Group #18017754 — subgroups

Subgroups — C₁₉×#11795 #18017754

Order 4864.

394 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2567	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1467	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1354	C₂	1	4	yes	maximal
5	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#432	—	2	1	no	—
8	C₂×C₁₉×#101	—	2	1	no	—
9	C₄×M₁₆×C₁₉	—	2	1	no	—
10	C₁₉×#395	C₄	1	2	yes	—
11	C₁₉×#395	C₂²	1	2	yes	—
12	C₁₉×#391	—	2	1	no	—
13	C₁₉×#389	—	2	1	no	—
14	C₁₉×#389	—	2	1	no	—
15	C₁₉×#384	—	2	1	no	—
16	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
17	C₁₉×#343	C₂²	1	2	yes	—
18	C₁₉×#324	—	2	1	no	—
19	C₁₉×#324	C₂²	1	2	yes	—
20	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	4	1	no	—
24	C₁₉×C₄⋊Q₈	—	4	1	no	—
25	C₄×Q₈×C₁₉	—	4	1	no	—
26	C₄×Q₈×C₁₉	—	4	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₁₉×C₄⋊C₈	—	4	1	no	—
40	C₁₉×#101	—	2	4	no	—
41	C₁₉×C₂²⋊C₈	—	2	2	no	—
42	C₁₉×#97	—	4	1	no	—
43	C₁₉×#97	—	4	1	no	—
44	C₄×C₈×C₁₉	—	4	1	no	—
45	C₁₉×#95	—	2	2	no	—
46	C₁₉×#95	—	2	2	no	—
47	C₁₉×#95	C₂×C₄	1	2	yes	—
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	4	1	no	—
51	C₂×Q₈×C₁₉	—	4	2	no	—
52	C₂×Q₈×C₁₉	—	8	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	M₁₆×C₁₉	—	2	4	no	—
63	M₁₆×C₁₉	—	4	2	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₄⋊C₄×C₁₉	—	4	1	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₄⋊C₄×C₁₉	—	4	1	no	—
72	C₄⋊C₄×C₁₉	—	4	1	no	—
73	C₄⋊C₄×C₁₉	—	8	2	no	—
74	C₄⋊C₄×C₁₉	—	8	2	no	—
75	C₄²×C₁₉	—	2	1	no	—
76	C₄²×C₁₉	—	2	1	no	—
77	C₄²×C₁₉	—	2	1	no	—
78	C₄²×C₁₉	—	2	1	no	—
79	C₄²×C₁₉	—	2	1	no	—
80	C₄²×C₁₉	—	2	1	no	—
81	C₄²×C₁₉	—	4	2	no	—
82	#11795	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	Q₈×C₁₉	—	4	4	no	—
85	Q₈×C₁₉	—	8	4	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	2	no	—
91	C₂×C₄×C₁₉	—	2	4	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#104	1	2	yes	—
109	C₂×C₄×C₁₉	#137	1	2	yes	—
110	C₈×C₁₉	—	4	4	no	—
111	C₈×C₁₉	—	8	2	no	—
112	#2567	C₂×C₁₉	1	1	yes	characteristic
113	C₄×#101	C₂×C₁₉	1	1	yes	characteristic
114	#1467	C₂×C₁₉	1	1	yes	characteristic
115	#1354	C₂×C₁₉	1	4	yes	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
119	C₂²×C₁₉	#419	1	1	yes	characteristic
120	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	—	2	2	no	—
124	C₄×C₁₉	—	4	4	no	—
125	C₄×C₁₉	—	4	1	no	—
126	C₄×C₁₉	—	4	1	no	—
127	C₄×C₁₉	—	4	1	no	—
128	C₄×C₁₉	—	4	1	no	—
129	C₄×C₁₉	—	8	2	no	—
130	C₄×C₁₉	#356	1	2	yes	—
131	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
132	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
133	#432	—	2	1	no	—
134	C₂×#101	—	2	1	no	—
135	C₄×M₁₆	—	2	1	no	—
136	#395	C₄×C₁₉	1	2	yes	—
137	#395	C₂²×C₁₉	1	2	yes	—
138	#391	—	2	1	no	—
139	#389	—	2	1	no	—
140	#389	—	2	1	no	—
141	#384	—	2	1	no	—
142	C₄×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
143	#343	C₂²×C₁₉	1	2	yes	—
144	#324	—	2	1	no	—
145	#324	C₂²×C₁₉	1	2	yes	—
146	C₂×C₁₉	—	2	1	no	—
147	C₂×C₁₉	—	2	1	no	—
