Group #18076400 — subgroups

Subgroups — #18076400

Order 4864.

482 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₄×#10597290	C₂	1	1	yes	maximal, characteristic
3	#14562385	C₂	1	2	yes	maximal, complemented
4	#14561472	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic
6	D₄×C₁₉⋊C₈	—	2	2	no	—
7	D₄×C₁₉⋊C₈	—	2	2	no	—
8	#11926597	C₂²	1	2	yes	—
9	C₂×#10597290	C₄	1	1	yes	characteristic
10	C₂×#10597290	C₄	1	1	yes	characteristic
11	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
12	C₄×#64520	C₂²	1	2	yes	—
13	#11926313	C₄	1	2	yes	—
14	#11926296	—	2	2	no	—
15	#11926294	—	2	2	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	D₄	1	2	yes	—
22	C₂²×C₈×C₁₉	—	2	1	no	—
23	C₂²×C₈×C₁₉	—	2	1	no	—
24	C₄×D₄×C₁₉	—	2	2	no	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×#64520	C₂×C₄	1	2	yes	—
30	C₂×#64520	C₂×C₄	1	2	yes	—
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	C₂²×C₁₉⋊C₈	—	2	2	no	—
33	C₁₉×C₄⋊C₈	—	2	2	no	—
34	C₁₉×C₂²⋊C₈	—	4	4	no	—
35	C₄×C₈×C₁₉	—	2	2	no	—
36	#10597290	—	2	2	no	—
37	#10597290	C₈	1	4	yes	complemented
38	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
39	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
41	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
42	#10597260	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₄×C₁₉⋊C₈	—	2	2	no	—
45	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
46	C₂×D₄×C₁₉	—	2	2	no	—
47	C₂×D₄×C₁₉	—	2	2	no	—
48	C₂×D₄×C₁₉	C₂×C₈	1	2	yes	—
49	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	C₄⋊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×Q₈	1	1	yes	characteristic
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₂×C₈×C₁₉	—	4	1	no	—
61	C₂×C₈×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	—	4	1	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂²⋊C₄×C₁₉	—	2	4	no	—
65	C₄²×C₁₉	C₂×D₄	1	2	yes	—
66	C₄²×C₁₉	#41	1	2	yes	—
67	#64520	—	2	2	no	—
68	#64520	—	2	2	no	—
69	#64520	—	2	2	no	—
70	#64520	C₂×C₈	1	4	yes	complemented
71	C₂×C₁₉⋊C₈	—	2	2	no	—
72	C₂×C₁₉⋊C₈	—	2	2	no	—
73	C₂×C₁₉⋊C₈	—	2	2	no	—
74	C₂×C₁₉⋊C₈	—	2	2	no	—
75	C₂×C₁₉⋊C₈	—	8	2	no	—
76	C₂×C₁₉⋊C₈	—	8	2	no	—
77	#8835	—	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	C₄⋊C₈	1	4	yes	—
83	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
84	D₄×C₁₉	—	2	4	no	—
85	D₄×C₁₉	—	2	4	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	8	2	no	—
94	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
95	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
97	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#131	1	2	yes	—
101	C₈×C₁₉	—	4	2	no	—
102	C₈×C₁₉	—	8	1	no	—
103	C₁₉⋊C₈	—	2	4	no	—
104	C₁₉⋊C₈	—	4	2	no	—
105	C₁₉⋊C₈	—	4	2	no	—
106	C₁₉⋊C₈	—	4	2	no	—
107	#2972	—	19	1	no	—
108	#1954	D₁₉	1	1	yes	characteristic
109	C₄×#100	—	19	1	no	—
110	#1565	—	19	2	no	—
111	#1278	—	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	#385	1	1	yes	characteristic
120	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
121	C₂²×C₁₉	#424	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	C₈×D₄	1	2	yes	—
126	C₄×C₁₉	#435	1	2	yes	—
127	C₄×C₁₉	#453	1	1	yes	characteristic
128	C₄×C₁₉	#455	1	1	yes	characteristic
129	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
130	C₈×D₄	—	38	2	no	—
131	C₈×D₄	—	38	2	no	—
132	#431	—	19	2	no	—
133	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
