Group #18074702 — subgroups

Subgroups — #18074702

Order 4864.

658 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 143 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	#14564576	C₂	1	1	yes	maximal, characteristic
2	#14562335	C₂	1	2	yes	maximal
3	#14562250	C₂	1	2	yes	maximal
4	#14561979	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#3502	C₂	1	1	yes	maximal, characteristic
6	#11926601	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×#10597260	C₂²	1	1	yes	characteristic
9	#11926299	—	2	2	no	—
10	#11926290	—	2	2	no	—
11	#11926290	—	2	2	no	—
12	#11926286	—	2	4	no	—
13	#11926270	—	2	2	no	—
14	Q₈²×C₁₉	—	2	2	no	—
15	C₁₉×#557	—	2	2	no	—
16	C₁₉×#557	—	2	4	no	—
17	C₁₉×#544	—	2	2	no	—
18	C₁₉×#544	C₄	1	2	yes	—
19	C₁₉×#533	—	2	2	no	—
20	C₁₉×#533	C₂²	1	2	yes	—
21	C₁₉×#519	C₄	1	2	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₁₉×C₄⋊Q₈	—	2	2	no	—
26	C₁₉×C₄⋊Q₈	—	2	8	no	—
27	C₁₉×C₄⋊Q₈	—	2	4	no	—
28	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
29	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
30	C₁₉×#125	—	2	4	no	—
31	C₁₉×#125	—	2	8	no	—
32	C₁₉×#125	—	2	4	no	—
33	C₁₉×#125	D₄	1	4	yes	—
34	C₁₉×C₂²⋊Q₈	—	2	4	no	—
35	C₁₉×C₂²⋊Q₈	—	2	2	no	—
36	C₁₉×C₂²⋊Q₈	—	2	2	no	—
37	C₄×Q₈×C₁₉	—	2	4	no	—
38	C₄×Q₈×C₁₉	—	2	4	no	—
39	C₄×Q₈×C₁₉	—	2	4	no	—
40	C₄×Q₈×C₁₉	—	2	4	no	—
41	C₄×Q₈×C₁₉	—	2	2	no	—
42	C₄×Q₈×C₁₉	—	2	2	no	—
43	C₄×Q₈×C₁₉	—	2	2	no	—
44	C₄×Q₈×C₁₉	—	2	2	no	—
45	C₁₉×#117	—	2	4	no	—
46	C₁₉×#117	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
49	C₂×C₄²×C₁₉	D₄	1	2	yes	—
50	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
55	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
56	#10597260	—	2	2	no	—
57	#10597260	—	2	2	no	—
58	C₂×Q₈×C₁₉	—	2	4	no	—
59	C₂×Q₈×C₁₉	—	2	4	no	—
60	C₂×Q₈×C₁₉	—	2	2	no	—
61	C₂×Q₈×C₁₉	—	2	2	no	—
62	C₂×Q₈×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄⋊C₄×C₁₉	—	2	4	no	—
69	C₄⋊C₄×C₁₉	—	2	4	no	—
70	C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₄⋊C₄×C₁₉	—	2	8	no	—
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄⋊C₄×C₁₉	—	2	4	no	—
78	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
79	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
80	C₂²⋊C₄×C₁₉	—	2	4	no	—
81	C₄²×C₁₉	—	2	8	no	—
82	C₄²×C₁₉	—	2	4	no	—
83	C₄²×C₁₉	—	2	2	no	—
84	C₄²×C₁₉	—	2	2	no	—
85	C₄²×C₁₉	C₂×D₄	1	2	yes	—
86	C₄²×C₁₉	C₂×D₄	1	2	yes	—
87	C₂×C₁₉⋊C₈	—	2	2	no	—
88	C₂×C₁₉⋊C₈	—	4	1	no	—
89	C₂×C₁₉⋊C₈	—	4	1	no	—
90	C₂×C₁₉⋊C₈	—	4	2	no	—
91	C₂×C₁₉⋊C₈	—	4	2	no	—
92	C₂×C₁₉⋊C₈	—	4	1	no	—
