Group #18016307 — subgroups

Subgroups — C₁₉×#10348 #18016307

Order 4864.

588 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 154 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×#2551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#1982	C₂	1	2	yes	maximal
3	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1279	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
7	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₁₉×#102	—	2	2	no	—
10	C₂×C₁₉×#102	—	2	2	no	—
11	C₂×C₁₉×#102	—	2	2	no	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#395	—	2	2	no	—
14	C₁₉×#389	—	2	2	no	—
15	C₁₉×#384	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×Q₈×C₁₉	—	2	2	no	—
18	C₂²×D₄×C₁₉	—	2	1	no	—
19	C₂²×D₄×C₁₉	—	2	2	no	—
20	C₂²×C₈×C₁₉	—	2	1	no	—
21	C₂²×C₈×C₁₉	—	2	2	no	—
22	C₁₉×C₄⋊Q₈	—	4	4	no	—
23	C₁₉×C₄⋊Q₈	—	4	4	no	—
24	C₁₉×#127	—	2	2	no	—
25	C₁₉×#127	—	2	1	no	—
26	C₁₉×#127	Q₈	1	2	yes	complemented
27	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
30	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
32	C₂×C₄²×C₁₉	—	2	2	no	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₁₉×C₄⋊C₈	—	2	2	no	—
35	C₁₉×C₄⋊C₈	—	2	2	no	—
36	C₁₉×#102	—	4	4	no	—
37	C₁₉×#102	—	4	4	no	—
38	C₁₉×#102	—	4	4	no	—
39	C₄×C₈×C₁₉	—	2	2	no	—
40	C₁₉×#95	—	2	2	no	—
41	C₁₉×#95	—	2	2	no	—
42	C₂⁴×C₁₉	—	4	1	no	—
43	C₂×Q₈×C₁₉	—	4	8	no	—
44	C₂×Q₈×C₁₉	—	8	2	no	—
45	C₂×D₄×C₁₉	—	2	2	no	—
46	C₂×D₄×C₁₉	—	2	4	no	—
47	C₂×D₄×C₁₉	—	4	2	no	—
48	C₂×D₄×C₁₉	—	4	2	no	—
49	C₂×D₄×C₁₉	—	4	1	no	—
50	C₂×D₄×C₁₉	—	4	2	no	—
51	C₂×D₄×C₁₉	—	4	2	no	—
52	C₂×D₄×C₁₉	—	4	2	no	—
53	C₂×D₄×C₁₉	—	4	2	no	—
54	C₂×D₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₁₉	—	2	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	2	no	—
66	C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	4	2	no	—
69	C₄⋊C₄×C₁₉	—	4	8	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₄⋊C₄×C₁₉	—	4	2	no	—
72	C₄⋊C₄×C₁₉	D₈	1	4	yes	—
73	C₄⋊C₄×C₁₉	SD₁₆	1	4	yes	—
74	C₄²×C₁₉	—	4	2	no	—
75	C₄²×C₁₉	—	4	2	no	—
76	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
77	C₄²×C₁₉	#41	1	2	yes	—
78	C₄²×C₁₉	#41	1	1	yes	characteristic
79	#10348	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂³×C₁₉	—	4	2	no	—
81	C₂³×C₁₉	—	8	2	no	—
82	C₂³×C₁₉	—	8	2	no	—
83	C₂³×C₁₉	—	8	1	no	—
84	C₂³×C₁₉	—	8	1	no	—
85	C₂³×C₁₉	#120	1	1	yes	characteristic
86	Q₈×C₁₉	—	8	8	no	—
87	D₄×C₁₉	—	4	4	no	—
88	D₄×C₁₉	—	4	4	no	—
89	D₄×C₁₉	—	4	4	no	—
90	D₄×C₁₉	—	8	2	no	—
91	D₄×C₁₉	—	8	2	no	—
92	D₄×C₁₉	—	8	2	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	4	no	—
96	C₂×C₄×C₁₉	—	2	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	2	no	—
103	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
105	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#124	1	2	yes	—
107	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
108	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
109	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
110	C₂×C₄×C₁₉	#137	1	2	yes	—
111	C₈×C₁₉	—	4	2	no	—
112	C₈×C₁₉	—	8	2	no	—
113	#2551	C₂×C₁₉	1	1	yes	characteristic, complemented
114	#1982	C₂×C₁₉	1	2	yes	—
115	#1957	C₂×C₁₉	1	1	yes	characteristic
116	#1296	C₂×C₁₉	1	1	yes	characteristic, complemented
117	#1279	C₂×C₁₉	1	2	yes	complemented
118	C₂²×C₁₉	—	8	4	no	—
119	C₂²×C₁₉	—	8	2	no	—
120	C₂²×C₁₉	—	16	1	no	—
121	C₂²×C₁₉	—	16	1	no	—
122	C₂²×C₁₉	—	16	2	no	—
123	C₂²×C₁₉	#393	1	1	yes	characteristic
124	C₂²×C₁₉	#447	1	2	yes	—
125	C₂²×C₁₉	#448	1	2	yes	—
126	C₂²×C₁₉	#453	1	1	yes	characteristic
127	C₂²×C₁₉	#454	1	1	yes	characteristic
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	4	4	no	—
131	C₄×C₁₉	—	4	4	no	—
132	C₄×C₁₉	—	8	2	no	—
133	C₄×C₁₉	#474	1	2	yes	—
134	C₄×C₁₉	#476	1	2	yes	—
135	C₄×C₁₉	#486	1	2	yes	—
136	C₄×C₁₉	#489	1	2	yes	—
