Group #14285410 — subgroups

Subgroups — C₅×#68389 #14285410

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	C₅×#5716	C₂	1	1	yes	maximal, characteristic
2	C₅×#4837	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4544	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4481	C₂	1	2	yes	maximal, complemented
6	C₅×#1560	—	3	1	no	maximal, Hall
7	C₂×C₅×#237	C₄	1	2	yes	—
8	C₃×C₅×#127	C₂²	1	1	yes	characteristic
9	C₅×#938	—	2	2	no	—
10	C₅×#936	C₄	1	2	yes	—
11	C₅×D₄×Dic₃	—	2	2	no	—
12	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
13	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₅×#869	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
16	C₅×Dic₃⋊C₈	—	2	2	no	—
17	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
18	#68389	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₅×#532	—	3	1	no	—
20	C₅×#423	—	3	2	no	—
21	C₅×#333	—	3	2	no	—
22	C₅×#331	—	3	1	no	—
23	C₅×#331	D₃	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×D₄	—	2	2	no	—
25	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
26	C₂×C₅×#67	—	2	2	no	—
27	C₂²×C₅×Dic₃	—	2	2	no	—
28	C₅×#237	—	4	4	no	—
29	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
31	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
32	C₂×C₃×C₅×C₈	—	2	2	no	—
33	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
34	C₅×#217	—	2	4	no	—
35	C₅×C₄⋊Dic₃	—	2	2	no	—
36	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
37	C₄×C₅×Dic₃	D₄	1	2	yes	—
38	C₂×C₅×C₃⋊C₈	—	2	2	no	—
39	C₅×ΓL(1,𝔽₂₅)	—	4	4	no	—
40	#5716	C₂×C₅	1	1	yes	characteristic
41	#4837	C₂×C₅	1	2	yes	complemented
42	C₃×#331	C₂×C₅	1	1	yes	characteristic, complemented
43	#4544	C₂×C₅	1	1	yes	characteristic, complemented
44	#4481	C₂×C₅	1	2	yes	complemented
45	C₂×C₅×#41	—	3	2	no	—
46	C₂×C₅×M₁₆	—	6	2	no	—
47	C₅×C₄⋊Q₈	—	3	1	no	—
48	C₅×#127	C₂×D₃	1	1	yes	characteristic
49	C₅×#124	—	3	2	no	—
50	C₅×#121	—	6	2	no	—
51	C₄×C₅×D₄	—	6	2	no	—
52	C₂×C₄²×C₅	—	3	1	no	—
53	C₅×C₄⋊C₈	—	3	2	no	—
54	C₅×C₄⋊C₈	—	6	2	no	—
55	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
56	#1560	—	3	1	no	Sylow
57	C₂³×C₃×C₅	—	2	2	no	—
58	C₂²×C₅×D₃	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	C₅×#67	—	4	4	no	—
65	C₂×C₅×Dic₃	—	2	2	no	—
66	C₂×C₅×Dic₃	—	4	4	no	—
67	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
68	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₄×C₅×D₃	—	2	2	no	—
70	C₄×C₅×D₃	—	2	2	no	—
71	C₄×C₅×D₃	—	2	2	no	—
72	C₅×Dic₆	—	4	2	no	—
73	C₃×C₅×C₈	—	4	2	no	—
74	C₅×C₃⋊C₈	—	4	2	no	—
75	C₂×#237	C₄×C₅	1	2	yes	—
76	C₃×#127	C₂²×C₅	1	1	yes	characteristic
77	#938	—	2	2	no	—
78	#936	C₄×C₅	1	2	yes	—
79	D₄×Dic₃	—	2	2	no	—
