Group #18073099 — subgroups

Subgroups — #100×C₁₉⋊C₈ #18073099

Order 4864.

542 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 193 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×D₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#14561956	C₂	1	1	yes	maximal, characteristic
3	M₁₆×C₁₉⋊C₈	C₂	1	2	yes	maximal, complemented
4	#14561486	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₄	1	2	yes	—
7	D₄×C₁₉⋊C₈	—	2	2	no	—
8	D₄×C₁₉⋊C₈	—	2	2	no	—
9	#11926597	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926268	C₄	1	4	yes	—
14	#11926265	—	2	2	no	—
15	C₈×C₁₉⋊C₈	—	2	2	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#100	C₄	1	2	yes	—
18	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#343	C₄	1	2	yes	—
20	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
23	C₄×D₄×C₁₉	—	2	2	no	—
24	C₄×D₄×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₁₉⋊C₈	—	2	2	no	—
29	C₂²×C₁₉⋊C₈	—	2	2	no	—
30	C₂²×C₁₉⋊C₈	—	4	4	no	—
31	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₁₉×#100	C₈	1	8	yes	complemented
35	C₁₉×#97	—	2	2	no	—
36	C₄×C₈×C₁₉	—	2	2	no	—
37	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
38	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄×C₁₉⋊C₈	—	2	2	no	—
42	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
43	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
44	C₂⁴×C₁₉	C₄²	1	2	yes	—
45	C₂×D₄×C₁₉	—	2	2	no	—
46	C₂×D₄×C₁₉	—	2	2	no	—
47	C₂×D₄×C₁₉	C₂×C₈	1	4	yes	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
53	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	M₁₆×C₁₉	—	2	4	no	—
57	M₁₆×C₁₉	C₂×C₈	1	8	yes	complemented
58	C₂×C₈×C₁₉	—	2	4	no	—
59	C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂²⋊C₄×C₁₉	—	2	4	no	—
61	C₄²×C₁₉	C₂×D₄	1	2	yes	—
62	C₄²×C₁₉	#41	1	2	yes	—
63	C₂×C₁₉⋊C₈	—	2	2	no	—
64	C₂×C₁₉⋊C₈	—	2	2	no	—
65	C₂×C₁₉⋊C₈	—	2	4	no	—
66	C₂×C₁₉⋊C₈	—	4	1	no	—
67	C₂×C₁₉⋊C₈	—	4	4	no	—
68	C₂×C₁₉⋊C₈	—	4	4	no	—
69	C₂×C₁₉⋊C₈	—	4	2	no	—
70	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
71	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
73	C₈×#100	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	—	2	2	no	—
75	C₂³×C₁₉	—	2	2	no	—
76	C₂³×C₁₉	—	4	2	no	—
77	C₂³×C₁₉	—	4	2	no	—
78	C₂³×C₁₉	C₄×C₈	1	4	yes	—
79	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
80	D₄×C₁₉	—	2	8	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	4	1	no	—
85	C₂×C₄×C₁₉	—	4	4	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
92	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
94	C₂×C₄×C₁₉	#131	1	2	yes	—
95	C₈×C₁₉	—	2	8	no	—
96	C₁₉⋊C₈	—	2	1	no	—
97	C₁₉⋊C₈	—	2	2	no	—
98	C₁₉⋊C₈	—	4	4	no	—
99	C₁₉⋊C₈	—	4	2	no	—
100	C₁₉⋊C₈	#100	1	2	yes	direct product factor
101	C₂×C₈×D₄	—	19	1	no	—
102	C₄×#100	D₁₉	1	1	yes	characteristic
103	#1460	—	19	1	no	—
104	C₈×M₁₆	—	19	2	no	—
105	#1283	—	19	2	no	—
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	—	2	4	no	—
109	C₂²×C₁₉	—	4	4	no	—
110	C₂²×C₁₉	—	4	4	no	—
111	C₂²×C₁₉	—	4	2	no	—
112	C₂²×C₁₉	—	4	2	no	—
113	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
115	C₂²×C₁₉	#405	1	1	yes	characteristic
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	2	no	—
118	C₄×C₁₉	—	4	2	no	—
119	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
120	C₄×C₁₉	#413	1	1	yes	characteristic
121	C₄×C₁₉	C₈×D₄	1	4	yes	—
122	C₂³×C₈	—	19	2	no	—
