Group #14285411 — subgroups

Subgroups — C₃×#10599182 #14285411

Order 1920.

508 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66050	C₂	1	1	yes	maximal, characteristic
2	C₃×#65126	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64764	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64701	C₂	1	2	yes	maximal, complemented
6	#10599182	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×#711	C₄	1	2	yes	—
8	C₃×C₅×#127	C₂²	1	1	yes	characteristic
9	C₃×#4084	—	2	2	no	—
10	C₃×#4082	C₄	1	2	yes	—
11	C₃×D₄×Dic₅	—	2	2	no	—
12	C₂×C₃×#676	—	2	2	no	—
13	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
14	C₃×#4015	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
16	C₃×#3946	—	2	2	no	—
17	C₃×C₄⋊#168	C₂²	1	2	yes	—
18	C₃×#1560	—	5	1	no	maximal, Hall
19	#66050	C₂×C₃	1	1	yes	characteristic
20	#65126	C₂×C₃	1	2	yes	complemented
21	C₅×#331	C₂×C₃	1	1	yes	characteristic, complemented
22	#64764	C₂×C₃	1	1	yes	characteristic, complemented
23	#64701	C₂×C₃	1	2	yes	complemented
24	C₂×C₃×C₅×D₄	—	2	2	no	—
25	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
26	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
27	C₂²×C₃×Dic₅	—	2	2	no	—
28	C₃×#711	—	4	4	no	—
29	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
31	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
32	C₂×C₃×C₅×C₈	—	2	2	no	—
33	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
34	C₃×C₂²⋊Dic₅	—	2	4	no	—
35	C₃×C₄⋊Dic₅	—	2	2	no	—
36	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
37	C₃×C₄×Dic₅	D₄	1	2	yes	—
38	C₂×C₃×#168	—	2	2	no	—
39	C₃×#676	—	4	4	no	—
40	C₃×#532	—	5	1	no	—
41	C₃×#423	—	5	2	no	—
42	C₃×#333	—	5	2	no	—
43	C₃×#331	—	5	1	no	—
44	C₃×#331	D₅	1	1	yes	characteristic, complemented
45	C₂×#711	C₃×C₄	1	2	yes	—
46	C₅×#127	C₂²×C₃	1	1	yes	characteristic
47	#4084	—	2	2	no	—
48	#4082	C₃×C₄	1	2	yes	—
49	D₄×Dic₅	—	2	2	no	—
50	C₂×#676	—	2	2	no	—
51	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
52	#4015	C₂²×C₃	1	1	yes	characteristic
53	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
54	#3946	—	2	2	no	—
55	C₄⋊#168	C₂²×C₃	1	2	yes	—
56	#1560	—	5	1	no	Sylow
57	C₂³×C₃×C₅	—	2	2	no	—
58	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
59	C₃×C₅×D₄	—	4	2	no	—
60	C₃×C₅×D₄	—	4	2	no	—
61	C₃×C₅×D₄	—	4	2	no	—
62	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
64	C₃×C₂²⋊D₅	—	4	4	no	—
65	C₂×C₃×Dic₅	—	2	2	no	—
66	C₂×C₃×Dic₅	—	4	4	no	—
67	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
68	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
69	C₃×C₄×D₅	—	2	2	no	—
70	C₃×C₄×D₅	—	2	2	no	—
71	C₃×C₄×D₅	—	2	2	no	—
72	C₃×Dic₁₀	—	4	2	no	—
73	C₃×C₅×C₈	—	4	2	no	—
74	C₃×#168	—	4	2	no	—
75	C₂×C₃×#41	—	5	2	no	—
76	C₂×C₃×M₁₆	—	10	2	no	—
77	C₃×C₄⋊Q₈	—	5	1	no	—
78	C₃×#127	C₂×D₅	1	1	yes	characteristic
