Group #18077843 — subgroups

Subgroups — #18077843

Order 4864.

570 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 147 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×#11926923	C₂	1	1	yes	maximal, characteristic
2	#14566725	C₂	1	1	yes	maximal, characteristic
3	#14564582	C₂	1	2	yes	maximal
4	#14561474	C₂	1	2	yes	maximal
5	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64528	—	2	2	no	—
7	C₂×#10597315	C₂²	1	1	yes	characteristic
8	#11926923	—	2	2	no	—
9	#11926923	C₄	1	4	yes	complemented
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	#11926451	—	2	2	no	—
12	#11926443	—	2	2	no	—
13	C₄⋊C₄×Dic₁₉	—	2	2	no	—
14	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
15	#11926307	—	2	2	no	—
16	#11926307	—	2	2	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₁₉×#333	—	2	2	no	—
20	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
21	C₂²×Dic₃₈	—	2	1	no	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
25	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×#64528	—	2	8	no	—
29	C₂×#64528	—	4	4	no	—
30	C₂×#64528	—	4	4	no	—
31	C₂×C₄⋊Dic₁₉	—	2	2	no	—
32	C₂×C₄⋊Dic₁₉	—	2	2	no	—
33	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
34	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
35	C₂×C₄×Dic₁₉	—	2	2	no	—
36	C₂×C₄×Dic₁₉	—	2	2	no	—
37	C₂²×C₁₉⋊C₈	—	2	1	no	—
38	#10597315	—	2	2	no	—
39	#10597315	—	2	1	no	—
40	#10597315	C₂×C₄	1	2	yes	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₁₉×C₄⋊C₈	—	2	2	no	—
43	C₁₉⋊#95	—	2	4	no	—
44	C₁₉⋊#95	—	2	2	no	—
45	C₄×C₁₉⋊C₈	—	2	1	no	—
46	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	4	2	no	—
49	C₂×Q₈×C₁₉	—	4	2	no	—
50	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂²×Dic₁₉	—	2	2	no	—
55	C₂²×Dic₁₉	—	2	2	no	—
56	C₂²×Dic₁₉	—	4	1	no	—
57	C₂×Dic₃₈	—	2	2	no	—
58	C₂×Dic₃₈	—	4	2	no	—
59	C₂×Dic₃₈	—	4	2	no	—
60	C₂×Dic₃₈	—	4	1	no	—
61	C₂×C₈×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	—	4	2	no	—
64	C₄⋊C₄×C₁₉	—	2	4	no	—
65	C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	2	yes	—
69	#64528	—	4	16	no	—
70	C₄⋊Dic₁₉	—	2	2	no	—
71	C₄⋊Dic₁₉	—	2	4	no	—
72	C₄⋊Dic₁₉	—	2	2	no	—
73	C₄⋊Dic₁₉	—	2	2	no	—
74	C₄⋊Dic₁₉	—	4	2	no	—
75	C₄⋊Dic₁₉	—	8	2	no	—
76	C₄⋊Dic₁₉	Q₁₆	1	4	yes	complemented
77	C₄×Dic₁₉	—	4	2	no	—
78	C₄×Dic₁₉	—	4	2	no	—
79	C₄×Dic₁₉	—	8	2	no	—
80	C₂×C₁₉⋊C₈	—	2	2	no	—
81	C₂×C₁₉⋊C₈	—	2	2	no	—
82	C₂×C₁₉⋊C₈	—	2	2	no	—
83	#9066	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	#120	1	1	yes	characteristic