134	C₂×#100	—	19	1	no	—
135	C₂×#100	—	19	1	no	—
136	C₂×C₂²⋊C₈	—	2	2	no	—
137	C₂×C₂²⋊C₈	—	38	2	no	—
138	C₄×M₁₆	—	19	2	no	—
139	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
140	#343	—	19	2	no	—
141	#335	—	38	2	no	—
142	#334	—	38	2	no	—
143	C₂×C₁₉	—	2	1	no	—
144	C₂×C₁₉	—	2	1	no	—
145	C₂×C₁₉	—	4	4	no	—
146	C₂×C₁₉	#1850	1	1	yes	characteristic
147	C₂×C₁₉	#1856	1	1	yes	characteristic
148	C₂×C₁₉	#1858	1	1	yes	characteristic
149	C₂²×D₄	C₄×D₁₉	1	1	yes	characteristic
150	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
151	C₂×M₁₆	—	19	2	no	—
152	C₂×M₁₆	—	19	2	no	—
153	C₂²×C₈	—	2	1	no	—
154	C₂²×C₈	—	2	1	no	—
155	C₂²×C₈	—	38	2	no	—
156	C₂²×C₈	—	38	2	no	—
157	C₄×D₄	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
160	C₂×C₂²⋊C₄	Dic₃₈	1	2	yes	—
161	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	19	2	no	—
164	C₄⋊C₈	—	19	2	no	—
165	#100	—	19	4	no	—
166	#100	—	38	2	no	—
167	C₂²⋊C₈	—	4	4	no	—
168	C₂²⋊C₈	—	38	4	no	—
169	C₂²⋊C₈	—	38	2	no	—
170	#97	—	38	2	no	—
171	C₄×C₈	—	2	2	no	—
172	C₄×C₈	—	38	2	no	—
173	C₄×C₈	—	38	2	no	—
174	C₁₉	#8835	1	1	yes	characteristic, complemented, Sylow
175	C₂⁴	Dic₁₉⋊C₄	1	2	yes	—
176	C₂×D₄	—	2	2	no	—
177	C₂×D₄	—	2	2	no	—
178	C₂×D₄	C₈×D₁₉	1	2	yes	—
179	C₂×D₄	#64515	1	2	yes	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	4	2	no	—
183	C₂²×C₄	—	4	2	no	—
184	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
185	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
187	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
188	M₁₆	—	19	4	no	—
189	M₁₆	—	38	2	no	—
190	M₁₆	—	38	2	no	—
191	M₁₆	—	38	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	4	1	no	—
194	C₂×C₈	—	4	1	no	—
195	C₂×C₈	—	4	2	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	38	2	no	—
198	C₂×C₈	—	38	2	no	—
199	C₂×C₈	—	38	2	no	—
200	C₂×C₈	—	38	2	no	—
201	C₂×C₈	—	152	2	no	—
202	C₂×C₈	—	152	2	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₂²⋊C₄	—	2	4	no	—
205	C₄²	D₄×D₁₉	1	2	yes	—
206	C₄²	#64543	1	2	yes	—
207	C₂³	—	2	2	no	—
208	C₂³	—	2	2	no	—
209	C₂³	—	4	2	no	—
210	C₂³	—	4	2	no	—
211	C₂³	Dic₁₉⋊C₈	1	4	yes	—
212	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
213	D₄	—	2	4	no	—
214	D₄	—	2	4	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	8	2	no	—
223	C₂×C₄	#10597324	1	2	yes	—
224	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
225	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
226	C₂×C₄	C₂×#64515	1	1	yes	characteristic
227	C₂×C₄	#10597353	1	2	yes	—
228	C₂×C₄	#10597381	1	1	yes	characteristic
229	C₂×C₄	#10597383	1	1	yes	characteristic
230	C₈	—	4	2	no	—
231	C₈	—	8	1	no	—
232	C₈	—	38	4	no	—
233	C₈	—	76	2	no	—
234	C₈	—	76	2	no	—
235	C₈	—	76	2	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	4	no	—
239	C₂²	—	4	4	no	—
240	C₂²	—	4	2	no	—
241	C₂²	—	4	2	no	—
242	C₂²	—	8	2	no	—
243	C₂²	#11926416	1	1	yes	characteristic
244	C₂²	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
245	C₂²	#11926572	1	1	yes	characteristic
246	C₄	—	2	1	no	—
247	C₄	—	2	2	no	—
248	C₄	—	4	2	no	—
249	C₄	(C₂²⋊D₁₉)⋊C₈	1	2	yes	—
250	C₄	#11926612	1	2	yes	—
251	C₄	#11926711	1	1	yes	characteristic
252	C₄	#11926721	1	1	yes	characteristic
253	C₂	—	2	1	no	—
254	C₂	—	2	1	no	—
255	C₂	—	4	4	no	—
256	C₂	#14563812	1	1	yes	characteristic
257	C₂	#14563844	1	1	yes	characteristic
258	C₂	#14563854	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572659

