Group #18075547 — subgroups

Subgroups — #18075547

Order 4864.

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

normal subgroups only

This group has 388 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	#14562398	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562398	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562270	C₂	1	2	yes	maximal
4	#14561546	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic
6	#11926601	C₂²	1	2	yes	—
7	#11926601	C₂²	1	2	yes	—
8	#11926297	—	2	1	no	—
9	#11926297	—	2	1	no	—
10	#11926295	—	2	1	no	—
11	#11926295	—	2	1	no	—
12	#11926284	—	2	4	no	—
13	C₂×C₁₉×#131	C₄	1	2	yes	—
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₁₉×#436	—	2	1	no	—
16	C₁₉×#436	—	2	1	no	—
17	C₈×D₄×C₁₉	—	2	1	no	—
18	C₈×D₄×C₁₉	—	2	1	no	—
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₁₉×#408	C₄	1	2	yes	—
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
23	C₁₉×#131	—	4	4	no	—
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₁₉	—	2	2	no	—
27	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₁₉×C₄⋊Q₈	Q₈	1	1	yes	characteristic
30	C₁₉×#127	Q₈	1	1	yes	characteristic
31	C₁₉×#124	D₄	1	2	yes	—
32	C₁₉×#121	—	2	1	no	—
33	C₁₉×#121	—	2	1	no	—
34	C₄×D₄×C₁₉	—	2	1	no	—
35	C₄×D₄×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₁₉×C₄⋊C₈	—	2	1	no	—
39	C₁₉×C₂²⋊C₈	—	2	2	no	—
40	C₁₉×C₂²⋊C₈	—	2	2	no	—
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	#10597260	—	2	2	no	—
50	#10597260	—	2	2	no	—
51	#41×C₁₉	—	4	2	no	—
52	#41×C₁₉	—	4	2	no	—
53	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	2	1	no	—
56	C₂×D₄×C₁₉	—	2	1	no	—
57	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
62	M₁₆×C₁₉	—	4	4	no	—
63	M₁₆×C₁₉	—	4	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	4	1	no	—
67	C₂×C₈×C₁₉	—	4	4	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	C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
80	C₂×C₁₉⋊C₈	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	4	2	no	—
82	#8634	—	19	1	no	maximal, Sylow
83	C₂³×C₁₉	—	2	2	no	—
84	C₂³×C₁₉	#117	1	1	yes	characteristic
85	Q₈×C₁₉	—	4	2	no	—
86	D₄×C₁₉	—	4	2	no	—
87	D₄×C₁₉	—	4	2	no	—
88	D₄×C₁₉	—	4	2	no	—
89	D₄×C₁₉	—	4	4	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
103	C₈×C₁₉	—	2	1	no	—
104	C₈×C₁₉	—	2	1	no	—
105	C₈×C₁₉	—	2	1	no	—
106	C₈×C₁₉	—	4	2	no	—
107	C₈×C₁₉	#100	1	2	yes	—
108	C₁₉⋊C₈	—	8	2	no	—
109	C₁₉⋊C₈	—	8	2	no	—
110	#2931	D₁₉	1	1	yes	characteristic
111	#1568	—	19	1	no	—
112	#1568	—	19	1	no	—
113	#1536	—	19	2	no	—
114	#1307	—	19	2	no	—
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	—	4	2	no	—
119	C₂²×C₁₉	—	4	2	no	—
120	C₂²×C₁₉	—	4	2	no	—
121	C₂²×C₁₉	#380	1	1	yes	characteristic
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	4	2	no	—
128	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
129	C₄×C₁₉	#413	1	1	yes	characteristic
130	C₂×#131	Dic₁₉	1	2	yes	—
131	#532	C₂×D₁₉	1	1	yes	characteristic
132	#436	—	2	1	no	—
133	#436	—	2	1	no	—
134	C₈×D₄	—	2	1	no	—
135	C₈×D₄	—	2	1	no	—
136	#432	—	19	2	no	—
137	#432	—	19	2	no	—
138	#423	C₂×D₁₉	1	1	yes	characteristic
139	#408	Dic₁₉	1	2	yes	—
140	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
141	#335	—	38	1	no	—
142	#335	—	38	1	no	—
143	#334	—	38	1	no	—
144	#334	—	38	1	no	—
145	#329	—	38	4	no	—
146	C₂×C₁₉	—	4	1	no	—