85	Q₈×C₁₉	—	4	4	no	—
86	Q₈×C₁₉	—	8	2	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	4	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
94	C₂×C₄×C₁₉	#121	1	2	yes	—
95	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
97	C₂×C₄×C₁₉	#135	1	2	yes	—
98	C₂×C₄×C₁₉	#137	1	2	yes	—
99	C₂×C₄×C₁₉	#137	1	2	yes	—
100	C₂×Dic₁₉	—	2	4	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	4	2	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	C₂×Dic₁₉	—	8	1	no	—
108	C₂×Dic₁₉	—	8	1	no	—
109	Dic₃₈	—	4	4	no	—
110	Dic₃₈	—	8	2	no	—
111	C₈×C₁₉	—	8	2	no	—
112	C₁₉⋊C₈	—	2	4	no	—
113	C₂×#494	—	19	1	no	—
114	#2369	—	19	1	no	—
115	#1987	—	19	2	no	—
116	C₂×#333	D₁₉	1	1	yes	characteristic
117	#1279	—	19	2	no	—
118	C₂²×C₁₉	#386	1	1	yes	characteristic
119	C₂²×C₁₉	#451	1	2	yes	—
120	C₂²×C₁₉	#452	1	2	yes	—
121	C₂²×C₁₉	#453	1	1	yes	characteristic
122	C₂²×C₁₉	#453	1	1	yes	characteristic
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	4	4	no	—
126	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
127	C₄×C₁₉	#441	1	2	yes	—
128	C₄×C₁₉	#462	1	2	yes	—
129	C₄×C₁₉	#464	1	2	yes	—
130	Dic₁₉	—	4	4	no	—
131	Dic₁₉	—	8	2	no	—
132	Dic₁₉	—	8	2	no	—
133	C₂²×Q₁₆	—	38	2	no	—
134	C₂×C₄⋊Q₈	—	19	1	no	—
135	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
136	#494	—	19	4	no	—
137	#494	—	38	2	no	—
138	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
139	C₂×C₄×C₈	—	19	1	no	—
140	#391	—	38	2	no	—
141	#389	—	38	2	no	—
142	C₄×C₄⋊C₄	—	19	2	no	—
143	C₄×C₄⋊C₄	—	38	2	no	—
144	#340	—	38	2	no	—
145	#340	—	38	2	no	—
146	#333	—	2	2	no	—
147	C₂×C₁₉	#1632	1	2	yes	—
148	C₂×C₁₉	#1633	1	1	yes	characteristic
149	C₂×C₁₉	#1634	1	1	yes	characteristic
150	C₂×C₁₉	#1878	1	2	yes	—
151	C₂×C₁₉	#1887	1	1	yes	characteristic
152	C₂²×Q₈	—	38	1	no	—
153	C₂²×Q₈	D₇₆	1	2	yes	—
154	C₂×Q₁₆	—	38	8	no	—
155	C₂×Q₁₆	—	76	4	no	—
156	C₂×Q₁₆	—	76	4	no	—
157	C₂²×C₈	—	2	2	no	—
158	C₂²×C₈	—	38	1	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₄⋊Q₈	—	19	2	no	—
161	C₄⋊Q₈	—	38	2	no	—
162	C₄⋊Q₈	—	38	1	no	—
163	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
164	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
165	C₂×C₄⋊C₄	—	2	2	no	—
166	C₂×C₄⋊C₄	—	19	2	no	—
167	C₂×C₄⋊C₄	—	19	2	no	—
168	C₂×C₄⋊C₄	—	38	2	no	—
169	C₂×C₄⋊C₄	—	38	2	no	—
170	C₂×C₄²	—	38	2	no	—
171	C₂×C₄²	—	38	2	no	—
172	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄×C₈	—	19	2	no	—
176	C₄×C₈	—	38	1	no	—
177	#95	—	38	4	no	—
