Group #18076942 — subgroups

Subgroups — #18076942

Order 4864.

392 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14564468	C₂	1	1	yes	maximal, characteristic
2	#14562403	C₂	1	2	yes	maximal, complemented
3	#14562227	C₂	1	1	yes	maximal, characteristic
4	#14561527	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2980	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	1	yes	characteristic
7	C₂×#10597294	—	2	1	no	—
8	C₂×#10597294	—	2	1	no	—
9	C₄×#64520	C₂²	1	2	yes	—
10	#11926390	C₂²	1	1	yes	characteristic
11	#11926296	—	2	2	no	—
12	#11926294	—	2	2	no	—
13	#11926284	C₄	1	1	yes	characteristic, complemented
14	#11926284	C₄	1	2	yes	complemented
15	#11926284	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₁₉×#435	—	2	2	no	—
18	C₁₉×#435	—	2	2	no	—
19	C₁₉×#432	C₂²	1	2	yes	—
20	C₁₉×#408	—	2	1	no	—
21	C₁₉×#408	—	2	1	no	—
22	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
23	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
24	C₂×M₁₆×C₁₉	—	2	1	no	—
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₂²×C₈×C₁₉	—	2	1	no	—
27	C₂²×C₈×C₁₉	—	2	1	no	—
28	C₁₉×C₄⋊Q₈	Q₈	1	1	yes	characteristic
29	C₁₉×#127	Q₈	1	1	yes	characteristic
30	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
31	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
32	C₁₉×#121	—	2	2	no	—
33	C₄×D₄×C₁₉	—	2	2	no	—
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉	—	2	1	no	—
36	C₂×#64520	—	2	2	no	—
37	C₂×#64520	—	2	1	no	—
38	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
39	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
40	C₁₉×C₂²⋊C₈	—	2	2	no	—
41	C₁₉×C₂²⋊C₈	—	2	2	no	—
42	C₁₉×C₂²⋊C₈	—	2	2	no	—
43	C₁₉×#97	—	2	2	no	—
44	#10597294	—	4	2	no	—
45	#10597294	—	4	2	no	—
46	C₁₉⋊#95	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	#10597260	C₂×C₄	1	2	yes	—
49	#10597260	C₂×C₄	1	2	yes	—
50	C₄×C₁₉⋊C₈	—	2	2	no	—
51	#41×C₁₉	—	4	1	no	—
52	#41×C₁₉	—	4	1	no	—
53	#41×C₁₉	—	4	1	no	—
54	#41×C₁₉	—	4	1	no	—
55	C₂×Q₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
56	C₂×Q₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
57	C₂×D₄×C₁₉	—	2	1	no	—
58	C₂×D₄×C₁₉	—	2	1	no	—
59	C₂×D₄×C₁₉	—	2	2	no	—
60	C₂×D₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
61	C₂×D₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	#41	1	2	yes	—
66	C₂²×Dic₁₉	—	4	1	no	—
67	M₁₆×C₁₉	—	8	1	no	—
68	M₁₆×C₁₉	—	8	1	no	—
69	C₂×C₈×C₁₉	—	2	2	no	—
70	C₂×C₈×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	—	8	1	no	—
72	C₂×C₈×C₁₉	—	8	1	no	—
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₁₉	C₂×D₄	1	2	yes	—
