Group #18069110 — subgroups

Subgroups — #18069110

Order 4864.

730 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
4	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	4	yes	complemented
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
8	C₂×C₁₉×#95	—	2	2	no	—
9	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂³×C₄×C₁₉	—	2	2	no	—
11	C₂³×C₄×C₁₉	—	4	4	no	—
12	C₂³×C₄×C₁₉	—	4	2	no	—
13	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
14	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	D₄	1	2	yes	—
16	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
18	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
19	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
20	C₂×C₂²⋊C₄×C₁₉	C₈	1	4	yes	complemented
21	C₂²×C₁₉⋊C₈	—	2	4	no	—
22	C₁₉×#95	—	4	4	no	—
23	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
24	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
25	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
26	C₂⁴×C₁₉	—	2	2	no	—
27	C₂⁴×C₁₉	—	2	1	no	—
28	C₂⁴×C₁₉	—	2	1	no	—
29	C₂⁴×C₁₉	—	4	2	no	—
30	C₂⁴×C₁₉	—	4	2	no	—
31	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
32	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂⁴×C₁₉	C₂×C₈	1	2	yes	—
35	C₂⁴×C₁₉	M₁₆	1	2	yes	—
36	C₂²×C₄×C₁₉	—	2	4	no	—
37	C₂²×C₄×C₁₉	—	2	4	no	—
38	C₂²×C₄×C₁₉	—	2	4	no	—
39	C₂²×C₄×C₁₉	—	2	4	no	—
40	C₂²×C₄×C₁₉	—	2	4	no	—
41	C₂²×C₄×C₁₉	—	4	2	no	—
42	C₂²×C₄×C₁₉	—	4	2	no	—
43	C₂²×C₄×C₁₉	—	4	1	no	—
44	C₂²×C₄×C₁₉	—	4	2	no	—
45	C₂²×C₄×C₁₉	—	4	2	no	—
46	C₂²×C₄×C₁₉	—	4	1	no	—
47	C₂²×C₄×C₁₉	—	4	16	no	—
48	C₂²×C₄×C₁₉	—	4	4	no	—
49	C₂²×C₄×C₁₉	—	4	4	no	—
50	C₂²×C₄×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
54	C₂²⋊C₄×C₁₉	—	4	4	no	—
55	C₂²⋊C₄×C₁₉	—	4	4	no	—
56	C₂×C₁₉⋊C₈	—	4	4	no	—
57	C₂×C₁₉⋊C₈	—	4	4	no	—
58	C₂×C₁₉⋊C₈	—	4	4	no	—
59	#7032	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	—	2	2	no	—
61	C₂³×C₁₉	—	2	2	no	—
62	C₂³×C₁₉	—	2	2	no	—
63	C₂³×C₁₉	—	2	2	no	—
64	C₂³×C₁₉	—	2	2	no	—
65	C₂³×C₁₉	—	2	2	no	—
66	C₂³×C₁₉	—	2	2	no	—
67	C₂³×C₁₉	—	2	2	no	—
68	C₂³×C₁₉	—	2	1	no	—
69	C₂³×C₁₉	—	2	1	no	—
70	C₂³×C₁₉	—	2	1	no	—
71	C₂³×C₁₉	—	2	1	no	—
72	C₂³×C₁₉	—	2	2	no	—
73	C₂³×C₁₉	—	2	2	no	—
74	C₂³×C₁₉	—	4	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	#95	1	1	yes	characteristic
81	C₂³×C₁₉	C₄×C₈	1	1	yes	characteristic
82	C₂³×C₁₉	#97	1	1	yes	characteristic
83	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
84	C₂³×C₁₉	#99	1	2	yes	—
85	C₂³×C₁₉	#100	1	1	yes	characteristic
86	C₂³×C₁₉	#101	1	1	yes	characteristic
87	C₂³×C₁₉	C₄⋊C₈	1	2	yes	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	4	4	no	—