80	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
81	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
82	#869	C₂²×C₅	1	1	yes	characteristic
83	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
84	Dic₃⋊C₈	—	2	2	no	—
85	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
86	C₅×#41	—	12	4	no	—
87	C₂×C₅×Q₈	—	3	2	no	—
88	C₂×C₅×D₄	—	2	2	no	—
89	C₂×C₅×D₄	—	6	2	no	—
90	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
91	C₂²×C₄×C₅	—	3	1	no	—
92	C₂²×C₄×C₅	—	3	2	no	—
93	C₂²×C₄×C₅	—	6	2	no	—
94	C₅×M₁₆	—	12	4	no	—
95	C₂×C₅×C₈	—	2	2	no	—
96	C₂×C₅×C₈	—	6	2	no	—
97	C₅×C₄⋊C₄	—	6	2	no	—
98	C₅×C₂²⋊C₄	—	6	4	no	—
99	C₄²×C₅	—	3	1	no	—
100	C₄²×C₅	—	3	2	no	—
101	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
102	#532	—	3	1	no	—
103	#423	—	3	2	no	—
104	#333	—	3	2	no	—
105	#331	—	3	1	no	—
106	#331	C₅×D₃	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×C₅×D₃	—	2	1	no	—
111	C₂×C₅×D₃	—	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	C₅×Dic₃	—	2	2	no	—
116	C₅×Dic₃	—	4	2	no	—
117	C₅×Dic₃	#100	1	2	yes	—
118	C₂×C₃×D₄	—	2	2	no	—
119	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
120	C₂×#67	—	2	2	no	—
121	C₂²×Dic₃	—	2	2	no	—
122	#237	—	4	4	no	—
123	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
124	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
125	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
126	C₂×C₃×C₈	—	2	2	no	—
127	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
128	#217	—	2	4	no	—
129	C₄⋊Dic₃	—	2	2	no	—
130	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
131	C₄×Dic₃	C₅×D₄	1	2	yes	—
132	C₂×C₃⋊C₈	—	2	2	no	—
133	ΓL(1,𝔽₂₅)	—	4	4	no	—
134	C₂³×C₅	—	2	2	no	—
135	C₂³×C₅	—	3	1	no	—
136	C₅×Q₈	—	12	2	no	—
137	C₅×D₄	—	4	2	no	—
138	C₅×D₄	—	4	2	no	—
139	C₅×D₄	—	4	2	no	—
140	C₅×D₄	—	12	4	no	—
141	C₂×C₄×C₅	—	3	1	no	—
142	C₂×C₄×C₅	—	3	2	no	—
143	C₂×C₄×C₅	—	6	2	no	—
144	C₂×C₄×C₅	—	6	2	no	—
145	C₂×C₄×C₅	—	6	2	no	—
146	C₂×C₄×C₅	—	6	2	no	—
147	C₂×C₄×C₅	—	12	4	no	—
148	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
149	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
150	C₅×C₈	—	4	2	no	—
151	C₅×C₈	—	12	2	no	—
152	C₂×#41	—	3	2	no	—
153	C₂×M₁₆	—	6	2	no	—
154	C₄⋊Q₈	—	3	1	no	—
155	#127	C₂×C₅×D₃	1	1	yes	characteristic
156	#124	—	3	2	no	—
157	#121	—	6	2	no	—
158	C₄×D₄	—	6	2	no	—
159	C₂×C₄²	—	3	1	no	—
160	C₄⋊C₈	—	3	2	no	—
161	C₄⋊C₈	—	6	2	no	—
162	C₄⋊C₈	C₂×C₅×D₃	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	C₅×D₃	—	4	1	no	—
167	C₂³×C₃	—	2	2	no	—
168	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
169	C₃×D₄	—	4	2	no	—
170	C₃×D₄	—	4	2	no	—
171	C₃×D₄	—	4	2	no	—
172	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