123	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
124	C₈×D₄	—	38	2	no	—
125	C₈×D₄	—	38	2	no	—
126	#431	—	19	2	no	—
127	C₂×C₄⋊C₈	—	19	1	no	—
128	C₂×#100	Dic₁₉	1	2	yes	—
129	C₂×C₂²⋊C₈	—	19	2	no	—
130	C₄×M₁₆	C₂×D₁₉	1	2	yes	—
131	C₂×C₄×C₈	—	19	1	no	—
132	#343	Dic₁₉	1	2	yes	—
133	#323	—	19	4	no	—
134	#322	—	38	2	no	—
135	C₈²	—	38	2	no	—
136	C₂×C₁₉	—	2	1	no	—
137	C₂×C₁₉	—	2	1	no	—
138	C₂×C₁₉	—	4	4	no	—
139	C₂×C₁₉	C₈×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₁₉	C₄×#100	1	1	yes	characteristic
141	C₂×C₁₉	#1757	1	1	yes	characteristic
142	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
143	C₂³×C₄	C₄×D₁₉	1	2	yes	—
144	C₂×M₁₆	C₂×Dic₁₉	1	4	yes	—
145	C₂²×C₈	—	19	1	no	—
146	C₂²×C₈	—	19	1	no	—
147	C₂²×C₈	—	19	2	no	—
148	C₂²×C₈	—	38	2	no	—
149	C₂²×C₈	—	38	2	no	—
150	C₂²×C₈	—	76	4	no	—
151	C₄×D₄	—	2	2	no	—
152	C₄×D₄	—	2	2	no	—
153	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
154	C₂×C₂²⋊C₄	C₄×D₁₉	1	2	yes	—
155	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
156	C₄⋊C₈	—	38	2	no	—
157	C₄⋊C₈	—	38	2	no	—
158	#100	C₁₉⋊C₈	1	8	yes	direct product factor
159	C₂²⋊C₈	—	19	4	no	—
160	C₂²⋊C₈	—	38	4	no	—
161	#97	—	2	2	no	—
162	C₄×C₈	—	2	2	no	—
163	C₄×C₈	—	19	2	no	—
164	C₄×C₈	—	19	2	no	—
165	C₄×C₈	—	38	2	no	—
166	C₁₉	C₈×#100	1	1	yes	characteristic, complemented, Sylow
167	C₂⁴	C₄×Dic₁₉	1	2	yes	—
168	C₂×D₄	—	2	2	no	—
169	C₂×D₄	—	2	2	no	—
170	C₂×D₄	C₂×C₁₉⋊C₈	1	4	yes	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	4	2	no	—
174	C₂²×C₄	—	4	2	no	—
175	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
176	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
179	M₁₆	—	2	4	no	—
180	M₁₆	C₂×C₁₉⋊C₈	1	8	yes	complemented
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	19	1	no	—
183	C₂×C₈	—	19	2	no	—
184	C₂×C₈	—	19	1	no	—
185	C₂×C₈	—	38	2	no	—
186	C₂×C₈	—	38	2	no	—
187	C₂×C₈	—	38	4	no	—
188	C₂×C₈	—	76	4	no	—
189	C₂×C₈	—	76	1	no	—
190	C₂×C₈	—	76	4	no	—
191	C₂×C₈	—	76	2	no	—
192	C₄⋊C₄	—	2	2	no	—
193	C₂²⋊C₄	—	2	4	no	—
194	C₄²	D₄×D₁₉	1	2	yes	—
195	C₄²	#64543	1	2	yes	—
196	C₂³	—	2	2	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	4	2	no	—
199	C₂³	—	4	2	no	—
200	C₂³	C₄×C₁₉⋊C₈	1	4	yes	—
201	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
202	D₄	—	2	8	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	#10597323	1	1	yes	characteristic
212	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
213	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
214	C₂×C₄	C₂²×C₁₉⋊C₈	1	2	yes	—
215	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
216	C₂×C₄	#10597394	1	2	yes	—
217	C₈	—	2	8	no	—
218	C₈	—	19	2	no	—
219	C₈	—	38	1	no	—
220	C₈	—	38	2	no	—
221	C₈	—	76	4	no	—
222	C₈	—	76	2	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	4	no	—
226	C₂²	—	4	4	no	—
227	C₂²	—	4	4	no	—
228	C₂²	—	4	2	no	—
229	C₂²	—	4	2	no	—
230	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
231	C₂²	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
232	C₂²	#11926500	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	2	no	—
235	C₄	—	4	2	no	—
236	C₄	#100×D₁₉	1	1	yes	characteristic
237	C₄	#11926525	1	1	yes	characteristic
238	C₄	D₄×C₁₉⋊C₈	1	4	yes	—
239	C₂	—	2	1	no	—
240	C₂	—	2	1	no	—
241	C₂	—	4	4	no	—
242	C₂	C₂²⋊C₄×C₁₉⋊C₈	1	1	yes	characteristic
243	C₂	#100×Dic₁₉	1	1	yes	characteristic
244	C₂	#14563438	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×C₁₉⋊C₈

