Group #18069679 — subgroups

Subgroups — #18069679

Order 4864.

302 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 91 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	C₂×#11926326	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1811	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	—	2	1	no	—
5	C₂×#10597269	—	2	1	no	—
6	#11926326	—	2	1	no	—
7	#11926326	C₄	1	2	yes	—
8	C₁₉⋊#338	—	2	1	no	—
9	C₁₉⋊#338	C₄	1	2	yes	—
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#108	C₄	1	1	yes	characteristic
12	C₂×C₁₉×#108	C₄	1	1	yes	characteristic
13	C₁₉×#407	—	2	1	no	—
14	C₁₉×#341	—	2	1	no	—
15	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂×M₁₆×C₁₉	—	2	1	no	—
17	C₂×M₁₆×C₁₉	—	2	1	no	—
18	C₂×M₁₆×C₁₉	—	4	1	no	—
19	C₂×M₁₆×C₁₉	—	4	1	no	—
20	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
23	C₂×M₁₆×C₁₉	Q₈	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂×#64520	—	2	2	no	—
27	C₂×#64520	—	2	2	no	—
28	C₂×#64520	—	4	1	no	—
29	C₂×#64520	—	4	1	no	—
30	C₂×#64520	—	4	1	no	—
31	C₂×#64520	—	4	1	no	—
32	C₂²×C₁₉⋊C₈	—	2	2	no	—
33	C₁₉×#108	—	4	1	no	—
34	C₁₉×#108	—	4	1	no	—
35	C₁₉×C₂²⋊C₈	—	4	1	no	—
36	C₁₉×C₂²⋊C₈	—	4	1	no	—
37	#10597269	—	2	2	no	—
38	#10597269	—	4	1	no	—
39	C₂×C₁₉⋊C₁₆	—	4	1	no	—
40	C₂⁴×C₁₉	Q₁₆	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	—	2	1	no	—
42	C₂²×C₄×C₁₉	—	2	1	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
51	M₁₆×C₁₉	—	4	1	no	—
52	M₁₆×C₁₉	—	4	1	no	—
53	M₁₆×C₁₉	—	4	1	no	—
54	M₁₆×C₁₉	—	4	1	no	—
55	M₁₆×C₁₉	—	4	1	no	—
56	M₁₆×C₁₉	—	4	1	no	—
57	M₁₆×C₁₉	—	4	1	no	—
58	M₁₆×C₁₉	—	4	1	no	—
59	C₂×C₈×C₁₉	—	2	1	no	—
60	C₂×C₈×C₁₉	—	2	1	no	—
61	C₂×C₈×C₁₉	—	2	1	no	—
62	C₂×C₈×C₁₉	—	2	1	no	—
63	C₂×C₈×C₁₉	—	4	1	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
69	#64520	—	4	2	no	—
70	#64520	—	4	2	no	—
71	#64520	—	4	2	no	—
72	#64520	—	4	2	no	—
73	C₂×C₁₉⋊C₈	—	2	4	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	C₁₉⋊C₁₆	—	4	2	no	—
77	#7257	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	—	2	1	no	—
79	C₂³×C₁₉	—	2	1	no	—
80	C₂³×C₁₉	—	8	1	no	—
81	C₂³×C₁₉	#103	1	1	yes	characteristic
82	C₂³×C₁₉	#103	1	1	yes	characteristic
83	C₂³×C₁₉	#107	1	1	yes	characteristic
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
102	C₈×C₁₉	—	2	1	no	—
103	C₈×C₁₉	—	2	1	no	—
104	C₈×C₁₉	—	2	1	no	—
105	C₈×C₁₉	—	2	1	no	—
106	C₈×C₁₉	—	8	1	no	—
107	C₈×C₁₉	—	8	1	no	—
108	C₁₉⋊C₈	—	4	4	no	—
109	C₂×#349	—	19	1	no	—
110	#1811	D₁₉	1	1	yes	characteristic
111	C₂×#338	—	19	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	—	2	1	no	—
114	C₂²×C₁₉	—	4	1	no	—
115	C₂²×C₁₉	—	4	1	no	—
116	C₂²×C₁₉	—	4	1	no	—
117	C₂²×C₁₉	—	4	2	no	—
118	C₂²×C₁₉	—	8	1	no	—
119	C₂²×C₁₉	#328	1	1	yes	characteristic
120	C₂²×C₁₉	#328	1	1	yes	characteristic
121	C₂²×C₁₉	#340	1	1	yes	characteristic
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	#327	1	1	yes	characteristic
125	C₄×C₁₉	#327	1	1	yes	characteristic
126	C₄×C₁₉	#339	1	1	yes	characteristic
127	C₄×C₁₉	#342	1	1	yes	characteristic
128	C₂²×M₁₆	—	38	1	no	—
129	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
130	C₂×M₃₂	—	38	1	no	—
131	C₂×#108	Dic₁₉	1	1	yes	characteristic
132	C₂×#108	Dic₁₉	1	1	yes	characteristic
133	#407	—	2	1	no	—
134	#349	—	19	2	no	—
135	#349	—	38	1	no	—
136	#341	—	2	1	no	—
137	#338	—	19	2	no	—
138	#338	—	38	1	no	—
139	C₂×C₁₉	—	2	1	no	—
