Group #18075880 — subgroups

Subgroups — #18075880

Order 4864.

830 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 147 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	#14563545	C₂	1	2	yes	maximal
2	#14561478	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
6	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
7	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
9	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
10	C₁₉×#380	—	2	2	no	—
11	C₁₉×#380	—	2	2	no	—
12	C₂×C₁₉×#95	C₂²	1	2	yes	—
13	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₁₉	—	2	4	no	—
15	C₂³×C₄×C₁₉	—	4	4	no	—
16	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
18	C₂³×C₄×C₁₉	D₄	1	2	yes	—
19	C₂³×C₄×C₁₉	D₄	1	2	yes	—
20	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
24	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
27	C₂²×C₁₉⋊C₈	—	2	4	no	—
28	C₁₉×#95	—	2	4	no	—
29	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
30	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
31	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
32	C₂⁴×C₁₉	—	2	2	no	—
33	C₂⁴×C₁₉	—	2	2	no	—
34	C₂⁴×C₁₉	—	2	2	no	—
35	C₂⁴×C₁₉	—	2	4	no	—
36	C₂⁴×C₁₉	—	4	2	no	—
37	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	—	2	4	no	—
42	C₂²×C₄×C₁₉	—	2	4	no	—
43	C₂²×C₄×C₁₉	—	2	4	no	—
44	C₂²×C₄×C₁₉	—	2	4	no	—
45	C₂²×C₄×C₁₉	—	2	4	no	—
46	C₂²×C₄×C₁₉	—	2	4	no	—
47	C₂²×C₄×C₁₉	—	2	8	no	—
48	C₂²×C₄×C₁₉	—	4	2	no	—
49	C₂²×C₄×C₁₉	—	4	2	no	—
50	C₂²×C₄×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	4	16	no	—
52	C₂²×C₄×C₁₉	—	4	4	no	—
53	C₂²×C₄×C₁₉	—	4	4	no	—
54	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂²×C₄×C₁₉	#41	1	4	yes	—
57	C₄⋊C₄×C₁₉	—	4	4	no	—
58	C₄⋊C₄×C₁₉	—	4	4	no	—
59	C₂²⋊C₄×C₁₉	—	4	4	no	—
60	C₂²⋊C₄×C₁₉	—	4	4	no	—
61	C₂×C₁₉⋊C₈	—	4	4	no	—
62	C₂×C₁₉⋊C₈	—	4	4	no	—
63	C₂×C₁₉⋊C₈	—	4	4	no	—
64	#8704	—	19	1	no	maximal, Sylow
65	C₂³×C₁₉	—	2	2	no	—
66	C₂³×C₁₉	—	2	1	no	—
67	C₂³×C₁₉	—	2	1	no	—
68	C₂³×C₁₉	—	2	8	no	—
69	C₂³×C₁₉	—	2	1	no	—
70	C₂³×C₁₉	—	2	1	no	—
71	C₂³×C₁₉	—	2	2	no	—
72	C₂³×C₁₉	—	2	2	no	—
73	C₂³×C₁₉	—	2	2	no	—
74	C₂³×C₁₉	—	2	2	no	—
75	C₂³×C₁₉	—	2	1	no	—
76	C₂³×C₁₉	—	2	1	no	—
77	C₂³×C₁₉	—	4	8	no	—
78	C₂³×C₁₉	—	4	8	no	—
79	C₂³×C₁₉	—	4	4	no	—
80	C₂³×C₁₉	—	4	4	no	—
81	C₂³×C₁₉	#100	1	2	yes	—
82	C₂³×C₁₉	#101	1	2	yes	—
83	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂³×C₁₉	#117	1	2	yes	—
