Group #18075800 — subgroups

Subgroups — #18075800

Order 4864.

414 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14572348	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926295	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562313	C₂	1	2	yes	maximal
4	#14561509	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597347	—	2	1	no	—
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926623	—	2	1	no	—
9	#11926623	C₄	1	2	yes	—
10	C₈×D₇₆	—	2	1	no	—
11	C₈×D₇₆	C₄	1	2	yes	—
12	#11926568	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
14	#11926510	—	2	1	no	—
15	#11926295	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926291	—	2	2	no	—
18	#11926287	—	2	2	no	—
19	C₁₉×#423	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#341	—	2	1	no	—
22	C₁₉×#341	—	2	1	no	—
23	C₂×#64541	—	2	1	no	—
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	#10597376	—	2	1	no	—
29	#10597376	Q₈	1	2	yes	—
30	C₂×#64520	—	2	1	no	—
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	#10597347	—	4	4	no	—
33	C₂×#64515	—	2	2	no	—
34	C₂×C₈×D₁₉	—	2	2	no	—
35	#10597321	—	2	1	no	—
36	#10597320	D₄	1	1	yes	characteristic
37	C₄×D₇₆	—	2	1	no	—
38	C₄×D₇₆	C₂×C₄	1	2	yes	—
39	#10597315	D₄	1	1	yes	characteristic
40	C₁₉×C₄⋊C₈	—	2	2	no	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	(C₂×D₁₉)⋊C₈	—	2	2	no	—
47	(C₂×D₁₉)⋊C₈	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂×C₂²⋊D₁₉	—	2	2	no	—
56	#64541	—	4	2	no	—
57	#64541	—	4	2	no	—
58	C₂×D₇₆	—	2	1	no	—
59	C₂×D₇₆	—	2	1	no	—
60	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
61	C₂×C₄×D₁₉	—	2	2	no	—
62	C₂×Dic₃₈	—	2	1	no	—
63	M₁₆×C₁₉	—	4	2	no	—
64	M₁₆×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	2	2	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₉	#41	1	1	yes	characteristic
76	(C₂×D₁₉)⋊C₄	—	2	2	no	—
77	(C₂×D₁₉)⋊C₄	—	2	2	no	—
78	C₄⋊Dic₁₉	—	2	1	no	—
79	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
80	#64520	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	2	2	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	8	2	no	—
84	#64515	—	4	4	no	—
85	C₈×D₁₉	—	4	4	no	—
86	#8686	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂²×D₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#135	1	2	yes	—
98	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
99	C₂²⋊D₁₉	—	4	4	no	—
100	C₂×Dic₁₉	—	2	2	no	—
101	D₇₆	—	4	2	no	—
102	D₇₆	—	4	2	no	—
103	D₇₆	—	4	2	no	—
104	C₄×D₁₉	—	4	2	no	—
105	C₄×D₁₉	—	4	2	no	—
106	Dic₃₈	—	4	2	no	—
107	C₈×C₁₉	—	2	1	no	—
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	8	2	no	—
112	C₁₉⋊C₈	—	4	2	no	—
113	C₁₉⋊C₈	—	8	2	no	—
114	#2931	—	19	1	no	—
115	#1837	D₁₉	1	1	yes	characteristic, complemented
116	C₂×#334	—	19	1	no	—
117	#1547	—	19	2	no	—
118	#1292	—	19	2	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	#380	1	1	yes	characteristic
122	C₂²×C₁₉	#478	1	2	yes	—
123	C₂×D₁₉	—	4	2	no	—
124	C₂×D₁₉	—	4	2	no	—
125	C₂×D₁₉	—	4	2	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	#416	1	1	yes	characteristic
130	C₄×C₁₉	#418	1	1	yes	characteristic
131	C₄×C₁₉	#463	1	2	yes	—
132	C₄×C₁₉	#471	1	2	yes	—
133	Dic₁₉	—	4	2	no	—
134	C₂×#131	—	38	1	no	—
135	#532	—	19	1	no	—
136	#436	—	19	2	no	—
137	#436	—	38	1	no	—
138	C₈×D₄	—	19	2	no	—
139	C₈×D₄	—	38	1	no	—
140	#423	—	19	1	no	—
141	#423	C₂×D₁₉	1	2	yes	—
142	C₂×C₄⋊C₈	—	19	2	no	—
143	#408	—	38	1	no	—
144	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
145	#341	—	2	1	no	—
146	#341	—	2	1	no	—
147	#334	—	38	1	no	—
148	#334	—	38	1	no	—