79	C₃×#124	—	5	2	no	—
80	C₃×#121	—	10	2	no	—
81	C₃×C₄×D₄	—	10	2	no	—
82	C₂×C₃×C₄²	—	5	1	no	—
83	C₃×C₄⋊C₈	—	5	2	no	—
84	C₃×C₄⋊C₈	—	10	2	no	—
85	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
86	C₂×C₅×D₄	—	2	2	no	—
87	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
88	C₂×C₂²⋊D₅	—	2	2	no	—
89	C₂²×Dic₅	—	2	2	no	—
90	#711	—	4	4	no	—
91	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
92	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
93	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
94	C₂×C₅×C₈	—	2	2	no	—
95	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
96	C₂²⋊Dic₅	—	2	4	no	—
97	C₄⋊Dic₅	—	2	2	no	—
98	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
99	C₄×Dic₅	C₃×D₄	1	2	yes	—
100	C₂×#168	—	2	2	no	—
101	#676	—	4	4	no	—
102	#532	—	5	1	no	—
103	#423	—	5	2	no	—
104	#333	—	5	2	no	—
105	#331	—	5	1	no	—
106	#331	C₃×D₅	1	1	yes	characteristic, complemented
107	C₂²×C₃×C₅	—	4	2	no	—
108	C₂²×C₃×C₅	—	4	4	no	—
109	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₃×D₅	—	2	1	no	—
111	C₂×C₃×D₅	—	2	2	no	—
112	C₃×C₄×C₅	—	2	1	no	—
113	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
114	C₃×C₄×C₅	#137	1	2	yes	—
115	C₃×Dic₅	—	2	2	no	—
116	C₃×Dic₅	—	4	2	no	—
117	C₃×Dic₅	#100	1	2	yes	—
118	C₃×#41	—	20	4	no	—
119	C₂×C₃×Q₈	—	5	2	no	—
120	C₂×C₃×D₄	—	2	2	no	—
121	C₂×C₃×D₄	—	10	2	no	—
122	C₂×C₃×D₄	C₄×D₅	1	2	yes	—
123	C₂²×C₃×C₄	—	5	1	no	—
124	C₂²×C₃×C₄	—	5	2	no	—
125	C₂²×C₃×C₄	—	10	2	no	—
126	C₃×M₁₆	—	20	4	no	—
127	C₂×C₃×C₈	—	2	2	no	—
128	C₂×C₃×C₈	—	10	2	no	—
129	C₃×C₄⋊C₄	—	10	2	no	—
130	C₃×C₂²⋊C₄	—	10	4	no	—
131	C₃×C₄²	—	5	1	no	—
132	C₃×C₄²	—	5	2	no	—
133	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
134	C₂³×C₅	—	2	2	no	—
135	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
136	C₅×D₄	—	4	2	no	—
137	C₅×D₄	—	4	2	no	—
138	C₅×D₄	—	4	2	no	—
139	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
140	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
141	C₂²⋊D₅	—	4	4	no	—
142	C₂×Dic₅	—	2	2	no	—
143	C₂×Dic₅	—	4	4	no	—
144	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
145	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
146	C₄×D₅	—	2	2	no	—
147	C₄×D₅	—	2	2	no	—
148	C₄×D₅	—	2	2	no	—
149	Dic₁₀	—	4	2	no	—
150	C₅×C₈	—	4	2	no	—
151	#168	—	4	2	no	—
152	C₂×#41	—	5	2	no	—
153	C₂×M₁₆	—	10	2	no	—
154	C₄⋊Q₈	—	5	1	no	—
155	#127	C₂×C₃×D₅	1	1	yes	characteristic
156	#124	—	5	2	no	—
157	#121	—	10	2	no	—
158	C₄×D₄	—	10	2	no	—
159	C₂×C₄²	—	5	1	no	—
160	C₄⋊C₈	—	5	2	no	—
161	C₄⋊C₈	—	10	2	no	—
162	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	—
163	C₂×C₃×C₅	—	8	2	no	—
164	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
165	C₂×C₃×C₅	#417	1	2	yes	—
166	C₃×D₅	—	4	1	no	—
167	C₂³×C₃	—	2	2	no	—
168	C₂³×C₃	—	5	1	no	—