94	C₂×C₄×C₁₉	—	4	8	no	—
95	C₂×C₄×C₁₉	—	4	8	no	—
96	C₂×C₄×C₁₉	—	4	4	no	—
97	C₂×C₄×C₁₉	—	4	8	no	—
98	C₂×C₄×C₁₉	—	4	4	no	—
99	C₂×C₄×C₁₉	—	8	2	no	—
100	C₂×C₄×C₁₉	—	8	4	no	—
101	C₂×C₄×C₁₉	—	8	2	no	—
102	C₂×C₄×C₁₉	#99	1	4	yes	—
103	C₁₉⋊C₈	—	8	4	no	—
104	#1779	—	19	2	no	—
105	C₂²⋊#95	D₁₉	1	1	yes	characteristic
106	C₂²×C₁₉	—	2	4	no	—
107	C₂²×C₁₉	—	2	2	no	—
108	C₂²×C₁₉	—	2	2	no	—
109	C₂²×C₁₉	—	2	2	no	—
110	C₂²×C₁₉	—	2	2	no	—
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	—	2	2	no	—
114	C₂²×C₁₉	—	2	2	no	—
115	C₂²×C₁₉	—	2	2	no	—
116	C₂²×C₁₉	—	2	4	no	—
117	C₂²×C₁₉	—	4	4	no	—
118	C₂²×C₁₉	—	4	4	no	—
119	C₂²×C₁₉	—	4	4	no	—
120	C₂²×C₁₉	—	4	4	no	—
121	C₂²×C₁₉	—	4	1	no	—
122	C₂²×C₁₉	—	4	1	no	—
123	C₂²×C₁₉	—	4	2	no	—
124	C₂²×C₁₉	—	4	2	no	—
125	C₂²×C₁₉	—	4	1	no	—
126	C₂²×C₁₉	—	4	1	no	—
127	C₂²×C₁₉	#323	1	2	yes	—
128	C₂²×C₁₉	#324	1	2	yes	—
129	C₂²×C₁₉	#336	1	1	yes	characteristic
130	C₂²×C₁₉	#342	1	2	yes	—
131	C₂²×C₁₉	#342	1	1	yes	characteristic
132	C₂²×C₁₉	#343	1	1	yes	characteristic
133	C₂²×C₁₉	#344	1	2	yes	—
134	C₄×C₁₉	—	2	4	no	—
135	C₄×C₁₉	—	4	2	no	—
136	C₄×C₁₉	—	8	4	no	—
137	C₂⁴×C₄	C₂×D₁₉	1	1	yes	characteristic
138	C₂²×C₂²⋊C₄	Dic₁₉	1	2	yes	—
139	C₂×C₂²⋊C₈	—	19	4	no	—
140	C₂×C₂²⋊C₈	—	38	2	no	—
141	C₂×C₂²⋊C₈	—	38	2	no	—
142	C₂×#95	—	2	2	no	—
143	C₂×C₁₉	—	2	2	no	—
144	C₂×C₁₉	—	2	2	no	—
145	C₂×C₁₉	—	4	1	no	—
146	C₂×C₁₉	—	4	1	no	—
147	C₂×C₁₉	—	4	2	no	—
148	C₂×C₁₉	#1280	1	1	yes	characteristic
149	C₂×C₁₉	#1282	1	2	yes	—
150	C₂×C₁₉	#1304	1	1	yes	characteristic
151	C₂×C₁₉	#1305	1	2	yes	—
152	C₂×C₁₉	#1306	1	1	yes	characteristic
153	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
154	C₂³×C₄	—	2	2	no	—
155	C₂³×C₄	—	4	4	no	—
156	C₂³×C₄	—	4	2	no	—
157	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
158	C₂³×C₄	C₄×D₁₉	1	2	yes	—
159	C₂³×C₄	D₇₆	1	1	yes	characteristic
160	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
161	C₂²×C₈	—	38	4	no	—
162	C₂×C₂²⋊C₄	—	2	2	no	—
163	C₂×C₂²⋊C₄	—	4	2	no	—
164	C₂×C₂²⋊C₄	—	4	2	no	—
165	C₂×C₂²⋊C₄	C₁₉⋊C₈	1	4	yes	complemented
166	C₂²⋊C₈	—	76	4	no	—
167	C₂²⋊C₈	—	76	4	no	—
168	C₂²⋊C₈	—	76	4	no	—
169	#95	—	4	4	no	—
170	C₁₉	#7032	1	1	yes	characteristic, complemented, Sylow
171	C₂⁴	—	2	1	no	—
172	C₂⁴	—	2	2	no	—
173	C₂⁴	—	2	1	no	—
174	C₂⁴	—	4	2	no	—
175	C₂⁴	—	4	2	no	—
176	C₂⁴	C₂×C₁₉⋊C₈	1	2	yes	—
177	C₂⁴	#64520	1	2	yes	—
178	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
179	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
180	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
181	C₂²×C₄	—	2	4	no	—
182	C₂²×C₄	—	2	4	no	—
183	C₂²×C₄	—	2	4	no	—
