Group #18076413 — subgroups

Subgroups — #18076413

Order 4864.

454 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14572676	C₂	1	1	yes	maximal, characteristic
2	#14564430	C₂	1	1	yes	maximal, characteristic
3	#14562387	C₂	1	2	yes	maximal, complemented
4	#14561473	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic
6	#11926622	—	2	2	no	—
7	#11926622	—	2	2	no	—
8	#11926597	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
10	#11926508	—	2	2	no	—
11	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926297	—	2	2	no	—
14	#11926295	—	2	2	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#100	C₄	1	2	yes	—
17	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#343	C₄	1	1	yes	characteristic
19	C₁₉×#343	C₄	1	1	yes	characteristic
20	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	D₄	1	2	yes	—
22	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
24	C₄×D₄×C₁₉	—	2	2	no	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×#64520	—	2	2	no	—
30	C₂×#64520	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	—	2	1	no	—
32	C₂²×C₁₉⋊C₈	—	2	1	no	—
33	C₁₉×#100	—	2	4	no	—
34	C₁₉×#97	—	2	2	no	—
35	C₄×C₈×C₁₉	—	2	2	no	—
36	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
37	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
41	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
45	C₂×D₄×C₁₉	—	2	2	no	—
46	C₂×D₄×C₁₉	—	2	2	no	—
47	C₂×D₄×C₁₉	—	2	1	no	—
48	C₂×D₄×C₁₉	—	2	1	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
57	M₁₆×C₁₉	—	2	2	no	—
58	M₁₆×C₁₉	—	2	2	no	—
59	M₁₆×C₁₉	—	2	2	no	—
60	M₁₆×C₁₉	M₁₆	1	4	yes	complemented
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂²⋊C₄×C₁₉	—	2	4	no	—
65	C₄²×C₁₉	C₂×D₄	1	2	yes	—
66	C₄²×C₁₉	#41	1	2	yes	—
67	#64520	—	8	2	no	—
68	#64520	—	8	2	no	—
69	C₂×C₁₉⋊C₈	—	2	2	no	—
70	C₂×C₁₉⋊C₈	—	2	2	no	—
71	C₂×C₁₉⋊C₈	—	2	2	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	C₂×C₁₉⋊C₈	—	4	1	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	1	no	—
76	#8837	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	—	2	2	no	—
78	C₂³×C₁₉	—	2	2	no	—
79	C₂³×C₁₉	—	2	2	no	—
80	C₂³×C₁₉	—	4	2	no	—
81	C₂³×C₁₉	—	4	2	no	—
82	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
83	D₄×C₁₉	—	4	2	no	—
84	D₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	8	2	no	—
93	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
94	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
96	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
98	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
100	C₈×C₁₉	—	2	4	no	—
101	C₈×C₁₉	—	4	2	no	—
102	C₁₉⋊C₈	—	4	2	no	—
103	C₁₉⋊C₈	—	4	2	no	—
104	C₁₉⋊C₈	—	4	2	no	—
105	C₁₉⋊C₈	—	8	1	no	—
106	#2975	—	19	1	no	—
107	#1954	—	19	1	no	—
108	C₄×#100	D₁₉	1	1	yes	characteristic
109	#1565	—	19	2	no	—
110	#1278	—	19	2	no	—
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	—	4	4	no	—
114	C₂²×C₁₉	—	4	2	no	—
115	C₂²×C₁₉	—	4	2	no	—
116	C₂²×C₁₉	—	4	2	no	—
117	C₂²×C₁₉	—	8	2	no	—
118	C₂²×C₁₉	#385	1	1	yes	characteristic
119	C₂²×C₁₉	#423	1	1	yes	characteristic
120	C₂²×C₁₉	#424	1	1	yes	characteristic
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	—	4	2	no	—
124	C₄×C₁₉	#435	1	2	yes	—
125	C₄×C₁₉	#436	1	2	yes	—
126	C₄×C₁₉	#453	1	1	yes	characteristic
127	C₄×C₁₉	#455	1	1	yes	characteristic
128	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
129	#436	—	38	2	no	—
130	#436	—	38	2	no	—
131	#431	—	19	2	no	—
