Group #18075868 — subgroups

Subgroups — #18075868

Order 4864.

898 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 179 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	#14563545	C₂	1	2	yes	maximal
2	#14561478	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
5	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
8	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
9	C₂²×C₄²×C₁₉	C₄	1	2	yes	—
10	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
11	C₂×C₁₉×#95	C₂²	1	2	yes	—
12	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂³×C₄×C₁₉	—	2	4	no	—
14	C₂³×C₄×C₁₉	—	4	4	no	—
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
17	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₉	D₄	1	4	yes	—
19	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
24	C₂×C₂²⋊C₄×C₁₉	C₈	1	4	yes	complemented
25	C₂×C₄²×C₁₉	—	2	2	no	—
26	C₂×C₄²×C₁₉	—	2	2	no	—
27	C₂×C₄²×C₁₉	—	4	4	no	—
28	C₂²×C₁₉⋊C₈	—	2	4	no	—
29	C₁₉×#95	—	2	4	no	—
30	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
31	C₂²⋊(C₁₉⋊C₈)	—	4	8	no	—
32	C₂⁴×C₁₉	—	2	2	no	—
33	C₂⁴×C₁₉	—	2	2	no	—
34	C₂⁴×C₁₉	—	4	2	no	—
35	C₂⁴×C₁₉	—	4	2	no	—
36	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
37	C₂⁴×C₁₉	C₂×C₈	1	2	yes	—
38	C₂⁴×C₁₉	M₁₆	1	2	yes	—
39	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	—	2	4	no	—
42	C₂²×C₄×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	8	no	—
47	C₂²×C₄×C₁₉	—	2	8	no	—
48	C₂²×C₄×C₁₉	—	4	4	no	—
49	C₂²×C₄×C₁₉	—	4	2	no	—
50	C₂²×C₄×C₁₉	—	4	16	no	—
51	C₂²×C₄×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
57	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
58	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
59	C₂²×C₄×C₁₉	#41	1	4	yes	—
60	C₂²⋊C₄×C₁₉	—	2	8	no	—
61	C₂²⋊C₄×C₁₉	—	2	8	no	—
62	C₄²×C₁₉	—	4	4	no	—
63	C₄²×C₁₉	—	4	4	no	—
64	C₂×C₁₉⋊C₈	—	4	8	no	—
65	C₂×C₁₉⋊C₈	—	4	4	no	—
66	#8700	—	19	1	no	maximal, Sylow
67	C₂³×C₁₉	—	2	2	no	—
68	C₂³×C₁₉	—	2	2	no	—
69	C₂³×C₁₉	—	2	2	no	—
70	C₂³×C₁₉	—	2	2	no	—
71	C₂³×C₁₉	—	2	4	no	—
72	C₂³×C₁₉	—	2	4	no	—
73	C₂³×C₁₉	—	2	4	no	—
74	C₂³×C₁₉	—	2	4	no	—
75	C₂³×C₁₉	—	4	4	no	—
76	C₂³×C₁₉	—	4	4	no	—
77	C₂³×C₁₉	—	4	4	no	—
78	C₂³×C₁₉	—	4	4	no	—
79	C₂³×C₁₉	—	4	4	no	—
80	C₂³×C₁₉	—	4	4	no	—
81	C₂³×C₁₉	C₂²⋊C₈	1	4	yes	—
82	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂³×C₁₉	#117	1	2	yes	—
84	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
85	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
86	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