148	C₂×C₁₉	#1508	1	1	yes	characteristic
149	C₂×C₁₉	#2122	1	1	yes	characteristic
150	C₂×C₁₉	C₂×#356	1	1	yes	characteristic
151	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
152	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
153	C₂×M₁₆	—	2	2	no	—
154	C₄⋊Q₈	—	4	1	no	—
155	C₄⋊Q₈	—	4	1	no	—
156	C₄×Q₈	—	4	1	no	—
157	C₄×Q₈	—	4	1	no	—
158	C₂×C₄⋊C₄	—	2	1	no	—
159	C₂×C₄⋊C₄	—	2	1	no	—
160	C₂×C₄⋊C₄	—	2	1	no	—
161	C₂×C₄⋊C₄	—	2	2	no	—
162	C₂×C₄⋊C₄	—	2	2	no	—
163	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
164	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
165	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
166	C₂×C₄²	—	2	1	no	—
167	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
168	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
169	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
170	C₄⋊C₈	—	4	1	no	—
171	#101	—	2	4	no	—
172	C₂²⋊C₈	—	2	2	no	—
173	#97	—	4	1	no	—
174	#97	—	4	1	no	—
175	C₄×C₈	—	4	1	no	—
176	#95	—	2	2	no	—
177	#95	—	2	2	no	—
178	#95	C₂×C₄×C₁₉	1	2	yes	—
179	C₁₉	#11795	1	1	yes	characteristic, direct product factor, Sylow
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	1	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	8	2	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
188	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
189	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
190	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
191	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
192	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
193	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
194	M₁₆	—	2	4	no	—
195	M₁₆	—	4	2	no	—
196	C₂×C₈	—	4	2	no	—
197	C₂×C₈	—	4	2	no	—
198	C₄⋊C₄	—	2	4	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	4	1	no	—
201	C₄⋊C₄	—	4	1	no	—
202	C₄⋊C₄	—	4	2	no	—
203	C₄⋊C₄	—	4	1	no	—
204	C₄⋊C₄	—	4	1	no	—
205	C₄⋊C₄	—	8	2	no	—
206	C₄⋊C₄	—	8	2	no	—
207	C₄²	—	2	1	no	—
208	C₄²	—	2	1	no	—
209	C₄²	—	2	1	no	—
210	C₄²	—	2	1	no	—
211	C₄²	—	2	1	no	—
212	C₄²	—	2	1	no	—
213	C₄²	—	4	2	no	—
214	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
215	Q₈	—	4	4	no	—
216	Q₈	—	8	4	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	4	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	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
238	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
239	C₂×C₄	C₁₉×#104	1	2	yes	—
240	C₂×C₄	C₁₉×#137	1	2	yes	—
241	C₈	—	4	4	no	—
242	C₈	—	8	2	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
246	C₂²	C₁₉×#419	1	1	yes	characteristic
247	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	1	no	—
251	C₄	—	4	4	no	—
252	C₄	—	4	1	no	—
253	C₄	—	4	1	no	—
254	C₄	—	4	1	no	—
255	C₄	—	4	1	no	—
256	C₄	—	8	2	no	—
257	C₄	C₁₉×#356	1	2	yes	—
258	C₂	—	2	1	no	—
259	C₂	—	2	1	no	—
260	C₂	C₁₉×#1508	1	1	yes	characteristic
261	C₂	C₁₉×#2122	1	1	yes	characteristic
262	C₂	C₂×C₁₉×#356	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2567