147	C₂×C₁₉	—	8	2	no	—
148	C₂×C₁₉	#1800	1	1	yes	characteristic
149	C₂×C₁₉	#1814	1	1	yes	characteristic
150	C₂×C₁₉	#1814	1	1	yes	characteristic
151	C₂×#41	C₂×Dic₁₉	1	2	yes	—
152	#131	—	4	4	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
155	C₂²×C₈	—	2	2	no	—
156	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
157	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
158	C₄⋊Q₈	Dic₃₈	1	1	yes	characteristic
159	#127	Dic₃₈	1	1	yes	characteristic
160	#124	D₇₆	1	2	yes	—
161	#121	—	2	1	no	—
162	#121	—	2	1	no	—
163	C₄×D₄	—	2	1	no	—
164	C₄×D₄	—	2	1	no	—
165	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
166	C₄⋊C₈	—	2	1	no	—
167	C₄⋊C₈	—	2	1	no	—
168	C₄⋊C₈	—	38	2	no	—
169	C₄⋊C₈	—	38	2	no	—
170	C₂²⋊C₈	—	2	2	no	—
171	C₂²⋊C₈	—	2	2	no	—
172	C₂²⋊C₈	—	38	2	no	—
173	C₂²⋊C₈	—	38	2	no	—
174	#97	—	38	2	no	—
175	#97	—	38	2	no	—
176	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
177	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
178	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
179	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
180	C₁₉	#8634	1	1	yes	characteristic, complemented, Sylow
181	#41	—	4	2	no	—
182	#41	—	4	2	no	—
183	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
184	C₂×D₄	—	2	2	no	—
185	C₂×D₄	—	2	1	no	—
186	C₂×D₄	—	2	1	no	—
187	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	#64541	1	1	yes	characteristic
190	C₂²×C₄	#64541	1	1	yes	characteristic
191	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
192	M₁₆	—	4	4	no	—
193	M₁₆	—	4	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	4	4	no	—
198	C₂×C₈	—	76	2	no	—
199	C₂×C₈	—	76	2	no	—
200	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
201	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
202	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
203	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
204	C₄⋊C₄	—	2	1	no	—
205	C₄⋊C₄	—	2	1	no	—
206	C₂²⋊C₄	—	2	2	no	—
207	C₂²⋊C₄	—	2	2	no	—
208	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
209	C₄²	C₂×D₇₆	1	1	yes	characteristic
210	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
211	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
212	C₂³	—	2	2	no	—
213	C₂³	#10597372	1	1	yes	characteristic
214	Q₈	—	4	2	no	—
215	D₄	—	4	2	no	—
216	D₄	—	4	2	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	4	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	#10597370	1	1	yes	characteristic
227	C₂×C₄	#10597370	1	1	yes	characteristic
228	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
229	C₂×C₄	#10597376	1	1	yes	characteristic
230	C₂×C₄	#10597376	1	1	yes	characteristic
231	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
232	C₈	—	2	1	no	—
233	C₈	—	2	1	no	—
234	C₈	—	2	1	no	—
235	C₈	—	4	2	no	—
236	C₈	—	152	2	no	—
237	C₈	—	152	2	no	—
238	C₈	#10597290	1	2	yes	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	4	2	no	—
244	C₂²	—	4	2	no	—
245	C₂²	#11926404	1	1	yes	characteristic
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	—	4	2	no	—
252	C₄	C₂×#10597290	1	1	yes	characteristic
253	C₄	#11926528	1	1	yes	characteristic
254	C₂	—	4	1	no	—
255	C₂	—	8	2	no	—
256	C₂	#14563627	1	1	yes	characteristic
257	C₂	#14563689	1	1	yes	characteristic
258	C₂	#14563689	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14562398

