Group #18076559 — subgroups

Subgroups — #18076559

Order 4864.

420 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14563619	C₂	1	1	yes	maximal, characteristic
2	#14562411	C₂	1	2	yes	maximal, complemented
3	#14561949	C₂	1	1	yes	maximal, characteristic
4	#14561530	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2905	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
10	#11926299	—	2	1	no	—
11	#11926296	—	2	4	no	—
12	#11926270	C₄	1	2	yes	—
13	#11926268	C₄	1	2	yes	—
14	C₂²×M₁₆×C₁₉	—	2	1	no	—
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₁₉×#424	—	2	4	no	—
17	C₁₉×#423	—	2	1	no	—
18	C₁₉×#423	C₂²	1	2	yes	—
19	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂×M₁₆×C₁₉	—	2	2	no	—
21	C₂×M₁₆×C₁₉	—	2	2	no	—
22	C₂×M₁₆×C₁₉	—	4	2	no	—
23	C₂×M₁₆×C₁₉	—	4	2	no	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₁₉×#117	—	2	2	no	—
26	C₁₉×#117	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	—	2	1	no	—
34	C₂²×C₁₉⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	4	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
38	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
39	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	—	2	1	no	—
48	C₂²×C₄×C₁₉	—	2	1	no	—
49	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	D₈	1	2	yes	—
53	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
54	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
57	M₁₆×C₁₉	—	4	4	no	—
58	M₁₆×C₁₉	—	4	2	no	—
59	M₁₆×C₁₉	—	4	2	no	—
60	C₂×C₈×C₁₉	—	2	4	no	—
61	C₂×C₈×C₁₉	—	4	4	no	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₄²×C₁₉	—	2	1	no	—
67	C₄²×C₁₉	—	2	1	no	—
68	C₄²×C₁₉	C₂×D₄	1	2	yes	—
69	C₄²×C₁₉	#41	1	2	yes	—
70	C₂×C₁₉⋊C₈	—	2	4	no	—
71	C₂×C₁₉⋊C₈	—	4	1	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	C₂×C₁₉⋊C₈	—	4	1	no	—
74	C₂×C₁₉⋊C₈	—	4	1	no	—
75	C₂×C₁₉⋊C₈	—	4	1	no	—
76	C₂×C₁₉⋊C₈	—	4	1	no	—
77	#8861	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	—	2	1	no	—
79	C₂³×C₁₉	—	2	1	no	—
80	C₂³×C₁₉	—	4	1	no	—
81	C₂³×C₁₉	—	4	1	no	—
82	C₂³×C₁₉	#107	1	2	yes	—
83	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	1	no	—
96	C₂×C₄×C₁₉	#107	1	2	yes	—
97	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
100	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
103	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
105	C₈×C₁₉	—	4	4	no	—
106	C₁₉⋊C₈	—	4	4	no	—
107	C₁₉⋊C₈	—	8	1	no	—
108	C₁₉⋊C₈	—	8	1	no	—
109	#2905	D₁₉	1	1	yes	characteristic
110	#1798	—	19	1	no	—
111	#1571	—	19	2	no	—
112	#1458	—	19	1	no	—
113	#1301	—	19	2	no	—
114	C₂²×C₁₉	—	2	1	no	—
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	—	2	2	no	—
117	C₂²×C₁₉	—	4	2	no	—
118	C₂²×C₁₉	—	4	1	no	—
119	C₂²×C₁₉	—	4	1	no	—
120	C₂²×C₁₉	—	8	1	no	—
121	C₂²×C₁₉	#385	1	1	yes	characteristic
122	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
123	C₂²×C₁₉	#428	1	1	yes	characteristic
124	C₄×C₁₉	—	2	2	no	—
125	C₄×C₁₉	—	2	2	no	—
126	C₄×C₁₉	—	2	2	no	—
127	C₄×C₁₉	—	4	1	no	—
128	C₄×C₁₉	—	4	1	no	—
129	C₄×C₁₉	#447	1	1	yes	characteristic
130	C₄×C₁₉	#451	1	1	yes	characteristic
131	C₄×C₁₉	#480	1	1	yes	characteristic
132	C₄×C₁₉	#484	1	1	yes	characteristic
133	C₂²×M₁₆	—	2	1	no	—
134	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
135	#431	—	19	2	no	—
136	#424	—	2	4	no	—
137	#423	—	2	1	no	—
138	#423	C₂×D₁₉	1	2	yes	—
139	C₂×C₄⋊C₈	—	19	1	no	—
140	C₂×C₄⋊C₈	—	19	1	no	—
141	C₂×C₂²⋊C₈	—	38	1	no	—