78	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
79	C₄×Dic₁₉	—	2	2	no	—
80	C₄×Dic₁₉	—	4	1	no	—
81	#64520	—	4	4	no	—
82	#64520	—	4	1	no	—
83	#64520	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	2	2	no	—
86	C₂×C₁₉⋊C₈	—	4	1	no	—
87	#8918	—	19	1	no	maximal, Sylow
88	C₂³×C₁₉	—	2	1	no	—
89	C₂³×C₁₉	—	2	1	no	—
90	C₂³×C₁₉	#123	1	1	yes	characteristic
91	Q₈×C₁₉	—	4	1	no	—
92	Q₈×C₁₉	—	4	1	no	—
93	D₄×C₁₉	—	4	1	no	—
94	D₄×C₁₉	—	4	1	no	—
95	D₄×C₁₉	—	8	2	no	—
96	D₄×C₁₉	—	8	1	no	—
97	D₄×C₁₉	—	8	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	—	4	1	no	—
107	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
109	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
111	C₂×Dic₁₉	—	4	2	no	—
112	C₂×Dic₁₉	—	8	2	no	—
113	C₈×C₁₉	—	4	2	no	—
114	C₈×C₁₉	—	4	2	no	—
115	C₁₉⋊C₈	—	2	4	no	—
116	C₁₉⋊C₈	—	4	2	no	—
117	C₁₉⋊C₈	—	8	1	no	—
118	#2980	D₁₉	1	1	yes	characteristic
119	#1963	—	19	1	no	—
120	#1569	—	19	2	no	—
121	#1525	—	19	1	no	—
122	#1300	—	19	2	no	—
123	C₂²×C₁₉	—	2	1	no	—
124	C₂²×C₁₉	—	2	2	no	—
125	C₂²×C₁₉	—	4	1	no	—
126	C₂²×C₁₉	—	4	1	no	—
127	C₂²×C₁₉	—	4	2	no	—
128	C₂²×C₁₉	—	4	2	no	—
129	C₂²×C₁₉	#385	1	1	yes	characteristic
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	2	no	—
132	C₄×C₁₉	—	2	2	no	—
133	C₄×C₁₉	—	4	1	no	—
134	C₄×C₁₉	—	4	1	no	—
135	C₄×C₁₉	#453	1	1	yes	characteristic
136	C₄×C₁₉	#455	1	1	yes	characteristic
137	Dic₁₉	—	8	2	no	—
138	#532	C₂×D₁₉	1	1	yes	characteristic
139	#435	—	2	2	no	—
140	#435	—	2	2	no	—
141	#432	C₂×D₁₉	1	2	yes	—
142	#423	—	19	1	no	—
143	C₂×#104	—	38	1	no	—
144	C₂×#104	—	38	1	no	—
145	#408	—	2	1	no	—
146	#408	—	2	1	no	—
147	C₄×M₁₆	—	19	2	no	—
148	#376	—	19	1	no	—
149	#335	—	38	2	no	—
150	#334	—	38	2	no	—
151	#329	—	19	1	no	—
152	#329	—	19	2	no	—
153	#329	—	19	1	no	—
154	C₂×C₁₉	—	4	1	no	—
155	C₂×C₁₉	—	8	1	no	—
156	C₂×C₁₉	—	8	1	no	—
157	C₂×C₁₉	#1856	1	1	yes	characteristic
158	C₂×C₁₉	#1861	1	2	yes	—
159	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
160	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
161	C₂×M₁₆	—	2	1	no	—
162	C₂×M₁₆	—	2	1	no	—
163	C₂×M₁₆	—	38	2	no	—
164	C₂×M₁₆	—	38	1	no	—
165	C₂²×C₈	—	2	1	no	—
166	C₂²×C₈	—	2	1	no	—
167	C₄⋊Q₈	Dic₃₈	1	1	yes	characteristic
168	#127	Dic₃₈	1	1	yes	characteristic
169	#124	C₄×D₁₉	1	1	yes	characteristic
170	#124	C₄×D₁₉	1	1	yes	characteristic
171	#121	—	2	2	no	—
172	C₄×D₄	—	2	2	no	—
173	C₂×C₄²	—	38	1	no	—
174	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
175	C₄⋊C₈	—	38	2	no	—
176	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
