₂×C₃×C₈	—	5	2	no	—
215	C₂×C₃×C₈	—	10	8	no	—
216	C₂×C₃×C₈	—	10	4	no	—
217	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
218	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
219	C₃×C₂²⋊C₄	—	5	4	no	—
220	C₃×C₂²⋊C₄	—	5	4	no	—
221	C₃×C₄²	—	5	1	no	—
222	C₃×C₄²	—	5	1	no	—
223	C₃×C₄²	—	5	1	no	—
224	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
225	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
226	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
227	C₅×Q₈	—	2	4	no	—
228	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
230	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
232	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
233	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
235	D₂₀	—	2	8	no	—
236	D₂₀	—	2	4	no	—
237	D₂₀	—	2	4	no	—
238	D₂₀	—	4	2	no	—
239	C₄×D₅	—	2	2	no	—
240	C₄×D₅	—	2	4	no	—
241	C₄×D₅	—	2	4	no	—
242	C₄×D₅	—	4	1	no	—
243	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
244	C₄×D₅	C₃×#41	1	2	yes	—
245	#170	—	2	2	no	—
246	#170	—	2	2	no	—
247	#170	—	2	2	no	—
248	#170	C₂×C₃×D₄	1	4	yes	—
249	C₂×#41	—	5	2	no	—
250	#131	—	10	8	no	—
251	C₂×M₁₆	—	5	1	no	—
252	C₂×M₁₆	—	5	4	no	—
253	C₂×M₁₆	—	5	1	no	—
254	C₂²×C₈	—	5	2	no	—
255	C₂²×C₈	—	5	4	no	—
256	C₄⋊Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
257	#127	—	5	1	no	—
258	#124	—	5	2	no	—
259	#121	—	5	2	no	—
260	#121	—	5	2	no	—
261	C₄×D₄	—	5	2	no	—
262	C₄×D₄	—	5	2	no	—
263	C₂×C₄²	—	5	1	no	—
264	C₄⋊C₈	—	5	1	no	—
265	C₄⋊C₈	—	5	1	no	—
266	C₄⋊C₈	—	5	2	no	—
267	C₂²⋊C₈	—	5	4	no	—
268	C₂²⋊C₈	—	5	4	no	—
269	#97	—	5	2	no	—
270	C₄×C₈	—	5	2	no	—
271	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
272	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
273	C₂×C₃×C₅	#568	1	1	yes	characteristic
274	C₃×D₅	—	2	2	no	—
275	C₃×D₅	—	4	4	no	—
276	C₂³×C₃	—	5	1	no	—
277	C₂³×C₃	—	5	4	no	—
278	C₃×Q₈	—	2	4	no	—
279	C₃×D₄	—	10	8	no	—
280	C₃×D₄	—	10	4	no	—
281	C₃×D₄	—	10	4	no	—
282	C₃×D₄	—	20	2	no	—
283	C₂×C₃×C₄	—	5	1	no	—
284	C₂×C₃×C₄	—	5	2	no	—
285	C₂×C₃×C₄	—	5	2	no	—
286	C₂×C₃×C₄	—	5	1	no	—
287	C₂×C₃×C₄	—	5	1	no	—
288	C₂×C₃×C₄	—	10	4	no	—
289	C₂×C₃×C₄	—	10	4	no	—
290	C₂×C₃×C₄	—	10	2	no	—
291	C₂×C₃×C₄	—	20	1	no	—
292	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	4	yes	—
294	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
296	C₃×C₈	—	5	4	no	—
297	C₃×C₈	—	10	2	no	—
298	C₃×C₈	—	10	2	no	—
299	C₃×C₈	—	10	2	no	—
300	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
301	C₂×D₅	—	2	1	no	—
302	C₂×D₅	—	2	1	no	—
303	C₂×D₅	—	2	4	no	—
304	C₂×D₅	—	2	4	no	—
305	C₂×D₅	—	2	4	no	—
306	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	4	no	—
309	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
310	C₄×C₅	C₃×#131	1	2	yes	complemented
311	Dic₅	—	2	1	no	—
312	Dic₅	—	2	1	no	—
313	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
314	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
315	#41	—	10	4	no	—
316	#41	—	10	4	no	—
317	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
318	C₂×D₄	—	5	2	no	—
319	C₂×D₄	—	5	4	no	—
320	C₂×D₄	—	5	2	no	—
321	C₂×D₄	—	5	2	no	—
322	C₂²×C₄	—	5	1	no	—
323	C₂²×C₄	—	5	4	no	—
324	C₂²×C₄	—	5	1	no	—
325	C₂²×C₄	—	5	1	no	—
326	M₁₆	—	5	4	no	—
327	M₁₆	—	10	8	no	—
328	M₁₆	—	10	2	no	—
329	C₂×C₈	—	5	2	no	—
330	C₂×C₈	—	5	2	no	—
331	C₂×C₈	—	5	2	no	—
332	C₂×C₈	—	5	2	no	—
333	C₂×C₈	—	10	8	no	—
334	C₂×C₈	—	10	4	no	—
335	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
