Group #18081565 — subgroups

Subgroups — #18081565

Order 4864.

456 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 127 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	#14571998	C₂	1	1	yes	maximal, characteristic
2	#14563488	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926285	C₂	1	4	yes	maximal
4	C₁₉×#1745	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597316	C₂²	1	2	yes	—
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×#10597260	C₂²	1	2	yes	—
8	#11926442	—	2	1	no	—
9	#11926442	—	2	1	no	—
10	#11926442	—	2	1	no	—
11	#11926442	—	2	1	no	—
12	#11926414	C₄	1	1	yes	characteristic
13	#11926414	C₄	1	1	yes	characteristic
14	#11926410	C₄	1	2	yes	—
15	#11926299	—	2	1	no	—
16	#11926285	—	2	8	no	—
17	C₂×C₁₉×#97	C₂²	1	2	yes	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	1	no	—
20	C₁₉×#336	—	2	1	no	—
21	C₂²×C₈×C₁₉	—	2	2	no	—
22	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	—	2	1	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	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
35	C₂×Dic₁₉⋊C₄	—	2	2	no	—
36	C₂×Dic₁₉⋊C₄	—	2	2	no	—
37	C₂²×C₁₉⋊C₈	—	2	2	no	—
38	#10597316	—	2	4	no	—
39	#10597316	—	2	4	no	—
40	C₁₉×#97	—	2	2	no	—
41	C₁₉×#97	D₄	1	4	yes	—
42	C₁₉⋊#95	—	2	2	no	—
43	C₁₉⋊#95	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
45	#10597260	—	2	4	no	—
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×Dic₁₉	—	2	2	no	—
54	C₂²×Dic₁₉	—	2	2	no	—
55	C₂×C₈×C₁₉	—	2	4	no	—
56	C₂×C₈×C₁₉	—	4	2	no	—
57	C₂×C₈×C₁₉	—	4	2	no	—
58	C₄²×C₁₉	—	2	2	no	—
59	C₄²×C₁₉	—	2	2	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	—	4	1	no	—
62	C₄²×C₁₉	—	4	1	no	—
63	C₄²×C₁₉	—	4	1	no	—
64	C₄²×C₁₉	C₂×D₄	1	2	yes	—
65	C₄²×C₁₉	#41	1	2	yes	—
66	C₄⋊Dic₁₉	—	2	4	no	—
67	C₄⋊Dic₁₉	—	2	4	no	—
68	C₄⋊Dic₁₉	—	4	2	no	—
69	C₄⋊Dic₁₉	—	4	2	no	—
70	C₄⋊Dic₁₉	—	4	2	no	—
71	C₄⋊Dic₁₉	—	4	2	no	—
72	Dic₁₉⋊C₄	—	4	4	no	—
73	Dic₁₉⋊C₄	—	4	2	no	—
74	Dic₁₉⋊C₄	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	2	4	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	C₂×C₁₉⋊C₈	—	4	2	no	—
78	#9690	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
95	C₂×C₄×C₁₉	#101	1	2	yes	—
96	C₂×C₄×C₁₉	#101	1	2	yes	—
97	C₂×C₄×C₁₉	#104	1	2	yes	—
98	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
99	C₂×C₄×C₁₉	#121	1	2	yes	—
100	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	4	2	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	C₂×Dic₁₉	—	4	2	no	—
108	C₈×C₁₉	—	4	4	no	—
109	C₁₉⋊C₈	—	4	4	no	—
110	#2859	—	19	1	no	—
111	#1767	—	19	1	no	—
112	#1745	D₁₉	1	1	yes	characteristic
113	C₂×#330	—	19	4	no	—
114	C₂²×C₁₉	#390	1	1	yes	characteristic
115	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
116	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
117	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
118	C₂²×C₁₉	#421	1	1	yes	characteristic
119	C₂²×C₁₉	#421	1	1	yes	characteristic
120	C₂²×C₁₉	#421	1	1	yes	characteristic
121	C₄×C₁₉	—	2	2	no	—
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	2	2	no	—
126	C₄×C₁₉	—	2	2	no	—
127	C₄×C₁₉	—	2	2	no	—
128	C₄×C₁₉	—	4	1	no	—
129	Dic₁₉	—	8	2	no	—
130	Dic₁₉	—	8	2	no	—
131	C₂×#125	—	19	2	no	—
132	C₂×C₄⋊C₈	—	38	1	no	—
133	C₂×#97	—	19	2	no	—
134	C₂×#97	C₂×D₁₉	1	2	yes	—
135	#389	—	38	1	no	—
136	#389	—	38	1	no	—
137	#389	—	38	1	no	—
138	#389	—	38	1	no	—
139	#384	—	19	1	no	—
140	#384	—	19	1	no	—
141	#382	—	19	2	no	—
142	C₄³	C₂×D₁₉	1	1	yes	characteristic