169	C₃×Q₈	—	20	2	no	—
170	C₃×D₄	—	4	2	no	—
171	C₃×D₄	—	4	2	no	—
172	C₃×D₄	—	4	2	no	—
173	C₃×D₄	—	20	4	no	—
174	C₂×C₃×C₄	—	5	1	no	—
175	C₂×C₃×C₄	—	5	2	no	—
176	C₂×C₃×C₄	—	10	2	no	—
177	C₂×C₃×C₄	—	10	2	no	—
178	C₂×C₃×C₄	—	10	2	no	—
179	C₂×C₃×C₄	—	10	2	no	—
180	C₂×C₃×C₄	—	20	4	no	—
181	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
182	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
183	C₃×C₈	—	4	2	no	—
184	C₃×C₈	—	20	2	no	—
185	C₂²×C₅	—	4	2	no	—
186	C₂²×C₅	—	4	4	no	—
187	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×D₅	—	2	1	no	—
189	C₂×D₅	—	2	2	no	—
190	C₄×C₅	—	2	1	no	—
191	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
192	C₄×C₅	C₃×#137	1	2	yes	—
193	Dic₅	—	2	2	no	—
194	Dic₅	—	4	2	no	—
195	Dic₅	C₃×#100	1	2	yes	—
196	#41	—	20	4	no	—
197	C₂×Q₈	—	5	2	no	—
198	C₂×D₄	—	2	2	no	—
199	C₂×D₄	—	10	2	no	—
200	C₂×D₄	C₃×C₄×D₅	1	2	yes	—
201	C₂²×C₄	—	5	1	no	—
202	C₂²×C₄	—	5	2	no	—
203	C₂²×C₄	—	10	2	no	—
204	M₁₆	—	20	4	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	10	2	no	—
207	C₄⋊C₄	—	10	2	no	—
208	C₂²⋊C₄	—	10	4	no	—
209	C₄²	—	5	1	no	—
210	C₄²	—	5	2	no	—
211	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
212	C₃×C₅	#1560	1	1	yes	characteristic, complemented, Hall
213	C₂²×C₃	—	4	2	no	—
214	C₂²×C₃	—	4	4	no	—
215	C₂²×C₃	—	10	1	no	—
216	C₂²×C₃	—	10	2	no	—
217	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
218	C₃×C₄	—	2	1	no	—
219	C₃×C₄	—	5	2	no	—
220	C₃×C₄	—	10	2	no	—
221	C₃×C₄	—	20	2	no	—
222	C₃×C₄	#4057	1	2	yes	—
223	C₃×C₄	#4061	1	2	yes	—
224	C₂×C₅	—	8	2	no	—
225	C₂×C₅	C₂×C₃×#100	1	1	yes	characteristic
226	C₂×C₅	C₃×#417	1	2	yes	—
227	D₅	—	4	1	no	—
228	C₂³	—	2	2	no	—
229	C₂³	—	5	1	no	—
230	Q₈	—	20	2	no	—
231	D₄	—	4	2	no	—
232	D₄	—	4	2	no	—
233	D₄	—	4	2	no	—
234	D₄	—	20	4	no	—
235	C₂×C₄	—	5	1	no	—
236	C₂×C₄	—	5	2	no	—
237	C₂×C₄	—	10	2	no	—
238	C₂×C₄	—	10	2	no	—
239	C₂×C₄	—	10	2	no	—
240	C₂×C₄	—	10	2	no	—
241	C₂×C₄	—	20	4	no	—
242	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
243	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
244	C₈	—	4	2	no	—
245	C₈	—	20	2	no	—
246	C₂×C₃	—	8	2	no	—
247	C₂×C₃	—	20	1	no	—
248	C₂×C₃	D₅×#100	1	1	yes	characteristic
249	C₂×C₃	#65060	1	2	yes	—
250	C₅	C₃×#1560	1	1	yes	characteristic, complemented, Sylow
251	C₂²	—	4	2	no	—
252	C₂²	—	4	4	no	—
253	C₂²	—	10	1	no	—
254	C₂²	—	10	2	no	—
255	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
256	C₄	—	2	1	no	—
257	C₄	—	5	2	no	—
258	C₄	—	10	2	no	—
259	C₄	—	20	2	no	—
260	C₄	C₃×#4057	1	2	yes	—
261	C₄	C₃×#4061	1	2	yes	—
262	C₃	#10599182	1	1	yes	characteristic, direct product factor, Sylow
263	C₂	—	8	2	no	—
264	C₂	—	20	1	no	—
265	C₂	C₃×D₅×#100	1	1	yes	characteristic
266	C₂	C₃×#65060	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#66050

