Group #18087316 — subgroups

Subgroups — #18087316

Order 4864.

292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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	#14564615	C₂	1	1	yes	maximal, characteristic
2	#14563788	C₂	1	1	yes	maximal, characteristic
3	#14562293	C₂	1	1	yes	maximal, characteristic
4	#14562290	C₂	1	1	yes	maximal, characteristic
5	#14561530	C₂	1	1	yes	maximal, characteristic
6	#14561463	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1301	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₈	—	2	1	no	—
12	C₂×Dic₁₉⋊C₈	—	2	1	no	—
13	#11926390	C₂²	1	1	yes	characteristic
14	#11926305	—	2	1	no	—
15	#11926305	—	2	1	no	—
16	#11926292	—	2	1	no	—
17	#11926292	—	2	1	no	—
18	#11926291	—	2	1	no	—
19	#11926289	—	2	1	no	—
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₁₉×#423	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	#10597372	—	2	1	no	—
27	#10597370	—	2	1	no	—
28	#10597370	—	2	1	no	—
29	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
30	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₁₉⋊C₈	—	2	1	no	—
32	#10597316	—	2	1	no	—
33	#10597315	D₄	1	1	yes	characteristic
34	#10597315	D₄	1	1	yes	characteristic
35	C₄×Dic₃₈	—	2	1	no	—
36	C₄×Dic₃₈	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₁₉×C₄⋊C₈	—	2	1	no	—
39	C₁₉×C₄⋊C₈	—	2	1	no	—
40	C₁₉×C₄⋊C₈	—	2	1	no	—
41	C₁₉×C₄⋊C₈	—	2	1	no	—
42	C₁₉×C₂²⋊C₈	—	2	1	no	—
43	C₄×C₈×C₁₉	—	2	1	no	—
44	C₁₉⋊#95	—	2	1	no	—
45	C₁₉⋊#95	—	2	1	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
47	Dic₁₉⋊C₈	—	4	2	no	—
48	Dic₁₉⋊C₈	—	4	2	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
52	C₄×C₁₉⋊C₈	—	2	1	no	—
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
56	C₂²×Dic₁₉	—	2	1	no	—
57	C₂²×Dic₁₉	—	2	1	no	—
58	C₂×Dic₃₈	—	2	1	no	—
59	C₂×Dic₃₈	—	2	1	no	—
60	M₁₆×C₁₉	—	4	1	no	—
61	M₁₆×C₁₉	—	4	1	no	—
62	C₂×C₈×C₁₉	—	4	1	no	—
63	C₂×C₈×C₁₉	—	4	1	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₂×C₈×C₁₉	—	4	1	no	—
66	C₂×C₈×C₁₉	—	4	1	no	—
67	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	1	yes	characteristic
69	C₄²×C₁₉	#41	1	1	yes	characteristic
70	C₄²×C₁₉	#41	1	1	yes	characteristic
71	C₂²⋊Dic₁₉	—	4	1	no	—
72	C₄⋊Dic₁₉	—	2	1	no	—
73	C₄⋊Dic₁₉	—	2	1	no	—
74	C₄⋊Dic₁₉	—	2	1	no	—
75	C₄⋊Dic₁₉	—	2	1	no	—
76	Dic₁₉⋊C₄	—	4	1	no	—
77	Dic₁₉⋊C₄	—	4	1	no	—
78	C₄×Dic₁₉	—	2	1	no	—
79	C₄×Dic₁₉	—	2	1	no	—
80	C₄×Dic₁₉	—	4	1	no	—
81	C₄×Dic₁₉	SD₁₆	1	2	yes	—
82	C₄×Dic₁₉	Q₁₆	1	2	yes	—
83	C₂×C₁₉⋊C₈	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	4	1	no	—