177	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
178	#104	—	76	2	no	—
179	#104	—	76	2	no	—
180	C₂²⋊C₈	—	2	2	no	—
181	C₂²⋊C₈	—	2	2	no	—
182	C₂²⋊C₈	—	2	2	no	—
183	#97	—	2	2	no	—
184	#97	—	19	2	no	—
185	#97	—	19	2	no	—
186	C₄×C₈	—	38	2	no	—
187	#95	—	38	2	no	—
188	C₁₉	#8918	1	1	yes	characteristic, complemented, Sylow
189	#41	—	4	1	no	—
190	#41	—	4	1	no	—
191	#41	—	4	1	no	—
192	#41	—	4	1	no	—
193	C₂×Q₈	Dic₁₉⋊C₄	1	1	yes	characteristic
194	C₂×Q₈	Dic₁₉⋊C₄	1	1	yes	characteristic
195	C₂×D₄	—	2	1	no	—
196	C₂×D₄	—	2	1	no	—
197	C₂×D₄	—	2	2	no	—
198	C₂×D₄	Dic₁₉⋊C₄	1	1	yes	characteristic
199	C₂×D₄	Dic₁₉⋊C₄	1	1	yes	characteristic
200	C₂²×C₄	—	2	1	no	—
201	C₂²×C₄	—	2	1	no	—
202	C₂²×C₄	—	76	1	no	—
203	C₂²×C₄	#64541	1	2	yes	—
204	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
205	M₁₆	—	8	1	no	—
206	M₁₆	—	8	1	no	—
207	M₁₆	—	76	4	no	—
208	M₁₆	—	76	1	no	—
209	M₁₆	—	76	1	no	—
210	C₂×C₈	—	2	2	no	—
211	C₂×C₈	—	2	2	no	—
212	C₂×C₈	—	8	1	no	—
213	C₂×C₈	—	8	1	no	—
214	C₂×C₈	—	38	2	no	—
215	C₂×C₈	—	38	2	no	—
216	C₂×C₈	—	76	1	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₂²⋊C₄	—	2	2	no	—
219	C₂²⋊C₄	—	2	2	no	—
220	C₄²	—	38	2	no	—
221	C₄²	—	76	1	no	—
222	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
223	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
224	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
225	C₂³	—	2	1	no	—
226	C₂³	—	2	1	no	—
227	C₂³	#10597375	1	1	yes	characteristic
228	Q₈	—	4	1	no	—
229	Q₈	—	4	1	no	—
230	D₄	—	4	1	no	—
231	D₄	—	4	1	no	—
232	D₄	—	8	2	no	—
233	D₄	—	8	1	no	—
234	D₄	—	8	1	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	1	no	—
241	C₂×C₄	—	4	1	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	76	2	no	—
245	C₂×C₄	—	152	2	no	—
246	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
247	C₂×C₄	#10597370	1	2	yes	—
248	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
249	C₂×C₄	#10597399	1	1	yes	characteristic
250	C₈	—	4	2	no	—
251	C₈	—	4	2	no	—
252	C₈	—	38	4	no	—
253	C₈	—	76	2	no	—
254	C₈	—	152	1	no	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	2	no	—
257	C₂²	—	4	1	no	—
258	C₂²	—	4	1	no	—
259	C₂²	—	4	2	no	—
260	C₂²	—	4	2	no	—
261	C₂²	#11926417	1	1	yes	characteristic
262	C₄	—	2	1	no	—
263	C₄	—	2	2	no	—
264	C₄	—	2	2	no	—
265	C₄	—	4	1	no	—
266	C₄	—	4	1	no	—
267	C₄	—	152	2	no	—
268	C₄	#11926712	1	1	yes	characteristic
269	C₄	#11926722	1	1	yes	characteristic
270	C₂	—	4	1	no	—
271	C₂	—	8	1	no	—
272	C₂	—	8	1	no	—
273	C₂	#14563845	1	1	yes	characteristic
274	C₂	#14563875	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564468