85	C₂³×C₁₉	#131	1	4	yes	—
86	C₂×C₄×C₁₉	—	2	8	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	4	4	no	—
92	C₂×C₄×C₁₉	—	4	8	no	—
93	C₂×C₄×C₁₉	—	4	8	no	—
94	C₂×C₄×C₁₉	—	4	4	no	—
95	C₂×C₄×C₁₉	—	4	4	no	—
96	C₂×C₄×C₁₉	—	4	4	no	—
97	C₂×C₄×C₁₉	—	8	8	no	—
98	C₂×C₄×C₁₉	#99	1	4	yes	—
99	C₂×C₄×C₁₉	#123	1	4	yes	—
100	C₁₉⋊C₈	—	8	4	no	—
101	C₂×#380	D₁₉	1	1	yes	characteristic
102	#1779	—	19	2	no	—
103	#1280	—	19	4	no	—
104	C₂²×C₁₉	—	2	2	no	—
105	C₂²×C₁₉	—	2	2	no	—
106	C₂²×C₁₉	—	2	4	no	—
107	C₂²×C₁₉	—	2	4	no	—
108	C₂²×C₁₉	—	2	2	no	—
109	C₂²×C₁₉	—	2	2	no	—
110	C₂²×C₁₉	—	2	4	no	—
111	C₂²×C₁₉	—	2	4	no	—
112	C₂²×C₁₉	—	4	16	no	—
113	C₂²×C₁₉	—	4	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	—	4	2	no	—
119	C₂²×C₁₉	#381	1	1	yes	characteristic
120	C₂²×C₁₉	#408	1	2	yes	—
121	C₂²×C₁₉	C₂×#99	1	2	yes	—
122	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
123	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
124	C₂²×C₁₉	#433	1	4	yes	—
125	C₄×C₁₉	—	2	4	no	—
126	C₄×C₁₉	—	2	4	no	—
127	C₄×C₁₉	—	8	4	no	—
128	C₂⁴×C₄	C₂×D₁₉	1	1	yes	characteristic
129	C₂²×C₄⋊C₄	Dic₁₉	1	2	yes	—
130	C₂²×C₂²⋊C₄	Dic₁₉	1	2	yes	—
131	C₂×C₂²⋊C₈	—	19	4	no	—
132	C₂×C₂²⋊C₈	—	38	2	no	—
133	C₂×C₂²⋊C₈	—	38	2	no	—
134	#380	—	2	2	no	—
135	#380	—	2	2	no	—
136	C₂×#95	C₂×D₁₉	1	2	yes	—
137	C₂×C₁₉	—	2	4	no	—
138	C₂×C₁₉	—	4	2	no	—
139	C₂×C₁₉	—	4	2	no	—
140	C₂×C₁₉	#1471	1	2	yes	—
141	C₂×C₁₉	#1472	1	2	yes	—
142	C₂×C₁₉	#1818	1	1	yes	characteristic
143	C₂×C₁₉	#1819	1	1	yes	characteristic
144	C₂×C₁₉	#1821	1	1	yes	characteristic
145	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
146	C₂³×C₄	—	2	4	no	—
147	C₂³×C₄	—	4	4	no	—
148	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
149	C₂³×C₄	C₂×Dic₁₉	1	4	yes	—
150	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
151	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
152	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
153	C₂²×C₈	—	38	4	no	—
154	C₂×C₄⋊C₄	—	2	2	no	—
155	C₂×C₄⋊C₄	—	2	2	no	—
156	C₂×C₄⋊C₄	—	4	4	no	—
157	C₂×C₂²⋊C₄	—	2	2	no	—
158	C₂×C₂²⋊C₄	—	2	2	no	—
159	C₂×C₂²⋊C₄	—	4	4	no	—
160	C₂²⋊C₈	—	38	8	no	—
161	C₂²⋊C₈	—	76	4	no	—
162	C₂²⋊C₈	—	76	4	no	—
163	#95	—	2	4	no	—
164	C₁₉	#8704	1	1	yes	characteristic, complemented, Sylow
165	C₂⁴	—	2	2	no	—
166	C₂⁴	—	2	2	no	—
167	C₂⁴	—	2	2	no	—
168	C₂⁴	—	2	4	no	—
169	C₂⁴	—	4	2	no	—
170	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