178	#95	—	38	2	no	—
179	C₁₉	#9066	1	1	yes	characteristic, complemented, Sylow
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	4	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	38	2	no	—
184	C₂×Q₈	—	76	2	no	—
185	C₂×Q₈	—	76	2	no	—
186	C₂×Q₈	—	76	1	no	—
187	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	—	38	2	no	—
190	C₂²×C₄	—	38	2	no	—
191	C₂²×C₄	—	76	1	no	—
192	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
193	C₂²×C₄	D₄×D₁₉	1	2	yes	—
194	Q₁₆	—	76	16	no	—
195	C₂×C₈	—	4	2	no	—
196	C₂×C₈	—	4	2	no	—
197	C₂×C₈	—	4	2	no	—
198	C₂×C₈	—	38	2	no	—
199	C₂×C₈	—	38	2	no	—
200	C₂×C₈	—	38	2	no	—
201	C₄⋊C₄	—	2	4	no	—
202	C₄⋊C₄	—	2	4	no	—
203	C₄⋊C₄	—	19	4	no	—
204	C₄⋊C₄	—	38	2	no	—
205	C₄⋊C₄	—	38	4	no	—
206	C₄⋊C₄	—	38	2	no	—
207	C₄⋊C₄	—	38	2	no	—
208	C₄⋊C₄	—	76	2	no	—
209	C₄⋊C₄	—	152	2	no	—
210	C₄²	—	76	2	no	—
211	C₄²	—	76	2	no	—
212	C₄²	—	152	2	no	—
213	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
214	C₄²	#64543	1	2	yes	—
215	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
216	C₂³	#10597328	1	1	yes	characteristic
217	Q₈	—	4	4	no	—
218	Q₈	—	8	2	no	—
219	Q₈	—	76	4	no	—
220	Q₈	—	152	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	4	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	38	4	no	—
227	C₂×C₄	—	76	2	no	—
228	C₂×C₄	—	76	2	no	—
229	C₂×C₄	—	76	2	no	—
230	C₂×C₄	—	76	2	no	—
231	C₂×C₄	—	76	2	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	—	152	1	no	—
234	C₂×C₄	—	152	1	no	—
235	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
236	C₂×C₄	#10597332	1	1	yes	characteristic
237	C₂×C₄	#10597361	1	2	yes	—
238	C₂×C₄	#10597362	1	2	yes	—
239	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
240	C₂×C₄	#10597364	1	2	yes	—
241	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
242	C₂×C₄	#10597385	1	2	yes	—
243	C₈	—	8	2	no	—
244	C₈	—	38	4	no	—
245	C₂²	#11926421	1	1	yes	characteristic
246	C₂²	#11926701	1	2	yes	—
247	C₂²	#11926709	1	2	yes	—
248	C₂²	#11926714	1	1	yes	characteristic
249	C₂²	#11926714	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	4	4	no	—
253	C₄	—	76	4	no	—
254	C₄	—	152	2	no	—
255	C₄	—	152	2	no	—
256	C₄	#11926636	1	2	yes	—
257	C₄	#11926648	1	2	yes	—
258	C₄	#11926752	1	2	yes	—
259	C₄	#11926764	1	2	yes	—
260	C₂	#14562770	1	2	yes	—
261	C₂	#14562776	1	1	yes	characteristic
262	C₂	#14562781	1	1	yes	characteristic
263	C₂	#14563974	1	2	yes	—
264	C₂	#14564031	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926923

