Group #18013206 — subgroups

Subgroups — C₁₉×#7247 #18013206

Order 4864.

322 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 78 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	C₁₉×#1869	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1466	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1465	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₁₉×#432	—	2	1	no	—
7	C₁₉×#407	—	2	1	no	—
8	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
9	C₂×C₁₉×C₂²⋊C₈	C₄	1	1	yes	characteristic
10	C₁₉×#336	—	2	1	no	—
11	C₁₉×#324	C₄	1	2	yes	—
12	C₁₉×#323	—	2	1	no	—
13	C₁₉×#323	—	2	1	no	—
14	C₁₉×#323	C₄	1	2	yes	—
15	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂×M₁₆×C₁₉	—	4	1	no	—
19	C₂²×C₈×C₁₉	—	2	1	no	—
20	C₂²×C₈×C₁₉	—	2	1	no	—
21	C₂²×C₈×C₁₉	—	4	2	no	—
22	C₂²×C₈×C₁₉	—	4	1	no	—
23	C₄×D₄×C₁₉	—	4	1	no	—
24	C₄×D₄×C₁₉	—	4	1	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₁₉×C₄⋊C₈	—	4	1	no	—
30	C₁₉×C₂²⋊C₈	—	2	2	no	—
31	C₁₉×C₂²⋊C₈	—	2	2	no	—
32	C₁₉×C₂²⋊C₈	—	4	2	no	—
33	C₁₉×C₂²⋊C₈	—	4	1	no	—
34	C₁₉×C₂²⋊C₈	—	4	1	no	—
35	C₁₉×#97	—	4	1	no	—
36	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂×D₄×C₁₉	—	2	2	no	—
39	C₂×D₄×C₁₉	—	4	1	no	—
40	C₂×D₄×C₁₉	—	4	1	no	—
41	C₂²×C₄×C₁₉	—	2	1	no	—
42	C₂²×C₄×C₁₉	—	2	1	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	—	4	1	no	—
46	C₂²×C₄×C₁₉	—	4	1	no	—
47	C₂²×C₄×C₁₉	—	4	1	no	—
48	C₂²×C₄×C₁₉	—	4	1	no	—
49	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
54	M₁₆×C₁₉	—	8	1	no	—
55	M₁₆×C₁₉	—	8	1	no	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	4	1	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₂×C₈×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	—	4	1	no	—
62	C₂×C₈×C₁₉	—	4	1	no	—
63	C₂×C₈×C₁₉	—	4	2	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	4	1	no	—
66	C₄⋊C₄×C₁₉	—	4	1	no	—
67	C₂²⋊C₄×C₁₉	—	4	1	no	—
68	C₂²⋊C₄×C₁₉	—	4	1	no	—
69	C₄²×C₁₉	—	2	1	no	—
70	C₄²×C₁₉	—	2	1	no	—
71	#7247	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂³×C₁₉	—	2	1	no	—
73	C₂³×C₁₉	—	2	1	no	—
74	C₂³×C₁₉	—	2	1	no	—
75	C₂³×C₁₉	—	2	1	no	—
76	C₂³×C₁₉	—	2	1	no	—
77	C₂³×C₁₉	—	4	1	no	—
78	C₂³×C₁₉	—	4	1	no	—
79	C₂³×C₁₉	—	4	1	no	—
80	C₂³×C₁₉	—	4	1	no	—
81	C₂³×C₁₉	#95	1	1	yes	characteristic
82	C₂³×C₁₉	#108	1	2	yes	—
83	D₄×C₁₉	—	4	4	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	4	2	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	—	4	1	no	—