171	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
172	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	4	no	—
175	C₂²×C₄	—	2	4	no	—
176	C₂²×C₄	—	2	4	no	—
177	C₂²×C₄	—	2	4	no	—
178	C₂²×C₄	—	2	4	no	—
179	C₂²×C₄	—	2	4	no	—
180	C₂²×C₄	—	2	8	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	—	4	2	no	—
183	C₂²×C₄	—	4	2	no	—
184	C₂²×C₄	—	4	16	no	—
185	C₂²×C₄	—	4	4	no	—
186	C₂²×C₄	—	4	4	no	—
187	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
188	C₂²×C₄	#64541	1	4	yes	—
189	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
190	C₂×C₈	—	76	4	no	—
191	C₂×C₈	—	76	4	no	—
192	C₂×C₈	—	76	4	no	—
193	C₄⋊C₄	—	4	4	no	—
194	C₄⋊C₄	—	4	4	no	—
195	C₂²⋊C₄	—	4	4	no	—
196	C₂²⋊C₄	—	4	4	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	2	1	no	—
199	C₂³	—	2	1	no	—
200	C₂³	—	2	8	no	—
201	C₂³	—	2	1	no	—
202	C₂³	—	2	1	no	—
203	C₂³	—	2	2	no	—
204	C₂³	—	2	2	no	—
205	C₂³	—	2	2	no	—
206	C₂³	—	2	2	no	—
207	C₂³	—	2	1	no	—
208	C₂³	—	2	1	no	—
209	C₂³	—	4	8	no	—
210	C₂³	—	4	8	no	—
211	C₂³	—	4	4	no	—
212	C₂³	—	4	4	no	—
213	C₂³	#10597290	1	2	yes	—
214	C₂³	#10597293	1	2	yes	—
215	C₂³	#10597372	1	2	yes	—
216	C₂³	#10597394	1	4	yes	—
217	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
218	C₂×C₄	—	2	8	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	4	4	no	—
224	C₂×C₄	—	4	8	no	—
225	C₂×C₄	—	4	8	no	—
226	C₂×C₄	—	4	4	no	—
227	C₂×C₄	—	4	4	no	—
228	C₂×C₄	—	4	4	no	—
229	C₂×C₄	—	8	8	no	—
230	C₂×C₄	#10597291	1	4	yes	—
231	C₂×C₄	#10597375	1	4	yes	—
232	C₈	—	152	4	no	—
233	C₂²	—	2	2	no	—
234	C₂²	—	2	2	no	—
235	C₂²	—	2	4	no	—
236	C₂²	—	2	4	no	—
237	C₂²	—	2	2	no	—
238	C₂²	—	2	2	no	—
239	C₂²	—	2	4	no	—
240	C₂²	—	2	4	no	—
241	C₂²	—	4	16	no	—
242	C₂²	—	4	1	no	—
243	C₂²	—	4	1	no	—
244	C₂²	—	4	1	no	—
245	C₂²	—	4	1	no	—
246	C₂²	—	4	2	no	—
247	C₂²	—	4	2	no	—
248	C₂²	#11926407	1	1	yes	characteristic
249	C₂²	#11926511	1	2	yes	—
250	C₂²	C₂×#10597291	1	2	yes	—
251	C₂²	C₂×#10597290	1	1	yes	characteristic
252	C₂²	C₂×#10597293	1	1	yes	characteristic
253	C₂²	#11926605	1	4	yes	—
254	C₄	—	2	4	no	—
255	C₄	—	2	4	no	—
256	C₄	—	8	4	no	—
257	C₂	—	2	4	no	—
258	C₂	—	4	2	no	—
259	C₂	—	4	2	no	—
260	C₂	#14561995	1	2	yes	—
261	C₂	#14561999	1	2	yes	—
262	C₂	#14563706	1	1	yes	characteristic
263	C₂	#14563709	1	1	yes	characteristic
264	C₂	#14563715	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563545