336	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
337	C₂²⋊C₄	—	5	4	no	—
338	C₂²⋊C₄	—	5	4	no	—
339	C₄²	—	5	1	no	—
340	C₄²	—	5	1	no	—
341	C₄²	—	5	1	no	—
342	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
343	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	5	2	no	—
345	C₂²×C₃	—	10	1	no	—
346	C₂²×C₃	—	10	1	no	—
347	C₂²×C₃	—	10	4	no	—
348	C₂²×C₃	—	10	4	no	—
349	C₂²×C₃	—	10	4	no	—
350	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	5	1	no	—
354	C₃×C₄	—	5	1	no	—
355	C₃×C₄	—	10	1	no	—
356	C₃×C₄	—	10	1	no	—
357	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
358	C₃×C₄	#4133	1	2	yes	complemented
359	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
360	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
361	C₂×C₅	C₃×#568	1	1	yes	characteristic
362	D₅	—	2	2	no	—
363	D₅	—	4	4	no	—
364	C₂³	—	5	1	no	—
365	C₂³	—	5	4	no	—
366	Q₈	—	2	4	no	—
367	D₄	—	10	8	no	—
368	D₄	—	10	4	no	—
369	D₄	—	10	4	no	—
370	D₄	—	20	2	no	—
371	C₂×C₄	—	5	1	no	—
372	C₂×C₄	—	5	2	no	—
373	C₂×C₄	—	5	2	no	—
374	C₂×C₄	—	5	1	no	—
375	C₂×C₄	—	5	1	no	—
376	C₂×C₄	—	10	4	no	—
377	C₂×C₄	—	10	4	no	—
378	C₂×C₄	—	10	2	no	—
379	C₂×C₄	—	20	1	no	—
380	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
382	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
384	C₈	—	5	4	no	—
385	C₈	—	10	2	no	—
386	C₈	—	10	2	no	—
387	C₈	—	10	2	no	—
388	C₂×C₃	—	10	2	no	—
389	C₂×C₃	—	20	4	no	—
390	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
391	C₂×C₃	C₂×#4133	1	1	yes	characteristic
392	C₂×C₃	#66260	1	1	yes	characteristic
393	C₅	C₃×#2935	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	5	2	no	—
395	C₂²	—	10	1	no	—
396	C₂²	—	10	1	no	—
397	C₂²	—	10	4	no	—
398	C₂²	—	10	4	no	—
399	C₂²	—	10	4	no	—
400	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	2	1	no	—
403	C₄	—	5	1	no	—
404	C₄	—	5	1	no	—
405	C₄	—	10	1	no	—
406	C₄	—	10	1	no	—
407	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
408	C₄	C₃×#4133	1	2	yes	complemented
409	C₃	#10617373	1	1	yes	characteristic, direct product factor, Sylow
410	C₂	—	10	2	no	—
411	C₂	—	20	4	no	—
412	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₂	C₂×C₃×#4133	1	1	yes	characteristic
414	C₂	C₃×#66260	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×C₄⋊Q₈	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#66059	C₂
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×C₄⋊Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2935
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4133	C₂	semidirect
3. C₃×#65787	C₂	semidirect
4. C₃×#65705	C₂	semidirect
5. C₃×#65704	C₂	semidirect
6. C₃×#65702	C₂	semidirect
7. C₃×D₅⋊(C₄⋊C₈)	C₂	semidirect
8. C₃×C₄×#700	C₂	semidirect
9. #10617373	C₃	direct (N × H)
33. C₂×#4133	C₂×C₃	semidirect
35. #65787	C₂×C₃	semidirect
36. #65705	C₂×C₃	semidirect
37. #65704	C₂×C₃	semidirect
38. #65702	C₂×C₃	semidirect
39. D₅⋊(C₄⋊C₈)	C₂×C₃	semidirect
40. C₄×#700	C₂×C₃	semidirect
58. C₃×#700	D₄	semidirect
163. #700	C₃×D₄	semidirect
192. C₃×C₄×C₅	#131	semidirect
310. C₄×C₅	C₃×#131	semidirect
343. C₃×C₅	#2935	semidirect
358. C₃×C₄	#4133	semidirect
393. C₅	C₃×#2935	semidirect
408. C₄	C₃×#4133	semidirect
409. C₃	#10617373	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×#4133	2
C₃×#66059	2
C₃×#65787	2
C₃×#65705	2
C₃×#65704	2
C₃×#65702	2
C₃×D₅⋊(C₄⋊C₈)	2
C₃×C₄×#700	2
#10617373	3
C₃×#2935	5

Subgroups — C3×#10617373 #14415857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617373 #14415857