Group #18017491 — subgroups

Subgroups — C₁₉×#11532 #18017491

Order 4864.

412 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 110 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	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1467	C₂	1	2	yes	maximal
3	C₁₉×#1325	C₂	1	2	yes	maximal
4	C₁₉×#1319	C₂	1	2	yes	maximal
5	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#432	—	2	2	no	—
9	C₁₉×#391	C₄	1	1	yes	characteristic
10	C₁₉×#391	C₂²	1	1	yes	characteristic
11	C₁₉×#389	—	2	2	no	—
12	C₁₉×#384	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
14	C₄³×C₁₉	C₄	1	1	yes	characteristic
15	C₁₉×#324	—	2	2	no	—
16	C₁₉×#324	C₂²	1	4	yes	—
17	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₁₉×C₄⋊Q₈	—	2	2	no	—
20	C₁₉×C₄⋊Q₈	—	2	2	no	—
21	C₄×Q₈×C₁₉	—	4	1	no	—
22	C₄×Q₈×C₁₉	—	4	1	no	—
23	C₄×Q₈×C₁₉	—	4	1	no	—
24	C₄×Q₈×C₁₉	—	4	1	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
30	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	—	2	1	no	—
32	C₂×C₄²×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	2	yes	—
38	C₁₉×C₄⋊C₈	—	4	2	no	—
39	C₁₉×C₂²⋊C₈	—	2	4	no	—
40	C₁₉×#97	—	4	2	no	—
41	C₁₉×#95	—	2	2	no	—
42	C₁₉×#95	—	2	2	no	—
43	C₂×Q₈×C₁₉	—	2	1	no	—
44	C₂×Q₈×C₁₉	—	2	1	no	—
45	C₂×Q₈×C₁₉	—	2	1	no	—
46	C₂×Q₈×C₁₉	—	4	1	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂×Q₈×C₁₉	—	4	1	no	—
49	C₂×Q₈×C₁₉	—	4	1	no	—
50	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
51	C₂²×C₄×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	—	2	1	no	—
53	C₂²×C₄×C₁₉	—	2	1	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₁₉	—	4	4	no	—
61	C₄⋊C₄×C₁₉	—	2	8	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄⋊C₄×C₁₉	—	4	1	no	—
64	C₄⋊C₄×C₁₉	—	4	1	no	—
65	C₄⋊C₄×C₁₉	—	4	4	no	—
66	C₄⋊C₄×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	—	2	4	no	—
68	C₄²×C₁₉	—	2	1	no	—
69	C₄²×C₁₉	—	2	1	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	2	1	no	—
73	C₄²×C₁₉	—	4	1	no	—
74	C₄²×C₁₉	—	4	2	no	—
75	C₄²×C₁₉	—	4	1	no	—
76	C₄²×C₁₉	—	4	1	no	—
77	C₄²×C₁₉	M₁₆	1	2	yes	—
78	#11532	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	Q₈×C₁₉	—	4	2	no	—
81	Q₈×C₁₉	—	4	2	no	—
82	Q₈×C₁₉	—	4	2	no	—
83	Q₈×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	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	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
109	C₈×C₁₉	—	8	4	no	—
110	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
111	#1467	C₂×C₁₉	1	2	yes	—
112	#1325	C₂×C₁₉	1	2	yes	—
113	#1319	C₂×C₁₉	1	2	yes	—
114	C₂²×C₁₉	—	2	1	no	—
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	#407	1	1	yes	characteristic
117	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
118	C₂²×C₁₉	#413	1	1	yes	characteristic
119	C₄×C₁₉	—	2	4	no	—
120	C₄×C₁₉	—	2	1	no	—
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	4	2	no	—
124	C₄×C₁₉	—	4	2	no	—
125	C₄×C₁₉	—	4	1	no	—
126	C₄×C₁₉	—	4	2	no	—
127	C₄×C₁₉	—	4	2	no	—
128	C₄×C₁₉	—	8	1	no	—
129	C₄×C₁₉	#356	1	2	yes	—
130	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
131	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
132	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
133	#432	—	2	2	no	—
134	#391	C₄×C₁₉	1	1	yes	characteristic