184	C₂²×C₄	—	2	4	no	—
185	C₂²×C₄	—	2	4	no	—
186	C₂²×C₄	—	4	2	no	—
187	C₂²×C₄	—	4	1	no	—
188	C₂²×C₄	—	4	2	no	—
189	C₂²×C₄	—	4	2	no	—
190	C₂²×C₄	—	4	1	no	—
191	C₂²×C₄	—	4	2	no	—
192	C₂²×C₄	—	4	16	no	—
193	C₂²×C₄	—	4	4	no	—
194	C₂²×C₄	—	4	4	no	—
195	C₂²×C₄	—	4	2	no	—
196	C₂²×C₄	—	4	2	no	—
197	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
198	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
199	C₂×C₈	—	76	4	no	—
200	C₂×C₈	—	76	4	no	—
201	C₂×C₈	—	76	4	no	—
202	C₂²⋊C₄	—	4	4	no	—
203	C₂²⋊C₄	—	4	4	no	—
204	C₂³	—	2	2	no	—
205	C₂³	—	2	2	no	—
206	C₂³	—	2	2	no	—
207	C₂³	—	2	2	no	—
208	C₂³	—	2	1	no	—
209	C₂³	—	2	1	no	—
210	C₂³	—	2	1	no	—
211	C₂³	—	2	1	no	—
212	C₂³	—	2	2	no	—
213	C₂³	—	2	2	no	—
214	C₂³	—	2	2	no	—
215	C₂³	—	2	2	no	—
216	C₂³	—	2	2	no	—
217	C₂³	—	2	2	no	—
218	C₂³	—	4	4	no	—
219	C₂³	—	4	4	no	—
220	C₂³	—	4	4	no	—
221	C₂³	—	4	4	no	—
222	C₂³	—	4	4	no	—
223	C₂³	—	4	4	no	—
224	C₂³	C₄×C₁₉⋊C₈	1	1	yes	characteristic
225	C₂³	#10597260	1	1	yes	characteristic
226	C₂³	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
227	C₂³	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
228	C₂³	C₁₉⋊#95	1	1	yes	characteristic
229	C₂³	#10597290	1	1	yes	characteristic
230	C₂³	#10597291	1	2	yes	—
231	C₂³	#10597293	1	1	yes	characteristic
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	4	4	no	—
238	C₂×C₄	—	4	8	no	—
239	C₂×C₄	—	4	8	no	—
240	C₂×C₄	—	4	4	no	—
241	C₂×C₄	—	4	8	no	—
242	C₂×C₄	—	4	4	no	—
243	C₂×C₄	—	8	2	no	—
244	C₂×C₄	—	8	4	no	—
245	C₂×C₄	—	8	2	no	—
246	C₂×C₄	#10597263	1	4	yes	—
247	C₈	—	152	4	no	—
248	C₂²	—	2	2	no	—
249	C₂²	—	2	2	no	—
250	C₂²	—	2	2	no	—
251	C₂²	—	2	2	no	—
252	C₂²	—	2	4	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	2	2	no	—
256	C₂²	—	2	2	no	—
257	C₂²	—	2	2	no	—
258	C₂²	—	2	4	no	—
259	C₂²	—	4	4	no	—
260	C₂²	—	4	4	no	—
261	C₂²	—	4	4	no	—
262	C₂²	—	4	4	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	4	1	no	—
265	C₂²	—	4	2	no	—
266	C₂²	—	4	2	no	—
267	C₂²	—	4	1	no	—
268	C₂²	—	4	1	no	—
269	C₂²	#11926268	1	2	yes	—
270	C₂²	#11926270	1	2	yes	—
271	C₂²	#11926299	1	1	yes	characteristic
272	C₂²	#11926310	1	2	yes	—
273	C₂²	#11926311	1	1	yes	characteristic
274	C₂²	#11926313	1	1	yes	characteristic
275	C₂²	#11926314	1	2	yes	—
276	C₄	—	2	4	no	—
277	C₄	—	4	2	no	—
278	C₄	—	8	4	no	—
279	C₂	—	2	2	no	—
280	C₂	—	2	2	no	—
281	C₂	—	4	1	no	—
282	C₂	—	4	1	no	—
283	C₂	—	4	2	no	—
284	C₂	#14561478	1	1	yes	characteristic
285	C₂	#14561483	1	2	yes	—
286	C₂	C₁₉⋊#1304	1	1	yes	characteristic
287	C₂	#14561541	1	2	yes	—
288	C₂	#14561543	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563545