C₂

yes

maximal, characteristic

#14562403

C₂

yes

maximal, complemented

#14562227

C₂

yes

maximal, characteristic

#14561527

C₂

yes

maximal, complemented

C₁₉×#2980

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

—

C₂²

yes

—

#11926390

C₂²

yes

—

—

C₄

yes

characteristic, complemented

#11926284

C₄

yes

complemented

#11926284

C₄

yes

characteristic, complemented

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#435

—

C₁₉×#435

—

C₁₉×#432

C₂²

yes

—

C₁₉×#408

—

C₁₉×#408

—

C₂×#41×C₁₉

D₄

yes

characteristic

C₂×#41×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

Q₈

yes

characteristic

C₁₉×#127

Q₈

yes

characteristic

C₁₉×#124

C₂×C₄

yes

characteristic

C₁₉×#124

C₂×C₄

yes

characteristic

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×#64520

—

C₂×#64520

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

#10597294

—

#10597294

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

C₂×C₄

yes

—

#10597260

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×Q₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×D₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8918

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

C₂×C₄⋊C₄

yes

characteristic

108

C₂×C₄×C₁₉

C₄×D₄

yes

—

109

C₂×C₄×C₁₉

#120

yes

characteristic

110

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

111

C₂×Dic₁₉

—

112

C₂×Dic₁₉

—

113

C₈×C₁₉

—

114

C₈×C₁₉

—

115

C₁₉⋊C₈

—

116

C₁₉⋊C₈

—

117

C₁₉⋊C₈

—

118

#2980

D₁₉

yes

characteristic

119

#1963

—

120

#1569

—

121

#1525

—

122

#1300

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

#385

yes

characteristic

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

#453

yes

characteristic

136

C₄×C₁₉

#455

yes

characteristic

137

Dic₁₉

—

138

#532

C₂×D₁₉

yes

characteristic

139

#435

—

140

#435

—

141

#432

C₂×D₁₉

yes

—

142

#423

—

143

C₂×#104

—

144

C₂×#104

—

145

#408

—

146

#408

—

147

C₄×M₁₆

—

148

#376

—

149

#335

—

150

#334

—

151

#329

—

152

#329

—

153

#329

—

154

C₂×C₁₉

—

155

C₂×C₁₉

—

156

C₂×C₁₉

—

157

C₂×C₁₉

#1856

yes

characteristic

158

C₂×C₁₉

#1861

yes

—

159

C₂×#41

C₂²⋊D₁₉

yes

characteristic

160

C₂×#41

C₂²⋊D₁₉

yes

characteristic

161

C₂×M₁₆

—

162

C₂×M₁₆

—

163

C₂×M₁₆

—

164

C₂×M₁₆

—

165

C₂²×C₈

—

166

C₂²×C₈

—

167

C₄⋊Q₈

Dic₃₈

yes

characteristic

168

#127

Dic₃₈

yes

characteristic

169

#124

C₄×D₁₉

yes

characteristic

170

#124

C₄×D₁₉

yes

characteristic

171

#121

—

172

C₄×D₄

—

173

C₂×C₄²

—

174

C₂×C₄²

C₂²×D₁₉

yes

characteristic

175

C₄⋊C₈

—

176

C₄⋊C₈

C₂²⋊D₁₉

yes

—

177

C₄⋊C₈

C₂²⋊D₁₉

yes

—

178

#104

—

179

#104

—

180

C₂²⋊C₈

—

181

C₂²⋊C₈

—

182

C₂²⋊C₈

—

183

#97

—

184

#97

—

185

#97

—

186

C₄×C₈

—

187

#95

—

188

C₁₉

#8918

yes

characteristic, complemented, Sylow

189

#41

—

190

#41

—

191

#41

—

192

#41

—

193

C₂×Q₈

Dic₁₉⋊C₄

yes

characteristic

194

C₂×Q₈

Dic₁₉⋊C₄

yes

characteristic

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

Dic₁₉⋊C₄

yes

characteristic

199

C₂×D₄

Dic₁₉⋊C₄

yes

characteristic

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

#64541

yes

—

204

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

205

M₁₆

—

206

M₁₆

—

207

M₁₆

—

208

M₁₆

—

209

M₁₆

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₄⋊C₄

—

218

C₂²⋊C₄

—

219

C₂²⋊C₄

—

220

C₄²

—

221

C₄²

—

222

C₄²

C₂×Dic₃₈

yes

characteristic

223

C₄²

C₂×C₄×D₁₉

yes

characteristic

224

C₄²

C₂×C₂²⋊D₁₉

yes

—

225

C₂³

—

226

C₂³

—

227

C₂³

#10597375

yes

characteristic

228

Q₈

—

229

Q₈

—

230

D₄

—

231

D₄

—

232

D₄

—

233

D₄

—

234

D₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

152

—

246

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

247

C₂×C₄

#10597370

yes

—

248

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

249

C₂×C₄

#10597399

yes

characteristic

250

C₈

—

251

C₈

—

252

C₈

—

253

C₈

—

254

C₈

—

152

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

#11926417

yes

characteristic

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

—

152

—

268

C₄

#11926712

yes

characteristic

269

C₄

#11926722

yes

characteristic

270

C₂

—

271

C₂

—

272

C₂

—

273

C₂

#14563845

yes

characteristic

274

C₂

#14563875

yes

—

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2980	C₂
socle	C₂²×C₁₉	#385
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2980	D₁₉
hypocenter	C₁₉	#8918
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2980

subgroup

G/H

center

C₂×C₄

#10597399

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2980

C₂

socle

C₂²×C₁₉

#385

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2980

N	H ≅ G/N	type
2. #14562403	C₂	semidirect
4. #14561527	C₂	semidirect
13. #11926284	C₄	semidirect
14. #11926284	C₄	semidirect
15. #11926284	C₄	semidirect
188. C₁₉	#8918	semidirect

H ≅ G/N

type

2. #14562403

C₂

semidirect

4. #14561527

C₂

semidirect

13. #11926284

C₄

semidirect

14. #11926284

C₄

semidirect

15. #11926284

C₄

semidirect

188. C₁₉

#8918

semidirect

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

subgroup	index
#14564468	2
#14562403	2
#14562227	2
#14561527	2
C₁₉×#2980	2
#8918	19

subgroup

index

C₁₉×#2980

Subgroups — #18076942

Conjugacy classes of subgroups

Complements

Maximal subgroups