142	#336	—	38	1	no	—
143	#335	—	38	4	no	—
144	#324	—	19	2	no	—
145	#323	—	19	2	no	—
146	C₂×C₁₉	—	2	1	no	—
147	C₂×C₁₉	—	2	1	no	—
148	C₂×C₁₉	—	4	2	no	—
149	C₂×C₁₉	#1852	1	1	yes	characteristic
150	C₂×C₁₉	#1858	1	1	yes	characteristic
151	C₂×C₁₉	#1868	1	1	yes	characteristic
152	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	2	2	no	—
155	C₂×M₁₆	—	4	2	no	—
156	C₂×M₁₆	—	4	2	no	—
157	C₂²×C₈	—	2	2	no	—
158	C₂²×C₈	—	38	1	no	—
159	C₂²×C₈	—	38	1	no	—
160	#117	—	2	2	no	—
161	#117	—	2	2	no	—
162	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
163	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
164	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
165	C₂×C₂²⋊C₄	C₄×D₁₉	1	1	yes	characteristic
166	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
167	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
168	C₄⋊C₈	—	2	4	no	—
169	C₄⋊C₈	—	2	2	no	—
170	C₄⋊C₈	—	38	2	no	—
171	C₄⋊C₈	—	38	2	no	—
172	C₄⋊C₈	—	38	2	no	—
173	C₄⋊C₈	C₂²⋊D₁₉	1	4	yes	—
174	C₂²⋊C₈	—	19	4	no	—
175	C₂²⋊C₈	—	76	2	no	—
176	C₄×C₈	—	38	2	no	—
177	C₁₉	#8861	1	1	yes	characteristic, complemented, Sylow
178	C₂⁴	Dic₁₉⋊C₄	1	1	yes	characteristic
179	C₂²×C₄	—	2	1	no	—
180	C₂²×C₄	—	2	1	no	—
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
184	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
185	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
186	C₂²×C₄	#64525	1	2	yes	—
187	C₂²×C₄	#64528	1	2	yes	—
188	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
190	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
191	M₁₆	—	4	4	no	—
192	M₁₆	—	4	2	no	—
193	M₁₆	—	4	2	no	—
194	C₂×C₈	—	2	4	no	—
195	C₂×C₈	—	4	4	no	—
196	C₂×C₈	—	38	4	no	—
197	C₂×C₈	—	76	1	no	—
198	C₂×C₈	—	76	1	no	—
199	C₂×C₈	—	76	1	no	—
200	C₂×C₈	—	76	1	no	—
201	C₂×C₈	—	76	1	no	—
202	C₂×C₈	—	76	1	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₂²⋊C₄	—	2	2	no	—
206	C₂²⋊C₄	—	2	2	no	—
207	C₄²	—	2	1	no	—
208	C₄²	—	2	1	no	—
209	C₄²	#64541	1	2	yes	—
210	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
211	C₂³	—	2	1	no	—
212	C₂³	—	2	1	no	—
213	C₂³	—	4	1	no	—
214	C₂³	—	4	1	no	—
215	C₂³	#10597264	1	2	yes	—
216	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	#10597264	1	2	yes	—
230	C₂×C₄	#10597370	1	2	yes	—
231	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
232	C₂×C₄	#10597375	1	1	yes	characteristic
233	C₂×C₄	C₂×#64525	1	1	yes	characteristic
234	C₂×C₄	#10597378	1	1	yes	characteristic
235	C₂×C₄	#10597388	1	1	yes	characteristic
236	C₂×C₄	C₂×#64528	1	1	yes	characteristic
237	C₂×C₄	#10597399	1	1	yes	characteristic
238	C₈	—	4	4	no	—
239	C₈	—	76	4	no	—
240	C₈	—	152	1	no	—
241	C₈	—	152	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	2	no	—
245	C₂²	—	4	2	no	—
246	C₂²	—	4	1	no	—
247	C₂²	—	4	1	no	—
248	C₂²	—	8	1	no	—
249	C₂²	#11926417	1	1	yes	characteristic
250	C₂²	C₂×#10597264	1	1	yes	characteristic
251	C₂²	#11926584	1	1	yes	characteristic
252	C₄	—	2	2	no	—
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	4	1	no	—
256	C₄	—	4	1	no	—
257	C₄	#11926678	1	1	yes	characteristic
258	C₄	#11926700	1	1	yes	characteristic
259	C₄	#11926857	1	1	yes	characteristic
260	C₄	#11926879	1	1	yes	characteristic
261	C₂	—	2	1	no	—
262	C₂	—	2	1	no	—
263	C₂	—	4	2	no	—
264	C₂	#14563823	1	1	yes	characteristic
265	C₂	#14563855	1	1	yes	characteristic
266	C₂	#14563921	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563619