173	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
174	#67	—	4	4	no	—
175	C₂×Dic₃	—	2	2	no	—
176	C₂×Dic₃	—	4	4	no	—
177	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
178	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
179	C₄×D₃	—	2	2	no	—
180	C₄×D₃	—	2	2	no	—
181	C₄×D₃	—	2	2	no	—
182	Dic₆	—	4	2	no	—
183	C₃×C₈	—	4	2	no	—
184	C₃⋊C₈	—	4	2	no	—
185	C₂²×C₅	—	4	2	no	—
186	C₂²×C₅	—	4	4	no	—
187	C₂²×C₅	—	6	1	no	—
188	C₂²×C₅	—	6	2	no	—
189	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
190	C₄×C₅	—	2	1	no	—
191	C₄×C₅	—	3	2	no	—
192	C₄×C₅	—	6	2	no	—
193	C₄×C₅	—	12	2	no	—
194	C₄×C₅	#911	1	2	yes	—
195	C₄×C₅	#915	1	2	yes	—
196	#41	—	12	4	no	—
197	C₂×Q₈	—	3	2	no	—
198	C₂×D₄	—	2	2	no	—
199	C₂×D₄	—	6	2	no	—
200	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
201	C₂²×C₄	—	3	1	no	—
202	C₂²×C₄	—	3	2	no	—
203	C₂²×C₄	—	6	2	no	—
204	M₁₆	—	12	4	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	6	2	no	—
207	C₄⋊C₄	—	6	2	no	—
208	C₂²⋊C₄	—	6	4	no	—
209	C₄²	—	3	1	no	—
210	C₄²	—	3	2	no	—
211	C₄²	C₂²×C₅×D₃	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	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×D₃	—	2	1	no	—
217	C₂×D₃	—	2	2	no	—
218	C₃×C₄	—	2	1	no	—
219	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
220	C₃×C₄	C₅×#137	1	2	yes	—
221	Dic₃	—	2	2	no	—
222	Dic₃	—	4	2	no	—
223	Dic₃	C₅×#100	1	2	yes	—
224	C₂×C₅	—	8	2	no	—
225	C₂×C₅	—	12	1	no	—
226	C₂×C₅	D₃×#100	1	1	yes	characteristic
227	C₂×C₅	#4771	1	2	yes	—
228	C₂³	—	2	2	no	—
229	C₂³	—	3	1	no	—
230	Q₈	—	12	2	no	—
231	D₄	—	4	2	no	—
232	D₄	—	4	2	no	—
233	D₄	—	4	2	no	—
234	D₄	—	12	4	no	—
235	C₂×C₄	—	3	1	no	—
236	C₂×C₄	—	3	2	no	—
237	C₂×C₄	—	6	2	no	—
238	C₂×C₄	—	6	2	no	—
239	C₂×C₄	—	6	2	no	—
240	C₂×C₄	—	6	2	no	—
241	C₂×C₄	—	12	4	no	—
242	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
243	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
244	C₈	—	4	2	no	—
245	C₈	—	12	2	no	—
246	C₂×C₃	—	8	2	no	—
247	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
248	C₂×C₃	C₅×#417	1	2	yes	—
249	D₃	—	4	1	no	—
250	C₅	#68389	1	1	yes	characteristic, direct product factor, Sylow
251	C₂²	—	4	2	no	—
252	C₂²	—	4	4	no	—
253	C₂²	—	6	1	no	—
254	C₂²	—	6	2	no	—
255	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
256	C₄	—	2	1	no	—
257	C₄	—	3	2	no	—
258	C₄	—	6	2	no	—
259	C₄	—	12	2	no	—
260	C₄	C₅×#911	1	2	yes	—
261	C₄	C₅×#915	1	2	yes	—
262	C₃	C₅×#1560	1	1	yes	characteristic, complemented, Sylow
263	C₂	—	8	2	no	—
264	C₂	—	12	1	no	—
265	C₂	C₅×D₃×#100	1	1	yes	characteristic
266	C₂	C₅×#4771	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#5716