C₂

yes

maximal

C₁₉×C₂²⋊#95

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

complemented

C₂⁴×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊C₄×C₁₉

C₄

yes

—

C₂×C₁₉×#95

—

C₂⁵×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

Q₈

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₈

yes

complemented

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₄²

yes

characteristic

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂⁴×C₁₉

C₂×C₈

yes

—

C₂⁴×C₁₉

M₁₆

yes

—

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×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7032

—

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

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

C₂³×C₁₉

C₄×C₈

yes

characteristic

C₂³×C₁₉

#97

yes

characteristic

C₂³×C₁₉

C₂²⋊C₈

yes

—

C₂³×C₁₉

#99

yes

—

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂³×C₁₉

C₄⋊C₈

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

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

#99

yes

—

103

C₁₉⋊C₈

—

104

#1779

—

105

C₂²⋊#95

D₁₉

yes

characteristic

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

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

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

#323

yes

—

128

C₂²×C₁₉

#324

yes

—

129

C₂²×C₁₉

#336

yes

characteristic

130

C₂²×C₁₉

#342

yes

—

131

C₂²×C₁₉

#342

yes

characteristic

132

C₂²×C₁₉

#343

yes

characteristic

133

C₂²×C₁₉

#344

yes

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₂⁴×C₄

C₂×D₁₉

yes

characteristic

138

C₂²×C₂²⋊C₄

Dic₁₉

yes

—

139

C₂×C₂²⋊C₈

—

140

C₂×C₂²⋊C₈

—

141

C₂×C₂²⋊C₈

—

142

C₂×#95

—

143

C₂×C₁₉

—

144

C₂×C₁₉

—

145

C₂×C₁₉

—

146

C₂×C₁₉

—

147

C₂×C₁₉

—

148

C₂×C₁₉

#1280

yes

characteristic

149

C₂×C₁₉

#1282

yes

—

150

C₂×C₁₉

#1304

yes

characteristic

151

C₂×C₁₉

#1305

yes

—

152

C₂×C₁₉

#1306

yes

characteristic

153

C₂⁵

C₂×Dic₁₉

yes

characteristic

154

C₂³×C₄

—

155

C₂³×C₄

—

156

C₂³×C₄

—

157

C₂³×C₄

Dic₃₈

yes

characteristic

158

C₂³×C₄

C₄×D₁₉

yes

—

159

C₂³×C₄

D₇₆

yes

characteristic

160

C₂³×C₄

C₂²⋊D₁₉

yes

—

161

C₂²×C₈

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₂²⋊C₄

—

164

C₂×C₂²⋊C₄

—

165

C₂×C₂²⋊C₄

C₁₉⋊C₈

yes

complemented

166

C₂²⋊C₈

—

167

C₂²⋊C₈

—

168

C₂²⋊C₈

—

169

#95

—

170

C₁₉

#7032

yes

characteristic, complemented, Sylow

171

C₂⁴

—

172

C₂⁴

—

173

C₂⁴

—

174

C₂⁴

—

175

C₂⁴

—

176

C₂⁴

C₂×C₁₉⋊C₈

yes

—

177

C₂⁴

#64520

yes

—

178

C₂⁴

C₄×Dic₁₉

yes