97	C₂×C₄×C₁₉	—	4	1	no	—
98	C₂×C₄×C₁₉	—	4	1	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	8	1	no	—
101	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
103	C₈×C₁₉	—	4	2	no	—
104	C₈×C₁₉	—	8	1	no	—
105	C₈×C₁₉	—	8	2	no	—
106	C₈×C₁₉	—	8	2	no	—
107	#1869	C₂×C₁₉	1	1	yes	characteristic
108	#1466	C₂×C₁₉	1	1	yes	characteristic
109	#1465	C₂×C₁₉	1	1	yes	characteristic
110	C₂²×C₁₉	—	2	1	no	—
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	—	2	2	no	—
113	C₂²×C₁₉	—	4	2	no	—
114	C₂²×C₁₉	—	4	2	no	—
115	C₂²×C₁₉	—	4	2	no	—
116	C₂²×C₁₉	—	4	1	no	—
117	C₂²×C₁₉	—	4	1	no	—
118	C₂²×C₁₉	—	4	1	no	—
119	C₂²×C₁₉	—	4	1	no	—
120	C₂²×C₁₉	—	4	1	no	—
121	C₂²×C₁₉	—	8	1	no	—
122	C₂²×C₁₉	#338	1	1	yes	characteristic
123	C₂²×C₁₉	#341	1	1	yes	characteristic
124	C₂²×C₁₉	#342	1	1	yes	characteristic
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	4	1	no	—
127	C₄×C₁₉	—	4	1	no	—
128	C₄×C₁₉	—	4	1	no	—
129	C₄×C₁₉	—	4	1	no	—
130	C₄×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
131	C₄×C₁₉	#352	1	1	yes	characteristic
132	C₂³×C₈	C₄×C₁₉	1	1	yes	characteristic
133	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
134	#432	—	2	1	no	—
135	#407	—	2	1	no	—
136	C₂×C₂²⋊C₈	—	2	1	no	—
137	C₂×C₂²⋊C₈	C₄×C₁₉	1	1	yes	characteristic
138	#336	—	2	1	no	—
139	#324	C₄×C₁₉	1	2	yes	—
140	#323	—	2	1	no	—
141	#323	—	2	1	no	—
142	#323	C₄×C₁₉	1	2	yes	—
143	C₂×C₁₉	—	2	1	no	—
144	C₂×C₁₉	—	2	1	no	—
145	C₂×C₁₉	—	4	2	no	—
146	C₂×C₁₉	—	8	1	no	—
147	C₂×C₁₉	#1293	1	1	yes	characteristic
148	C₂×C₁₉	#1390	1	1	yes	characteristic
149	C₂×C₁₉	#1395	1	1	yes	characteristic
150	C₂²×D₄	Q₈×C₁₉	1	1	yes	characteristic
151	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
152	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
153	C₂×M₁₆	—	4	1	no	—
154	C₂²×C₈	—	2	1	no	—
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	—	4	2	no	—
157	C₂²×C₈	—	4	1	no	—
158	C₄×D₄	—	4	1	no	—
159	C₄×D₄	—	4	1	no	—
160	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
161	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
162	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
163	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
164	C₄⋊C₈	—	4	1	no	—
165	C₂²⋊C₈	—	2	2	no	—
166	C₂²⋊C₈	—	2	2	no	—
167	C₂²⋊C₈	—	4	2	no	—
168	C₂²⋊C₈	—	4	1	no	—
169	C₂²⋊C₈	—	4	1	no	—
170	#97	—	4	1	no	—
171	C₁₉	#7247	1	1	yes	characteristic, direct product factor, Sylow
