Group #18075502 — subgroups

Subgroups — #18075502

Order 4864.

418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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	C₂×#11926623	C₂	1	1	yes	maximal, characteristic
2	#14562398	C₂	1	1	yes	maximal, characteristic, complemented
3	#14561975	C₂	1	2	yes	maximal
4	#14561504	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#64515	C₄	1	2	yes	—
7	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
8	#11926623	—	2	1	no	—
9	#11926623	—	2	1	no	—
10	#11926623	—	2	1	no	—
11	#11926623	—	2	1	no	—
12	#11926601	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₈	C₄	1	2	yes	—
15	#11926297	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926267	—	2	4	no	—
18	C₁₉×#432	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#335	—	2	1	no	—
21	C₁₉×#334	—	2	1	no	—
22	C₂²×D₇₆	Q₈	1	1	yes	characteristic
23	C₂²×C₄×D₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×(C₂×D₁₉)⋊C₄	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₁₉	Q₈	1	1	yes	characteristic
29	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
30	C₂×#64515	—	2	2	no	—
31	C₂×#64515	—	2	2	no	—
32	C₂×#64515	—	4	4	no	—
33	C₄×D₇₆	—	2	1	no	—
34	C₄×D₇₆	—	2	1	no	—
35	C₄×D₇₆	—	2	1	no	—
36	C₄×D₇₆	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₂²⋊C₈	—	2	2	no	—
39	C₁₉×#97	—	2	2	no	—
40	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
45	(C₂×D₁₉)⋊C₈	—	2	2	no	—
46	(C₂×D₁₉)⋊C₈	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	#10597260	—	2	2	no	—
51	C₂³×D₁₉	C₄⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
56	C₂×D₇₆	—	2	1	no	—
57	C₂×D₇₆	—	2	1	no	—
58	C₂×D₇₆	—	4	2	no	—
59	C₂×C₄×D₁₉	—	2	2	no	—
60	C₂×C₄×D₁₉	—	2	2	no	—
61	C₂×C₄×D₁₉	—	4	2	no	—
62	C₂×C₄×D₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	#41	1	1	yes	characteristic
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	(C₂×D₁₉)⋊C₄	—	2	2	no	—
75	(C₂×D₁₉)⋊C₄	—	2	2	no	—
76	C₄⋊Dic₁₉	—	2	1	no	—
77	C₄⋊Dic₁₉	—	2	1	no	—
78	C₂×C₁₉⋊C₈	—	2	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	C₂×C₁₉⋊C₈	—	4	2	no	—
81	#64515	—	4	4	no	—
82	#64515	—	4	4	no	—
83	#8624	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂²×D₁₉	—	2	2	no	—
86	C₂²×D₁₉	—	2	4	no	—
87	C₂²×D₁₉	—	4	2	no	—
88	C₂²×D₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
99	C₂×Dic₁₉	—	2	2	no	—
100	C₂×Dic₁₉	—	4	2	no	—
101	D₇₆	—	4	2	no	—
102	D₇₆	—	4	2	no	—
103	C₄×D₁₉	—	4	4	no	—
104	C₄×D₁₉	—	4	2	no	—
105	C₄×D₁₉	—	4	2	no	—
106	C₈×C₁₉	—	2	1	no	—
107	C₈×C₁₉	—	2	1	no	—
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	8	2	no	—
110	C₈×C₁₉	#100	1	2	yes	—
111	C₁₉⋊C₈	—	4	2	no	—
112	C₁₉⋊C₈	—	8	2	no	—
113	C₂×#436	—	19	1	no	—
114	#1568	—	19	1	no	—
115	#1568	D₁₉	1	1	yes	characteristic, complemented
116	#1466	—	19	2	no	—
117	#1290	—	19	2	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	#380	1	1	yes	characteristic
121	C₂²×C₁₉	#430	1	2	yes	—
122	C₂×D₁₉	—	4	2	no	—
123	C₂×D₁₉	—	4	2	no	—
124	C₂×D₁₉	—	4	2	no	—
125	C₂×D₁₉	—	8	4	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
132	C₄×C₁₉	#413	1	1	yes	characteristic
133	Dic₁₉	—	4	2	no	—
134	C₂²×M₁₆	—	19	2	no	—
135	C₂×C₄×D₄	—	19	1	no	—
136	#436	—	38	1	no	—
137	#436	—	38	1	no	—
138	#436	—	38	1	no	—
139	#436	—	38	1	no	—
140	#432	—	19	2	no	—
141	#432	C₂×D₁₉	1	2	yes	—
142	C₂×C₄⋊C₈	—	19	1	no	—
143	C₂×C₂²⋊C₈	—	19	2	no	—
144	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
145	#335	—	2	1	no	—
146	#335	—	38	1	no	—
147	#334	—	2	1	no	—