140	C₂×C₁₉	—	2	1	no	—
141	C₂×C₁₉	—	2	1	no	—
142	C₂×C₁₉	—	4	1	no	—
143	C₂×C₁₉	—	4	1	no	—
144	C₂×C₁₉	#1294	1	1	yes	characteristic
145	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
146	C₂×M₁₆	—	2	1	no	—
147	C₂×M₁₆	—	2	1	no	—
148	C₂×M₁₆	—	4	1	no	—
149	C₂×M₁₆	—	4	1	no	—
150	C₂×M₁₆	—	38	2	no	—
151	C₂×M₁₆	—	38	2	no	—
152	C₂×M₁₆	—	76	1	no	—
153	C₂×M₁₆	—	76	1	no	—
154	C₂×M₁₆	—	76	1	no	—
155	C₂×M₁₆	—	76	1	no	—
156	C₂×M₁₆	Dic₃₈	1	1	yes	characteristic
157	C₂×M₁₆	C₄×D₁₉	1	1	yes	characteristic
158	C₂×M₁₆	C₄×D₁₉	1	1	yes	characteristic
159	C₂×M₁₆	D₇₆	1	1	yes	characteristic
160	C₂²×C₈	—	38	2	no	—
161	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
162	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
163	M₃₂	—	38	2	no	—
164	M₃₂	—	76	1	no	—
165	C₂×C₁₆	—	76	1	no	—
166	#108	—	4	1	no	—
167	#108	—	4	1	no	—
168	C₂²⋊C₈	—	4	1	no	—
169	C₂²⋊C₈	—	4	1	no	—
170	C₁₉	#7257	1	1	yes	characteristic, complemented, Sylow
171	C₂⁴	#64528	1	1	yes	characteristic
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
177	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
178	C₂²×C₄	#64525	1	1	yes	characteristic
179	C₂²×C₄	#64526	1	1	yes	characteristic
180	C₂²×C₄	#64527	1	1	yes	characteristic
181	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
182	M₁₆	—	4	1	no	—
183	M₁₆	—	4	1	no	—
184	M₁₆	—	4	1	no	—
185	M₁₆	—	4	1	no	—
186	M₁₆	—	4	1	no	—
187	M₁₆	—	4	1	no	—
188	M₁₆	—	4	1	no	—
189	M₁₆	—	4	1	no	—
190	M₁₆	—	76	2	no	—
191	M₁₆	—	76	2	no	—
192	M₁₆	—	76	2	no	—
193	M₁₆	—	76	2	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	—	2	1	no	—
197	C₂×C₈	—	2	1	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	38	4	no	—
201	C₂×C₈	—	76	2	no	—
202	C₂×C₈	—	76	2	no	—
203	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
204	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
205	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
206	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
207	C₁₆	—	76	2	no	—
208	C₂³	—	2	1	no	—
209	C₂³	—	2	1	no	—
210	C₂³	—	8	1	no	—
211	C₂³	#10597264	1	1	yes	characteristic
212	C₂³	#10597267	1	1	yes	characteristic
213	C₂³	#10597292	1	1	yes	characteristic
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	#10597265	1	1	yes	characteristic
225	C₂×C₄	#10597266	1	1	yes	characteristic
226	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
227	C₂×C₄	#10597289	1	1	yes	characteristic
228	C₂×C₄	#10597291	1	1	yes	characteristic
229	C₂×C₄	#10597291	1	1	yes	characteristic
230	C₂×C₄	#10597294	1	1	yes	characteristic
231	C₂×C₄	#10597294	1	1	yes	characteristic
232	C₈	—	2	1	no	—
233	C₈	—	2	1	no	—
234	C₈	—	2	1	no	—
235	C₈	—	2	1	no	—
236	C₈	—	8	1	no	—
237	C₈	—	8	1	no	—
238	C₈	—	76	4	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	—	4	1	no	—
242	C₂²	—	4	1	no	—
243	C₂²	—	4	1	no	—
244	C₂²	—	4	2	no	—
245	C₂²	—	8	1	no	—
246	C₂²	#11926281	1	1	yes	characteristic
247	C₂²	#11926281	1	1	yes	characteristic
248	C₂²	#11926306	1	1	yes	characteristic
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	#11926278	1	1	yes	characteristic
252	C₄	#11926278	1	1	yes	characteristic
253	C₄	#11926303	1	1	yes	characteristic
254	C₄	#11926311	1	1	yes	characteristic
255	C₂	—	2	1	no	—
256	C₂	—	2	1	no	—
257	C₂	—	2	1	no	—
258	C₂	—	4	1	no	—
259	C₂	—	4	1	no	—
260	C₂	#14561513	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926326

