Group #18085157 — subgroups

Subgroups — #18085157

Order 4864.

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

normal subgroups only

This group has 562 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	C₂×#11926831	C₂	1	2	yes	maximal
2	#14564429	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926293	C₂	1	2	yes	maximal, complemented
4	#14561470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
7	#11926831	—	2	4	no	—
8	#11926831	—	2	4	no	—
9	C₂×#10597265	—	2	2	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
12	C₂×#10597266	—	2	2	no	—
13	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
14	#11926293	—	2	4	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₁₉×#500	—	2	4	no	—
17	C₂×C₁₉×#107	—	2	2	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₁₉	—	2	2	no	—
20	C₂²×D₇₆	D₄	1	1	yes	characteristic
21	C₂²×C₄×D₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₁₉×C₄⋊Q₈	—	2	2	no	—
26	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₁₉⋊C₈	—	2	2	no	—
33	C₂²×C₁₉⋊C₈	—	2	1	no	—
34	C₄×D₇₆	—	2	2	no	—
35	C₄×D₇₆	—	2	2	no	—
36	C₁₉×#107	—	2	8	no	—
37	C₄×C₈×C₁₉	—	2	2	no	—
38	(C₂×D₁₉)⋊C₈	—	4	4	no	—
39	#10597266	—	2	8	no	—
40	#10597265	—	2	8	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
44	C₂³×D₁₉	—	2	1	no	—
45	C₂×Q₈×C₁₉	—	2	4	no	—
46	C₂×Q₈×C₁₉	—	4	2	no	—
47	C₂×Q₈×C₁₉	—	8	4	no	—
48	C₂²×C₄×C₁₉	—	4	2	no	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
52	C₂²×Dic₁₉	—	2	1	no	—
53	C₂×D₇₆	—	2	2	no	—
54	C₂×D₇₆	—	2	2	no	—
55	C₂×D₇₆	—	2	1	no	—
56	C₂×D₇₆	Q₁₆	1	2	yes	—
57	C₂×C₄×D₁₉	—	4	1	no	—
58	C₂×C₄×D₁₉	—	4	1	no	—
59	C₂×C₄×D₁₉	—	4	2	no	—
60	C₂×C₄×D₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
64	C₄⋊C₄×C₁₉	—	2	4	no	—
65	C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₄⋊C₄×C₁₉	—	4	2	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₄²×C₁₉	C₂×D₄	1	2	yes	—
69	C₄²×C₁₉	C₂×D₄	1	2	yes	—
70	(C₂×D₁₉)⋊C₄	—	4	2	no	—
71	C₄⋊Dic₁₉	—	2	2	no	—
72	C₂×C₁₉⋊C₈	—	2	4	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	1	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	#10278	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	#121	1	1	yes	characteristic
79	C₂²×D₁₉	—	2	2	no	—
80	C₂²×D₁₉	—	4	1	no	—
81	C₂²×D₁₉	—	4	2	no	—
82	C₂²×D₁₉	—	4	1	no	—
83	C₂²×D₁₉	—	4	2	no	—
84	Q₈×C₁₉	—	8	4	no	—
85	Q₈×C₁₉	—	8	4	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	4	4	no	—
88	C₂×C₄×C₁₉	—	8	4	no	—
89	C₂×C₄×C₁₉	#120	1	2	yes	—