132	C₂×C₄⋊C₈	—	19	1	no	—
133	C₂×#100	Dic₁₉	1	2	yes	—
134	#407	—	38	2	no	—
135	C₂×C₂²⋊C₈	—	38	2	no	—
136	C₄×M₁₆	C₂×D₁₉	1	2	yes	—
137	C₂×C₄×C₈	—	19	1	no	—
138	#343	Dic₁₉	1	1	yes	characteristic
139	#343	Dic₁₉	1	1	yes	characteristic
140	#335	—	38	2	no	—
141	#334	—	38	2	no	—
142	C₂×C₁₉	—	2	1	no	—
143	C₂×C₁₉	—	2	1	no	—
144	C₂×C₁₉	—	8	2	no	—
145	C₂×C₁₉	#1851	1	1	yes	characteristic
146	C₂×C₁₉	#1856	1	1	yes	characteristic
147	C₂×C₁₉	#1858	1	1	yes	characteristic
148	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
149	C₂³×C₄	D₇₆	1	2	yes	—
150	C₂×M₁₆	—	38	2	no	—
151	C₂×M₁₆	—	38	2	no	—
152	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
153	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
154	C₂²×C₈	—	38	1	no	—
155	C₂²×C₈	—	38	1	no	—
156	C₄×D₄	—	2	2	no	—
157	C₄×D₄	—	2	2	no	—
158	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
159	C₂×C₂²⋊C₄	Dic₃₈	1	2	yes	—
160	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
161	C₄⋊C₈	—	19	2	no	—
162	C₄⋊C₈	—	19	2	no	—
163	C₄⋊C₈	—	38	2	no	—
164	#100	—	2	4	no	—
165	C₂²⋊C₈	—	38	4	no	—
166	C₂²⋊C₈	—	38	2	no	—
167	C₂²⋊C₈	—	76	4	no	—
168	#97	—	2	2	no	—
169	C₄×C₈	—	2	2	no	—
170	C₄×C₈	—	38	2	no	—
171	C₄×C₈	—	38	2	no	—
172	C₁₉	#8837	1	1	yes	characteristic, complemented, Sylow
173	C₂⁴	C₄⋊Dic₁₉	1	2	yes	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	1	no	—
176	C₂×D₄	—	2	1	no	—
177	C₂×D₄	—	2	2	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
183	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
184	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
185	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	2	no	—
188	M₁₆	—	2	2	no	—
189	M₁₆	—	152	2	no	—
190	M₁₆	—	152	2	no	—
191	M₁₆	#64520	1	4	yes	complemented
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	38	2	no	—
195	C₂×C₈	—	38	2	no	—
196	C₂×C₈	—	38	2	no	—
197	C₂×C₈	—	76	1	no	—
198	C₂×C₈	—	76	1	no	—
199	C₂×C₈	—	76	2	no	—
200	C₂×C₈	—	76	1	no	—
201	C₄⋊C₄	—	2	2	no	—
202	C₂²⋊C₄	—	2	4	no	—
203	C₄²	D₄×D₁₉	1	2	yes	—
204	C₄²	#64543	1	2	yes	—
205	C₂³	—	2	2	no	—
206	C₂³	—	2	2	no	—
207	C₂³	—	2	2	no	—
208	C₂³	—	4	2	no	—
209	C₂³	—	4	2	no	—
210	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
211	D₄	—	4	2	no	—
212	D₄	—	4	2	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	1	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	#10597324	1	2	yes	—
222	C₂×C₄	#10597328	1	1	yes	characteristic
223	C₂×C₄	#10597332	1	1	yes	characteristic
224	C₂×C₄	C₂×#64520	1	2	yes	—
225	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
226	C₂×C₄	#10597394	1	1	yes	characteristic
227	C₂×C₄	#10597394	1	1	yes	characteristic
228	C₈	—	2	4	no	—
229	C₈	—	4	2	no	—
230	C₈	—	76	2	no	—
231	C₈	—	76	2	no	—
232	C₈	—	76	2	no	—
233	C₈	—	152	1	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	4	4	no	—
237	C₂²	—	4	2	no	—
238	C₂²	—	4	2	no	—
239	C₂²	—	4	2	no	—
240	C₂²	—	8	2	no	—
241	C₂²	#11926419	1	1	yes	characteristic
242	C₂²	#11926568	1	1	yes	characteristic
243	C₂²	#11926571	1	1	yes	characteristic
244	C₄	—	2	1	no	—
245	C₄	—	2	2	no	—
246	C₄	—	4	2	no	—
247	C₄	#11926616	1	2	yes	—
248	C₄	#11926622	1	2	yes	—
249	C₄	#11926714	1	1	yes	characteristic
250	C₄	#11926724	1	1	yes	characteristic
251	C₂	—	2	1	no	—
252	C₂	—	2	1	no	—
253	C₂	—	8	2	no	—
254	C₂	#14563820	1	1	yes	characteristic
255	C₂	#14563847	1	1	yes	characteristic
256	C₂	#14563857	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572676