C₂

yes

maximal, characteristic

C₂×C₁₉⋊#338

C₂

yes

maximal, characteristic

C₁₉×#1811

C₂

yes

maximal, characteristic

C₂²×#64520

—

C₂×#10597269

—

#11926326

—

#11926326

C₄

yes

—

C₁₉⋊#338

—

C₁₉⋊#338

C₄

yes

—

C₂²×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#108

C₄

yes

characteristic

C₂×C₁₉×#108

C₄

yes

characteristic

C₁₉×#407

—

C₁₉×#341

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

—

—

—

—

—

—

C₂²×C₁₉⋊C₈

—

C₁₉×#108

—

C₁₉×#108

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

#10597269

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₂⁴×C₁₉

Q₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

#7257

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂³×C₁₉

yes

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

100

C₂×C₄×C₁₉

#104

yes

characteristic

101

C₂×C₄×C₁₉

#106

yes

characteristic

102

C₈×C₁₉

—

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₈×C₁₉

—

106

C₈×C₁₉

—

107

C₈×C₁₉

—

108

C₁₉⋊C₈

—

109

C₂×#349

—

110

#1811

D₁₉

yes

characteristic

111

C₂×#338

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

#328

yes

characteristic

120

C₂²×C₁₉

#328

yes

characteristic

121

C₂²×C₁₉

#340

yes

characteristic

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

#327

yes

characteristic

125

C₄×C₁₉

#327

yes

characteristic

126

C₄×C₁₉

#339

yes

characteristic

127

C₄×C₁₉

#342

yes

characteristic

128

C₂²×M₁₆

—

129

C₂²×M₁₆

C₂×D₁₉

yes

characteristic

130

C₂×M₃₂

—

131

C₂×#108

Dic₁₉

yes

characteristic

132

C₂×#108

Dic₁₉

yes

characteristic

133

#407

—

134

#349

—

135

#349

—

136

#341

—

137

#338

—

138

#338

—

139

C₂×C₁₉

—

140

C₂×C₁₉

—

141

C₂×C₁₉

—

142

C₂×C₁₉

—

143

C₂×C₁₉

—

144

C₂×C₁₉

#1294

yes

characteristic

145

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

146

C₂×M₁₆

—

147

C₂×M₁₆

—

148

C₂×M₁₆

—

149

C₂×M₁₆

—

150

C₂×M₁₆

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

154

C₂×M₁₆

—

155

C₂×M₁₆

—

156

C₂×M₁₆

Dic₃₈

yes

characteristic

157

C₂×M₁₆

C₄×D₁₉

yes

characteristic

158

C₂×M₁₆

C₄×D₁₉

yes

characteristic

159

C₂×M₁₆

D₇₆

yes

characteristic

160

C₂²×C₈

—

161

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

162

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

163

M₃₂

—

164

M₃₂

—

165

C₂×C₁₆

—

166

#108

—

167

#108

—

168

C₂²⋊C₈

—

169

C₂²⋊C₈

—

170

C₁₉

#7257

yes

characteristic, complemented, Sylow

171

C₂⁴

#64528

yes

characteristic

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

177

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