148	#334	—	38	1	no	—
149	#323	—	38	4	no	—
150	C₂×C₁₉	—	2	2	no	—
151	C₂×C₁₉	#1800	1	1	yes	characteristic
152	C₂×C₁₉	#1811	1	1	yes	characteristic
153	C₂×C₁₉	#1812	1	1	yes	characteristic
154	D₁₉	—	8	2	no	—
155	C₂²×D₄	—	19	1	no	—
156	C₂³×C₄	—	19	2	no	—
157	C₂×M₁₆	—	38	2	no	—
158	C₂×M₁₆	—	38	2	no	—
159	C₂×M₁₆	—	76	4	no	—
160	C₂²×C₈	—	19	2	no	—
161	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
162	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
163	C₄×D₄	—	38	1	no	—
164	C₄×D₄	—	38	1	no	—
165	C₄×D₄	—	38	1	no	—
166	C₄×D₄	—	38	1	no	—
167	C₂×C₄⋊C₄	—	19	1	no	—
168	C₂×C₂²⋊C₄	—	19	2	no	—
169	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
170	C₄⋊C₈	—	2	2	no	—
171	C₄⋊C₈	—	38	1	no	—
172	C₄⋊C₈	—	38	2	no	—
173	C₄⋊C₈	—	38	1	no	—
174	C₂²⋊C₈	—	2	2	no	—
175	C₂²⋊C₈	—	38	2	no	—
176	C₂²⋊C₈	—	38	2	no	—
177	C₂²⋊C₈	—	38	2	no	—
178	#97	—	2	2	no	—
179	#97	—	38	2	no	—
180	C₄×C₈	D₇₆	1	1	yes	characteristic
181	C₄×C₈	D₇₆	1	1	yes	characteristic
182	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
183	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
184	C₁₉	#8624	1	1	yes	characteristic, complemented, Sylow
185	C₂⁴	—	19	2	no	—
186	C₂×D₄	—	38	1	no	—
187	C₂×D₄	—	38	1	no	—
188	C₂×D₄	—	76	2	no	—
189	C₂²×C₄	—	19	2	no	—
190	C₂²×C₄	—	38	2	no	—
191	C₂²×C₄	—	38	2	no	—
192	C₂²×C₄	—	76	2	no	—
193	C₂²×C₄	—	76	2	no	—
194	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
195	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
196	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
197	M₁₆	—	76	4	no	—
198	M₁₆	—	76	4	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	4	2	no	—
202	C₂×C₈	—	38	2	no	—
203	C₂×C₈	—	76	2	no	—
204	C₂×C₈	—	76	2	no	—
205	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
206	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
208	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
209	C₄⋊C₄	—	38	1	no	—
210	C₄⋊C₄	—	38	1	no	—
211	C₂²⋊C₄	—	38	2	no	—
212	C₂²⋊C₄	—	38	2	no	—
213	C₄²	C₂×D₇₆	1	1	yes	characteristic
214	C₄²	#64543	1	1	yes	characteristic
215	C₄²	#64545	1	1	yes	characteristic
216	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
217	C₂³	—	38	2	no	—
218	C₂³	—	38	4	no	—
219	C₂³	—	76	2	no	—
220	C₂³	—	76	2	no	—
221	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
222	D₄	—	76	2	no	—
223	D₄	—	76	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	38	2	no	—
229	C₂×C₄	—	76	4	no	—
230	C₂×C₄	—	76	2	no	—
231	C₂×C₄	—	76	2	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	#10597338	1	1	yes	characteristic
234	C₂×C₄	#10597341	1	1	yes	characteristic
235	C₂×C₄	#10597343	1	1	yes	characteristic
236	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
237	C₂×C₄	#10597384	1	1	yes	characteristic
238	C₂×C₄	#10597392	1	1	yes	characteristic
239	C₈	—	2	1	no	—
240	C₈	—	2	1	no	—
241	C₈	—	2	1	no	—
242	C₈	—	8	2	no	—
243	C₈	—	76	2	no	—
244	C₈	—	152	2	no	—
245	C₈	#10597280	1	2	yes	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	76	2	no	—
249	C₂²	—	76	2	no	—
250	C₂²	—	76	2	no	—
251	C₂²	—	152	4	no	—
252	C₂²	#11926401	1	1	yes	characteristic
253	C₂²	#11926591	1	2	yes	—
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	76	2	no	—
260	C₄	C₂×#10597280	1	1	yes	characteristic
261	C₄	#11926526	1	1	yes	characteristic
262	C₂	—	2	2	no	—
263	C₂	—	152	2	no	—
264	C₂	#14563624	1	1	yes	characteristic
265	C₂	#14563674	1	1	yes	characteristic
266	C₂	#14563678	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926623