137	C₂×C₄⋊Q₈	—	2	2	no	—
138	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
139	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
140	C₂×#102	—	2	2	no	—
141	C₂×#102	—	2	2	no	—
142	C₂×#102	—	2	2	no	—
143	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
144	#395	—	2	2	no	—
145	#389	—	2	2	no	—
146	#384	C₂²×C₁₉	1	1	yes	characteristic
147	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
148	C₂×C₁₉	—	16	2	no	—
149	C₂×C₁₉	#1619	1	1	yes	characteristic
150	C₂×C₁₉	#1623	1	1	yes	characteristic
151	C₂×C₁₉	#1627	1	2	yes	—
152	C₂×C₁₉	#2023	1	2	yes	—
153	C₂×C₁₉	#2027	1	1	yes	characteristic
154	C₂²×Q₈	—	2	2	no	—
155	C₂²×D₄	—	2	1	no	—
156	C₂²×D₄	—	2	2	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	—	2	2	no	—
159	C₄⋊Q₈	—	4	4	no	—
160	C₄⋊Q₈	—	4	4	no	—
161	#127	—	2	2	no	—
162	#127	—	2	1	no	—
163	#127	Q₈×C₁₉	1	2	yes	complemented
164	C₂×C₄⋊C₄	—	2	4	no	—
165	C₂×C₄⋊C₄	—	2	2	no	—
166	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
167	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
168	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
169	C₂×C₄²	—	2	2	no	—
170	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
171	C₄⋊C₈	—	2	2	no	—
172	C₄⋊C₈	—	2	2	no	—
173	#102	—	4	4	no	—
174	#102	—	4	4	no	—
175	#102	—	4	4	no	—
176	C₄×C₈	—	2	2	no	—
177	#95	—	2	2	no	—
178	#95	—	2	2	no	—
179	C₁₉	#10348	1	1	yes	characteristic, direct product factor, Sylow
180	C₂⁴	—	4	1	no	—
181	C₂×Q₈	—	4	8	no	—
182	C₂×Q₈	—	8	2	no	—
183	C₂×D₄	—	2	2	no	—
184	C₂×D₄	—	2	4	no	—
185	C₂×D₄	—	4	2	no	—
186	C₂×D₄	—	4	2	no	—
187	C₂×D₄	—	4	1	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂×D₄	—	4	2	no	—
190	C₂×D₄	—	4	2	no	—
191	C₂×D₄	—	4	2	no	—
192	C₂×D₄	—	4	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	—	2	2	no	—
196	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
197	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	4	2	no	—
202	C₂×C₈	—	4	2	no	—
203	C₂×C₈	—	4	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	4	8	no	—
208	C₄⋊C₄	—	4	2	no	—
209	C₄⋊C₄	—	4	2	no	—
210	C₄⋊C₄	D₈×C₁₉	1	4	yes	—
211	C₄⋊C₄	SD₁₆×C₁₉	1	4	yes	—
212	C₄²	—	4	2	no	—
213	C₄²	—	4	2	no	—
214	C₄²	C₂×Q₈×C₁₉	1	1	yes	characteristic
215	C₄²	#41×C₁₉	1	2	yes	—
216	C₄²	#41×C₁₉	1	1	yes	characteristic
217	C₂³	—	4	2	no	—
218	C₂³	—	8	2	no	—
219	C₂³	—	8	2	no	—
220	C₂³	—	8	1	no	—
221	C₂³	—	8	1	no	—
222	C₂³	C₁₉×#120	1	1	yes	characteristic
223	Q₈	—	8	8	no	—
224	D₄	—	4	4	no	—
225	D₄	—	4	4	no	—
226	D₄	—	4	4	no	—
227	D₄	—	8	2	no	—
228	D₄	—	8	2	no	—
229	D₄	—	8	2	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	4	no	—
233	C₂×C₄	—	2	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	2	no	—
240	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
242	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
243	C₂×C₄	C₁₉×#124	1	2	yes	—
244	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
245	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
246	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
247	C₂×C₄	C₁₉×#137	1	2	yes	—
248	C₈	—	4	2	no	—
249	C₈	—	8	2	no	—
250	C₂²	—	8	4	no	—
251	C₂²	—	8	2	no	—
252	C₂²	—	16	1	no	—
253	C₂²	—	16	1	no	—
254	C₂²	—	16	2	no	—
255	C₂²	C₁₉×#393	1	1	yes	characteristic
256	C₂²	C₁₉×#447	1	2	yes	—
257	C₂²	C₁₉×#448	1	2	yes	—
258	C₂²	C₁₉×#453	1	1	yes	characteristic
259	C₂²	C₁₉×#454	1	1	yes	characteristic
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	4	4	no	—
263	C₄	—	4	4	no	—
264	C₄	—	8	2	no	—
265	C₄	C₁₉×#474	1	2	yes	—
266	C₄	C₁₉×#476	1	2	yes	—
267	C₄	C₁₉×#486	1	2	yes	—
268	C₄	C₁₉×#489	1	2	yes	—
269	C₂	—	16	2	no	—
270	C₂	C₁₉×#1619	1	1	yes	characteristic
271	C₂	C₁₉×#1623	1	1	yes	characteristic
272	C₂	C₁₉×#1627	1	2	yes	—
273	C₂	C₁₉×#2023	1	2	yes	—
274	C₂	C₁₉×#2027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2551