C₂

yes

maximal, characteristic

#14561956

C₂

yes

maximal, characteristic

M₁₆×C₁₉⋊C₈

C₂

yes

maximal, complemented

#14561486

C₂

yes

maximal, complemented

C₄×C₁₉×#100

C₂

yes

maximal, characteristic

C₂³×C₁₉⋊C₈

C₄

yes

—

D₄×C₁₉⋊C₈

—

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926268

C₄

yes

—

#11926265

—

C₈×C₁₉⋊C₈

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#100

C₄

yes

—

C₄×M₁₆×C₁₉

C₂²

yes

—

C₁₉×#343

C₄

yes

—

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×#100

C₈

yes

complemented

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂⁴×C₁₉

C₄²

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂×C₈

yes

complemented

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×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

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₈×#100

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₄×C₈

yes

—

C₂³×C₁₉

C₂×C₄²

yes

characteristic

D₄×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×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#117

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₂²×C₈

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

100

C₁₉⋊C₈

#100

yes

direct product factor

101

C₂×C₈×D₄

—

102

C₄×#100

D₁₉

yes

characteristic

103

#1460

—

104

C₈×M₁₆

—

105

#1283

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

114

C₂²×C₁₉

C₂×C₄×C₈

yes

characteristic

115

C₂²×C₁₉

#405

yes

characteristic

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

C₂×#100

yes

characteristic

120

C₄×C₁₉

#413

yes

characteristic

121

C₄×C₁₉

C₈×D₄

yes

—

122

C₂³×C₈

—

123

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

124

C₈×D₄

—

125

C₈×D₄

—

126

#431

—

127

C₂×C₄⋊C₈

—

128

C₂×#100

Dic₁₉

yes

—

129

C₂×C₂²⋊C₈

—

130

C₄×M₁₆

C₂×D₁₉

yes

—

131

C₂×C₄×C₈

—

132

#343

Dic₁₉

yes

—

133

#323

—

134

#322

—

135

C₈²

—

136

C₂×C₁₉

—

137

C₂×C₁₉

—

138

C₂×C₁₉

—

139

C₂×C₁₉

C₈×C₂²⋊C₄

yes

characteristic

140

C₂×C₁₉

C₄×#100

yes

characteristic

141

C₂×C₁₉

#1757

yes

characteristic

142

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

143

C₂³×C₄

C₄×D₁₉

yes

—

144

C₂×M₁₆

C₂×Dic₁₉

yes

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

—

148

C₂²×C₈

—

149

C₂²×C₈

—

150

C₂²×C₈

—

151

C₄×D₄

—

152

C₄×D₄

—

153

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

154

C₂×C₂²⋊C₄

C₄×D₁₉

yes

—

155

C₂×C₄²

C₂²×D₁₉

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

#100

C₁₉⋊C₈

yes

direct product factor

159

C₂²⋊C₈

—

160

C₂²⋊C₈

—

161

#97

—

162

C₄×C₈

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₄×C₈

—

166

C₁₉

C₈×#100

yes

characteristic, complemented, Sylow

167

C₂⁴

C₄×Dic₁₉