90	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#121	1	2	yes	—
92	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
94	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#137	1	2	yes	—
97	C₂×C₄×C₁₉	#137	1	2	yes	—
98	C₂×Dic₁₉	—	4	1	no	—
99	C₂×Dic₁₉	—	4	2	no	—
100	D₇₆	—	2	4	no	—
101	D₇₆	—	4	2	no	—
102	C₄×D₁₉	—	8	2	no	—
103	C₄×D₁₉	—	8	1	no	—
104	C₄×D₁₉	—	8	1	no	—
105	C₈×C₁₉	—	2	4	no	—
106	C₁₉⋊C₈	—	4	4	no	—
107	C₁₉⋊C₈	—	8	1	no	—
108	C₂×#500	D₁₉	1	1	yes	characteristic, complemented
109	C₂×#476	—	19	2	no	—
110	#1954	—	19	1	no	—
111	C₂×#333	—	19	2	no	—
112	#1277	—	19	1	no	—
113	C₂²×C₁₉	#392	1	1	yes	characteristic
114	C₂²×C₁₉	#461	1	2	yes	—
115	C₂²×C₁₉	#467	1	1	yes	characteristic
116	C₂²×C₁₉	#470	1	1	yes	characteristic
117	C₂²×C₁₉	#472	1	2	yes	—
118	C₂×D₁₉	—	4	4	no	—
119	C₂×D₁₉	—	4	2	no	—
120	C₂×D₁₉	—	8	2	no	—
121	C₂×D₁₉	—	8	1	no	—
122	C₂×D₁₉	—	8	1	no	—
123	C₄×C₁₉	—	2	2	no	—
124	C₄×C₁₉	—	8	4	no	—
125	C₄×C₁₉	#448	1	2	yes	—
126	C₄×C₁₉	#451	1	2	yes	—
127	C₄×C₁₉	#452	1	2	yes	—
128	C₄×C₁₉	#492	1	1	yes	characteristic
129	C₄×C₁₉	#497	1	1	yes	characteristic
130	Dic₁₉	—	8	1	no	—
131	C₂×C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
132	C₂×C₄×D₄	—	19	1	no	—
133	#500	—	2	4	no	—
134	#476	—	38	4	no	—
135	#476	—	38	4	no	—
136	C₂×#107	—	2	2	no	—
137	C₂×#106	—	38	2	no	—
138	C₂×C₄⋊C₈	—	19	2	no	—
139	C₂×C₄⋊C₈	—	19	1	no	—
140	C₂×#102	—	38	2	no	—
141	C₂×C₂²⋊C₈	—	38	2	no	—
142	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
143	#333	—	38	4	no	—
144	C₂×C₁₉	#1675	1	2	yes	—
145	C₂×C₁₉	#1695	1	2	yes	—
146	C₂×C₁₉	#2001	1	1	yes	characteristic
147	C₂×C₁₉	#2013	1	1	yes	characteristic
148	C₂×C₁₉	#2018	1	1	yes	characteristic
149	D₁₉	—	8	2	no	—
150	C₂²×Q₈	—	2	2	no	—
151	C₂²×D₄	—	19	1	no	—
152	C₂³×C₄	—	38	1	no	—
153	C₂²×C₈	—	38	2	no	—
154	C₂²×C₈	—	38	1	no	—
155	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
156	C₄⋊Q₈	—	2	2	no	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄⋊Q₈	—	2	2	no	—
159	C₄⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
160	C₄×D₄	—	38	2	no	—
161	C₄×D₄	—	38	2	no	—
162	C₂×C₄⋊C₄	—	2	2	no	—
163	C₂×C₄⋊C₄	—	2	2	no	—
164	C₂×C₄⋊C₄	—	19	1	no	—
165	C₂×C₂²⋊C₄	—	38	1	no	—
166	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
167	#107	—	2	8	no	—
168	#106	—	38	8	no	—
169	C₄⋊C₈	—	19	4	no	—
170	C₄⋊C₈	—	38	2	no	—
171	C₄⋊C₈	—	38	2	no	—
172	#102	—	38	8	no	—
173	C₂²⋊C₈	—	76	4	no	—
174	C₄×C₈	—	2	2	no	—
