Group #18080244 — subgroups

Subgroups — #18080244

Order 4864.

432 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 111 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	#14572720	C₂	1	1	yes	maximal, characteristic
2	#14562352	C₂	1	2	yes	maximal
3	#14561979	C₂	1	1	yes	maximal, characteristic
4	#14561491	C₂	1	2	yes	maximal
5	C₁₉×#2568	C₂	1	1	yes	maximal, characteristic
6	#11926675	—	2	4	no	—
7	#11926601	—	2	1	no	—
8	#11926601	C₂²	1	2	yes	—
9	#11926601	C₂²	1	2	yes	—
10	#11926597	—	2	1	no	—
11	#11926290	—	2	4	no	—
12	#11926270	—	2	1	no	—
13	#11926270	—	2	1	no	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#400	—	2	1	no	—
17	C₁₉×#400	—	2	1	no	—
18	C₁₉×#391	—	2	1	no	—
19	C₁₉×#391	—	2	1	no	—
20	C₁₉×#391	C₄	1	2	yes	—
21	C₁₉×#382	C₄	1	2	yes	—
22	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×Q₈×C₁₉	—	2	1	no	—
24	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₁₉×C₄⋊Q₈	—	2	2	no	—
26	C₁₉×C₄⋊Q₈	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₁₉×#95	—	2	2	no	—
40	C₁₉×#95	—	2	2	no	—
41	C₁₉×#95	—	2	2	no	—
42	C₁₉×#95	—	2	2	no	—
43	C₁₉×#95	—	2	1	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
50	#10597260	—	2	2	no	—
51	#10597260	—	2	2	no	—
52	#10597260	—	2	2	no	—
53	C₄×C₁₉⋊C₈	—	2	2	no	—
54	C₂×Q₈×C₁₉	—	2	2	no	—
55	C₂×Q₈×C₁₉	—	2	2	no	—
56	C₂×Q₈×C₁₉	—	4	1	no	—
57	C₂×Q₈×C₁₉	—	4	4	no	—
58	C₂×Q₈×C₁₉	—	4	1	no	—
59	C₂×Q₈×C₁₉	—	4	1	no	—
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄⋊C₄×C₁₉	—	2	4	no	—
73	C₄⋊C₄×C₁₉	—	4	2	no	—
74	C₄⋊C₄×C₁₉	—	4	2	no	—
75	C₄²×C₁₉	—	2	1	no	—
76	C₄²×C₁₉	—	2	1	no	—
77	C₄²×C₁₉	—	2	1	no	—
78	C₄²×C₁₉	—	2	1	no	—
79	C₄²×C₁₉	—	4	2	no	—
80	C₄²×C₁₉	C₂×D₄	1	2	yes	—
81	C₄²×C₁₉	#41	1	2	yes	—
82	C₂×C₁₉⋊C₈	—	2	4	no	—
83	C₂×C₁₉⋊C₈	—	4	2	no	—
84	#9456	—	19	1	no	maximal, Sylow
85	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	Q₈×C₁₉	—	4	4	no	—
87	Q₈×C₁₉	—	8	2	no	—
88	Q₈×C₁₉	—	8	2	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	2	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	4	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	#101	1	2	yes	—
108	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
109	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
110	C₂×C₄×C₁₉	#121	1	2	yes	—
111	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
112	C₁₉⋊C₈	—	4	4	no	—
113	C₁₉⋊C₈	—	8	2	no	—
114	#2983	—	19	1	no	—
115	#2568	D₁₉	1	1	yes	characteristic
116	#1556	—	19	2	no	—
117	#1467	—	19	1	no	—
118	#1285	—	19	2	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	#386	1	1	yes	characteristic
122	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
123	C₂²×C₁₉	#413	1	1	yes	characteristic
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	C₄×C₁₉	—	4	1	no	—
130	C₄×C₁₉	—	4	1	no	—
131	C₄×C₁₉	—	8	2	no	—
132	C₄×C₁₉	—	8	2	no	—
133	C₄×C₁₉	#454	1	2	yes	—
134	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
135	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
136	#446	—	38	4	no	—
137	#432	—	19	2	no	—
138	#432	—	19	2	no	—
139	#432	—	38	1	no	—
140	#431	—	38	1	no	—
141	#400	—	2	1	no	—
142	#400	—	2	1	no	—
143	#391	—	2	1	no	—
144	#391	—	2	1	no	—
145	#391	Dic₁₉	1	2	yes	—
146	#382	Dic₁₉	1	2	yes	—
147	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
148	#332	—	38	4	no	—
149	#324	—	38	1	no	—
150	#324	—	38	1	no	—
151	C₂×C₁₉	—	2	1	no	—