C₂

yes

maximal, characteristic

C₅×#4837

C₂

yes

maximal, complemented

C₃×C₅×#331

C₂

yes

maximal, characteristic, complemented

C₅×#4544

C₂

yes

maximal, characteristic, complemented

C₅×#4481

C₂

yes

maximal, complemented

C₅×#1560

—

maximal, Hall

C₂×C₅×#237

C₄

yes

—

C₃×C₅×#127

C₂²

yes

characteristic

C₅×#938

—

C₅×#936

C₄

yes

—

C₅×D₄×Dic₃

—

C₂×C₅×ΓL(1,𝔽₂₅)

—

C₄²×C₅×D₃

C₂²

yes

characteristic

C₅×#869

C₂²

yes

characteristic

C₃×C₅×C₄⋊C₈

C₂²

yes

—

C₅×Dic₃⋊C₈

—

C₅×C₄⋊(C₃⋊C₈)

C₂²

yes

—

#68389

C₅

yes

maximal, characteristic, direct product factor, Hall

—

—

—

—

D₃

yes

characteristic, complemented

C₂×C₃×C₅×D₄

—

C₂×C₃×C₅×D₄

C₂×C₄

yes

—

C₂×C₅×#67

—

C₂²×C₅×Dic₃

—

C₅×#237

—

C₂×C₄×C₅×D₃

C₂×C₄

yes

characteristic

C₂×C₄×C₅×D₃

D₄

yes

—

C₂×C₅×Dic₆

C₂×C₄

yes

—

C₂×C₃×C₅×C₈

—

C₃×C₄²×C₅

C₂³

yes

characteristic

C₅×#217

—

C₅×C₄⋊Dic₃

—

C₄×C₅×Dic₃

C₂×C₄

yes

characteristic

C₄×C₅×Dic₃

D₄

yes

—

C₂×C₅×C₃⋊C₈

—

C₅×ΓL(1,𝔽₂₅)

—

#5716

C₂×C₅

yes

characteristic

#4837

C₂×C₅

yes

complemented

C₃×#331

C₂×C₅

yes

characteristic, complemented

#4544

C₂×C₅

yes

characteristic, complemented

#4481

C₂×C₅

yes

complemented

C₂×C₅×#41

—

C₂×C₅×M₁₆

—

C₅×C₄⋊Q₈

—

C₅×#127

C₂×D₃

yes

characteristic

C₅×#124

—

C₅×#121

—

C₄×C₅×D₄

—

C₂×C₄²×C₅

—

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

C₂×D₃

yes

—

#1560

—

Sylow

C₂³×C₃×C₅

—

C₂²×C₅×D₃

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

—

C₅×#67

—

C₂×C₅×Dic₃

—

C₂×C₅×Dic₃

—

C₂×C₅×Dic₃

C₂²⋊C₄

yes

—

C₂×C₅×Dic₃

C₂²⋊C₄

yes

characteristic

C₄×C₅×D₃

—

C₄×C₅×D₃

—

C₄×C₅×D₃

—

C₅×Dic₆

—

C₃×C₅×C₈

—

C₅×C₃⋊C₈

—

C₂×#237

C₄×C₅

yes

—

C₃×#127

C₂²×C₅

yes

characteristic

#938

—

#936

C₄×C₅

yes

—

D₄×Dic₃

—

C₂×ΓL(1,𝔽₂₅)

—

C₄²×D₃

C₂²×C₅

yes

characteristic

#869

C₂²×C₅

yes

characteristic

C₃×C₄⋊C₈

C₂²×C₅

yes

—

Dic₃⋊C₈

—

C₄⋊(C₃⋊C₈)