C₂

yes

maximal

#14561478

C₂

yes

maximal, complemented

C₂×C₁₉×#380

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂⁴×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₄⋊C₄×C₁₉

C₄

yes

—

C₂²×C₂²⋊C₄×C₁₉

C₄

yes

—

C₁₉×#380

—

C₁₉×#380

—

C₂×C₁₉×#95

C₂²

yes

—

C₂⁵×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8704

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#100

yes

—

C₂³×C₁₉

#101

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

C₂³×C₁₉

#131

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

—

C₂×C₄×C₁₉

#123

yes

—

100

C₁₉⋊C₈

—

101

C₂×#380

D₁₉

yes

characteristic

102

#1779

—

103

#1280

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

#381

yes

characteristic

120

C₂²×C₁₉

#408

yes

—

121

C₂²×C₁₉

C₂×#99

yes

—

122

C₂²×C₁₉

C₂×#100

yes

characteristic

123

C₂²×C₁₉

C₂×#101

yes

characteristic

124

C₂²×C₁₉

#433

yes

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₂⁴×C₄

C₂×D₁₉

yes

characteristic

129

C₂²×C₄⋊C₄

Dic₁₉

yes

—

130

C₂²×C₂²⋊C₄

Dic₁₉

yes

—

131

C₂×C₂²⋊C₈

—

132

C₂×C₂²⋊C₈

—

133

C₂×C₂²⋊C₈

—

134

#380

—

135

#380

—

136

C₂×#95

C₂×D₁₉

yes

—

137

C₂×C₁₉

—

138

C₂×C₁₉

—

139

C₂×C₁₉

—

140

C₂×C₁₉

#1471

yes

—

141

C₂×C₁₉

#1472

yes

—

142

C₂×C₁₉

#1818

yes

characteristic

143

C₂×C₁₉

#1819

yes

characteristic

144

C₂×C₁₉

#1821

yes

characteristic

145

C₂⁵

C₂×Dic₁₉

yes

characteristic

146

C₂³×C₄

—

147

C₂³×C₄

—

148

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

149

C₂³×C₄

C₂×Dic₁₉

yes

—

150

C₂³×C₄

C₂²⋊D₁₉

yes

—

151

C₂³×C₄

C₂²⋊D₁₉

yes

—

152

C₂³×C₄

C₂²×D₁₉

yes

characteristic

153

C₂²×C₈

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₂²⋊C₄

—

158

C₂×C₂²⋊C₄

—

159

C₂×C₂²⋊C₄

—

160

C₂²⋊C₈

—

161

C₂²⋊C₈

—

162

C₂²⋊C₈

—

163

#95

—

164

C₁₉

#8704

yes

characteristic, complemented, Sylow

165

C₂⁴

—

166

C₂⁴

—

167

C₂⁴

—

168

C₂⁴

—

169

C₂⁴

—

170

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

171

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

172

C₂⁴

C₂²×Dic₁₉

yes

characteristic

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

188

C₂²×C₄

#64541

yes

—

189

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₂²⋊C₄

—

196

C₂²⋊C₄

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

#10597290

yes

—

214

C₂³

#10597293

yes

—

215

C₂³

#10597372

yes

—

216

C₂³

#10597394

yes

—

217

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

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

#10597291

yes

—

231

C₂×C₄

#10597375

yes

—

232

C₈

—

152

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

#11926407

yes

characteristic

249

C₂²

#11926511

yes

—

250

C₂²

C₂×#10597291

yes

—

251

C₂²

C₂×#10597290

yes

characteristic

252

C₂²

C₂×#10597293

yes

characteristic

253

C₂²

#11926605

yes

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₂

—

258

C₂

—

259

C₂

—

260

C₂

#14561995

yes

—

261

C₂

#14561999

yes

—

262

C₂

#14563706

yes

characteristic

263

C₂

#14563709

yes

characteristic

264

C₂

#14563715

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#380	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₁₉	C₂×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#380	D₁₉
hypocenter	C₁₉	#8704
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×#380

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#380

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁵×C₁₉

C₂×C₄

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×#380

N	H ≅ G/N	type
2. #14561478	C₂	semidirect
164. C₁₉	#8704	semidirect

H ≅ G/N

type

2. #14561478

C₂

semidirect

164. C₁₉

#8704

semidirect

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

subgroup	index
#14563545	2
#14561478	2
C₂×C₁₉×#380	2
#8704	19

subgroup

index

#14563545

#14561478

C₂×C₁₉×#380

#8704

Subgroups — #18075880

Conjugacy classes of subgroups

Complements

Maximal subgroups