87	C₂×C₄×C₁₉	—	2	8	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	4	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	4	no	—
92	C₂×C₄×C₁₉	—	2	4	no	—
93	C₂×C₄×C₁₉	—	4	4	no	—
94	C₂×C₄×C₁₉	—	4	16	no	—
95	C₂×C₄×C₁₉	—	4	4	no	—
96	C₂×C₄×C₁₉	—	4	4	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	4	4	no	—
102	C₂×C₄×C₁₉	—	4	4	no	—
103	C₂×C₄×C₁₉	#99	1	4	yes	—
104	C₂×C₄×C₁₉	#123	1	4	yes	—
105	C₁₉⋊C₈	—	8	4	no	—
106	C₂×C₄×C₂²⋊C₄	D₁₉	1	1	yes	characteristic
107	#1779	—	19	2	no	—
108	#1280	—	19	4	no	—
109	C₂²×C₁₉	—	2	2	no	—
110	C₂²×C₁₉	—	2	2	no	—
111	C₂²×C₁₉	—	2	2	no	—
112	C₂²×C₁₉	—	2	2	no	—
113	C₂²×C₁₉	—	2	2	no	—
114	C₂²×C₁₉	—	2	2	no	—
115	C₂²×C₁₉	—	2	4	no	—
116	C₂²×C₁₉	—	2	8	no	—
117	C₂²×C₁₉	—	4	8	no	—
118	C₂²×C₁₉	—	4	8	no	—
119	C₂²×C₁₉	—	4	2	no	—
120	C₂²×C₁₉	—	4	2	no	—
121	C₂²×C₁₉	—	4	4	no	—
122	C₂²×C₁₉	#381	1	1	yes	characteristic
123	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
124	C₂²×C₁₉	#407	1	1	yes	characteristic
125	C₂²×C₁₉	C₂×#99	1	2	yes	—
126	C₂²×C₁₉	#413	1	2	yes	—
127	C₂²×C₁₉	#431	1	2	yes	—
128	C₂²×C₁₉	#432	1	2	yes	—
129	C₄×C₁₉	—	2	4	no	—
130	C₄×C₁₉	—	2	4	no	—
131	C₄×C₁₉	—	4	4	no	—
132	C₄×C₁₉	—	4	4	no	—
133	C₂⁴×C₄	C₂×D₁₉	1	1	yes	characteristic
134	C₂²×C₂²⋊C₄	Dic₁₉	1	1	yes	characteristic
135	C₂²×C₂²⋊C₄	Dic₁₉	1	1	yes	characteristic
136	C₂²×C₄²	Dic₁₉	1	2	yes	—
137	C₂×C₂²⋊C₈	—	19	4	no	—
138	C₂×C₂²⋊C₈	—	38	4	no	—
139	C₄×C₂²⋊C₄	—	2	4	no	—
140	C₂×#95	C₂×D₁₉	1	2	yes	—
141	C₂×C₁₉	—	2	2	no	—
142	C₂×C₁₉	—	2	2	no	—
143	C₂×C₁₉	—	4	4	no	—
144	C₂×C₁₉	#1459	1	2	yes	—
145	C₂×C₁₉	#1465	1	2	yes	—
146	C₂×C₁₉	#1817	1	1	yes	characteristic
147	C₂×C₁₉	#1819	1	1	yes	characteristic
148	C₂×C₁₉	#1822	1	1	yes	characteristic
149	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
150	C₂³×C₄	—	2	4	no	—
151	C₂³×C₄	—	4	4	no	—
152	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
153	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
154	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
155	C₂³×C₄	C₂²⋊D₁₉	1	4	yes	—
156	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
157	C₂²×C₈	—	38	4	no	—
158	C₂×C₂²⋊C₄	—	2	2	no	—
159	C₂×C₂²⋊C₄	—	2	2	no	—
160	C₂×C₂²⋊C₄	—	2	2	no	—
161	C₂×C₂²⋊C₄	—	2	4	no	—
162	C₂×C₂²⋊C₄	C₁₉⋊C₈	1	4	yes	complemented
163	C₂×C₄²	—	2	2	no	—
164	C₂×C₄²	—	2	2	no	—
165	C₂×C₄²	—	4	4	no	—
166	C₂²⋊C₈	—	38	8	no	—
167	C₂²⋊C₈	—	76	8	no	—
168	#95	—	2	4	no	—
169	C₁₉	#8700	1	1	yes	characteristic, complemented, Sylow
170	C₂⁴	—	2	2	no	—
171	C₂⁴	—	2	2	no	—
172	C₂⁴	—	4	2	no	—
173	C₂⁴	—	4	2	no	—
174	C₂⁴	C₂×C₁₉⋊C₈	1	2	yes	—