85	C₂×C₁₉⋊C₈	—	4	1	no	—
86	C₂×C₁₉⋊C₈	—	4	1	no	—
87	#10628	—	19	1	no	maximal, Sylow
88	C₂³×C₁₉	#123	1	1	yes	characteristic
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
99	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
101	C₂×Dic₁₉	—	2	2	no	—
102	C₂×Dic₁₉	—	2	2	no	—
103	C₂×Dic₁₉	—	4	1	no	—
104	C₂×Dic₁₉	—	4	1	no	—
105	C₂×Dic₁₉	—	4	1	no	—
106	C₂×Dic₁₉	—	4	1	no	—
107	C₂×Dic₁₉	—	4	1	no	—
108	C₂×Dic₁₉	—	4	1	no	—
109	Dic₃₈	—	8	1	no	—
110	Dic₃₈	—	8	1	no	—
111	C₈×C₁₉	—	8	1	no	—
112	C₈×C₁₉	—	8	1	no	—
113	C₈×C₁₉	—	8	1	no	—
114	C₁₉⋊C₈	—	8	1	no	—
115	C₁₉⋊C₈	—	8	1	no	—
116	#1995	—	19	1	no	—
117	#1843	—	19	1	no	—
118	#1542	—	19	1	no	—
119	#1542	—	19	1	no	—
120	#1301	—	19	1	no	—
121	#1301	D₁₉	1	1	yes	characteristic
122	#1274	—	19	1	no	—
123	C₂²×C₁₉	—	2	1	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	#397	1	1	yes	characteristic
126	C₂²×C₁₉	#483	1	1	yes	characteristic
127	C₂²×C₁₉	#484	1	1	yes	characteristic
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	#460	1	1	yes	characteristic
133	C₄×C₁₉	#462	1	1	yes	characteristic
134	C₄×C₁₉	#487	1	1	yes	characteristic
135	C₄×C₁₉	#489	1	1	yes	characteristic
136	Dic₁₉	—	4	2	no	—
137	Dic₁₉	—	4	2	no	—
138	Dic₁₉	—	8	1	no	—
139	Dic₁₉	—	8	1	no	—
140	#533	—	19	1	no	—
141	#431	—	19	1	no	—
142	#431	C₂×D₁₉	1	1	yes	characteristic
143	#423	C₂×D₁₉	1	1	yes	characteristic
144	C₂×C₄⋊C₈	—	19	1	no	—
145	C₂×C₄⋊C₈	—	38	1	no	—
146	C₂×C₄⋊C₈	—	38	1	no	—
147	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
148	#376	—	19	1	no	—
149	#339	—	38	1	no	—
150	#339	—	38	1	no	—
151	#333	—	38	1	no	—
152	#333	—	38	1	no	—
153	#332	—	38	1	no	—
154	#332	—	38	1	no	—
155	C₂×C₁₉	—	2	1	no	—
156	C₂×C₁₉	—	2	1	no	—
157	C₂×C₁₉	#2072	1	1	yes	characteristic
158	C₂×C₁₉	#2080	1	1	yes	characteristic
159	C₂×C₁₉	#2080	1	1	yes	characteristic
160	C₂×M₁₆	—	2	1	no	—
161	C₂²×C₈	—	2	1	no	—
162	C₂²×C₈	—	38	1	no	—
163	C₄⋊Q₈	—	19	1	no	—
164	C₄⋊Q₈	—	19	1	no	—
165	#125	—	38	1	no	—
166	C₂²⋊Q₈	—	38	1	no	—
167	C₂²⋊Q₈	—	38	1	no	—
168	C₄×Q₈	—	38	1	no	—
169	C₄×Q₈	—	38	1	no	—
170	#117	—	38	1	no	—
171	C₂×C₄²	—	19	1	no	—
172	C₂×C₄²	—	19	1	no	—
173	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
174	C₄⋊C₈	—	2	1	no	—
175	C₄⋊C₈	—	2	1	no	—
176	C₄⋊C₈	—	2	1	no	—
177	C₄⋊C₈	—	2	1	no	—
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	38	1	no	—
180	C₄⋊C₈	—	38	1	no	—
181	C₄⋊C₈	—	38	1	no	—
182	C₄⋊C₈	—	76	2	no	—
183	C₄⋊C₈	—	76	2	no	—
184	C₂²⋊C₈	—	2	1	no	—
185	C₂²⋊C₈	—	38	1	no	—
186	C₄×C₈	—	2	1	no	—
187	C₄×C₈	—	38	1	no	—