C₂

yes

maximal, characteristic, complemented

C₁₉×#1982

C₂

yes

maximal

C₁₉×#1957

C₂

yes

maximal, characteristic

C₁₉×#1296

C₂

yes

maximal, characteristic, complemented

C₁₉×#1279

C₂

yes

maximal, complemented

C₂×C₁₉×C₄⋊Q₈

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₁₉×#102

—

C₂×C₁₉×#102

—

C₂×C₁₉×#102

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#395

—

C₁₉×#389

—

C₁₉×#384

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×Q₈×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

Q₈

yes

complemented

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#102

—

C₁₉×#102

—

C₁₉×#102

—

C₄×C₈×C₁₉

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₈

yes

—

C₄⋊C₄×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

#10348

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

C₂²⋊Q₈

yes

characteristic

104

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

105

C₂×C₄×C₁₉

#124

yes

characteristic

106

C₂×C₄×C₁₉

#124

yes

—

107

C₂×C₄×C₁₉

C₂×D₈

yes

—

108

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

109

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

110

C₂×C₄×C₁₉

#137

yes

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

#2551

C₂×C₁₉

yes

characteristic, complemented

114

#1982

C₂×C₁₉

yes

—

115

#1957

C₂×C₁₉

yes

characteristic

116

#1296

C₂×C₁₉

yes

characteristic, complemented

117

#1279

C₂×C₁₉

yes

complemented

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

#393

yes

characteristic

124

C₂²×C₁₉

#447

yes

—

125

C₂²×C₁₉

#448

yes

—

126

C₂²×C₁₉

#453

yes

characteristic

127

C₂²×C₁₉

#454

yes

characteristic

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

#474

yes

—

134

C₄×C₁₉

#476

yes

—

135

C₄×C₁₉

#486

yes

—

136

C₄×C₁₉

#489

yes

—

137

C₂×C₄⋊Q₈

—

138

C₂×#127

C₂²×C₁₉

yes

characteristic

139

C₂×C₄⋊C₈

C₂²×C₁₉

yes

—

140

C₂×#102

—

141

C₂×#102

—

142

C₂×#102

—

143

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

144

#395

—

145

#389

—

146

#384

C₂²×C₁₉

yes

characteristic

147

C₄×C₄⋊C₄

C₂²×C₁₉

yes

—

148

C₂×C₁₉

—

149

C₂×C₁₉

#1619

yes

characteristic

150

C₂×C₁₉

#1623

yes

characteristic

151

C₂×C₁₉

#1627

yes

—

152

C₂×C₁₉

#2023

yes

—

153

C₂×C₁₉

#2027

yes

characteristic

154

C₂²×Q₈

—

155

C₂²×D₄

—

156

C₂²×D₄

—

157

C₂²×C₈

—

158

C₂²×C₈

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

#127

—

162

#127

—

163

#127

Q₈×C₁₉

yes

complemented

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

167

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

168

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

169

C₂×C₄²

—

170

C₂×C₄²

C₂³×C₁₉

yes

characteristic