93	#8460	—	19	1	no	maximal, Sylow
94	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	Q₈×C₁₉	—	2	8	no	—
96	Q₈×C₁₉	—	4	2	no	—
97	Q₈×C₁₉	—	4	2	no	—
98	Q₈×C₁₉	—	8	2	no	—
99	Q₈×C₁₉	—	8	4	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	4	no	—
106	C₂×C₄×C₁₉	—	2	4	no	—
107	C₂×C₄×C₁₉	—	2	2	no	—
108	C₂×C₄×C₁₉	—	4	1	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	#101	1	4	yes	—
111	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
112	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#120	1	2	yes	—
114	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
115	C₁₉⋊C₈	—	4	2	no	—
116	C₁₉⋊C₈	—	8	2	no	—
117	C₁₉⋊C₈	—	8	1	no	—
118	#3502	D₁₉	1	1	yes	characteristic
119	#1985	—	19	1	no	—
120	#1552	—	19	2	no	—
121	#1531	—	19	2	no	—
122	#1467	—	19	1	no	—
123	C₂²×C₁₉	—	2	1	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	#379	1	1	yes	characteristic
126	C₂²×C₁₉	C₂×#101	1	2	yes	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	2	no	—
129	C₄×C₁₉	—	2	4	no	—
130	C₄×C₁₉	—	2	2	no	—
131	C₄×C₁₉	—	4	4	no	—
132	C₄×C₁₉	—	4	2	no	—
133	C₄×C₁₉	—	4	4	no	—
134	C₄×C₁₉	#454	1	1	yes	characteristic
135	C₄×C₁₉	#456	1	1	yes	characteristic
136	Q₈²	—	2	2	no	—
137	#557	—	2	2	no	—
138	#557	—	2	4	no	—
139	#544	—	2	2	no	—
140	#544	Dic₁₉	1	2	yes	—
141	#533	—	2	2	no	—
142	#533	C₂×D₁₉	1	2	yes	—
143	#519	Dic₁₉	1	2	yes	—
144	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
145	#432	—	19	2	no	—
146	C₂×C₄⋊C₈	—	19	1	no	—
147	C₂×#97	—	19	1	no	—
148	#336	—	38	2	no	—
149	#332	—	38	2	no	—
150	#332	—	38	2	no	—
151	#330	—	38	4	no	—
152	#324	—	38	2	no	—
153	C₂×C₁₉	—	2	2	no	—
154	C₂×C₁₉	#1784	1	1	yes	characteristic
155	C₂×C₁₉	#1793	1	1	yes	characteristic
156	C₂×C₁₉	#1794	1	1	yes	characteristic
157	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
158	C₂²×C₈	—	38	1	no	—
159	C₂²×C₈	—	38	1	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	—	2	2	no	—
162	C₄⋊Q₈	—	2	8	no	—
163	C₄⋊Q₈	—	2	4	no	—
164	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
165	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
166	#125	—	2	4	no	—
167	#125	—	2	8	no	—
168	#125	—	2	4	no	—
169	#125	C₂²⋊D₁₉	1	4	yes	—
170	C₂²⋊Q₈	—	2	4	no	—
171	C₂²⋊Q₈	—	2	2	no	—
172	C₂²⋊Q₈	—	2	2	no	—
173	C₄×Q₈	—	2	4	no	—
174	C₄×Q₈	—	2	4	no	—
175	C₄×Q₈	—	2	4	no	—
176	C₄×Q₈	—	2	4	no	—
177	C₄×Q₈	—	2	2	no	—
178	C₄×Q₈	—	2	2	no	—
179	C₄×Q₈	—	2	2	no	—
180	C₄×Q₈	—	2	2	no	—
181	#117	—	2	4	no	—
182	#117	C₂×Dic₁₉	1	4	yes	—
183	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