188	#95	—	38	1	no	—
189	#95	—	38	1	no	—
190	C₁₉	#10628	1	1	yes	characteristic, complemented, Sylow
191	C₂×Q₈	—	38	1	no	—
192	C₂×Q₈	—	38	1	no	—
193	C₂²×C₄	—	38	1	no	—
194	C₂²×C₄	—	38	1	no	—
195	C₂²×C₄	#64541	1	1	yes	characteristic
196	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
197	C₂²×C₄	#64545	1	1	yes	characteristic
198	M₁₆	—	4	1	no	—
199	M₁₆	—	4	1	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	4	1	no	—
203	C₂×C₈	—	4	1	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	76	1	no	—
206	C₂×C₈	—	76	1	no	—
207	C₂×C₈	—	76	1	no	—
208	C₂×C₈	—	76	1	no	—
209	C₄⋊C₄	—	38	1	no	—
210	C₄⋊C₄	—	38	1	no	—
211	C₄⋊C₄	—	38	1	no	—
212	C₄⋊C₄	—	38	1	no	—
213	C₄⋊C₄	—	76	1	no	—
214	C₄⋊C₄	—	76	1	no	—
215	C₂²⋊C₄	—	76	1	no	—
216	C₄²	—	19	2	no	—
217	C₄²	—	19	2	no	—
218	C₄²	—	38	1	no	—
219	C₄²	—	38	1	no	—
220	C₄²	—	76	1	no	—
221	C₄²	#64541	1	1	yes	characteristic
222	C₄²	#64541	1	1	yes	characteristic
223	C₄²	D₄×D₁₉	1	1	yes	characteristic
224	C₄²	#64543	1	1	yes	characteristic
225	C₂³	#10597340	1	1	yes	characteristic
226	Q₈	—	152	1	no	—
227	Q₈	—	152	1	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	38	2	no	—
231	C₂×C₄	—	38	2	no	—
232	C₂×C₄	—	76	1	no	—
233	C₂×C₄	—	76	1	no	—
234	C₂×C₄	—	76	1	no	—
235	C₂×C₄	—	76	1	no	—
236	C₂×C₄	—	76	1	no	—
237	C₂×C₄	—	76	1	no	—
238	C₂×C₄	#10597322	1	1	yes	characteristic
239	C₂×C₄	#10597329	1	1	yes	characteristic
240	C₂×C₄	#10597330	1	1	yes	characteristic
241	C₂×C₄	#10597331	1	1	yes	characteristic
242	C₂×C₄	#10597340	1	1	yes	characteristic
243	C₂×C₄	#10597344	1	1	yes	characteristic
244	C₂×C₄	#10597357	1	1	yes	characteristic
245	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
246	C₂×C₄	#10597361	1	1	yes	characteristic
247	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
248	C₈	—	8	1	no	—
249	C₈	—	8	1	no	—
250	C₈	—	8	1	no	—
251	C₈	—	152	1	no	—
252	C₈	—	152	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	#11926473	1	1	yes	characteristic
256	C₂²	#11926876	1	1	yes	characteristic
257	C₂²	#11926881	1	1	yes	characteristic
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	76	2	no	—
263	C₄	—	76	2	no	—
264	C₄	—	152	1	no	—
265	C₄	—	152	1	no	—
266	C₄	#11926743	1	1	yes	characteristic
267	C₄	#11926753	1	1	yes	characteristic
268	C₄	#11926893	1	1	yes	characteristic
269	C₄	#11926902	1	1	yes	characteristic
270	C₂	—	2	1	no	—
271	C₂	—	2	1	no	—
272	C₂	#14565047	1	1	yes	characteristic
273	C₂	#14565090	1	1	yes	characteristic
274	C₂	#14565091	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564615