C₂

yes

maximal, characteristic, complemented

#14562398

C₂

yes

maximal, characteristic, complemented

#14562270

C₂

yes

maximal

#14561546

C₂

yes

maximal, complemented

C₁₉×#2931

C₂

yes

maximal, characteristic

#11926601

C₂²

yes

—

#11926601

C₂²

yes

—

—

—

—

—

—

C₂×C₁₉×#131

C₄

yes

—

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#436

—

C₁₉×#436

—

C₈×D₄×C₁₉

—

C₈×D₄×C₁₉

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#408

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

C₂×C₄

yes

—

C₁₉×#131

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

Q₈

yes

characteristic

C₁₉×#127

Q₈

yes

characteristic

C₁₉×#124

D₄

yes

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×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

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8634

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#117

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

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×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#121

yes

characteristic

100

C₂×C₄×C₁₉

#121

yes

characteristic

101

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

102

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₈×C₁₉

—

106

C₈×C₁₉

—

107

C₈×C₁₉

#100

yes

—

108

C₁₉⋊C₈

—

109

C₁₉⋊C₈

—

110

#2931

D₁₉

yes

characteristic

111

#1568

—

112

#1568

—

113

#1536

—

114

#1307

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#380

yes

characteristic

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

C₂×#100

yes

characteristic

129

C₄×C₁₉

#413

yes

characteristic

130

C₂×#131

Dic₁₉

yes

—

131

#532

C₂×D₁₉

yes

characteristic

132

#436

—

133

#436

—

134

C₈×D₄

—

135

C₈×D₄

—

136

#432

—

137

#432

—

138

#423

C₂×D₁₉

yes

characteristic

139

#408

Dic₁₉

yes

—

140

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

141

#335

—

142

#335

—

143

#334

—

144

#334

—

145

#329

—

146

C₂×C₁₉

—

147

C₂×C₁₉

—

148

C₂×C₁₉

#1800

yes

characteristic

149

C₂×C₁₉

#1814

yes

characteristic

150

C₂×C₁₉

#1814

yes

characteristic

151

C₂×#41

C₂×Dic₁₉

yes

—

152

#131

—

153

C₂×M₁₆

—

154

C₂×M₁₆

C₂×Dic₁₉

yes

—

155

C₂²×C₈

—

156

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

157

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

158

C₄⋊Q₈

Dic₃₈

yes

characteristic

159

#127

Dic₃₈

yes

characteristic

160

#124

D₇₆

yes

—

161

#121

—

162

#121

—

163

C₄×D₄

—

164

C₄×D₄

—

165

C₂×C₄²

C₂²×D₁₉

yes

characteristic

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₂²⋊C₈

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

173

C₂²⋊C₈

—

174

#97

—

175

#97

—

176

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

177

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

178

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

179

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

180

C₁₉

#8634

yes

characteristic, complemented, Sylow

181

#41

—

182

#41

—

183

C₂×Q₈

C₄⋊Dic₁₉

yes

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

C₄⋊Dic₁₉

yes

—

188

C₂²×C₄

—

189

C₂²×C₄

#64541

yes

characteristic

190

C₂²×C₄

#64541

yes

characteristic

191

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

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

C₂²⋊Dic₁₉

yes

characteristic

201

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

202

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

203

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

C₂×Dic₃₈

yes

characteristic

209

C₄²

C₂×D₇₆

yes

characteristic

210

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

211

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

212

C₂³

—

213

C₂³

#10597372

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

D₄

—

218

D₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

#10597370

yes

characteristic

227

C₂×C₄

#10597370

yes

characteristic

228

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

229

C₂×C₄

#10597376

yes

characteristic

230

C₂×C₄

#10597376

yes

characteristic

231

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

236

C₈

—

152

—

237

C₈

—

152

—

238

C₈

#10597290

yes

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

#11926404

yes

characteristic

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

C₂×#10597290

yes

characteristic

253

C₄

#11926528

yes

characteristic

254

C₂

—

255

C₂

—

256

C₂

#14563627

yes

characteristic

257

C₂

#14563689

yes

characteristic

258

C₂

#14563689

yes

characteristic

	subgroup	G/H
center	C₂²	#11926404
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2931	C₂
socle	C₂²×C₁₉	#380
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2931	D₁₉
hypocenter	C₁₉	#8634
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2931

subgroup

G/H

center

C₂²

#11926404

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2931

C₂

socle

C₂²×C₁₉

#380

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2931

N	H ≅ G/N	type
1. #14562398	C₂	semidirect
2. #14562398	C₂	semidirect
4. #14561546	C₂	semidirect
180. C₁₉	#8634	semidirect

H ≅ G/N

type

1. #14562398

C₂

semidirect

2. #14562398

C₂

semidirect

4. #14561546

C₂

semidirect

180. C₁₉

#8634

semidirect

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

subgroup	index
#14562398	2
#14562270	2
#14561546	2
C₁₉×#2931	2
#8634	19

subgroup

index

C₁₉×#2931

Subgroups — #18075547

Conjugacy classes of subgroups

Complements

Maximal subgroups