175	C₁₉	#10278	1	1	yes	characteristic, complemented, Sylow
176	C₂⁴	—	38	1	no	—
177	C₂×Q₈	—	2	4	no	—
178	C₂×Q₈	—	4	2	no	—
179	C₂×Q₈	—	8	4	no	—
180	C₂×D₄	—	19	2	no	—
181	C₂×D₄	—	38	2	no	—
182	C₂×D₄	—	38	2	no	—
183	C₂×D₄	—	38	1	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	—	38	1	no	—
186	C₂²×C₄	—	76	1	no	—
187	C₂²×C₄	—	76	2	no	—
188	C₂²×C₄	—	76	2	no	—
189	C₂²×C₄	—	76	1	no	—
190	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
191	C₂²×C₄	#64543	1	1	yes	characteristic
192	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	38	4	no	—
196	C₂×C₈	—	76	2	no	—
197	C₂×C₈	—	76	2	no	—
198	C₂×C₈	—	76	1	no	—
199	C₂×C₈	—	76	2	no	—
200	C₂×C₈	#64527	1	4	yes	—
201	C₄⋊C₄	—	2	4	no	—
202	C₄⋊C₄	—	2	4	no	—
203	C₄⋊C₄	—	4	2	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	38	2	no	—
206	C₂²⋊C₄	—	76	2	no	—
207	C₄²	D₄×D₁₉	1	2	yes	—
208	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
209	C₂³	—	38	2	no	—
210	C₂³	—	76	1	no	—
211	C₂³	—	76	2	no	—
212	C₂³	—	76	1	no	—
213	C₂³	—	76	2	no	—
214	C₂³	#10597384	1	1	yes	characteristic
215	Q₈	—	8	4	no	—
216	Q₈	—	8	4	no	—
217	D₄	—	38	4	no	—
218	D₄	—	76	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	8	4	no	—
222	C₂×C₄	—	76	1	no	—
223	C₂×C₄	—	76	2	no	—
224	C₂×C₄	—	152	1	no	—
225	C₂×C₄	—	152	1	no	—
226	C₂×C₄	—	152	2	no	—
227	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
228	C₂×C₄	#10597364	1	2	yes	—
229	C₂×C₄	#10597365	1	1	yes	characteristic
230	C₂×C₄	#10597383	1	2	yes	—
231	C₂×C₄	#10597385	1	2	yes	—
232	C₂×C₄	#10597386	1	1	yes	characteristic
233	C₂×C₄	C₂×#64527	1	2	yes	—
234	C₂×C₄	#10597388	1	2	yes	—
235	C₂×C₄	#10597399	1	1	yes	characteristic
236	C₈	—	2	4	no	—
237	C₈	—	76	4	no	—
238	C₈	—	152	1	no	—
239	C₂²	—	76	2	no	—
240	C₂²	—	76	4	no	—
241	C₂²	—	152	2	no	—
242	C₂²	—	152	1	no	—
243	C₂²	—	152	1	no	—
244	C₂²	#11926452	1	1	yes	characteristic
245	C₂²	#11926746	1	2	yes	—
246	C₂²	#11926782	1	1	yes	characteristic
247	C₂²	#11926799	1	1	yes	characteristic
248	C₂²	#11926811	1	2	yes	—
249	C₄	—	2	2	no	—
250	C₄	—	8	4	no	—
251	C₄	—	152	1	no	—
252	C₄	#11926683	1	2	yes	—
253	C₄	#11926698	1	2	yes	—
254	C₄	#11926705	1	2	yes	—
255	C₄	#11926918	1	1	yes	characteristic
256	C₄	#11926936	1	1	yes	characteristic
257	C₂	—	152	2	no	—
258	C₂	#14563031	1	2	yes	—
259	C₂	#14563155	1	2	yes	—
260	C₂	#14564642	1	1	yes	characteristic
261	C₂	#14564718	1	1	yes	characteristic
262	C₂	#14564742	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926831