149	#332	—	38	2	no	—
150	#331	—	38	2	no	—
151	C₂×C₁₉	—	2	2	no	—
152	C₂×C₁₉	#1804	1	1	yes	characteristic
153	C₂×C₁₉	#1813	1	1	yes	characteristic
154	C₂×C₁₉	#1815	1	1	yes	characteristic
155	D₁₉	—	8	2	no	—
156	C₂×#41	—	38	1	no	—
157	#131	—	76	4	no	—
158	C₂×M₁₆	—	2	2	no	—
159	C₂×M₁₆	—	38	1	no	—
160	C₂×M₁₆	—	38	2	no	—
161	C₂²×C₈	—	38	2	no	—
162	C₂²×C₈	—	38	2	no	—
163	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
164	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
165	C₄⋊Q₈	—	19	1	no	—
166	#127	—	19	1	no	—
167	#124	—	38	1	no	—
168	#121	—	19	2	no	—
169	#121	—	38	1	no	—
170	C₄×D₄	—	19	2	no	—
171	C₄×D₄	—	38	1	no	—
172	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	—	19	2	no	—
176	C₄⋊C₈	—	38	1	no	—
177	C₄⋊C₈	—	38	2	no	—
178	C₄⋊C₈	—	38	2	no	—
179	C₂²⋊C₈	—	38	2	no	—
180	C₂²⋊C₈	—	38	2	no	—
181	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
182	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
183	C₄×C₈	D₇₆	1	1	yes	characteristic
184	C₄×C₈	D₇₆	1	1	yes	characteristic
185	C₁₉	#8686	1	1	yes	characteristic, complemented, Sylow
186	#41	—	76	2	no	—
187	#41	—	76	2	no	—
188	C₂×Q₈	—	38	1	no	—
189	C₂×D₄	—	19	2	no	—
190	C₂×D₄	—	38	2	no	—
191	C₂×D₄	—	38	1	no	—
192	C₂×D₄	—	38	1	no	—
193	C₂²×C₄	—	38	2	no	—
194	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
195	C₂²×C₄	#64545	1	1	yes	characteristic
196	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
197	M₁₆	—	4	2	no	—
198	M₁₆	—	4	2	no	—
199	M₁₆	—	76	4	no	—
200	M₁₆	—	76	2	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	4	2	no	—
204	C₂×C₈	—	38	2	no	—
205	C₂×C₈	—	76	4	no	—
206	C₂×C₈	—	76	2	no	—
207	C₂×C₈	—	152	2	no	—
208	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
209	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
210	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
211	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
212	C₄⋊C₄	—	19	2	no	—
213	C₄⋊C₄	—	38	1	no	—
214	C₂²⋊C₄	—	38	2	no	—
215	C₂²⋊C₄	—	38	2	no	—
216	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
217	C₄²	C₂×D₇₆	1	1	yes	characteristic
218	C₄²	D₄×D₁₉	1	1	yes	characteristic
219	C₄²	#64543	1	1	yes	characteristic
220	C₂³	—	38	2	no	—
221	C₂³	#10597392	1	1	yes	characteristic
222	Q₈	—	76	2	no	—
223	D₄	—	76	2	no	—
224	D₄	—	76	4	no	—
225	D₄	—	76	2	no	—
226	D₄	—	76	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	38	2	no	—
230	C₂×C₄	—	76	2	no	—
231	C₂×C₄	—	76	2	no	—
232	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
233	C₂×C₄	#10597338	1	1	yes	characteristic
234	C₂×C₄	#10597341	1	1	yes	characteristic
235	C₂×C₄	#10597343	1	1	yes	characteristic
236	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
237	C₂×C₄	#10597384	1	1	yes	characteristic
238	C₂×C₄	#10597395	1	2	yes	—
239	C₂×C₄	#10597396	1	2	yes	—
240	C₈	—	2	1	no	—
241	C₈	—	2	1	no	—
242	C₈	—	2	1	no	—
243	C₈	—	2	1	no	—
244	C₈	—	8	2	no	—
245	C₈	—	76	2	no	—
246	C₈	—	152	2	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	76	2	no	—
250	C₂²	—	76	2	no	—
251	C₂²	—	76	2	no	—
252	C₂²	#11926401	1	1	yes	characteristic
253	C₂²	#11926841	1	2	yes	—
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	76	2	no	—
258	C₄	#11926538	1	1	yes	characteristic
259	C₄	#11926548	1	1	yes	characteristic
260	C₄	#11926756	1	2	yes	—
261	C₄	#11926808	1	2	yes	—
262	C₂	—	2	2	no	—
263	C₂	—	152	2	no	—
264	C₂	#14563642	1	1	yes	characteristic
265	C₂	#14563682	1	1	yes	characteristic
266	C₂	#14563691	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572348