184	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
185	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
186	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
187	C₄⋊C₈	—	38	2	no	—
188	C₄⋊C₈	—	38	2	no	—
189	C₂²⋊C₈	—	38	2	no	—
190	#97	—	38	2	no	—
191	#97	—	38	2	no	—
192	C₁₉	#8460	1	1	yes	characteristic, complemented, Sylow
193	C₂×Q₈	—	2	4	no	—
194	C₂×Q₈	—	2	2	no	—
195	C₂×Q₈	—	2	2	no	—
196	C₂×Q₈	—	2	2	no	—
197	C₂×Q₈	—	2	4	no	—
198	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
199	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
200	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
201	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
202	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
203	C₂×C₈	—	38	2	no	—
204	C₂×C₈	—	76	1	no	—
205	C₂×C₈	—	76	1	no	—
206	C₂×C₈	—	76	2	no	—
207	C₂×C₈	—	76	2	no	—
208	C₂×C₈	—	76	1	no	—
209	C₄⋊C₄	—	2	4	no	—
210	C₄⋊C₄	—	2	4	no	—
211	C₄⋊C₄	—	2	4	no	—
212	C₄⋊C₄	—	2	8	no	—
213	C₄⋊C₄	—	2	2	no	—
214	C₄⋊C₄	—	2	4	no	—
215	C₄⋊C₄	—	2	4	no	—
216	C₄⋊C₄	—	2	2	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₄⋊C₄	—	2	4	no	—
219	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
220	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
221	C₂²⋊C₄	—	2	4	no	—
222	C₄²	—	2	8	no	—
223	C₄²	—	2	4	no	—
224	C₄²	—	2	2	no	—
225	C₄²	—	2	2	no	—
226	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
227	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
228	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
229	Q₈	—	2	8	no	—
230	Q₈	—	4	2	no	—
231	Q₈	—	4	2	no	—
232	Q₈	—	8	2	no	—
233	Q₈	—	8	4	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	4	no	—
240	C₂×C₄	—	2	4	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	#10597293	1	4	yes	—
245	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
246	C₂×C₄	#10597399	1	1	yes	characteristic
247	C₂×C₄	#10597399	1	2	yes	—
248	C₂×C₄	#10597399	1	1	yes	characteristic
249	C₈	—	76	2	no	—
250	C₈	—	152	2	no	—
251	C₈	—	152	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	#11926400	1	1	yes	characteristic
255	C₂²	C₂×#10597293	1	2	yes	—
256	C₄	—	2	1	no	—
257	C₄	—	2	2	no	—
258	C₄	—	2	2	no	—
259	C₄	—	2	4	no	—
260	C₄	—	4	4	no	—
261	C₄	—	4	2	no	—
262	C₄	—	4	4	no	—
263	C₄	#11926717	1	1	yes	characteristic
264	C₄	#11926727	1	1	yes	characteristic
265	C₂	—	2	2	no	—
266	C₂	#14563559	1	1	yes	characteristic
267	C₂	#14563594	1	1	yes	characteristic
268	C₂	#14563599	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564576