characteristic

179

C₂⁴

C₄⋊Dic₁₉

yes

characteristic

180

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

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

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

Dic₁₉⋊C₄

yes

—

198

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

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

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

C₄×C₁₉⋊C₈

yes

characteristic

225

C₂³

#10597260

yes

characteristic

226

C₂³

C₄⋊(C₁₉⋊C₈)

yes

—

227

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

—

228

C₂³

C₁₉⋊#95

yes

characteristic

229

C₂³

#10597290

yes

characteristic

230

C₂³

#10597291

yes

—

231

C₂³

#10597293

yes

characteristic

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

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

#10597263

yes

—

247

C₈

—

152

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

#11926268

yes

—

270

C₂²

#11926270

yes

—

271

C₂²

#11926299

yes

characteristic

272

C₂²

#11926310

yes

—

273

C₂²

#11926311

yes

characteristic

274

C₂²

#11926313

yes

characteristic

275

C₂²

#11926314

yes

—

276

C₄

—

277

C₄

—

278

C₄

—

279

C₂

—

280

C₂

—

281

C₂

—

282

C₂

—

283

C₂

—

284

C₂

#14561478

yes

characteristic

285

C₂

#14561483

yes

—

286

C₂

C₁₉⋊#1304

yes

characteristic

287

C₂

#14561541

yes

—

288

C₂

#14561543

yes

characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂³×C₁₉	C₄×C₈
Frattini	C₂⁴×C₄	C₂×D₁₉
Fitting	C₁₉×C₂²⋊#95	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁵×C₁₉	C₂×C₄
cosocle	C₂⁴×C₄×C₁₉	C₂²
hypercenter	C₂²⋊#95	D₁₉
hypocenter	C₁₉	#7032
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂²⋊#95

subgroup

G/H

center

C₂³

C₁₉⋊#95

commutator

C₂³×C₁₉

C₄×C₈

Frattini

C₂⁴×C₄

C₂×D₁₉

Fitting

C₁₉×C₂²⋊#95

C₂

socle

C₂³×C₁₉

#95

prime radical

C₂⁵×C₁₉

C₂×C₄

cosocle

C₂⁴×C₄×C₁₉

C₂²

hypercenter

C₂²⋊#95

D₁₉

hypocenter

C₁₉

#7032

LCS

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂²⋊#95

N	H ≅ G/N	type
5. C₂×C₂²⋊(C₁₉⋊C₈)	C₄	semidirect
20. C₂×C₂²⋊C₄×C₁₉	C₈	semidirect
165. C₂×C₂²⋊C₄	C₁₉⋊C₈	semidirect
170. C₁₉	#7032	semidirect

H ≅ G/N

type

5. C₂×C₂²⋊(C₁₉⋊C₈)

C₄

semidirect

20. C₂×C₂²⋊C₄×C₁₉

C₈

semidirect

165. C₂×C₂²⋊C₄

C₁₉⋊C₈

semidirect

170. C₁₉

#7032

semidirect

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

subgroup	index
#14563545	2
C₁₉×C₂²⋊#95	2
#7032	19

subgroup

index

#14563545

C₁₉×C₂²⋊#95

#7032

Subgroups — #18069110

Conjugacy classes of subgroups

Complements

Maximal subgroups