C₂

yes

maximal, characteristic

#14562411

C₂

yes

maximal, complemented

#14561949

C₂

yes

maximal, characteristic

#14561530

C₂

yes

maximal, complemented

C₁₉×#2905

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926299

—

#11926296

—

#11926270

C₄

yes

—

#11926268

C₄

yes

—

C₂²×M₁₆×C₁₉

—

C₂×C₁₉×#117

C₂²

yes

characteristic

C₁₉×#424

—

C₁₉×#423

—

C₁₉×#423

C₂²

yes

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

—

C₂²×C₄×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8861

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#107

yes

—

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#107

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

100

C₂×C₄×C₁₉

#123

yes

characteristic

101

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

102

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

103

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

104

C₂×C₄×C₁₉

#137

yes

characteristic

105

C₈×C₁₉

—

106

C₁₉⋊C₈

—

107

C₁₉⋊C₈

—

108

C₁₉⋊C₈

—

109

#2905

D₁₉

yes

characteristic

110

#1798

—

111

#1571

—

112

#1458

—

113

#1301

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#385

yes

characteristic

122

C₂²×C₁₉

C₂×#107

yes

characteristic

123

C₂²×C₁₉

#428

yes

characteristic

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

#447

yes

characteristic

130

C₄×C₁₉

#451

yes

characteristic

131

C₄×C₁₉

#480

yes

characteristic

132

C₄×C₁₉

#484

yes

characteristic

133

C₂²×M₁₆

—

134

C₂×#117

C₂×D₁₉

yes

characteristic

135

#431

—

136

#424

—

137

#423

—

138

#423

C₂×D₁₉

yes

—

139

C₂×C₄⋊C₈

—

140

C₂×C₄⋊C₈

—

141

C₂×C₂²⋊C₈

—

142

#336

—

143

#335

—

144

#324

—

145

#323

—

146

C₂×C₁₉

—

147

C₂×C₁₉

—

148

C₂×C₁₉

—

149

C₂×C₁₉

#1852

yes

characteristic

150

C₂×C₁₉

#1858

yes

characteristic

151

C₂×C₁₉

#1868

yes

characteristic

152

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

153

C₂×M₁₆

—

154

C₂×M₁₆

—

155

C₂×M₁₆

—

156

C₂×M₁₆

—

157

C₂²×C₈

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

#117

—

161

#117

—

162

C₂×C₄⋊C₄

Dic₃₈

yes

characteristic

163

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

164

C₂×C₂²⋊C₄

Dic₃₈

yes

characteristic

165

C₂×C₂²⋊C₄

C₄×D₁₉

yes

characteristic

166

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

167

C₂×C₄²

C₂²×D₁₉

yes

characteristic

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

C₂²⋊D₁₉

yes

—

174

C₂²⋊C₈

—

175

C₂²⋊C₈

—

176

C₄×C₈

—

177

C₁₉

#8861

yes

characteristic, complemented, Sylow

178

C₂⁴

Dic₁₉⋊C₄

yes

characteristic

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

184

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

185

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

186

C₂²×C₄

#64525

yes

—

187

C₂²×C₄

#64528

yes

—

188

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

189

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

190

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

191

M₁₆

—

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

—

208

C₄²

—

209

C₄²

#64541

yes

—

210

C₄²

C₂×C₂²⋊D₁₉

yes

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

—

215

C₂³

#10597264

yes

—

216

C₂³

C₂×Dic₁₉⋊C₄

yes

characteristic

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

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

#10597264

yes

—

230

C₂×C₄

#10597370

yes

—

231

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

232

C₂×C₄

#10597375

yes

characteristic

233

C₂×C₄

C₂×#64525

yes

characteristic

234

C₂×C₄

#10597378

yes

characteristic

235

C₂×C₄

#10597388

yes

characteristic

236

C₂×C₄

C₂×#64528

yes

characteristic

237

C₂×C₄

#10597399

yes

characteristic

238

C₈

—

239

C₈

—

240

C₈

—

152

—

241

C₈

—

152

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

#11926417

yes

characteristic

250

C₂²

C₂×#10597264

yes

characteristic

251

C₂²

#11926584

yes

characteristic

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

#11926678

yes

characteristic

258

C₄

#11926700

yes

characteristic

259

C₄

#11926857

yes

characteristic

260

C₄

#11926879

yes

characteristic

261

C₂

—

262

C₂

—

263

C₂

—

264

C₂

#14563823

yes

characteristic

265

C₂

#14563855

yes

characteristic

266

C₂

#14563921

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2905	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2905	D₁₉
hypocenter	C₁₉	#8861
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2905

subgroup

G/H

center

C₂×C₄

#10597399

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2905

C₂

socle

C₂²×C₁₉

#385

prime radical

C₂⁴×C₁₉

C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2905

N	H ≅ G/N	type
2. #14562411	C₂	semidirect
4. #14561530	C₂	semidirect
177. C₁₉	#8861	semidirect

H ≅ G/N

type

2. #14562411

C₂

semidirect

4. #14561530

C₂

semidirect

177. C₁₉

#8861

semidirect

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

subgroup	index
#14563619	2
#14562411	2
#14561949	2
#14561530	2
C₁₉×#2905	2
#8861	19

subgroup

index

C₁₉×#2905

Subgroups — #18076559

Conjugacy classes of subgroups

Complements

Maximal subgroups