C₂

yes

maximal, characteristic

#14563788

C₂

yes

maximal, characteristic

#14562293

C₂

yes

maximal, characteristic

#14562290

C₂

yes

maximal, characteristic

#14561530

C₂

yes

maximal, characteristic

#14561463

C₂

yes

maximal, characteristic

C₁₉×#1301

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₈

—

C₂×Dic₁₉⋊C₈

—

#11926390

C₂²

yes

—

—

—

—

—

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597315

D₄

yes

characteristic

#10597315

D₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

SD₁₆

yes

—

C₄×Dic₁₉

Q₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

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

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

100

C₂×C₄×C₁₉

#137

yes

characteristic

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

C₂×Dic₁₉

—

108

C₂×Dic₁₉

—

109

Dic₃₈

—

110

Dic₃₈

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₈×C₁₉

—

114

C₁₉⋊C₈

—

115

C₁₉⋊C₈

—

116

#1995

—

117

#1843

—

118

#1542

—

119

#1542

—

120

#1301

—

121

#1301

D₁₉

yes

characteristic

122

#1274

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

#397

yes

characteristic

126

C₂²×C₁₉

#483

yes

characteristic

127

C₂²×C₁₉

#484

yes

characteristic

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

#460

yes

characteristic

133

C₄×C₁₉

#462

yes

characteristic

134

C₄×C₁₉

#487

yes

characteristic

135

C₄×C₁₉

#489

yes

characteristic

136

Dic₁₉

—

137

Dic₁₉

—

138

Dic₁₉

—

139

Dic₁₉

—

140

#533

—

141

#431

—

142

#431

C₂×D₁₉

yes

characteristic

143

#423

C₂×D₁₉

yes

characteristic

144

C₂×C₄⋊C₈

—

145

C₂×C₄⋊C₈

—

146

C₂×C₄⋊C₈

—

147

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

148

#376

—

149

#339

—

150

#339

—

151

#333

—

152

#333

—

153

#332

—

154

#332

—

155

C₂×C₁₉

—

156

C₂×C₁₉

—

157

C₂×C₁₉

#2072

yes

characteristic

158

C₂×C₁₉

#2080

yes

characteristic

159

C₂×C₁₉

#2080

yes

characteristic

160

C₂×M₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

—

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

165

#125

—

166

C₂²⋊Q₈

—

167

C₂²⋊Q₈

—

168

C₄×Q₈

—

169

C₄×Q₈

—

170

#117

—

171

C₂×C₄²

—

172

C₂×C₄²

—

173

C₂×C₄²

C₂²×D₁₉

yes

characteristic

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₂²⋊C₈

—

185

C₂²⋊C₈

—

186

C₄×C₈

—

187

C₄×C₈

—

188

#95

—

189

#95

—

190

C₁₉

#10628

yes

characteristic, complemented, Sylow

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

#64541

yes

characteristic

196

C₂²×C₄

D₄×D₁₉

yes

characteristic

197

C₂²×C₄

#64545

yes

characteristic

198

M₁₆

—

199

M₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₂²⋊C₄

—

216

C₄²

—

217

C₄²

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₄²

#64541

yes

characteristic

222

C₄²

#64541

yes

characteristic

223

C₄²

D₄×D₁₉

yes

characteristic

224

C₄²

#64543

yes

characteristic

225

C₂³

#10597340

yes

characteristic

226

Q₈

—

152

—

227

Q₈

—

152

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

#10597322

yes

characteristic

239

C₂×C₄

#10597329

yes

characteristic

240

C₂×C₄

#10597330

yes

characteristic

241

C₂×C₄

#10597331

yes

characteristic

242

C₂×C₄

#10597340

yes

characteristic

243

C₂×C₄

#10597344

yes

characteristic

244

C₂×C₄

#10597357

yes

characteristic

245

C₂×C₄

SD₁₆×D₁₉

yes

characteristic

246

C₂×C₄

#10597361

yes

characteristic

247

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

152

—

252

C₈

—

152

—

253

C₂²

—

254

C₂²

—

255

C₂²

#11926473

yes

characteristic

256

C₂²

#11926876

yes

characteristic

257

C₂²

#11926881

yes

characteristic

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

152

—

265

C₄

—

152

—

266

C₄

#11926743

yes

characteristic

267

C₄

#11926753

yes

characteristic

268

C₄

#11926893

yes

characteristic

269

C₄

#11926902

yes

characteristic

270

C₂

—

271

C₂

—

272

C₂

#14565047

yes

characteristic

273

C₂

#14565090

yes

characteristic

274

C₂

#14565091

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597331
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1301	C₂
socle	C₂²×C₁₉	#397
prime radical	C₂³×C₁₉	#123
hypercenter	#1301	D₁₉
hypocenter	C₁₉	#10628
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

subgroup

G/H

center

C₂×C₄

#10597331

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1301

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

N	H ≅ G/N	type
190. C₁₉	#10628	semidirect

H ≅ G/N

type

190. C₁₉

#10628

semidirect

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

subgroup	index
#14564615	2
#14563788	2
#14562293	2
#14562290	2
#14561530	2
#14561463	2
C₁₉×#1301	2
#10628	19

subgroup

index

C₁₉×#1301

Subgroups — #18087316

Conjugacy classes of subgroups

Complements

Maximal subgroups