178

C₂²×C₄

#64525

yes

characteristic

179

C₂²×C₄

#64526

yes

characteristic

180

C₂²×C₄

#64527

yes

characteristic

181

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

182

M₁₆

—

183

M₁₆

—

184

M₁₆

—

185

M₁₆

—

186

M₁₆

—

187

M₁₆

—

188

M₁₆

—

189

M₁₆

—

190

M₁₆

—

191

M₁₆

—

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

C₄×Dic₁₉

yes

characteristic

204

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

205

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

206

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

207

C₁₆

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

#10597264

yes

characteristic

212

C₂³

#10597267

yes

characteristic

213

C₂³

#10597292

yes

characteristic

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

#10597265

yes

characteristic

225

C₂×C₄

#10597266

yes

characteristic

226

C₂×C₄

C₁₉⋊#95

yes

characteristic

227

C₂×C₄

#10597289

yes

characteristic

228

C₂×C₄

#10597291

yes

characteristic

229

C₂×C₄

#10597291

yes

characteristic

230

C₂×C₄

#10597294

yes

characteristic

231

C₂×C₄

#10597294

yes

characteristic

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

236

C₈

—

237

C₈

—

238

C₈

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

#11926281

yes

characteristic

247

C₂²

#11926281

yes

characteristic

248

C₂²

#11926306

yes

characteristic

249

C₄

—

250

C₄

—

251

C₄

#11926278

yes

characteristic

252

C₄

#11926278

yes

characteristic

253

C₄

#11926303

yes

characteristic

254

C₄

#11926311

yes

characteristic

255

C₂

—

256

C₂

—

257

C₂

—

258

C₂

—

259

C₂

—

260

C₂

#14561513

yes

characteristic

	subgroup	G/H
center	C₄	#11926278
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂²×M₁₆	C₂×D₁₉
Fitting	C₁₉×#1811	C₂
socle	C₂×C₁₉	#1294
prime radical	C₂⁴×C₁₉	Q₁₆
cosocle	C₂²×M₁₆×C₁₉	C₂²
hypercenter	#1811	D₁₉
hypocenter	C₁₉	#7257
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ #1811

subgroup

G/H

center

C₄

#11926278

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₂²×M₁₆

C₂×D₁₉

Fitting

C₁₉×#1811

C₂

socle

C₂×C₁₉

#1294

prime radical

C₂⁴×C₁₉

Q₁₆

cosocle

C₂²×M₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ #1811

N	H ≅ G/N	type
170. C₁₉	#7257	semidirect

H ≅ G/N

type

170. C₁₉

#7257

semidirect

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

subgroup	index
C₂×#11926326	2
C₂×C₁₉⋊#338	2
C₁₉×#1811	2
#7257	19

subgroup

index

C₂×#11926326

C₂×C₁₉⋊#338

C₁₉×#1811

#7257

Subgroups — #18069679

Conjugacy classes of subgroups

Complements

Maximal subgroups