C₂

yes

maximal, characteristic

#14562398

C₂

yes

maximal, characteristic, complemented

#14561975

C₂

yes

maximal

#14561504

C₂

yes

maximal, complemented

C₁₉×#1568

C₂

yes

maximal, characteristic, complemented

C₂²×#64515

C₄

yes

—

C₂×C₄×D₇₆

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₈

C₄

yes

—

#11926297

—

#11926295

—

#11926267

—

C₁₉×#432

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂²×D₇₆

Q₈

yes

characteristic

C₂²×C₄×D₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

D₄

yes

—

C₂×C₄⋊Dic₁₉

Q₈

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×#64515

—

C₂×#64515

—

C₂×#64515

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

(C₂×D₁₉)⋊C₈

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂³×D₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

—

—

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

D₇₆

—

102

D₇₆

—

103

C₄×D₁₉

—

104

C₄×D₁₉

—

105

C₄×D₁₉

—

106

C₈×C₁₉

—

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

#100

yes

—

111

C₁₉⋊C₈

—

112

C₁₉⋊C₈

—

113

C₂×#436

—

114

#1568

—

115

#1568

D₁₉

yes

characteristic, complemented

116

#1466

—

117

#1290

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

#380

yes

characteristic

121

C₂²×C₁₉

#430

yes

—

122

C₂×D₁₉

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

C₂×#100

yes

characteristic

132

C₄×C₁₉

#413

yes

characteristic

133

Dic₁₉

—

134

C₂²×M₁₆

—

135

C₂×C₄×D₄

—

136

#436

—

137

#436

—

138

#436

—

139

#436

—

140

#432

—

141

#432

C₂×D₁₉

yes

—

142

C₂×C₄⋊C₈

—

143

C₂×C₂²⋊C₈

—

144

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

145

#335

—

146

#335

—

147

#334

—

148

#334

—

149

#323

—

150

C₂×C₁₉

—

151

C₂×C₁₉

#1800

yes

characteristic

152

C₂×C₁₉

#1811

yes

characteristic

153

C₂×C₁₉

#1812

yes

characteristic

154

D₁₉

—

155

C₂²×D₄

—

156

C₂³×C₄

—

157

C₂×M₁₆

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂²×C₈

—

161

C₂²×C₈

C₄×D₁₉

yes

characteristic

162

C₂²×C₈

C₄×D₁₉

yes

characteristic

163

C₄×D₄

—

164

C₄×D₄

—

165

C₄×D₄

—

166

C₄×D₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₂²⋊C₄

—

169

C₂×C₄²

C₂²×D₁₉

yes

characteristic

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₂²⋊C₈

—

175

C₂²⋊C₈

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

#97

—

179

#97

—

180

C₄×C₈

D₇₆

yes

characteristic

181

C₄×C₈

D₇₆

yes

characteristic

182

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

183

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

184

C₁₉

#8624

yes

characteristic, complemented, Sylow

185

C₂⁴

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

195

C₂²×C₄

D₄×D₁₉

yes

characteristic

196

C₂²×C₄

Q₈×D₁₉

yes

characteristic

197

M₁₆

—

198

M₁₆

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

206

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

207

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

208

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₂²⋊C₄

—

212

C₂²⋊C₄

—

213

C₄²

C₂×D₇₆

yes

characteristic

214

C₄²

#64543

yes

characteristic

215

C₄²

#64545

yes

characteristic

216

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

C₄⋊C₄×D₁₉

yes

characteristic

222

D₄

—

223

D₄

—

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

#10597338

yes

characteristic

234

C₂×C₄

#10597341

yes

characteristic

235

C₂×C₄

#10597343

yes

characteristic

236

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

237

C₂×C₄

#10597384

yes

characteristic

238

C₂×C₄

#10597392

yes

characteristic

239

C₈

—

240

C₈

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

152

—

245

C₈

#10597280

yes

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

152

—

252

C₂²

#11926401

yes

characteristic

253

C₂²

#11926591

yes

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

C₂×#10597280

yes

characteristic

261

C₄

#11926526

yes

characteristic

262

C₂

—

263

C₂

—

152

—

264

C₂

#14563624

yes

characteristic

265

C₂

#14563674

yes

characteristic

266

C₂

#14563678

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1568	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₇₆	Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1568	D₁₉
hypocenter	C₁₉	#8624
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#11926401

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1568

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂²×D₇₆

Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
2. #14562398	C₂	semidirect
4. #14561504	C₂	semidirect
5. C₁₉×#1568	C₂	semidirect
115. #1568	D₁₉	semidirect
184. C₁₉	#8624	semidirect

H ≅ G/N

type

2. #14562398

C₂

semidirect

4. #14561504

C₂

semidirect

5. C₁₉×#1568

C₂

semidirect

115. #1568

D₁₉

semidirect

184. C₁₉

#8624

semidirect

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

subgroup	index
C₂×#11926623	2
#14562398	2
#14561975	2
#14561504	2
C₁₉×#1568	2
#8624	19

subgroup

index

C₁₉×#1568

Subgroups — #18075502

Conjugacy classes of subgroups

Complements

Maximal subgroups