C₂²×C₅

yes

—

C₅×#41

—

C₂×C₅×Q₈

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

C₄×D₃

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₄²×C₅

—

100

C₄²×C₅

—

101

C₄²×C₅

C₂²×D₃

yes

characteristic

102

#532

—

103

#423

—

104

#333

—

105

#331

—

106

#331

C₅×D₃

yes

characteristic, complemented

107

C₂²×C₃×C₅

—

108

C₂²×C₃×C₅

—

109

C₂²×C₃×C₅

C₂×C₂²⋊C₄

yes

characteristic

110

C₂×C₅×D₃

—

111

C₂×C₅×D₃

—

112

C₃×C₄×C₅

—

113

C₃×C₄×C₅

AGL(1,ℤ/8)

yes

—

114

C₃×C₄×C₅

#137

yes

—

115

C₅×Dic₃

—

116

C₅×Dic₃

—

117

C₅×Dic₃

#100

yes

—

118

C₂×C₃×D₄

—

119

C₂×C₃×D₄

C₂×C₄×C₅

yes

—

120

C₂×#67

—

121

C₂²×Dic₃

—

122

#237

—

123

C₂×C₄×D₃

C₂×C₄×C₅

yes

characteristic

124

C₂×C₄×D₃

C₅×D₄

yes

—

125

C₂×Dic₆

C₂×C₄×C₅

yes

—

126

C₂×C₃×C₈

—

127

C₃×C₄²

C₂³×C₅

yes

characteristic

128

#217

—

129

C₄⋊Dic₃

—

130

C₄×Dic₃

C₂×C₄×C₅

yes

characteristic

131

C₄×Dic₃

C₅×D₄

yes

—

132

C₂×C₃⋊C₈

—

133

ΓL(1,𝔽₂₅)

—

134

C₂³×C₅

—

135

C₂³×C₅

—

136

C₅×Q₈

—

137

C₅×D₄

—

138

C₅×D₄

—

139

C₅×D₄

—

140

C₅×D₄

—

141

C₂×C₄×C₅

—

142

C₂×C₄×C₅

—

143

C₂×C₄×C₅

—

144

C₂×C₄×C₅

—

145

C₂×C₄×C₅

—

146

C₂×C₄×C₅

—

147

C₂×C₄×C₅

—

148

C₂×C₄×C₅

C₂×C₄×D₃

yes

characteristic

149

C₂×C₄×C₅

D₃×D₄

yes

—

150

C₅×C₈

—

151

C₅×C₈

—

152

C₂×#41

—

153

C₂×M₁₆

—

154

C₄⋊Q₈

—

155

#127

C₂×C₅×D₃

yes

characteristic

156

#124

—

157

#121

—

158

C₄×D₄

—

159

C₂×C₄²

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

C₂×C₅×D₃

yes

—

163

C₂×C₃×C₅

—

164

C₂×C₃×C₅

C₂×#100

yes

characteristic

165

C₂×C₃×C₅

#417

yes

—

166

C₅×D₃

—

167

C₂³×C₃

—

168

C₂²×D₃

C₅×C₂²⋊C₄

yes

characteristic

169

C₃×D₄

—

170

C₃×D₄

—

171

C₃×D₄

—

172

C₂×C₃×C₄

C₂²×C₄×C₅

yes

characteristic

173

C₂×C₃×C₄

C₂×C₅×D₄

yes

—

174

#67

—

175

C₂×Dic₃

—

176

C₂×Dic₃

—

177

C₂×Dic₃

C₅×C₂²⋊C₄

yes

—

178

C₂×Dic₃

C₅×C₂²⋊C₄

yes

characteristic

179

C₄×D₃

—

180

C₄×D₃

—

181

C₄×D₃

—

182

Dic₆

—

183

C₃×C₈

—

184

C₃⋊C₈

—

185

C₂²×C₅

—

186

C₂²×C₅

—

187

C₂²×C₅

—

188

C₂²×C₅

—

189

C₂²×C₅

D₃×C₂²⋊C₄

yes

characteristic

190

C₄×C₅

—

191

C₄×C₅

—

192

C₄×C₅

—

193

C₄×C₅

—

194

C₄×C₅

#911

yes

—

195

C₄×C₅

#915

yes

—

196

#41

—

197

C₂×Q₈

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

C₄×C₅×D₃

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×C₅×D₃

yes

characteristic

212

C₃×C₅

#1560

yes

characteristic, complemented, Hall

213

C₂²×C₃

—

214

C₂²×C₃

—

215

C₂²×C₃

C₂×C₅×C₂²⋊C₄

yes

characteristic

216

C₂×D₃

—

217

C₂×D₃

—

218

C₃×C₄

—

219

C₃×C₄

C₅×AGL(1,ℤ/8)