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

#102

—

174

#102

—

175

#102

—

176

C₄×C₈

—

177

#95

—

178

#95

—

179

C₁₉

#10348

yes

characteristic, direct product factor, Sylow

180

C₂⁴

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

197

C₂²×C₄

C₂×D₄×C₁₉

yes

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

D₈×C₁₉

yes

—

211

C₄⋊C₄

SD₁₆×C₁₉

yes

—

212

C₄²

—

213

C₄²

—

214

C₄²

C₂×Q₈×C₁₉

yes

characteristic

215

C₄²

#41×C₁₉

yes

—

216

C₄²

#41×C₁₉

yes

characteristic

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

C₁₉×#120

yes

characteristic

223

Q₈

—

224

D₄

—

225

D₄

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

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

C₁₉×C₂²⋊Q₈

yes

characteristic

241

C₂×C₄

C₁₉×C₂²⋊Q₈

yes

—

242

C₂×C₄

C₁₉×#124

yes

characteristic

243

C₂×C₄

C₁₉×#124

yes

—

244

C₂×C₄

C₂×D₈×C₁₉

yes

—

245

C₂×C₄

C₂×SD₁₆×C₁₉

yes

—

246

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

—

247

C₂×C₄

C₁₉×#137

yes

—

248

C₈

—

249

C₈

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

C₁₉×#393

yes

characteristic

256

C₂²

C₁₉×#447

yes

—

257

C₂²

C₁₉×#448

yes

—

258

C₂²

C₁₉×#453

yes

characteristic

259

C₂²

C₁₉×#454

yes

characteristic

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

C₁₉×#474

yes

—

266

C₄

C₁₉×#476

yes

—

267

C₄

C₁₉×#486

yes

—

268

C₄

C₁₉×#489

yes

—

269

C₂

—

270

C₂

C₁₉×#1619

yes

characteristic

271

C₂

C₁₉×#1623

yes

characteristic

272

C₂

C₁₉×#1627

yes

—

273

C₂

C₁₉×#2023

yes

—

274

C₂

C₁₉×#2027

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂×C₁₉×#127

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#2551	C₂	semidirect
4. C₁₉×#1296	C₂	semidirect
5. C₁₉×#1279	C₂	semidirect
26. C₁₉×#127	Q₈	semidirect
79. #10348	C₁₉	direct (N × H)
113. #2551	C₂×C₁₉	semidirect
116. #1296	C₂×C₁₉	semidirect
117. #1279	C₂×C₁₉	semidirect
163. #127	Q₈×C₁₉	semidirect
179. C₁₉	#10348	direct (N × H)

H ≅ G/N

type

1. C₁₉×#2551

C₂

semidirect

4. C₁₉×#1296

C₂

semidirect

5. C₁₉×#1279

C₂

semidirect

26. C₁₉×#127

Q₈

semidirect

79. #10348

C₁₉

direct (N × H)

113. #2551

C₂×C₁₉

semidirect

116. #1296

C₂×C₁₉

semidirect

117. #1279

C₂×C₁₉

semidirect

163. #127

Q₈×C₁₉

semidirect

179. C₁₉

#10348

direct (N × H)

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

subgroup	index
C₁₉×#2551	2
C₁₉×#1982	2
C₁₉×#1957	2
C₁₉×#1296	2
C₁₉×#1279	2
#10348	19

subgroup

index

C₁₉×#2551

C₁₉×#1982

C₁₉×#1957

C₁₉×#1296

C₁₉×#1279

#10348

Subgroups — C₁₉×#10348 #18016307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10348 #18016307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10348 #18016307