C₂

yes

maximal, characteristic

#14564430

C₂

yes

maximal, characteristic

#14562387

C₂

yes

maximal, complemented

#14561473

C₂

yes

maximal, complemented

C₄×C₁₉×#100

C₂

yes

maximal, characteristic

#11926622

—

#11926622

—

#11926597

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

#11926508

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926297

—

#11926295

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#100

C₄

yes

—

C₄×M₁₆×C₁₉

C₂²

yes

—

C₁₉×#343

C₄

yes

characteristic

C₁₉×#343

C₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×#100

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₄⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

M₁₆

yes

complemented

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8837

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

100

C₈×C₁₉

—

101

C₈×C₁₉

—

102

C₁₉⋊C₈

—

103

C₁₉⋊C₈

—

104

C₁₉⋊C₈

—

105

C₁₉⋊C₈

—

106

#2975

—

107

#1954

—

108

C₄×#100

D₁₉

yes

characteristic

109

#1565

—

110

#1278

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

#385

yes

characteristic

119

C₂²×C₁₉

#423

yes

characteristic

120

C₂²×C₁₉

#424

yes

characteristic

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

#435

yes

—

125

C₄×C₁₉

#436

yes

—

126

C₄×C₁₉

#453

yes

characteristic

127

C₄×C₁₉

#455

yes

characteristic

128

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

129

#436

—

130

#436

—

131

#431

—

132

C₂×C₄⋊C₈

—

133

C₂×#100

Dic₁₉

yes

—

134

#407

—

135

C₂×C₂²⋊C₈

—

136

C₄×M₁₆

C₂×D₁₉

yes

—

137

C₂×C₄×C₈

—

138

#343

Dic₁₉

yes

characteristic

139

#343

Dic₁₉

yes

characteristic

140

#335

—

141

#334

—

142

C₂×C₁₉

—

143

C₂×C₁₉

—

144

C₂×C₁₉

—

145

C₂×C₁₉

#1851

yes

characteristic

146

C₂×C₁₉

#1856

yes

characteristic

147

C₂×C₁₉

#1858

yes

characteristic

148

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

149

C₂³×C₄

D₇₆

yes

—

150

C₂×M₁₆

—

151

C₂×M₁₆

—

152

C₂×M₁₆

C₂×Dic₁₉

yes

—

153

C₂×M₁₆

C₂×Dic₁₉

yes

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₄×D₄

—

157

C₄×D₄

—

158

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

159

C₂×C₂²⋊C₄

Dic₃₈

yes

—

160

C₂×C₄²

C₂²×D₁₉

yes

characteristic

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

#100

—

165

C₂²⋊C₈

—

166

C₂²⋊C₈

—

167

C₂²⋊C₈

—

168

#97

—

169

C₄×C₈

—

170

C₄×C₈

—

171

C₄×C₈

—

172

C₁₉

#8837

yes

characteristic, complemented, Sylow

173

C₂⁴

C₄⋊Dic₁₉

yes

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

C₄⋊Dic₁₉

yes

—

183

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

184

C₂²×C₄

C₂×D₇₆

yes

characteristic

185

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

186

M₁₆

—

187

M₁₆

—

188

M₁₆

—

189

M₁₆

—

152

—

190

M₁₆

—

152

—

191

M₁₆

#64520

yes

complemented

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₄⋊C₄

—

202

C₂²⋊C₄

—

203

C₄²

D₄×D₁₉

yes

—

204

C₄²

#64543

yes

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

211

D₄

—

212

D₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

#10597324

yes

—

222

C₂×C₄

#10597328

yes

characteristic

223

C₂×C₄

#10597332

yes

characteristic

224

C₂×C₄

C₂×#64520

yes

—

225

C₂×C₄

D₄×Dic₁₉

yes

—

226

C₂×C₄

#10597394

yes

characteristic

227

C₂×C₄

#10597394

yes

characteristic

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

232

C₈

—

233

C₈

—

152

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

#11926419

yes

characteristic

242

C₂²

#11926568

yes

characteristic

243

C₂²

#11926571

yes

characteristic

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

#11926616

yes

—

248

C₄

#11926622

yes

—

249

C₄

#11926714

yes

characteristic

250

C₄

#11926724

yes

characteristic

251

C₂

—

252

C₂

—

253

C₂

—

254

C₂

#14563820

yes

characteristic

255

C₂

#14563847

yes

characteristic

256

C₂

#14563857

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#100	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#100	D₁₉
hypocenter	C₁₉	#8837
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

subgroup

G/H

center

C₂×C₄

#10597328

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#100

C₂

socle

C₂²×C₁₉

#385

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

N	H ≅ G/N	type
3. #14562387	C₂	semidirect
4. #14561473	C₂	semidirect
60. M₁₆×C₁₉	M₁₆	semidirect
172. C₁₉	#8837	semidirect
191. M₁₆	#64520	semidirect

H ≅ G/N

type

3. #14562387

C₂

semidirect

4. #14561473

C₂

semidirect

60. M₁₆×C₁₉

M₁₆

semidirect

172. C₁₉

#8837

semidirect

191. M₁₆

#64520

semidirect

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

subgroup	index
#14572676	2
#14564430	2
#14562387	2
#14561473	2
C₄×C₁₉×#100	2
#8837	19

subgroup

index

C₄×C₁₉×#100

Subgroups — #18076413

Conjugacy classes of subgroups

Complements

Maximal subgroups