135	#391	C₂²×C₁₉	1	1	yes	characteristic
136	#389	—	2	2	no	—
137	#384	C₂²×C₁₉	1	1	yes	characteristic
138	C₄×C₄⋊C₄	—	2	2	no	—
139	C₄³	C₄×C₁₉	1	1	yes	characteristic
140	#324	—	2	2	no	—
141	#324	C₂²×C₁₉	1	4	yes	—
142	C₂×C₁₉	—	2	1	no	—
143	C₂×C₁₉	—	2	1	no	—
144	C₂×C₁₉	#1465	1	1	yes	characteristic
145	C₂×C₁₉	#2126	1	1	yes	characteristic
146	C₂×C₁₉	C₂×#356	1	1	yes	characteristic
147	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
148	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₄×Q₈	—	4	1	no	—
152	C₄×Q₈	—	4	1	no	—
153	C₄×Q₈	—	4	1	no	—
154	C₄×Q₈	—	4	1	no	—
155	C₂×C₄⋊C₄	—	2	2	no	—
156	C₂×C₄⋊C₄	—	2	1	no	—
157	C₂×C₄⋊C₄	—	2	2	no	—
158	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
159	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
160	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
161	C₂×C₄²	—	2	1	no	—
162	C₂×C₄²	—	2	1	no	—
163	C₂×C₄²	—	2	1	no	—
164	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
165	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
166	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
167	C₂×C₄²	D₄×C₁₉	1	2	yes	—
168	C₄⋊C₈	—	4	2	no	—
169	C₂²⋊C₈	—	2	4	no	—
170	#97	—	4	2	no	—
171	#95	—	2	2	no	—
172	#95	—	2	2	no	—
173	C₁₉	#11532	1	1	yes	characteristic, direct product factor, Sylow
174	C₂×Q₈	—	2	1	no	—
175	C₂×Q₈	—	2	1	no	—
176	C₂×Q₈	—	2	1	no	—
177	C₂×Q₈	—	4	1	no	—
178	C₂×Q₈	—	4	1	no	—
179	C₂×Q₈	—	4	1	no	—
180	C₂×Q₈	—	4	1	no	—
181	C₂×Q₈	M₁₆×C₁₉	1	2	yes	—
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	2	1	no	—
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
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	C₂×D₄×C₁₉	1	2	yes	—
191	C₂×C₈	—	4	4	no	—
192	C₄⋊C₄	—	2	8	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₄⋊C₄	—	4	1	no	—
195	C₄⋊C₄	—	4	1	no	—
196	C₄⋊C₄	—	4	4	no	—
197	C₄⋊C₄	—	4	2	no	—
198	C₄²	—	2	4	no	—
199	C₄²	—	2	1	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	1	no	—
203	C₄²	—	2	1	no	—
204	C₄²	—	4	1	no	—
205	C₄²	—	4	2	no	—
206	C₄²	—	4	1	no	—
207	C₄²	—	4	1	no	—
208	C₄²	M₁₆×C₁₉	1	2	yes	—
209	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
210	Q₈	—	4	2	no	—
211	Q₈	—	4	2	no	—
212	Q₈	—	4	2	no	—
213	Q₈	—	4	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	4	1	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	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	4	1	no	—
235	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
236	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
237	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
238	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
239	C₈	—	8	4	no	—
240	C₂²	—	2	1	no	—
241	C₂²	—	2	1	no	—
242	C₂²	C₁₉×#407	1	1	yes	characteristic
243	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
244	C₂²	C₁₉×#413	1	1	yes	characteristic
245	C₄	—	2	4	no	—
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	4	2	no	—
250	C₄	—	4	2	no	—
251	C₄	—	4	2	no	—
252	C₄	—	4	2	no	—
253	C₄	—	4	1	no	—
254	C₄	—	8	1	no	—
255	C₄	C₁₉×#356	1	2	yes	—
256	C₂	—	2	1	no	—
257	C₂	—	2	1	no	—
258	C₂	C₁₉×#1465	1	1	yes	characteristic
259	C₂	C₁₉×#2126	1	1	yes	characteristic
260	C₂	C₂×C₁₉×#356	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₁₉×#1467