172	C₂⁴	C₄⋊C₄×C₁₉	1	1	yes	characteristic
173	C₂⁴	C₄⋊C₄×C₁₉	1	1	yes	characteristic
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	4	1	no	—
176	C₂×D₄	—	4	1	no	—
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	—	2	1	no	—
180	C₂²×C₄	—	2	1	no	—
181	C₂²×C₄	—	4	1	no	—
182	C₂²×C₄	—	4	1	no	—
183	C₂²×C₄	—	4	1	no	—
184	C₂²×C₄	—	4	1	no	—
185	C₂²×C₄	C₄²×C₁₉	1	1	yes	characteristic
186	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
187	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
188	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
189	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
190	M₁₆	—	8	1	no	—
191	M₁₆	—	8	1	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	4	1	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	4	1	no	—
196	C₂×C₈	—	4	2	no	—
197	C₂×C₈	—	4	2	no	—
198	C₂×C₈	—	4	2	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	4	1	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₂²⋊C₄	—	4	1	no	—
204	C₂²⋊C₄	—	4	1	no	—
205	C₄²	—	2	1	no	—
206	C₄²	—	2	1	no	—
207	C₂³	—	2	1	no	—
208	C₂³	—	2	1	no	—
209	C₂³	—	2	1	no	—
210	C₂³	—	2	1	no	—
211	C₂³	—	2	1	no	—
212	C₂³	—	4	1	no	—
213	C₂³	—	4	1	no	—
214	C₂³	—	4	1	no	—
215	C₂³	—	4	1	no	—
216	C₂³	C₁₉×#95	1	1	yes	characteristic
217	C₂³	C₁₉×#108	1	2	yes	—
218	D₄	—	4	4	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	4	1	no	—
235	C₂×C₄	—	8	1	no	—
236	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
237	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
238	C₈	—	4	2	no	—
239	C₈	—	8	1	no	—
240	C₈	—	8	2	no	—
241	C₈	—	8	2	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	2	no	—
245	C₂²	—	4	2	no	—
246	C₂²	—	4	2	no	—
247	C₂²	—	4	2	no	—
248	C₂²	—	4	1	no	—
249	C₂²	—	4	1	no	—
250	C₂²	—	4	1	no	—
251	C₂²	—	4	1	no	—
252	C₂²	—	4	1	no	—
253	C₂²	—	8	1	no	—
254	C₂²	C₁₉×#338	1	1	yes	characteristic
255	C₂²	C₁₉×#341	1	1	yes	characteristic
256	C₂²	C₁₉×#342	1	1	yes	characteristic
257	C₄	—	2	1	no	—
258	C₄	—	4	1	no	—
259	C₄	—	4	1	no	—
260	C₄	—	4	1	no	—
261	C₄	—	4	1	no	—
262	C₄	C₁₉×AΣL(1,𝔽₁₆)	1	1	yes	characteristic
263	C₄	C₁₉×#352	1	1	yes	characteristic
264	C₂	—	2	1	no	—
265	C₂	—	2	1	no	—
266	C₂	—	4	2	no	—
267	C₂	—	8	1	no	—
268	C₂	C₁₉×#1293	1	1	yes	characteristic
269	C₂	C₁₉×#1390	1	1	yes	characteristic
270	C₂	C₁₉×#1395	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1869