C₂

yes

maximal, characteristic

C₃×#65126

C₂

yes

maximal, complemented

C₃×C₅×#331

C₂

yes

maximal, characteristic, complemented

C₃×#64764

C₂

yes

maximal, characteristic, complemented

C₃×#64701

C₂

yes

maximal, complemented

#10599182

C₃

yes

maximal, characteristic, direct product factor, Hall

C₂×C₃×#711

C₄

yes

—

C₃×C₅×#127

C₂²

yes

characteristic

C₃×#4084

—

C₃×#4082

C₄

yes

—

C₃×D₄×Dic₅

—

C₂×C₃×#676

—

C₃×C₄²×D₅

C₂²

yes

characteristic

C₃×#4015

C₂²

yes

characteristic

C₃×C₅×C₄⋊C₈

C₂²

yes

—

C₃×#3946

—

C₃×C₄⋊#168

C₂²

yes

—

C₃×#1560

—

maximal, Hall

#66050

C₂×C₃

yes

characteristic

#65126

C₂×C₃

yes

complemented

C₅×#331

C₂×C₃

yes

characteristic, complemented

#64764

C₂×C₃

yes

characteristic, complemented

#64701

C₂×C₃

yes

complemented

C₂×C₃×C₅×D₄

—

C₂×C₃×C₅×D₄

C₂×C₄

yes

—

C₂×C₃×C₂²⋊D₅

—

C₂²×C₃×Dic₅

—

C₃×#711

—

C₂×C₃×C₄×D₅

C₂×C₄

yes

characteristic

C₂×C₃×C₄×D₅

D₄

yes

—

C₂×C₃×Dic₁₀

C₂×C₄

yes

—

C₂×C₃×C₅×C₈

—

C₃×C₄²×C₅

C₂³

yes

characteristic

C₃×C₂²⋊Dic₅

—

C₃×C₄⋊Dic₅

—

C₃×C₄×Dic₅

C₂×C₄

yes

characteristic

C₃×C₄×Dic₅

D₄

yes

—

C₂×C₃×#168

—

—

—

—

—

—

D₅

yes

characteristic, complemented

C₂×#711

C₃×C₄

yes

—

C₅×#127

C₂²×C₃

yes

characteristic

#4084

—

#4082

C₃×C₄

yes

—

D₄×Dic₅

—

C₂×#676

—

C₄²×D₅

C₂²×C₃

yes

characteristic

#4015

C₂²×C₃

yes

characteristic

C₅×C₄⋊C₈

C₂²×C₃

yes

—

#3946

—

C₄⋊#168

C₂²×C₃

yes

—

#1560

—

Sylow

C₂³×C₃×C₅

—

C₂²×C₃×D₅

C₂²⋊C₄

yes

characteristic

C₃×C₅×D₄

—

C₃×C₅×D₄

—

C₃×C₅×D₄

—

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂×D₄

yes

—

C₃×C₂²⋊D₅

—

C₂×C₃×Dic₅

—

C₂×C₃×Dic₅

—

C₂×C₃×Dic₅

C₂²⋊C₄

yes

—

C₂×C₃×Dic₅

C₂²⋊C₄

yes

characteristic

C₃×C₄×D₅

—

C₃×C₄×D₅

—

C₃×C₄×D₅

—

C₃×Dic₁₀

—

C₃×C₅×C₈

—

C₃×#168

—

C₂×C₃×#41

—

C₂×C₃×M₁₆

—

C₃×C₄⋊Q₈

—

C₃×#127

C₂×D₅

yes

characteristic

C₃×#124

—

C₃×#121

—

C₃×C₄×D₄

—

C₂×C₃×C₄²

—

C₃×C₄⋊C₈

—

C₃×C₄⋊C₈

—

C₃×C₄⋊C₈

C₂×D₅

yes

—

C₂×C₅×D₄

—

C₂×C₅×D₄

C₂×C₃×C₄

yes

—

C₂×C₂²⋊D₅

—

C₂²×Dic₅

—

#711

—

C₂×C₄×D₅

C₂×C₃×C₄

yes

characteristic

C₂×C₄×D₅