C₂

yes

maximal

C₁₉×#1325

C₂

yes

maximal

C₁₉×#1319

C₂

yes

maximal

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#432

—

C₁₉×#391

C₄

yes

characteristic

C₁₉×#391

C₂²

yes

characteristic

C₁₉×#389

—

C₁₉×#384

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

—

C₄³×C₁₉

C₄

yes

characteristic

C₁₉×#324

—

C₁₉×#324

C₂²

yes

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×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

—

C₂×C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#95

—

C₁₉×#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

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

—

C₂×C₈×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

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

M₁₆

yes

—

#11532

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

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

—

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

#99

yes

characteristic

106

C₂×C₄×C₁₉

#99

yes

characteristic

107

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

108

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

109

C₈×C₁₉

—

110

C₄×C₄⋊Q₈

C₂×C₁₉

yes

characteristic

111

#1467

C₂×C₁₉

yes

—

112

#1325

C₂×C₁₉

yes

—

113

#1319

C₂×C₁₉

yes

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

#407

yes

characteristic

117

C₂²×C₁₉

C₂×#99

yes

characteristic

118

C₂²×C₁₉

#413

yes

characteristic

119

C₄×C₁₉

—

120

C₄×C₁₉

—

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

#356

yes

—

130

C₂×C₄⋊Q₈

C₄×C₁₉

yes

characteristic

131

C₂×C₄×Q₈

C₄×C₁₉

yes

characteristic

132

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

133

#432

—

134

#391

C₄×C₁₉

yes

characteristic

135

#391

C₂²×C₁₉

yes

characteristic

136

#389

—

137

#384

C₂²×C₁₉

yes

characteristic

138

C₄×C₄⋊C₄

—

139

C₄³

C₄×C₁₉

yes

characteristic

140

#324

—

141

#324

C₂²×C₁₉

yes

—

142

C₂×C₁₉

—

143

C₂×C₁₉

—

144

C₂×C₁₉

#1465

yes

characteristic

145

C₂×C₁₉

#2126

yes

characteristic

146

C₂×C₁₉

C₂×#356

yes

characteristic

147

C₂²×Q₈

C₂×C₄×C₁₉

yes

characteristic

148

C₂²×Q₈

C₂×C₄×C₁₉

yes

characteristic

149

C₄⋊Q₈

—

150

C₄⋊Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

C₄×Q₈

—

154

C₄×Q₈

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

159

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

160

C₂×C₄⋊C₄

C₂³×C₁₉

yes

characteristic

161

C₂×C₄²

—

162

C₂×C₄²

—

163

C₂×C₄²

—

164

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

165

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

166

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

167

C₂×C₄²

D₄×C₁₉

yes

—

168

C₄⋊C₈

—

169

C₂²⋊C₈

—

170

#97

—

171

#95

—

172

#95

—

173

C₁₉

#11532

yes

characteristic, direct product factor, Sylow

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

M₁₆×C₁₉

yes

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

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

C₂×D₄×C₁₉

yes

—

191

C₂×C₈

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

M₁₆×C₁₉

yes

—

209

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

210

Q₈

—

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

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

C₁₉×#99

yes

characteristic

236

C₂×C₄

C₁₉×#99

yes

characteristic

237

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

238

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

239

C₈

—

240

C₂²

—

241

C₂²

—

242

C₂²

C₁₉×#407

yes

characteristic

243

C₂²

C₂×C₁₉×#99

yes

characteristic

244

C₂²

C₁₉×#413

yes

characteristic

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

C₁₉×#356

yes

—

256

C₂

—

257

C₂

—

258

C₂

C₁₉×#1465

yes

characteristic

259

C₂

C₁₉×#2126

yes

characteristic

260

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 ▷ C₂² ▷ 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 ▷ C₂² ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
78. #11532	C₁₉	direct (N × H)
173. C₁₉	#11532	direct (N × H)

H ≅ G/N

type

78. #11532

C₁₉

direct (N × H)

173. C₁₉

#11532

direct (N × H)

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

subgroup	index
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#1467	2
C₁₉×#1325	2
C₁₉×#1319	2
#11532	19

subgroup

index

C₄×C₁₉×C₄⋊Q₈

C₁₉×#1467

C₁₉×#1325

C₁₉×#1319

#11532

Subgroups — C₁₉×#11532 #18017491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11532 #18017491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11532 #18017491