C₂

yes

maximal, characteristic

C₄×C₁₉×#101

C₂

yes

maximal, characteristic

C₁₉×#1467

C₂

yes

maximal, characteristic

C₁₉×#1354

C₂

yes

maximal

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#432

—

C₂×C₁₉×#101

—

C₄×M₁₆×C₁₉

—

C₁₉×#395

C₄

yes

—

C₁₉×#395

C₂²

yes

—

C₁₉×#391

—

C₁₉×#389

—

C₁₉×#389

—

C₁₉×#384

—

C₄×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₁₉×#343

C₂²

yes

—

C₁₉×#324

—

C₁₉×#324

C₂²

yes

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

C₂×C₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

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

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×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

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#11795

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×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

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

#99

yes

characteristic

107

C₂×C₄×C₁₉

#99

yes

characteristic

108

C₂×C₄×C₁₉

#104

yes

—

109

C₂×C₄×C₁₉

#137

yes

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

#2567

C₂×C₁₉

yes

characteristic

113

C₄×#101

C₂×C₁₉

yes

characteristic

114

#1467

C₂×C₁₉

yes

characteristic

115

#1354

C₂×C₁₉

yes

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

C₂×#99

yes

characteristic

119

C₂²×C₁₉

#419

yes

characteristic

120

C₂²×C₁₉

C₂×#104

yes

characteristic

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

#356

yes

—

131

C₂×C₄⋊Q₈

C₄×C₁₉

yes

characteristic

132

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

133

#432

—

134

C₂×#101

—

135

C₄×M₁₆

—

136

#395

C₄×C₁₉

yes

—

137

#395

C₂²×C₁₉

yes

—

138

#391

—

139

#389

—

140

#389

—

141

#384

—

142

C₄×C₄⋊C₄

C₄×C₁₉

yes

characteristic

143

#343

C₂²×C₁₉

yes

—

144

#324

—

145

#324

C₂²×C₁₉

yes

—

146

C₂×C₁₉

—

147

C₂×C₁₉

—

148

C₂×C₁₉

#1508

yes

characteristic

149

C₂×C₁₉

#2122

yes

characteristic

150

C₂×C₁₉

C₂×#356

yes

characteristic

151

C₂²×Q₈

C₂×C₄×C₁₉

yes

—

152

C₂²×Q₈

D₄×C₁₉

yes

characteristic

153

C₂×M₁₆

—

154

C₄⋊Q₈

—

155

C₄⋊Q₈

—

156

C₄×Q₈

—

157

C₄×Q₈

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

164

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

165

C₂×C₄⋊C₄

C₂³×C₁₉

yes

characteristic

166

C₂×C₄²

—

167

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

168

C₂×C₄²

D₄×C₁₉

yes

characteristic

169

C₂×C₄²

D₄×C₁₉

yes

characteristic

170

C₄⋊C₈

—

171

#101

—

172

C₂²⋊C₈

—

173

#97

—

174

#97

—

175

C₄×C₈

—

176

#95

—

177

#95

—

178

#95

C₂×C₄×C₁₉

yes

—

179

C₁₉

#11795

yes

characteristic, direct product factor, Sylow

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

188

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

189

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

190

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

191

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

192

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

193

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

194

M₁₆

—

195

M₁₆

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

215

Q₈

—

216

Q₈

—

217

C₂×C₄

—

218

C₂×C₄

—

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

—

237

C₂×C₄

C₁₉×#99

yes

characteristic

238

C₂×C₄

C₁₉×#99

yes

characteristic

239

C₂×C₄

C₁₉×#104

yes

—

240

C₂×C₄

C₁₉×#137

yes

—

241

C₈

—

242

C₈

—

243

C₂²

—

244

C₂²

—

245

C₂²

C₂×C₁₉×#99

yes

characteristic

246

C₂²

C₁₉×#419

yes

characteristic

247

C₂²

C₂×C₁₉×#104

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

C₁₉×#356

yes

—

258

C₂

—

259

C₂

—

260

C₂

C₁₉×#1508

yes

characteristic

261

C₂

C₁₉×#2122

yes

characteristic

262

C₂

C₂×C₁₉×#356

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×#99

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄⋊C₄

C₂³×C₁₉

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

N	H ≅ G/N	type
82. #11795	C₁₉	direct (N × H)
179. C₁₉	#11795	direct (N × H)

H ≅ G/N

type

82. #11795

C₁₉

direct (N × H)

179. C₁₉

#11795

direct (N × H)

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

subgroup	index
C₁₉×#2567	2
C₄×C₁₉×#101	2
C₁₉×#1467	2
C₁₉×#1354	2
#11795	19

subgroup

index

C₁₉×#2567

C₄×C₁₉×#101

C₁₉×#1467

C₁₉×#1354

#11795

Subgroups — C₁₉×#11795 #18017754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11795 #18017754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11795 #18017754