C₂

yes

maximal

#14564429

C₂

yes

maximal, characteristic

C₂×#11926293

C₂

yes

maximal, complemented

#14561470

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#500

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₇₆

C₂²

yes

—

—

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597266

—

C₂×(C₂×D₁₉)⋊C₈

—

#11926293

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

—

C₁₉×#500

—

C₂×C₁₉×#107

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×D₇₆

D₄

yes

characteristic

C₂²×C₄×D₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₄×D₇₆

—

C₄×D₇₆

—

C₁₉×#107

—

C₄×C₈×C₁₉

—

(C₂×D₁₉)⋊C₈

—

#10597266

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

Q₁₆

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

D₇₆

—

101

D₇₆

—

102

C₄×D₁₉

—

103

C₄×D₁₉

—

104

C₄×D₁₉

—

105

C₈×C₁₉

—

106

C₁₉⋊C₈

—

107

C₁₉⋊C₈

—

108

C₂×#500

D₁₉

yes

characteristic, complemented

109

C₂×#476

—

110

#1954

—

111

C₂×#333

—

112

#1277

—

113

C₂²×C₁₉

#392

yes

characteristic

114

C₂²×C₁₉

#461

yes

—

115

C₂²×C₁₉

#467

yes

characteristic

116

C₂²×C₁₉

#470

yes

characteristic

117

C₂²×C₁₉

#472

yes

—

118

C₂×D₁₉

—

119

C₂×D₁₉

—

120

C₂×D₁₉

—

121

C₂×D₁₉

—

122

C₂×D₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

#448

yes

—

126

C₄×C₁₉

#451

yes

—

127

C₄×C₁₉

#452

yes

—

128

C₄×C₁₉

#492

yes

characteristic

129

C₄×C₁₉

#497

yes

characteristic

130

Dic₁₉

—

131

C₂×C₄⋊Q₈

C₂×D₁₉

yes

—

132

C₂×C₄×D₄

—

133

#500

—

134

#476

—

135

#476

—

136

C₂×#107

—

137

C₂×#106

—

138

C₂×C₄⋊C₈

—

139

C₂×C₄⋊C₈

—

140

C₂×#102

—

141

C₂×C₂²⋊C₈

—

142

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

143

#333

—

144

C₂×C₁₉

#1675

yes

—

145

C₂×C₁₉

#1695

yes

—

146

C₂×C₁₉

#2001

yes

characteristic

147

C₂×C₁₉

#2013

yes

characteristic

148

C₂×C₁₉

#2018

yes

characteristic

149

D₁₉

—

150

C₂²×Q₈

—

151

C₂²×D₄

—

152

C₂³×C₄

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

C₂²⋊D₁₉

yes

—

156

C₄⋊Q₈

—

157

C₄⋊Q₈

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

160

C₄×D₄

—

161

C₄×D₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₂²⋊C₄

—

166

C₂×C₄²

C₂²×D₁₉

yes

characteristic

167

#107

—

168

#106

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

#102

—

173

C₂²⋊C₈

—

174

C₄×C₈

—

175

C₁₉

#10278

yes

characteristic, complemented, Sylow

176

C₂⁴

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

D₄×D₁₉

yes

characteristic

191

C₂²×C₄

#64543

yes

characteristic

192

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

#64527

yes

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

D₄×D₁₉

yes

—

208

C₄²

C₂×C₂²⋊D₁₉

yes

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

#10597384

yes

characteristic

215

Q₈

—

216

Q₈

—

217

D₄

—

218

D₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

152

—

225

C₂×C₄

—

152

—

226

C₂×C₄

—

152

—

227

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

228

C₂×C₄

#10597364

yes

—

229

C₂×C₄

#10597365

yes

characteristic

230

C₂×C₄

#10597383

yes

—

231

C₂×C₄

#10597385

yes

—

232

C₂×C₄

#10597386

yes

characteristic

233

C₂×C₄

C₂×#64527

yes

—

234

C₂×C₄

#10597388

yes

—

235

C₂×C₄

#10597399

yes

characteristic

236

C₈

—

237

C₈

—

238

C₈

—

152

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

152

—

242

C₂²

—

152

—

243

C₂²

—

152

—

244

C₂²

#11926452

yes

characteristic

245

C₂²

#11926746

yes

—

246

C₂²

#11926782

yes

characteristic

247

C₂²

#11926799

yes

characteristic

248

C₂²

#11926811

yes

—

249

C₄

—

250

C₄

—

251

C₄

—

152

—

252

C₄

#11926683

yes

—

253

C₄

#11926698

yes

—

254

C₄

#11926705

yes

—

255

C₄

#11926918

yes

characteristic

256

C₄

#11926936

yes

characteristic

257

C₂

—

152

—

258

C₂

#14563031

yes

—

259

C₂

#14563155

yes

—

260

C₂

#14564642

yes

characteristic

261

C₂

#14564718

yes

characteristic

262

C₂

#14564742

yes

characteristic

	subgroup	G/H
center	C₂³	#10597384
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#500	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₇₆	D₄
hypercenter	C₂×#500	D₁₉
hypocenter	C₁₉	#10278
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

subgroup

G/H

center

C₂³

#10597384

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#500

C₂

socle

C₂³×C₁₉

#121

prime radical

C₂²×D₇₆

D₄

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

N	H ≅ G/N	type
3. C₂×#11926293	C₂	semidirect
4. #14561470	C₂	semidirect
5. C₂×C₁₉×#500	C₂	semidirect
108. C₂×#500	D₁₉	semidirect
175. C₁₉	#10278	semidirect

H ≅ G/N

type

3. C₂×#11926293

C₂

semidirect

4. #14561470

C₂

semidirect

5. C₂×C₁₉×#500

C₂

semidirect

108. C₂×#500

D₁₉

semidirect

175. C₁₉

#10278

semidirect

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

subgroup	index
C₂×#11926831	2
#14564429	2
C₂×#11926293	2
#14561470	2
C₂×C₁₉×#500	2
#10278	19

subgroup

index

C₂×C₁₉×#500

Subgroups — #18085157

Conjugacy classes of subgroups

Complements

Maximal subgroups