175	C₂⁴	#64520	1	2	yes	—
176	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
177	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	4	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	2	8	no	—
185	C₂²×C₄	—	2	8	no	—
186	C₂²×C₄	—	4	4	no	—
187	C₂²×C₄	—	4	2	no	—
188	C₂²×C₄	—	4	16	no	—
189	C₂²×C₄	—	4	2	no	—
190	C₂²×C₄	—	4	2	no	—
191	C₂²×C₄	—	4	2	no	—
192	C₂²×C₄	—	4	2	no	—
193	C₂²×C₄	C₂×C₁₉⋊C₈	1	4	yes	—
194	C₂²×C₄	#64520	1	4	yes	—
195	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
196	C₂²×C₄	#64541	1	4	yes	—
197	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
198	C₂×C₈	—	76	8	no	—
199	C₂×C₈	—	76	4	no	—
200	C₂²⋊C₄	—	2	8	no	—
201	C₂²⋊C₄	—	2	8	no	—
202	C₄²	—	4	4	no	—
203	C₄²	—	4	4	no	—
204	C₂³	—	2	2	no	—
205	C₂³	—	2	2	no	—
206	C₂³	—	2	4	no	—
207	C₂³	—	2	4	no	—
208	C₂³	—	2	4	no	—
209	C₂³	—	2	2	no	—
210	C₂³	—	2	2	no	—
211	C₂³	—	2	4	no	—
212	C₂³	—	4	4	no	—
213	C₂³	—	4	4	no	—
214	C₂³	—	4	4	no	—
215	C₂³	—	4	4	no	—
216	C₂³	—	4	4	no	—
217	C₂³	—	4	4	no	—
218	C₂³	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
219	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
220	C₂³	C₂×#64520	1	2	yes	—
221	C₂³	C₂×#64520	1	1	yes	characteristic
222	C₂³	#10597372	1	2	yes	—
223	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
224	C₂×C₄	—	2	8	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	4	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	2	4	no	—
230	C₂×C₄	—	4	4	no	—
231	C₂×C₄	—	4	16	no	—
232	C₂×C₄	—	4	4	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	4	no	—
239	C₂×C₄	—	4	4	no	—
240	C₂×C₄	#10597291	1	4	yes	—
241	C₂×C₄	#10597375	1	4	yes	—
242	C₈	—	152	4	no	—
243	C₂²	—	2	2	no	—
244	C₂²	—	2	2	no	—
245	C₂²	—	2	2	no	—
246	C₂²	—	2	2	no	—
247	C₂²	—	2	2	no	—
248	C₂²	—	2	2	no	—
249	C₂²	—	2	4	no	—
250	C₂²	—	2	8	no	—
251	C₂²	—	4	8	no	—
252	C₂²	—	4	8	no	—
253	C₂²	—	4	2	no	—
254	C₂²	—	4	2	no	—
255	C₂²	—	4	4	no	—
256	C₂²	#11926407	1	1	yes	characteristic
257	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
258	C₂²	#11926508	1	1	yes	characteristic
259	C₂²	C₂×#10597291	1	2	yes	—
260	C₂²	#11926528	1	2	yes	—
261	C₂²	#11926597	1	2	yes	—
262	C₂²	#11926601	1	2	yes	—
263	C₄	—	2	4	no	—
264	C₄	—	2	4	no	—
265	C₄	—	4	4	no	—
266	C₄	—	4	4	no	—
267	C₂	—	2	2	no	—
268	C₂	—	2	2	no	—
269	C₂	—	4	4	no	—
270	C₂	#14561953	1	2	yes	—
271	C₂	#14561973	1	2	yes	—
272	C₂	#14563703	1	1	yes	characteristic
273	C₂	#14563709	1	1	yes	characteristic
274	C₂	#14563718	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563545