143	#336	—	2	1	no	—
144	#336	—	2	1	no	—
145	#336	—	38	1	no	—
146	#330	—	38	8	no	—
147	C₂×C₁₉	#1528	1	1	yes	characteristic
148	C₂×C₁₉	#1531	1	1	yes	characteristic
149	C₂×C₁₉	#1534	1	1	yes	characteristic
150	C₂×C₁₉	#1537	1	1	yes	characteristic
151	C₂×C₁₉	#1963	1	1	yes	characteristic
152	C₂×C₁₉	#1966	1	1	yes	characteristic
153	C₂×C₁₉	#1980	1	1	yes	characteristic
154	C₂²×C₈	—	2	2	no	—
155	C₂²×C₈	—	38	2	no	—
156	#125	—	38	4	no	—
157	#125	—	38	4	no	—
158	C₂×C₄⋊C₄	—	19	2	no	—
159	C₂×C₄⋊C₄	—	19	2	no	—
160	C₂×C₄⋊C₄	—	38	1	no	—
161	C₂×C₄⋊C₄	—	38	1	no	—
162	C₂×C₄⋊C₄	—	38	1	no	—
163	C₂×C₄⋊C₄	—	38	1	no	—
164	C₂×C₄⋊C₄	—	38	2	no	—
165	C₂×C₄⋊C₄	—	38	2	no	—
166	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
167	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
168	C₂×C₄²	D₇₆	1	1	yes	characteristic
169	C₂×C₄²	D₇₆	1	1	yes	characteristic
170	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
171	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
172	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	C₄⋊C₈	—	38	4	no	—
174	#97	—	2	2	no	—
175	#97	—	38	4	no	—
176	#97	D₇₆	1	4	yes	—
177	#95	—	38	2	no	—
178	#95	—	38	2	no	—
179	C₁₉	#9690	1	1	yes	characteristic, complemented, Sylow
180	C₂²×C₄	—	38	2	no	—
181	C₂²×C₄	—	38	2	no	—
182	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
183	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
184	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
185	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
187	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	—	38	4	no	—
193	C₂×C₈	—	76	2	no	—
194	C₂×C₈	—	76	2	no	—
195	C₄⋊C₄	—	38	4	no	—
196	C₄⋊C₄	—	38	4	no	—
197	C₄⋊C₄	—	76	2	no	—
198	C₄⋊C₄	—	76	2	no	—
199	C₄⋊C₄	—	76	2	no	—
200	C₄⋊C₄	—	76	4	no	—
201	C₄⋊C₄	—	76	2	no	—
202	C₄⋊C₄	—	76	2	no	—
203	C₄⋊C₄	—	76	2	no	—
204	C₄²	—	2	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	2	2	no	—
207	C₄²	—	4	1	no	—
208	C₄²	—	4	1	no	—
209	C₄²	—	4	1	no	—
210	C₄²	C₂×D₇₆	1	2	yes	—
211	C₄²	#64541	1	2	yes	—
212	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
213	C₂×C₄	—	2	1	no	—
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	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	76	2	no	—
229	C₂×C₄	—	76	2	no	—
230	C₂×C₄	—	76	2	no	—
231	C₂×C₄	—	76	2	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	—	76	2	no	—
234	C₂×C₄	#10597281	1	2	yes	—
235	C₂×C₄	#10597281	1	2	yes	—
236	C₂×C₄	#10597282	1	2	yes	—
237	C₂×C₄	C₄×D₇₆	1	2	yes	—
238	C₂×C₄	#10597320	1	1	yes	characteristic
239	C₂×C₄	#10597321	1	1	yes	characteristic
240	C₂×C₄	#10597376	1	2	yes	—
241	C₈	—	4	4	no	—
242	C₈	—	76	4	no	—
243	C₂²	#11926446	1	1	yes	characteristic
244	C₂²	C₂×#10597281	1	1	yes	characteristic
245	C₂²	C₂×#10597281	1	1	yes	characteristic
246	C₂²	C₂×#10597282	1	1	yes	characteristic
247	C₂²	#11926560	1	1	yes	characteristic
248	C₂²	#11926562	1	1	yes	characteristic
249	C₂²	#11926562	1	1	yes	characteristic
250	C₄	—	2	2	no	—
251	C₄	—	2	2	no	—
252	C₄	—	2	2	no	—
253	C₄	—	2	1	no	—
254	C₄	—	2	1	no	—
255	C₄	—	2	2	no	—
256	C₄	—	2	2	no	—
257	C₄	—	4	1	no	—
258	C₄	—	152	2	no	—
259	C₄	—	152	2	no	—
260	C₂	#14562238	1	1	yes	characteristic
261	C₂	#14562251	1	1	yes	characteristic
262	C₂	#14562261	1	1	yes	characteristic
263	C₂	#14562272	1	1	yes	characteristic
264	C₂	#14564467	1	1	yes	characteristic
265	C₂	#14564479	1	1	yes	characteristic
266	C₂	#14564554	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14571998