yes

—

220

C₃×C₄

C₅×#137

yes

—

221

Dic₃

—

222

Dic₃

—

223

Dic₃

C₅×#100

yes

—

224

C₂×C₅

—

225

C₂×C₅

—

226

C₂×C₅

D₃×#100

yes

characteristic

227

C₂×C₅

#4771

yes

—

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×C₄×C₅×D₃

yes

characteristic

243

C₂×C₄

C₅×D₃×D₄

yes

—

244

C₈

—

245

C₈

—

246

C₂×C₃

—

247

C₂×C₃

C₂×C₅×#100

yes

characteristic

248

C₂×C₃

C₅×#417

yes

—

249

D₃

—

250

C₅

#68389

yes

characteristic, direct product factor, Sylow

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

C₅×D₃×C₂²⋊C₄

yes

characteristic

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

C₅×#911

yes

—

261

C₄

C₅×#915

yes

—

262

C₃

C₅×#1560

yes

characteristic, complemented, Sylow

263

C₂

—

264

C₂

—

265

C₂

C₅×D₃×#100

yes

characteristic

266

C₂

C₅×#4771

yes

—

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#331	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#5716	C₂
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#331	D₃
hypocenter	C₃	C₅×#1560
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#331

subgroup

G/H

center

C₂²×C₅

D₃×C₂²⋊C₄

commutator

C₂×C₃×C₄

C₂²×C₄×C₅

Frattini

C₄²

C₂²×C₅×D₃

Fitting

C₃×C₅×#331

C₂

socle

C₂²×C₃×C₅

C₂×C₂²⋊C₄

prime radical

C₅×#5716

C₂

cosocle

C₃×C₄²

C₂³×C₅

D₃

C₃

G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃

UCS

C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#331

N	H ≅ G/N	type
2. C₅×#4837	C₂	semidirect
3. C₃×C₅×#331	C₂	semidirect
4. C₅×#4544	C₂	semidirect
5. C₅×#4481	C₂	semidirect
18. #68389	C₅	direct (N × H)
23. C₅×#331	D₃	semidirect
41. #4837	C₂×C₅	semidirect
42. C₃×#331	C₂×C₅	semidirect
43. #4544	C₂×C₅	semidirect
44. #4481	C₂×C₅	semidirect
106. #331	C₅×D₃	semidirect
212. C₃×C₅	#1560	semidirect
250. C₅	#68389	direct (N × H)
262. C₃	C₅×#1560	semidirect

H ≅ G/N

type

2. C₅×#4837

C₂

semidirect

3. C₃×C₅×#331

C₂

semidirect

4. C₅×#4544

C₂

semidirect

5. C₅×#4481

C₂

semidirect

18. #68389

C₅

direct (N × H)

23. C₅×#331

D₃

semidirect

41. #4837

C₂×C₅

semidirect

42. C₃×#331

C₂×C₅

semidirect

43. #4544

C₂×C₅

semidirect

44. #4481

C₂×C₅

semidirect

106. #331

C₅×D₃

semidirect

212. C₃×C₅

#1560

semidirect

250. C₅

#68389

direct (N × H)

262. C₃

C₅×#1560

semidirect

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

subgroup	index
C₅×#5716	2
C₅×#4837	2
C₃×C₅×#331	2
C₅×#4544	2
C₅×#4481	2
C₅×#1560	3
#68389	5

subgroup

index

C₃×C₅×#331

Subgroups — C₅×#68389 #14285410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#68389 #14285410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68389 #14285410