C₂

yes

maximal, characteristic

C₂×#11926295

C₂

yes

maximal, characteristic, complemented

#14562313

C₂

yes

maximal

#14561509

C₂

yes

maximal, complemented

C₁₉×#1837

C₂

yes

maximal, characteristic, complemented

C₂×#10597347

—

#11927094

C₂²

yes

characteristic

#11926623

—

#11926623

C₄

yes

—

C₈×D₇₆

—

C₈×D₇₆

C₄

yes

—

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

—

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#341

—

C₁₉×#341

—

C₂×#64541

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

#10597376

Q₈

yes

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

#10597347

—

C₂×#64515

—

C₂×C₈×D₁₉

—

#10597321

—

#10597320

D₄

yes

characteristic

C₄×D₇₆

—

C₄×D₇₆

C₂×C₄

yes

—

#10597315

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

(C₂×D₁₉)⋊C₈

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₄⋊C₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#64515

—

C₈×D₁₉

—

#8686

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²⋊D₁₉

—

100

C₂×Dic₁₉

—

101

D₇₆

—

102

D₇₆

—

103

D₇₆

—

104

C₄×D₁₉

—

105

C₄×D₁₉

—

106

Dic₃₈

—

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₁₉⋊C₈

—

113

C₁₉⋊C₈

—

114

#2931

—

115

#1837

D₁₉

yes

characteristic, complemented

116

C₂×#334

—

117

#1547

—

118

#1292

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#380

yes

characteristic

122

C₂²×C₁₉

#478

yes

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

#416

yes

characteristic

130

C₄×C₁₉

#418

yes

characteristic

131

C₄×C₁₉

#463

yes

—

132

C₄×C₁₉

#471

yes

—

133

Dic₁₉

—

134

C₂×#131

—

135

#532

—

136

#436

—

137

#436

—

138

C₈×D₄

—

139

C₈×D₄

—

140

#423

—

141

#423

C₂×D₁₉

yes

—

142

C₂×C₄⋊C₈

—

143

#408

—

144

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

145

#341

—

146

#341

—

147

#334

—

148

#334

—

149

#332

—

150

#331

—

151

C₂×C₁₉

—

152

C₂×C₁₉

#1804

yes

characteristic

153

C₂×C₁₉

#1813

yes

characteristic

154

C₂×C₁₉

#1815

yes

characteristic

155

D₁₉

—

156

C₂×#41

—

157

#131

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂×M₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

—

163

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

164

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

165

C₄⋊Q₈

—

166

#127

—

167

#124

—

168

#121

—

169

#121

—

170

C₄×D₄

—

171

C₄×D₄

—

172

C₂×C₄²

C₂²×D₁₉

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₂²⋊C₈

—

180

C₂²⋊C₈

—

181

C₄×C₈

C₄×D₁₉

yes

characteristic

182

C₄×C₈

C₄×D₁₉

yes

characteristic

183

C₄×C₈

D₇₆

yes

characteristic

184

C₄×C₈

D₇₆

yes

characteristic

185

C₁₉

#8686

yes

characteristic, complemented, Sylow

186

#41

—

187

#41

—

188

C₂×Q₈

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂²×C₄

—

194

C₂²×C₄

Q₈×D₁₉

yes

characteristic

195

C₂²×C₄

#64545

yes

characteristic

196

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

197

M₁₆

—

198

M₁₆

—

199

M₁₆

—

200

M₁₆

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

152

—

208

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

209

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

210

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

211

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₂²⋊C₄

—

215

C₂²⋊C₄

—

216

C₄²

C₂×C₄×D₁₉

yes

characteristic

217

C₄²

C₂×D₇₆

yes

characteristic

218

C₄²

D₄×D₁₉

yes

characteristic

219

C₄²

#64543

yes

characteristic

220

C₂³

—

221

C₂³

#10597392

yes

characteristic

222

Q₈

—

223

D₄

—

224

D₄

—

225

D₄

—

226

D₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

233

C₂×C₄

#10597338

yes

characteristic

234

C₂×C₄

#10597341

yes

characteristic

235

C₂×C₄

#10597343

yes

characteristic

236

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

237

C₂×C₄

#10597384

yes

characteristic

238

C₂×C₄

#10597395

yes

—

239

C₂×C₄

#10597396

yes

—

240

C₈

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

—

246

C₈

—

152

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

#11926401

yes

characteristic

253

C₂²

#11926841

yes

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

#11926538

yes

characteristic

259

C₄

#11926548

yes

characteristic

260

C₄

#11926756

yes

—

261

C₄

#11926808

yes

—

262

C₂

—

263

C₂

—

152

—

264

C₂

#14563642

yes

characteristic

265

C₂

#14563682

yes

characteristic

266

C₂

#14563691

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1837	C₂
socle	C₂²×C₁₉	#380
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1837	D₁₉
hypocenter	C₁₉	#8686
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂²

#11926401

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1837

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
2. C₂×#11926295	C₂	semidirect
4. #14561509	C₂	semidirect
5. C₁₉×#1837	C₂	semidirect
115. #1837	D₁₉	semidirect
185. C₁₉	#8686	semidirect

H ≅ G/N

type

2. C₂×#11926295

C₂

semidirect

4. #14561509

C₂

semidirect

5. C₁₉×#1837

C₂

semidirect

115. #1837

D₁₉

semidirect

185. C₁₉

#8686

semidirect

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

subgroup	index
#14572348	2
C₂×#11926295	2
#14562313	2
#14561509	2
C₁₉×#1837	2
#8686	19

subgroup

index

C₁₉×#1837

Subgroups — #18075800

Conjugacy classes of subgroups

Complements

Maximal subgroups