C₃×D₄

yes

—

C₂×Dic₁₀

C₂×C₃×C₄

yes

—

C₂×C₅×C₈

—

C₄²×C₅

C₂³×C₃

yes

characteristic

C₂²⋊Dic₅

—

C₄⋊Dic₅

—

C₄×Dic₅

C₂×C₃×C₄

yes

characteristic

C₄×Dic₅

C₃×D₄

yes

—

100

C₂×#168

—

101

#676

—

102

#532

—

103

#423

—

104

#333

—

105

#331

—

106

#331

C₃×D₅

yes

characteristic, complemented

107

C₂²×C₃×C₅

—

108

C₂²×C₃×C₅

—

109

C₂²×C₃×C₅

C₂×C₂²⋊C₄

yes

characteristic

110

C₂×C₃×D₅

—

111

C₂×C₃×D₅

—

112

C₃×C₄×C₅

—

113

C₃×C₄×C₅

AGL(1,ℤ/8)

yes

—

114

C₃×C₄×C₅

#137

yes

—

115

C₃×Dic₅

—

116

C₃×Dic₅

—

117

C₃×Dic₅

#100

yes

—

118

C₃×#41

—

119

C₂×C₃×Q₈

—

120

C₂×C₃×D₄

—

121

C₂×C₃×D₄

—

122

C₂×C₃×D₄

C₄×D₅

yes

—

123

C₂²×C₃×C₄

—

124

C₂²×C₃×C₄

—

125

C₂²×C₃×C₄

—

126

C₃×M₁₆

—

127

C₂×C₃×C₈

—

128

C₂×C₃×C₈

—

129

C₃×C₄⋊C₄

—

130

C₃×C₂²⋊C₄

—

131

C₃×C₄²

—

132

C₃×C₄²

—

133

C₃×C₄²

C₂²×D₅

yes

characteristic

134

C₂³×C₅

—

135

C₂²×D₅

C₃×C₂²⋊C₄

yes

characteristic

136

C₅×D₄

—

137

C₅×D₄

—

138

C₅×D₄

—

139

C₂×C₄×C₅

C₂²×C₃×C₄

yes

characteristic

140

C₂×C₄×C₅

C₂×C₃×D₄

yes

—

141

C₂²⋊D₅

—

142

C₂×Dic₅

—

143

C₂×Dic₅

—

144

C₂×Dic₅

C₃×C₂²⋊C₄

yes

—

145

C₂×Dic₅

C₃×C₂²⋊C₄

yes

characteristic

146

C₄×D₅

—

147

C₄×D₅

—

148

C₄×D₅

—

149

Dic₁₀

—

150

C₅×C₈

—

151

#168

—

152

C₂×#41

—

153

C₂×M₁₆

—

154

C₄⋊Q₈

—

155

#127

C₂×C₃×D₅

yes

characteristic

156

#124

—

157

#121

—

158

C₄×D₄

—

159

C₂×C₄²

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

C₂×C₃×D₅

yes

—

163

C₂×C₃×C₅

—

164

C₂×C₃×C₅

C₂×#100

yes

characteristic

165

C₂×C₃×C₅

#417

yes

—

166

C₃×D₅

—

167

C₂³×C₃

—

168

C₂³×C₃

—

169

C₃×Q₈

—

170

C₃×D₄

—

171

C₃×D₄

—

172

C₃×D₄

—

173

C₃×D₄

—

174

C₂×C₃×C₄

—

175

C₂×C₃×C₄

—

176

C₂×C₃×C₄

—

177

C₂×C₃×C₄

—

178

C₂×C₃×C₄

—

179

C₂×C₃×C₄

—

180

C₂×C₃×C₄

—

181

C₂×C₃×C₄

C₂×C₄×D₅

yes

characteristic

182

C₂×C₃×C₄

D₄×D₅

yes

—

183

C₃×C₈

—

184

C₃×C₈

—

185

C₂²×C₅

—

186

C₂²×C₅

—

187

C₂²×C₅

C₂×C₃×C₂²⋊C₄

yes

characteristic

188

C₂×D₅

—

189

C₂×D₅

—

190

C₄×C₅

—

191

C₄×C₅

C₃×AGL(1,ℤ/8)

