Group #18079892 — subgroups

Subgroups — #18079892

Order 4864.

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

normal subgroups only

This group has 538 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	#14572659	C₂	1	1	yes	maximal, characteristic
2	#14568808	C₂	1	1	yes	maximal, characteristic
3	#14562317	C₂	1	2	yes	maximal, complemented
4	#14561536	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	D₄×C₁₉⋊C₈	—	2	4	no	—
8	#11926597	C₂²	1	2	yes	—
9	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
10	#11926456	C₄	1	4	yes	—
11	#11926447	—	2	1	no	—
12	#11926409	—	2	1	no	—
13	#11926404	—	2	2	no	—
14	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	#11926292	—	2	4	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#423	C₂²	1	2	yes	—
18	C₂×C₁₉×#100	—	2	1	no	—
19	C₁₉×#343	—	2	1	no	—
20	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	D₄	1	2	yes	—
22	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₄×D₄×C₁₉	—	2	2	no	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₁₉	—	2	4	no	—
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	—	2	1	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄×Dic₁₉	—	2	1	no	—
34	C₂²×C₁₉⋊C₈	—	2	4	no	—
35	#10597315	—	2	2	no	—
36	#10597315	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×#100	—	4	2	no	—
40	C₁₉⋊#95	—	2	4	no	—
41	C₁₉⋊#95	C₂×C₄	1	2	yes	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
45	C₄×C₁₉⋊C₈	—	2	2	no	—
46	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
47	C₂×D₄×C₁₉	—	2	2	no	—
48	C₂×D₄×C₁₉	—	2	2	no	—
49	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
50	C₂×D₄×C₁₉	Q₁₆	1	2	yes	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	4	4	no	—
54	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×Dic₁₉	—	2	2	no	—
59	C₂²×Dic₁₉	—	2	2	no	—
60	C₂×Dic₃₈	—	2	4	no	—
61	C₂×Dic₃₈	—	8	2	no	—
62	M₁₆×C₁₉	—	4	2	no	—
63	M₁₆×C₁₉	—	4	2	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₄²×C₁₉	C₂×D₄	1	2	yes	—
68	C₄²×C₁₉	#41	1	2	yes	—
69	C₂²⋊Dic₁₉	—	8	4	no	—
70	C₄⋊Dic₁₉	—	4	2	no	—
71	C₄⋊Dic₁₉	—	4	1	no	—
72	C₄⋊Dic₁₉	—	4	2	no	—
73	C₄⋊Dic₁₉	—	4	1	no	—
74	C₄×Dic₁₉	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	2	4	no	—
76	C₂×C₁₉⋊C₈	—	8	4	no	—
77	#9391	—	19	1	no	maximal, Sylow
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	#103	1	4	yes	—
83	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	D₄×C₁₉	—	2	4	no	—
85	D₄×C₁₉	—	2	4	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	—	4	4	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	8	2	no	—
92	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#121	1	2	yes	—
95	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#135	1	2	yes	—
99	C₂×Dic₁₉	—	4	2	no	—
100	C₂×Dic₁₉	—	4	2	no	—
101	C₂×Dic₁₉	—	4	4	no	—
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	4	2	no	—
104	Dic₃₈	—	8	4	no	—
105	C₈×C₁₉	—	8	2	no	—
106	C₁₉⋊C₈	—	4	4	no	—
107	#2972	—	19	1	no	—
108	#2563	—	19	1	no	—
109	#1800	D₁₉	1	1	yes	characteristic
110	#1548	—	19	2	no	—
111	#1303	—	19	2	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	—	2	1	no	—
114	C₂²×C₁₉	—	2	4	no	—
115	C₂²×C₁₉	—	4	4	no	—
116	C₂²×C₁₉	—	4	2	no	—
117	C₂²×C₁₉	—	4	2	no	—
118	C₂²×C₁₉	—	8	2	no	—
119	C₂²×C₁₉	#386	1	1	yes	characteristic
120	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
121	C₂²×C₁₉	#416	1	1	yes	characteristic
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	2	no	—
124	C₄×C₁₉	—	4	2	no	—
125	C₄×C₁₉	#455	1	2	yes	—
126	C₄×C₁₉	#465	1	2	yes	—
127	C₄×C₁₉	#467	1	2	yes	—
128	Dic₁₉	—	8	2	no	—
129	Dic₁₉	—	8	2	no	—
130	C₂×C₄⋊Q₈	—	19	1	no	—