152	C₂×C₁₉	—	2	1	no	—
153	C₂×C₁₉	#1888	1	1	yes	characteristic
154	C₂×C₁₉	#1901	1	1	yes	characteristic
155	C₂×C₁₉	#1909	1	1	yes	characteristic
156	C₂²×Q₈	—	2	1	no	—
157	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
158	C₄⋊Q₈	—	2	2	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₄×Q₈	—	2	2	no	—
161	C₄×Q₈	—	2	2	no	—
162	C₂×C₄⋊C₄	—	2	1	no	—
163	C₂×C₄⋊C₄	—	2	1	no	—
164	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
165	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
166	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
167	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
168	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
169	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
170	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	C₄⋊C₈	—	19	4	no	—
173	C₄⋊C₈	—	38	2	no	—
174	C₄⋊C₈	—	38	2	no	—
175	C₄⋊C₈	—	38	2	no	—
176	C₂²⋊C₈	—	38	2	no	—
177	C₂²⋊C₈	—	38	2	no	—
178	#97	—	38	2	no	—
179	#97	—	38	2	no	—
180	#97	—	38	2	no	—
181	C₄×C₈	—	38	2	no	—
182	#95	—	2	2	no	—
183	#95	—	2	2	no	—
184	#95	—	2	2	no	—
185	#95	—	2	2	no	—
186	#95	—	2	1	no	—
187	C₁₉	#9456	1	1	yes	characteristic, complemented, Sylow
188	C₂×Q₈	—	2	2	no	—
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	—	4	1	no	—
191	C₂×Q₈	—	4	4	no	—
192	C₂×Q₈	—	4	1	no	—
193	C₂×Q₈	—	4	1	no	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	—	2	2	no	—
196	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
197	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
198	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
199	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
200	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
201	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
202	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
203	C₂×C₈	—	38	4	no	—
204	C₂×C₈	—	76	2	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	2	2	no	—
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	2	4	no	—
209	C₄⋊C₄	—	4	2	no	—
210	C₄⋊C₄	—	4	2	no	—
211	C₄²	—	2	1	no	—
212	C₄²	—	2	1	no	—
213	C₄²	—	2	1	no	—
214	C₄²	—	2	1	no	—
215	C₄²	—	4	2	no	—
216	C₄²	D₄×D₁₉	1	2	yes	—
217	C₄²	#64543	1	2	yes	—
218	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
219	Q₈	—	4	4	no	—
220	Q₈	—	8	2	no	—
221	Q₈	—	8	2	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	2	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	4	1	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	4	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	#10597293	1	2	yes	—
241	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
242	C₂×C₄	#10597381	1	1	yes	characteristic
243	C₂×C₄	#10597383	1	1	yes	characteristic
244	C₂×C₄	#10597385	1	2	yes	—
245	C₈	—	76	4	no	—
246	C₈	—	152	2	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	#11926424	1	1	yes	characteristic
250	C₂²	C₂×#10597293	1	1	yes	characteristic
251	C₂²	#11926528	1	1	yes	characteristic
252	C₄	—	2	2	no	—
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	2	1	no	—
256	C₄	—	4	1	no	—
257	C₄	—	4	1	no	—
258	C₄	—	4	1	no	—
259	C₄	—	8	2	no	—
260	C₄	—	8	2	no	—
261	C₄	#11926716	1	2	yes	—
262	C₂	—	2	1	no	—
263	C₂	—	2	1	no	—
264	C₂	#14564039	1	1	yes	characteristic
265	C₂	#14564104	1	1	yes	characteristic
266	C₂	#14564158	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572720