C₂

yes

maximal, characteristic

#14562335

C₂

yes

maximal

#14562250

C₂

yes

maximal

#14561979

C₂

yes

maximal, characteristic

C₁₉×#3502

C₂

yes

maximal, characteristic

#11926601

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597260

C₂²

yes

—

—

—

—

—

Q₈²×C₁₉

—

C₁₉×#557

—

C₁₉×#557

—

C₁₉×#544

—

C₁₉×#544

C₄

yes

—

C₁₉×#533

—

C₁₉×#533

C₂²

yes

—

C₁₉×#519

C₄

yes

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

D₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₁₉×#117

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

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

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8460

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

#101

yes

—

111

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

112

C₂×C₄×C₁₉

#120

yes

characteristic

113

C₂×C₄×C₁₉

#120

yes

—

114

C₂×C₄×C₁₉

#120

yes

characteristic

115

C₁₉⋊C₈

—

116

C₁₉⋊C₈

—

117

C₁₉⋊C₈

—

118

#3502

D₁₉

yes

characteristic

119

#1985

—

120

#1552

—

121

#1531

—

122

#1467

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

#379

yes

characteristic

126

C₂²×C₁₉

C₂×#101

yes

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

#454

yes

characteristic

135

C₄×C₁₉

#456

yes

characteristic

136

Q₈²

—

137

#557

—

138

#557

—

139

#544

—

140

#544

Dic₁₉

yes

—

141

#533

—

142

#533

C₂×D₁₉

yes

—

143

#519

Dic₁₉

yes

—

144

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

145

#432

—

146

C₂×C₄⋊C₈

—

147

C₂×#97

—

148

#336

—

149

#332

—

150

#332

—

151

#330

—

152

#324

—

153

C₂×C₁₉

—

154

C₂×C₁₉

#1784

yes

characteristic

155

C₂×C₁₉

#1793

yes

characteristic

156

C₂×C₁₉

#1794

yes

characteristic

157

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

164

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

165

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

166

#125

—

167

#125

—

168

#125

—

169

#125

C₂²⋊D₁₉

yes

—

170

C₂²⋊Q₈

—

171

C₂²⋊Q₈

—

172

C₂²⋊Q₈

—

173

C₄×Q₈

—

174

C₄×Q₈

—

175

C₄×Q₈

—

176

C₄×Q₈

—

177

C₄×Q₈

—

178

C₄×Q₈

—

179

C₄×Q₈

—

180

C₄×Q₈

—

181

#117

—

182

#117

C₂×Dic₁₉

yes

—

183

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

184

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

185

C₂×C₄²

C₂²⋊D₁₉

yes

—

186

C₂×C₄²

C₂²×D₁₉

yes

characteristic

187

C₄⋊C₈

—

188

C₄⋊C₈

—

189

C₂²⋊C₈

—

190

#97

—

191

#97

—

192

C₁₉

#8460

yes

characteristic, complemented, Sylow

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

199

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

200

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

201

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

202

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

220

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

221

C₂²⋊C₄

—

222

C₄²

—

223

C₄²

—

224

C₄²

—

225

C₄²

—

226

C₄²

C₂×C₂²⋊D₁₉

yes

—

227

C₄²

C₂×C₂²⋊D₁₉

yes

—

228

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

229

Q₈

—

230

Q₈

—

231

Q₈

—

232

Q₈

—

233

Q₈

—

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

#10597293

yes

—

245

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

—

246

C₂×C₄

#10597399

yes

characteristic

247

C₂×C₄

#10597399

yes

—

248

C₂×C₄

#10597399

yes

characteristic

249

C₈

—

250

C₈

—

152

—

251

C₈

—

152

—

252

C₂²

—

253

C₂²

—

254

C₂²

#11926400

yes

characteristic

255

C₂²

C₂×#10597293

yes

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

#11926717

yes

characteristic

264

C₄

#11926727

yes

characteristic

265

C₂

—

266

C₂

#14563559

yes

characteristic

267

C₂

#14563594

yes

characteristic

268

C₂

#14563599

yes

characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3502	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3502	D₁₉
hypocenter	C₁₉	#8460
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3502

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3502

C₂

socle

C₂²×C₁₉

#379

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3502

N	H ≅ G/N	type
192. C₁₉	#8460	semidirect

H ≅ G/N

type

192. C₁₉

#8460

semidirect

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

subgroup	index
#14564576	2
#14562335	2
#14562250	2
#14561979	2
C₁₉×#3502	2
#8460	19

subgroup

index

C₁₉×#3502

Subgroups — #18074702

Conjugacy classes of subgroups

Complements

Maximal subgroups