131	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
132	C₈×D₄	—	38	4	no	—
133	#431	—	19	2	no	—
134	#423	C₂×D₁₉	1	2	yes	—
135	C₂×#100	—	2	1	no	—
136	C₂×C₂²⋊C₈	—	38	2	no	—
137	#393	—	19	4	no	—
138	#390	—	38	1	no	—
139	#382	—	38	1	no	—
140	#380	—	38	2	no	—
141	C₄×C₄⋊C₄	—	19	1	no	—
142	#343	—	2	1	no	—
143	#333	—	38	4	no	—
144	C₂×C₁₉	—	2	1	no	—
145	C₂×C₁₉	—	2	1	no	—
146	C₂×C₁₉	—	4	4	no	—
147	C₂×C₁₉	#1885	1	1	yes	characteristic
148	C₂×C₁₉	#1892	1	1	yes	characteristic
149	C₂×C₁₉	#1914	1	1	yes	characteristic
150	C₂²×Q₈	—	19	2	no	—
151	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
152	C₂³×C₄	D₇₆	1	2	yes	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂²×C₈	—	38	4	no	—
155	C₄⋊Q₈	—	38	2	no	—
156	C₄⋊Q₈	—	38	2	no	—
157	C₄×D₄	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	38	1	no	—
160	C₂×C₄⋊C₄	—	38	1	no	—
161	C₂×C₄⋊C₄	—	38	1	no	—
162	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
163	C₂×C₂²⋊C₄	—	38	4	no	—
164	C₂×C₂²⋊C₄	C₄×D₁₉	1	2	yes	—
165	C₂×C₄²	—	38	1	no	—
166	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	19	4	no	—
170	#100	—	4	2	no	—
171	C₂²⋊C₈	—	38	4	no	—
172	C₂²⋊C₈	—	38	2	no	—
173	C₄×C₈	—	38	2	no	—
174	#95	—	19	2	no	—
175	#95	—	38	4	no	—
176	C₁₉	#9391	1	1	yes	characteristic, complemented, Sylow
177	C₂⁴	(C₂×D₁₉)⋊C₄	1	2	yes	—
178	C₂×Q₈	—	38	4	no	—
179	C₂×Q₈	—	152	2	no	—
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	—	2	2	no	—
182	C₂×D₄	#64526	1	2	yes	—
183	C₂×D₄	#64528	1	2	yes	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	4	4	no	—
187	C₂²×C₄	—	38	2	no	—
188	C₂²×C₄	—	38	2	no	—
189	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
190	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
191	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
192	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
193	M₁₆	—	4	2	no	—
194	M₁₆	—	4	2	no	—
195	C₂×C₈	—	4	2	no	—
196	C₂×C₈	—	38	4	no	—
197	C₂×C₈	—	152	4	no	—
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	76	2	no	—
200	C₄⋊C₄	—	76	2	no	—
201	C₄⋊C₄	—	76	1	no	—
202	C₄⋊C₄	—	76	1	no	—
203	C₂²⋊C₄	—	2	4	no	—
204	C₂²⋊C₄	—	152	4	no	—
205	C₄²	—	76	2	no	—
206	C₄²	D₄×D₁₉	1	2	yes	—
207	C₄²	#64543	1	2	yes	—
208	C₂³	—	2	2	no	—
209	C₂³	—	2	2	no	—
210	C₂³	—	4	2	no	—
211	C₂³	—	4	2	no	—
212	C₂³	#10597267	1	4	yes	—
213	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
214	Q₈	—	152	4	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	4	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	8	2	no	—
223	C₂×C₄	—	76	2	no	—
224	C₂×C₄	—	76	4	no	—
225	C₂×C₄	—	76	2	no	—
226	C₂×C₄	—	76	2	no	—
227	C₂×C₄	—	76	2	no	—
228	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
229	C₂×C₄	#10597328	1	1	yes	characteristic
230	C₂×C₄	#10597332	1	1	yes	characteristic
231	C₂×C₄	C₂×#64526	1	1	yes	characteristic
232	C₂×C₄	#10597385	1	2	yes	—
233	C₂×C₄	C₂×#64528	1	1	yes	characteristic
234	C₂×C₄	#10597396	1	2	yes	—
235	C₈	—	8	2	no	—
236	C₈	—	76	4	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	2	4	no	—
240	C₂²	—	4	4	no	—
241	C₂²	—	4	2	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	8	2	no	—
244	C₂²	#11926421	1	1	yes	characteristic
245	C₂²	C₂×#10597267	1	1	yes	characteristic
246	C₂²	#11926538	1	1	yes	characteristic
247	C₄	—	2	2	no	—
248	C₄	—	2	1	no	—
249	C₄	—	4	2	no	—
250	C₄	—	152	2	no	—
251	C₄	—	152	2	no	—
252	C₄	#11926724	1	2	yes	—
253	C₄	#11926771	1	2	yes	—
254	C₄	#11926783	1	2	yes	—
255	C₂	—	2	1	no	—
256	C₂	—	2	1	no	—
257	C₂	—	4	4	no	—
258	C₂	#14564021	1	1	yes	characteristic
259	C₂	#14564056	1	1	yes	characteristic
260	C₂	#14564180	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572659