C₂

yes

maximal, characteristic

C₄×#10597290

C₂

yes

maximal, characteristic

#14562385

C₂

yes

maximal, complemented

#14561472

C₂

yes

maximal, complemented

C₁₉×#1954

C₂

yes

maximal, characteristic

D₄×C₁₉⋊C₈

—

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

C₂×#10597290

C₄

yes

characteristic

C₂×#10597290

C₄

yes

characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₄×#64520

C₂²

yes

—

#11926313

C₄

yes

—

#11926296

—

#11926294

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

C₂×C₄

yes

—

C₂×#64520

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597290

—

#10597290

C₈

yes

complemented

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₄⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₈

yes

—

C₂×D₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

—

—

—

C₂×C₈

yes

complemented

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8835

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₄⋊C₈

yes

—

C₂³×C₁₉

C₂×C₄⋊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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

100

C₂×C₄×C₁₉

#131

yes

—

101

C₈×C₁₉

—

102

C₈×C₁₉

—

103

C₁₉⋊C₈

—

104

C₁₉⋊C₈

—

105

C₁₉⋊C₈

—

106

C₁₉⋊C₈

—

107

#2972

—

108

#1954

D₁₉

yes

characteristic

109

C₄×#100

—

110

#1565

—

111

#1278

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

#385

yes

characteristic

120

C₂²×C₁₉

C₂×C₄⋊C₈

yes

characteristic

121

C₂²×C₁₉

#424

yes

characteristic

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

C₈×D₄

yes

—

126

C₄×C₁₉

#435

yes

—

127

C₄×C₁₉

#453

yes

characteristic

128

C₄×C₁₉

#455

yes

characteristic

129

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

130

C₈×D₄

—

131

C₈×D₄

—

132

#431

—

133

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

134

C₂×#100

—

135

C₂×#100

—

136

C₂×C₂²⋊C₈

—

137

C₂×C₂²⋊C₈

—

138

C₄×M₁₆

—

139

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

140

#343

—

141

#335

—

142

#334

—

143

C₂×C₁₉

—

144

C₂×C₁₉

—

145

C₂×C₁₉

—

146

C₂×C₁₉

#1850

yes

characteristic

147

C₂×C₁₉

#1856

yes

characteristic

148

C₂×C₁₉

#1858

yes

characteristic

149

C₂²×D₄

C₄×D₁₉

yes

characteristic

150

C₂³×C₄

C₂²⋊D₁₉

yes

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₄×D₄

—

158

C₄×D₄

—

159

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

160

C₂×C₂²⋊C₄

Dic₃₈

yes

—

161

C₂×C₄²

C₂²×D₁₉

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

#100

—

166

#100

—

167

C₂²⋊C₈

—

168

C₂²⋊C₈

—

169

C₂²⋊C₈

—

170

#97

—

171

C₄×C₈

—

172

C₄×C₈

—

173

C₄×C₈

—

174

C₁₉

#8835

yes

characteristic, complemented, Sylow

175

C₂⁴

Dic₁₉⋊C₄

yes

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

C₈×D₁₉

yes

—

179

C₂×D₄

#64515

yes

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

Dic₁₉⋊C₄

yes

—

185

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

186

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

187

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

188

M₁₆

—

189

M₁₆

—

190

M₁₆

—

191

M₁₆

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

152

—

202

C₂×C₈

—

152

—

203

C₄⋊C₄

—

204

C₂²⋊C₄

—

205

C₄²

D₄×D₁₉

yes

—

206

C₄²

#64543

yes

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

Dic₁₉⋊C₈

yes

—

212

C₂³

C₂×Dic₁₉⋊C₄

yes

characteristic

213

D₄

—

214

D₄

—

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

#10597324

yes

—

224

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

225

C₂×C₄

C₂×C₈×D₁₉

yes

characteristic

226

C₂×C₄

C₂×#64515

yes

characteristic

227

C₂×C₄

#10597353

yes

—

228

C₂×C₄

#10597381

yes

characteristic

229

C₂×C₄

#10597383

yes

characteristic

230

C₈

—

231

C₈

—

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

#11926416

yes

characteristic

244

C₂²

C₂×Dic₁₉⋊C₈

yes

characteristic

245

C₂²

#11926572

yes

characteristic

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

(C₂²⋊D₁₉)⋊C₈

yes

—

250

C₄

#11926612

yes

—

251

C₄

#11926711

yes

characteristic

252

C₄

#11926721

yes

characteristic

253

C₂

—

254

C₂

—

255

C₂

—

256

C₂

#14563812

yes

characteristic

257

C₂

#14563844

yes

characteristic

258

C₂

#14563854

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1954	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1954	D₁₉
hypocenter	C₁₉	#8835
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂×C₄

#10597383

commutator

C₂×C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1954

C₂

socle

C₂²×C₁₉

#385

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
3. #14562385	C₂	semidirect
4. #14561472	C₂	semidirect
37. #10597290	C₈	semidirect
70. #64520	C₂×C₈	semidirect
174. C₁₉	#8835	semidirect

H ≅ G/N

type

3. #14562385

C₂

semidirect

4. #14561472

C₂

semidirect

37. #10597290

C₈

semidirect

70. #64520

C₂×C₈

semidirect

174. C₁₉

#8835

semidirect

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

subgroup	index
#14572659	2
C₄×#10597290	2
#14562385	2
#14561472	2
C₁₉×#1954	2
#8835	19

subgroup

index

C₁₉×#1954

Subgroups — #18076400

Conjugacy classes of subgroups

Complements

Maximal subgroups