yes

—

192

C₄×C₅

C₃×#137

yes

—

193

Dic₅

—

194

Dic₅

—

195

Dic₅

C₃×#100

yes

—

196

#41

—

197

C₂×Q₈

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

C₃×C₄×D₅

yes

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

M₁₆

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

C₂²×C₃×D₅

yes

characteristic

212

C₃×C₅

#1560

yes

characteristic, complemented, Hall

213

C₂²×C₃

—

214

C₂²×C₃

—

215

C₂²×C₃

—

216

C₂²×C₃

—

217

C₂²×C₃

D₅×C₂²⋊C₄

yes

characteristic

218

C₃×C₄

—

219

C₃×C₄

—

220

C₃×C₄

—

221

C₃×C₄

—

222

C₃×C₄

#4057

yes

—

223

C₃×C₄

#4061

yes

—

224

C₂×C₅

—

225

C₂×C₅

C₂×C₃×#100

yes

characteristic

226

C₂×C₅

C₃×#417

yes

—

227

D₅

—

228

C₂³

—

229

C₂³

—

230

Q₈

—

231

D₄

—

232

D₄

—

233

D₄

—

234

D₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

C₂×C₃×C₄×D₅

yes

characteristic

243

C₂×C₄

C₃×D₄×D₅

yes

—

244

C₈

—

245

C₈

—

246

C₂×C₃

—

247

C₂×C₃

—

248

C₂×C₃

D₅×#100

yes

characteristic

249

C₂×C₃

#65060

yes

—

250

C₅

C₃×#1560

yes

characteristic, complemented, Sylow

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

C₃×D₅×C₂²⋊C₄

yes

characteristic

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

C₃×#4057

yes

—

261

C₄

C₃×#4061

yes

—

262

C₃

#10599182

yes

characteristic, direct product factor, Sylow

263

C₂

—

264

C₂

—

265

C₂

C₃×D₅×#100

yes

characteristic

266

C₂

C₃×#65060

yes

—

	subgroup	G/H
center	C₂²×C₃	D₅×C₂²⋊C₄
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×#331	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×#66050	C₂
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₃×#331	D₅
hypocenter	C₅	C₃×#1560
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#331

subgroup

G/H

center

C₂²×C₃

D₅×C₂²⋊C₄

commutator

C₂×C₄×C₅

C₂²×C₃×C₄

Frattini

C₄²

C₂²×C₃×D₅

Fitting

C₃×C₅×#331

C₂

socle

C₂²×C₃×C₅

C₂×C₂²⋊C₄

prime radical

C₃×#66050

C₂

cosocle

C₄²×C₅

C₂³×C₃

D₅

C₅

G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅

UCS

C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#331

N	H ≅ G/N	type
2. C₃×#65126	C₂	semidirect
3. C₃×C₅×#331	C₂	semidirect
4. C₃×#64764	C₂	semidirect
5. C₃×#64701	C₂	semidirect
6. #10599182	C₃	direct (N × H)
20. #65126	C₂×C₃	semidirect
21. C₅×#331	C₂×C₃	semidirect
22. #64764	C₂×C₃	semidirect
23. #64701	C₂×C₃	semidirect
44. C₃×#331	D₅	semidirect
106. #331	C₃×D₅	semidirect
212. C₃×C₅	#1560	semidirect
250. C₅	C₃×#1560	semidirect
262. C₃	#10599182	direct (N × H)

H ≅ G/N

type

2. C₃×#65126

C₂

semidirect

3. C₃×C₅×#331

C₂

semidirect

4. C₃×#64764

C₂

semidirect

5. C₃×#64701

C₂

semidirect

6. #10599182

C₃

direct (N × H)

20. #65126

C₂×C₃

semidirect

21. C₅×#331

C₂×C₃

semidirect

22. #64764

C₂×C₃

semidirect

23. #64701

C₂×C₃

semidirect

44. C₃×#331

D₅

semidirect

106. #331

C₃×D₅

semidirect

212. C₃×C₅

#1560

semidirect

250. C₅

C₃×#1560

semidirect

262. C₃

#10599182

direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#66050	2
C₃×#65126	2
C₃×C₅×#331	2
C₃×#64764	2
C₃×#64701	2
#10599182	3
C₃×#1560	5

subgroup

index

C₃×C₅×#331

Subgroups — C₃×#10599182 #14285411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#10599182 #14285411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599182 #14285411