C₂

yes

maximal, characteristic

#14562352

C₂

yes

maximal

#14561979

C₂

yes

maximal, characteristic

#14561491

C₂

yes

maximal

C₁₉×#2568

C₂

yes

maximal, characteristic

#11926675

—

#11926601

—

#11926601

C₂²

yes

—

#11926601

C₂²

yes

—

—

—

—

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#400

—

C₁₉×#400

—

C₁₉×#391

—

C₁₉×#391

—

C₁₉×#391

C₄

yes

—

C₁₉×#382

C₄

yes

—

C₄×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

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

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9456

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

#101

yes

—

108

C₂×C₄×C₁₉

C₄×D₄

yes

—

109

C₂×C₄×C₁₉

#120

yes

characteristic

110

C₂×C₄×C₁₉

#121

yes

—

111

C₂×C₄×C₁₉

#123

yes

characteristic

112

C₁₉⋊C₈

—

113

C₁₉⋊C₈

—

114

#2983

—

115

#2568

D₁₉

yes

characteristic

116

#1556

—

117

#1467

—

118

#1285

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#386

yes

characteristic

122

C₂²×C₁₉

C₂×#101

yes

characteristic

123

C₂²×C₁₉

#413

yes

characteristic

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

#454

yes

—

134

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

135

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

136

#446

—

137

#432

—

138

#432

—

139

#432

—

140

#431

—

141

#400

—

142

#400

—

143

#391

—

144

#391

—

145

#391

Dic₁₉

yes

—

146

#382

Dic₁₉

yes

—

147

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

148

#332

—

149

#324

—

150

#324

—

151

C₂×C₁₉

—

152

C₂×C₁₉

—

153

C₂×C₁₉

#1888

yes

characteristic

154

C₂×C₁₉

#1901

yes

characteristic

155

C₂×C₁₉

#1909

yes

characteristic

156

C₂²×Q₈

—

157

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

158

C₄⋊Q₈

—

159

C₄⋊Q₈

—

160

C₄×Q₈

—

161

C₄×Q₈

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

165

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

166

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

167

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

168

C₂×C₄²

C₂×Dic₁₉

yes

—

169

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

170

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

171

C₂×C₄²

C₂²×D₁₉

yes

characteristic

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

#97

—

179

#97

—

180

#97

—

181

C₄×C₈

—

182

#95

—

183

#95

—

184

#95

—

185

#95

—

186

#95

—

187

C₁₉

#9456

yes

characteristic, complemented, Sylow

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

197

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

198

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

199

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

200

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

201

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

202

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

203

C₂×C₈

—

204

C₂×C₈

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

—

216

C₄²

D₄×D₁₉

yes

—

217

C₄²

#64543

yes

—

218

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

219

Q₈

—

220

Q₈

—

221

Q₈

—

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

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

#10597293

yes

—

241

C₂×C₄

D₄×Dic₁₉

yes

—

242

C₂×C₄

#10597381

yes

characteristic

243

C₂×C₄

#10597383

yes

characteristic

244

C₂×C₄

#10597385

yes

—

245

C₈

—

246

C₈

—

152

—

247

C₂²

—

248

C₂²

—

249

C₂²

#11926424

yes

characteristic

250

C₂²

C₂×#10597293

yes

characteristic

251

C₂²

#11926528

yes

characteristic

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

#11926716

yes

—

262

C₂

—

263

C₂

—

264

C₂

#14564039

yes

characteristic

265

C₂

#14564104

yes

characteristic

266

C₂

#14564158

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2568	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2568	D₁₉
hypocenter	C₁₉	#9456
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2568

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2568

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2568

N	H ≅ G/N	type
187. C₁₉	#9456	semidirect

H ≅ G/N

type

187. C₁₉

#9456

semidirect

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

subgroup	index
#14572720	2
#14562352	2
#14561979	2
#14561491	2
C₁₉×#2568	2
#9456	19

subgroup

index

C₁₉×#2568

Subgroups — #18080244

Conjugacy classes of subgroups

Complements

Maximal subgroups