C₂

yes

maximal, characteristic

#14563488

C₂

yes

maximal, characteristic

C₂×#11926285

C₂

yes

maximal

C₁₉×#1745

C₂

yes

maximal, characteristic

C₂×#10597316

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×#10597260

C₂²

yes

—

—

—

—

—

C₄

yes

characteristic

#11926414

C₄

yes

characteristic

#11926410

C₄

yes

—

#11926299

—

#11926285

—

C₂×C₁₉×#97

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×#336

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597316

—

C₁₉×#97

—

C₁₉×#97

D₄

yes

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

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×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9690

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

100

C₂×C₄×C₁₉

#124

yes

characteristic

101

C₂×C₄×C₁₉

#127

yes

characteristic

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

C₂×Dic₁₉

—

108

C₈×C₁₉

—

109

C₁₉⋊C₈

—

110

#2859

—

111

#1767

—

112

#1745

D₁₉

yes

characteristic

113

C₂×#330

—

114

C₂²×C₁₉

#390

yes

characteristic

115

C₂²×C₁₉

C₂×#101

yes

characteristic

116

C₂²×C₁₉

C₂×#101

yes

characteristic

117

C₂²×C₁₉

C₂×#104

yes

characteristic

118

C₂²×C₁₉

#421

yes

characteristic

119

C₂²×C₁₉

#421

yes

characteristic

120

C₂²×C₁₉

#421

yes

characteristic

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

Dic₁₉

—

130

Dic₁₉

—

131

C₂×#125

—

132

C₂×C₄⋊C₈

—

133

C₂×#97

—

134

C₂×#97

C₂×D₁₉

yes

—

135

#389

—

136

#389

—

137

#389

—

138

#389

—

139

#384

—

140

#384

—

141

#382

—

142

C₄³

C₂×D₁₉

yes

characteristic

143

#336

—

144

#336

—

145

#336

—

146

#330

—

147

C₂×C₁₉

#1528

yes

characteristic

148

C₂×C₁₉

#1531

yes

characteristic

149

C₂×C₁₉

#1534

yes

characteristic

150

C₂×C₁₉

#1537

yes

characteristic

151

C₂×C₁₉

#1963

yes

characteristic

152

C₂×C₁₉

#1966

yes

characteristic

153

C₂×C₁₉

#1980

yes

characteristic

154

C₂²×C₈

—

155

C₂²×C₈

—

156

#125

—

157

#125

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄²

C₄×D₁₉

yes

characteristic

167

C₂×C₄²

C₄×D₁₉

yes

characteristic

168

C₂×C₄²

D₇₆

yes

characteristic

169

C₂×C₄²

D₇₆

yes

characteristic

170

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

171

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

172

C₂×C₄²

C₂²×D₁₉

yes

characteristic

173

C₄⋊C₈

—

174

#97

—

175

#97

—

176

#97

D₇₆

yes

—

177

#95

—

178

#95

—

179

C₁₉

#9690

yes

characteristic, complemented, Sylow

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

183

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

184

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

185

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

186

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

187

C₂²×C₄

C₂×D₇₆

yes

characteristic

188

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₄²

C₂×D₇₆

yes

—

211

C₄²

#64541

yes

—

212

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

213

C₂×C₄

—

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

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

#10597281

yes

—

235

C₂×C₄

#10597281

yes

—

236

C₂×C₄

#10597282

yes

—

237

C₂×C₄

C₄×D₇₆

yes

—

238

C₂×C₄

#10597320

yes

characteristic

239

C₂×C₄

#10597321

yes

characteristic

240

C₂×C₄

#10597376

yes

—

241

C₈

—

242

C₈

—

243

C₂²

#11926446

yes

characteristic

244

C₂²

C₂×#10597281

yes

characteristic

245

C₂²

C₂×#10597281

yes

characteristic

246

C₂²

C₂×#10597282

yes

characteristic

247

C₂²

#11926560

yes

characteristic

248

C₂²

#11926562

yes

characteristic

249

C₂²

#11926562

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

152

—

259

C₄

—

152

—

260

C₂

#14562238

yes

characteristic

261

C₂

#14562251

yes

characteristic

262

C₂

#14562261

yes

characteristic

263

C₂

#14562272

yes

characteristic

264

C₂

#14564467

yes

characteristic

265

C₂

#14564479

yes

characteristic

266

C₂

#14564554

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1745	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1745	D₁₉
hypocenter	C₁₉	#9690
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1745

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1745

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1745

N	H ≅ G/N	type
179. C₁₉	#9690	semidirect

H ≅ G/N

type

179. C₁₉

#9690

semidirect

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

subgroup	index
#14571998	2
#14563488	2
C₂×#11926285	2
C₁₉×#1745	2
#9690	19

subgroup

index

C₁₉×#1745

Subgroups — #18081565

Conjugacy classes of subgroups

Complements

Maximal subgroups