C₂

yes

maximal

#14561478

C₂

yes

maximal, complemented

C₂×C₄×C₂²⋊C₄×C₁₉

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂⁴×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊C₄×C₁₉

C₄

yes

characteristic

C₂²×C₂²⋊C₄×C₁₉

C₄

yes

characteristic

C₂²×C₄²×C₁₉

C₄

yes

—

C₄×C₂²⋊C₄×C₁₉

—

C₂×C₁₉×#95

C₂²

yes

—

C₂⁵×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₈

yes

complemented

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₉

C₂×C₈

yes

—

C₂⁴×C₁₉

M₁₆

yes

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8700

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

C₂³×C₁₉

C₂²×C₈

yes

characteristic

C₂³×C₁₉

C₂×M₁₆

yes

characteristic

C₂³×C₁₉

C₂×M₁₆

yes

—

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

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

#99

yes

—

104

C₂×C₄×C₁₉

#123

yes

—

105

C₁₉⋊C₈

—

106

C₂×C₄×C₂²⋊C₄

D₁₉

yes

characteristic

107

#1779

—

108

#1280

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

#381

yes

characteristic

123

C₂²×C₁₉

C₂×C₂²⋊C₈

yes

characteristic

124

C₂²×C₁₉

#407

yes

characteristic

125

C₂²×C₁₉

C₂×#99

yes

—

126

C₂²×C₁₉

#413

yes

—

127

C₂²×C₁₉

#431

yes

—

128

C₂²×C₁₉

#432

yes

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₂⁴×C₄

C₂×D₁₉

yes

characteristic

134

C₂²×C₂²⋊C₄

Dic₁₉

yes

characteristic

135

C₂²×C₂²⋊C₄

Dic₁₉

yes

characteristic

136

C₂²×C₄²

Dic₁₉

yes

—

137

C₂×C₂²⋊C₈

—

138

C₂×C₂²⋊C₈

—

139

C₄×C₂²⋊C₄

—

140

C₂×#95

C₂×D₁₉

yes

—

141

C₂×C₁₉

—

142

C₂×C₁₉

—

143

C₂×C₁₉

—

144

C₂×C₁₉

#1459

yes

—

145

C₂×C₁₉

#1465

yes

—

146

C₂×C₁₉

#1817

yes

characteristic

147

C₂×C₁₉

#1819

yes

characteristic

148

C₂×C₁₉

#1822

yes

characteristic

149

C₂⁵

C₂×Dic₁₉

yes

characteristic

150

C₂³×C₄

—

151

C₂³×C₄

—

152

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

153

C₂³×C₄

C₂×Dic₁₉

yes

—

154

C₂³×C₄

C₂×Dic₁₉

yes

—

155

C₂³×C₄

C₂²⋊D₁₉

yes

—

156

C₂³×C₄

C₂²×D₁₉

yes

characteristic

157

C₂²×C₈

—

158

C₂×C₂²⋊C₄

—

159

C₂×C₂²⋊C₄

—

160

C₂×C₂²⋊C₄

—

161

C₂×C₂²⋊C₄

—

162

C₂×C₂²⋊C₄

C₁₉⋊C₈

yes

complemented

163

C₂×C₄²

—

164

C₂×C₄²

—

165

C₂×C₄²

—

166

C₂²⋊C₈

—

167

C₂²⋊C₈

—

168

#95

—

169

C₁₉

#8700

yes

characteristic, complemented, Sylow

170

C₂⁴

—

171

C₂⁴

—

172

C₂⁴

—

173

C₂⁴

—

174

C₂⁴

C₂×C₁₉⋊C₈

yes

—

175

C₂⁴

#64520

yes

—

176

C₂⁴

C₂²⋊Dic₁₉

yes

—

177

C₂⁴

C₂²×Dic₁₉

yes

characteristic

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

C₂×C₁₉⋊C₈

yes

—

194

C₂²×C₄

#64520

yes

—

195

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

196

C₂²×C₄

#64541

yes

—

197

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₄²

—

203

C₄²

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

—

219

C₂³

C₂²×C₁₉⋊C₈

yes

characteristic

220

C₂³

C₂×#64520

yes

—

221

C₂³

C₂×#64520

yes

characteristic

222

C₂³

#10597372

yes

—

223

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

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

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

#10597291

yes

—

241

C₂×C₄

#10597375

yes

—

242

C₈

—

152

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

#11926407

yes

characteristic

257

C₂²

C₂×C₂²⋊(C₁₉⋊C₈)

yes

characteristic

258

C₂²

#11926508

yes

characteristic

259

C₂²

C₂×#10597291

yes

—

260

C₂²

#11926528

yes

—

261

C₂²

#11926597

yes

—

262

C₂²

#11926601

yes

—

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₂

—

268

C₂

—

269

C₂

—

270

C₂

#14561953

yes

—

271

C₂

#14561973

yes

—

272

C₂

#14563703

yes

characteristic

273

C₂

#14563709

yes

characteristic

274

C₂

#14563718

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂³×C₁₉	C₂²×C₈
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₄×C₂²⋊C₄×C₁₉	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₁₉	C₂×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₂²⋊C₄	D₁₉
hypocenter	C₁₉	#8700
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×C₄×C₂²⋊C₄

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂³×C₁₉

C₂²×C₈

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₂×C₄×C₂²⋊C₄×C₁₉

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁵×C₁₉

C₂×C₄

cosocle

C₂³×C₄×C₁₉

C₂³

hypercenter

C₂×C₄×C₂²⋊C₄

D₁₉

hypocenter

C₁₉

#8700

LCS

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×C₄×C₂²⋊C₄

N	H ≅ G/N	type
2. #14561478	C₂	semidirect
24. C₂×C₂²⋊C₄×C₁₉	C₈	semidirect
162. C₂×C₂²⋊C₄	C₁₉⋊C₈	semidirect
169. C₁₉	#8700	semidirect

H ≅ G/N

type

2. #14561478

C₂

semidirect

24. C₂×C₂²⋊C₄×C₁₉

C₈

semidirect

162. C₂×C₂²⋊C₄

C₁₉⋊C₈

semidirect

169. C₁₉

#8700

semidirect

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

subgroup	index
#14563545	2
#14561478	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
#8700	19

subgroup

index

#14563545

#14561478

C₂×C₄×C₂²⋊C₄×C₁₉

#8700

Subgroups — #18075868

Conjugacy classes of subgroups

Complements

Maximal subgroups