C₂

yes

maximal, characteristic

#14568808

C₂

yes

maximal, characteristic

#14562317

C₂

yes

maximal, complemented

#14561536

C₂

yes

maximal, complemented

C₁₉×#1800

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926456

C₄

yes

—

#11926447

—

#11926409

—

#11926404

—

C₄×C₄⋊Dic₁₉

C₂²

yes

characteristic

#11926292

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#100

—

C₁₉×#343

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂²×Dic₃₈

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

#10597315

—

#10597315

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#100

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂×C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

SD₁₆

yes

—

C₂×D₄×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9391

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#103

yes

—

C₂³×C₁₉

C₂×C₂²⋊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

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

Dic₃₈

—

105

C₈×C₁₉

—

106

C₁₉⋊C₈

—

107

#2972

—

108

#2563

—

109

#1800

D₁₉

yes

characteristic

110

#1548

—

111

#1303

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

#386

yes

characteristic

120

C₂²×C₁₉

C₂×#103

yes

characteristic

121

C₂²×C₁₉

#416

yes

characteristic

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

#455

yes

—

126

C₄×C₁₉

#465

yes

—

127

C₄×C₁₉

#467

yes

—

128

Dic₁₉

—

129

Dic₁₉

—

130

C₂×C₄⋊Q₈

—

131

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

132

C₈×D₄

—

133

#431

—

134

#423

C₂×D₁₉

yes

—

135

C₂×#100

—

136

C₂×C₂²⋊C₈

—

137

#393

—

138

#390

—

139

#382

—

140

#380

—

141

C₄×C₄⋊C₄

—

142

#343

—

143

#333

—

144

C₂×C₁₉

—

145

C₂×C₁₉

—

146

C₂×C₁₉

—

147

C₂×C₁₉

#1885

yes

characteristic

148

C₂×C₁₉

#1892

yes

characteristic

149

C₂×C₁₉

#1914

yes

characteristic

150

C₂²×Q₈

—

151

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

152

C₂³×C₄

D₇₆

yes

—

153

C₂×M₁₆

—

154

C₂²×C₈

—

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

157

C₄×D₄

—

158

C₄×D₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

163

C₂×C₂²⋊C₄

—

164

C₂×C₂²⋊C₄

C₄×D₁₉

yes

—

165

C₂×C₄²

—

166

C₂×C₄²

C₂²×D₁₉

yes

characteristic

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

#100

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

173

C₄×C₈

—

174

#95

—

175

#95

—

176

C₁₉

#9391

yes

characteristic, complemented, Sylow

177

C₂⁴

(C₂×D₁₉)⋊C₄

yes

—

178

C₂×Q₈

—

179

C₂×Q₈

—

152

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

#64526

yes

—

183

C₂×D₄

#64528

yes

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

190

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

191

C₂²×C₄

C₂×D₇₆

yes

characteristic

192

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

193

M₁₆

—

194

M₁₆

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

152

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

152

—

205

C₄²

—

206

C₄²

D₄×D₁₉

yes

—

207

C₄²

#64543

yes

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

#10597267

yes

—

213

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

214

Q₈

—

152

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

229

C₂×C₄

#10597328

yes

characteristic

230

C₂×C₄

#10597332

yes

characteristic

231

C₂×C₄

C₂×#64526

yes

characteristic

232

C₂×C₄

#10597385

yes

—

233

C₂×C₄

C₂×#64528

yes

characteristic

234

C₂×C₄

#10597396

yes

—

235

C₈

—

236

C₈

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

#11926421

yes

characteristic

245

C₂²

C₂×#10597267

yes

characteristic

246

C₂²

#11926538

yes

characteristic

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

152

—

251

C₄

—

152

—

252

C₄

#11926724

yes

—

253

C₄

#11926771

yes

—

254

C₄

#11926783

yes

—

255

C₂

—

256

C₂

—

257

C₂

—

258

C₂

#14564021

yes

characteristic

259

C₂

#14564056

yes

characteristic

260

C₂

#14564180

yes

characteristic

	subgroup	G/H
center	C₂²	#11926421
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1800	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1800	D₁₉
hypocenter	C₁₉	#9391
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

subgroup

G/H

center

C₂²

#11926421

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1800

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂²×D₄×C₁₉

D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

N	H ≅ G/N	type
3. #14562317	C₂	semidirect
4. #14561536	C₂	semidirect
176. C₁₉	#9391	semidirect

H ≅ G/N

type

3. #14562317

C₂

semidirect

4. #14561536

C₂

semidirect

176. C₁₉

#9391

semidirect

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

subgroup	index
#14572659	2
#14568808	2
#14562317	2
#14561536	2
C₁₉×#1800	2
#9391	19

subgroup

index

C₁₉×#1800

Subgroups — #18079892

Conjugacy classes of subgroups

Complements

Maximal subgroups