C₂

yes

maximal, characteristic

#14566725

C₂

yes

maximal, characteristic

#14564582

C₂

yes

maximal

#14561474

C₂

yes

maximal

C₂×C₁₉×#333

C₂

yes

maximal, characteristic

C₂²×#64528

—

C₂×#10597315

C₂²

yes

characteristic

#11926923

—

#11926923

C₄

yes

complemented

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926451

—

#11926443

—

C₄⋊C₄×Dic₁₉

—

C₄×C₄⋊Dic₁₉

C₂²

yes

—

#11926307

—

#11926307

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#333

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

#10597315

—

#10597315

—

#10597315

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

Q₁₆

yes

complemented

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

C₂×Dic₁₉

—

108

C₂×Dic₁₉

—

109

Dic₃₈

—

110

Dic₃₈

—

111

C₈×C₁₉

—

112

C₁₉⋊C₈

—

113

C₂×#494

—

114

#2369

—

115

#1987

—

116

C₂×#333

D₁₉

yes

characteristic

117

#1279

—

118

C₂²×C₁₉

#386

yes

characteristic

119

C₂²×C₁₉

#451

yes

—

120

C₂²×C₁₉

#452

yes

—

121

C₂²×C₁₉

#453

yes

characteristic

122

C₂²×C₁₉

#453

yes

characteristic

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

C₄×Q₁₆

yes

—

127

C₄×C₁₉

#441

yes

—

128

C₄×C₁₉

#462

yes

—

129

C₄×C₁₉

#464

yes

—

130

Dic₁₉

—

131

Dic₁₉

—

132

Dic₁₉

—

133

C₂²×Q₁₆

—

134

C₂×C₄⋊Q₈

—

135

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

136

#494

—

137

#494

—

138

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

139

C₂×C₄×C₈

—

140

#391

—

141

#389

—

142

C₄×C₄⋊C₄

—

143

C₄×C₄⋊C₄

—

144

#340

—

145

#340

—

146

#333

—

147

C₂×C₁₉

#1632

yes

—

148

C₂×C₁₉

#1633

yes

characteristic

149

C₂×C₁₉

#1634

yes

characteristic

150

C₂×C₁₉

#1878

yes

—

151

C₂×C₁₉

#1887

yes

characteristic

152

C₂²×Q₈

—

153

C₂²×Q₈

D₇₆

yes

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂²×C₈

—

158

C₂²×C₈

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

C₄×D₁₉

yes

—

164

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄²

—

171

C₂×C₄²

—

172

C₂×C₄²

C₂²×D₁₉

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄×C₈

—

176

C₄×C₈

—

177

#95

—

178

#95

—

179

C₁₉

#9066

yes

characteristic, complemented, Sylow

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

(C₂×D₁₉)⋊C₄

yes

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

C₂×D₇₆

yes

characteristic

193

C₂²×C₄

D₄×D₁₉

yes

—

194

Q₁₆

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

152

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

152

—

213

C₄²

C₂×C₄×D₁₉

yes

characteristic

214

C₄²

#64543

yes

—

215

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

216

C₂³

#10597328

yes

characteristic

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

152

—

221

C₂×C₄

—

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

—

152

—

234

C₂×C₄

—

152

—

235

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

236

C₂×C₄

#10597332

yes

characteristic

237

C₂×C₄

#10597361

yes

—

238

C₂×C₄

#10597362

yes

—

239

C₂×C₄

Q₁₆×D₁₉

yes

—

240

C₂×C₄

#10597364

yes

—

241

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

242

C₂×C₄

#10597385

yes

—

243

C₈

—

244

C₈

—

245

C₂²

#11926421

yes

characteristic

246

C₂²

#11926701

yes

—

247

C₂²

#11926709

yes

—

248

C₂²

#11926714

yes

characteristic

249

C₂²

#11926714

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

152

—

255

C₄

—

152

—

256

C₄

#11926636

yes

—

257

C₄

#11926648

yes

—

258

C₄

#11926752

yes

—

259

C₄

#11926764

yes

—

260

C₂

#14562770

yes

—

261

C₂

#14562776

yes

characteristic

262

C₂

#14562781

yes

characteristic

263

C₂

#14563974

yes

—

264

C₂

#14564031

yes

characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#333	C₂
socle, prime radical	C₂³×C₁₉	#120
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#333	D₁₉
hypocenter	C₁₉	#9066
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

#10597328

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#333

C₂

socle, prime radical

C₂³×C₁₉

#120

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

N	H ≅ G/N	type
9. #11926923	C₄	semidirect
76. C₄⋊Dic₁₉	Q₁₆	semidirect
179. C₁₉	#9066	semidirect

H ≅ G/N

type

9. #11926923

C₄

semidirect

76. C₄⋊Dic₁₉

Q₁₆

semidirect

179. C₁₉

#9066

semidirect

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

subgroup	index
C₂×#11926923	2
#14566725	2
#14564582	2
#14561474	2
C₂×C₁₉×#333	2
#9066	19

subgroup

index

C₂×C₁₉×#333

Subgroups — #18077843

Conjugacy classes of subgroups

Complements

Maximal subgroups