yes

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

C₂×C₁₉⋊C₈

yes

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₄×Dic₁₉

yes

—

176

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

177

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

178

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

179

M₁₆

—

180

M₁₆

C₂×C₁₉⋊C₈

yes

complemented

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₄⋊C₄

—

193

C₂²⋊C₄

—

194

C₄²

D₄×D₁₉

yes

—

195

C₄²

#64543

yes

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

C₄×C₁₉⋊C₈

yes

—

201

C₂³

C₂×C₄×Dic₁₉

yes

characteristic

202

D₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

#10597323

yes

characteristic

212

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

213

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

214

C₂×C₄

C₂²×C₁₉⋊C₈

yes

—

215

C₂×C₄

D₄×Dic₁₉

yes

—

216

C₂×C₄

#10597394

yes

—

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₂²⋊C₄×Dic₁₉

yes

characteristic

231

C₂²

C₂×C₄×C₁₉⋊C₈

yes

characteristic

232

C₂²

#11926500

yes

characteristic

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

#100×D₁₉

yes

characteristic

237

C₄

#11926525

yes

characteristic

238

C₄

D₄×C₁₉⋊C₈

yes

—

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

C₂²⋊C₄×C₁₉⋊C₈

yes

characteristic

243

C₂

#100×Dic₁₉

yes

characteristic

244

C₂

#14563438

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator	C₂²×C₁₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#100	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#100	D₁₉
hypocenter	C₁₉	C₈×#100
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₁₉

commutator

C₂²×C₁₉

C₂×C₄×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#100

C₂

socle

C₂²×C₁₉

C₄×C₂²⋊C₄

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

N	H ≅ G/N	type
3. M₁₆×C₁₉⋊C₈	C₂	semidirect
4. #14561486	C₂	semidirect
34. C₁₉×#100	C₈	semidirect
57. M₁₆×C₁₉	C₂×C₈	semidirect
100. C₁₉⋊C₈	#100	direct (N × H)
158. #100	C₁₉⋊C₈	direct (N × H)
166. C₁₉	C₈×#100	semidirect
180. M₁₆	C₂×C₁₉⋊C₈	semidirect

H ≅ G/N

type

3. M₁₆×C₁₉⋊C₈

C₂

semidirect

4. #14561486

C₂

semidirect

34. C₁₉×#100

C₈

semidirect

57. M₁₆×C₁₉

C₂×C₈

semidirect

100. C₁₉⋊C₈

#100

direct (N × H)

158. #100

C₁₉⋊C₈

direct (N × H)

166. C₁₉

C₈×#100

semidirect

180. M₁₆

C₂×C₁₉⋊C₈

semidirect

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

subgroup	index
C₂×D₄×C₁₉⋊C₈	2
#14561956	2
M₁₆×C₁₉⋊C₈	2
#14561486	2
C₄×C₁₉×#100	2
C₈×#100	19

subgroup

index

C₂×D₄×C₁₉⋊C₈

#14561956

M₁₆×C₁₉⋊C₈

#14561486

C₄×C₁₉×#100

C₈×#100

Subgroups — #100×C₁₉⋊C₈ #18073099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #100×C19⋊C8 #18073099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #100×C₁₉⋊C₈ #18073099