C₂

yes

maximal, characteristic

C₁₉×#1466

C₂

yes

maximal, characteristic

C₁₉×#1465

C₂

yes

maximal, characteristic

C₂³×C₈×C₁₉

C₄

yes

characteristic

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#432

—

C₁₉×#407

—

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×C₂²⋊C₈

C₄

yes

characteristic

C₁₉×#336

—

C₁₉×#324

C₄

yes

—

C₁₉×#323

—

C₁₉×#323

—

C₁₉×#323

C₄

yes

—

C₂²×D₄×C₁₉

Q₈

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×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

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#7247

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

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

#108

yes

—

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×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

#99

yes

characteristic

102

C₂×C₄×C₁₉

#99

yes

characteristic

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₈×C₁₉

—

106

C₈×C₁₉

—

107

#1869

C₂×C₁₉

yes

characteristic

108

#1466

C₂×C₁₉

yes

characteristic

109

#1465

C₂×C₁₉

yes

characteristic

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

#338

yes

characteristic

123

C₂²×C₁₉

#341

yes

characteristic

124

C₂²×C₁₉

#342

yes

characteristic

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

131

C₄×C₁₉

#352

yes

characteristic

132

C₂³×C₈

C₄×C₁₉

yes

characteristic

133

C₂×C₄×D₄

C₂²×C₁₉

yes

characteristic

134

#432

—

135

#407

—

136

C₂×C₂²⋊C₈

—

137

C₂×C₂²⋊C₈

C₄×C₁₉

yes

characteristic

138

#336

—

139

#324

C₄×C₁₉

yes

—

140

#323

—

141

#323

—

142

#323

C₄×C₁₉

yes

—

143

C₂×C₁₉

—

144

C₂×C₁₉

—

145

C₂×C₁₉

—

146

C₂×C₁₉

—

147

C₂×C₁₉

#1293

yes

characteristic

148

C₂×C₁₉

#1390

yes

characteristic

149

C₂×C₁₉

#1395

yes

characteristic

150

C₂²×D₄

Q₈×C₁₉

yes

characteristic

151

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

152

C₂³×C₄

D₄×C₁₉

yes

characteristic

153

C₂×M₁₆

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₄×D₄

—

159

C₄×D₄

—

160

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

161

C₂×C₂²⋊C₄

C₂×C₄×C₁₉

yes

characteristic

162

C₂×C₂²⋊C₄

D₄×C₁₉

yes

characteristic

163

C₂×C₄²

D₄×C₁₉

yes

characteristic

164

C₄⋊C₈

—

165

C₂²⋊C₈

—

166

C₂²⋊C₈

—

167

C₂²⋊C₈

—

168

C₂²⋊C₈

—

169

C₂²⋊C₈

—

170

#97

—

171

C₁₉

#7247

yes

characteristic, direct product factor, Sylow

172

C₂⁴

C₄⋊C₄×C₁₉

yes

characteristic

173

C₂⁴

C₄⋊C₄×C₁₉

yes

characteristic

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

C₄²×C₁₉

yes

characteristic

186

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

187

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

188

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

189

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

190

M₁₆

—

191

M₁₆

—

192

C₂×C₈

—

193

C₂×C₈

—

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

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₄²

—

206

C₄²

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

C₁₉×#95

yes

characteristic

217

C₂³

C₁₉×#108

yes

—

218

D₄

—

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

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

C₁₉×#99

yes

characteristic

237

C₂×C₄

C₁₉×#99

yes

characteristic

238

C₈

—

239

C₈

—

240

C₈

—

241

C₈

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

C₁₉×#338

yes

characteristic

255

C₂²

C₁₉×#341

yes

characteristic

256

C₂²

C₁₉×#342

yes

characteristic

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

C₁₉×AΣL(1,𝔽₁₆)

yes

characteristic

263

C₄

C₁₉×#352

yes

characteristic

264

C₂

—

265

C₂

—

266

C₂

—

267

C₂

—

268

C₂

C₁₉×#1293

yes

characteristic

269

C₂

C₁₉×#1390

yes

characteristic

270

C₂

C₁₉×#1395

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#342
commutator	C₂²×C₄	C₄²×C₁₉
Frattini, cosocle	C₂×C₄×D₄	C₂²×C₁₉
prime radical	C₂²×D₄×C₁₉	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#342

commutator

C₂²×C₄

C₄²×C₁₉

Frattini, cosocle

C₂×C₄×D₄

C₂²×C₁₉

prime radical

C₂²×D₄×C₁₉

Q₈

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

N	H ≅ G/N	type
71. #7247	C₁₉	direct (N × H)
171. C₁₉	#7247	direct (N × H)

H ≅ G/N

type

71. #7247

C₁₉

direct (N × H)

171. C₁₉

#7247

direct (N × H)

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

subgroup	index
C₁₉×#1869	2
C₁₉×#1466	2
C₁₉×#1465	2
#7247	19

subgroup

index

C₁₉×#1869

C₁₉×#1466

C₁₉×#1465

#7247

Subgroups — C₁₉×#7247 #18013206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7247 #18013206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7247 #18013206