Group #18073461 — subgroups

Subgroups — #18073461

Order 4864.

528 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 151 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	#14563384	C₂	1	2	yes	maximal, complemented
2	C₂×#11926284	C₂	1	2	yes	maximal
3	#14561516	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597260	C₂²	1	4	yes	—
6	#11926299	—	2	2	no	—
7	#11926299	—	2	2	no	—
8	#11926284	C₄	1	8	yes	complemented
9	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
12	C₁₉×#391	C₄	1	1	yes	characteristic
13	C₁₉×#390	C₄	1	1	yes	characteristic
14	C₁₉×#388	—	2	2	no	—
15	C₁₉×#382	C₂²	1	1	yes	characteristic
16	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
17	C₄³×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	—	2	1	no	—
21	C₁₉×#124	—	2	2	no	—
22	C₁₉×#124	C₂×C₄	1	4	yes	—
23	C₄×Q₈×C₁₉	—	4	2	no	—
24	C₄×D₄×C₁₉	—	4	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄²×C₁₉	—	2	1	no	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	D₄	1	2	yes	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₁₉⋊C₈	—	2	4	no	—
38	C₁₉×#95	—	2	2	no	—
39	C₁₉×#95	—	2	2	no	—
40	#10597260	—	2	4	no	—
41	#10597260	C₂×C₄	1	8	yes	complemented
42	C₂⁴×C₁₉	—	2	1	no	—
43	C₂×Q₈×C₁₉	—	2	1	no	—
44	C₂×Q₈×C₁₉	—	4	1	no	—
45	C₂×Q₈×C₁₉	—	4	1	no	—
46	C₂×Q₈×C₁₉	C₄²	1	2	yes	—
47	C₂×D₄×C₁₉	—	2	1	no	—
48	C₂×D₄×C₁₉	—	4	1	no	—
49	C₂×D₄×C₁₉	—	4	1	no	—
50	C₂×D₄×C₁₉	C₄²	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	—	4	4	no	—
55	C₂²×C₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
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	2	yes	—
61	C₄⋊C₄×C₁₉	—	4	1	no	—
62	C₄⋊C₄×C₁₉	—	4	1	no	—
63	C₄⋊C₄×C₁₉	—	4	2	no	—
64	C₂²⋊C₄×C₁₉	—	2	8	no	—
65	C₂²⋊C₄×C₁₉	—	4	4	no	—
66	C₂²⋊C₄×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	—	2	2	no	—
68	C₄²×C₁₉	—	4	1	no	—
69	C₄²×C₁₉	—	4	2	no	—
70	C₄²×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	—	4	2	no	—
72	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
73	C₄²×C₁₉	#41	1	2	yes	—
74	C₂×C₁₉⋊C₈	—	2	8	no	—
75	C₂×C₁₉⋊C₈	—	4	4	no	—
76	C₂×C₁₉⋊C₈	—	4	4	no	—
77	#8224	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	—	2	2	no	—
79	C₂³×C₁₉	—	4	1	no	—
80	C₂³×C₁₉	—	4	1	no	—
81	C₂³×C₁₉	—	4	2	no	—
82	C₂³×C₁₉	—	4	2	no	—
83	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	Q₈×C₁₉	—	4	2	no	—
85	Q₈×C₁₉	—	4	2	no	—
86	D₄×C₁₉	—	4	2	no	—
87	D₄×C₁₉	—	4	2	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	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	2	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	1	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	8	4	no	—
106	C₂×C₄×C₁₉	#100	1	2	yes	—
107	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
109	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
110	C₁₉⋊C₈	—	4	8	no	—
111	C₄×#124	D₁₉	1	1	yes	characteristic
112	#1745	—	19	2	no	—
113	C₂×#329	—	19	2	no	—
114	#1295	—	19	2	no	—
115	C₂²×C₁₉	—	4	2	no	—
116	C₂²×C₁₉	—	4	4	no	—
117	C₂²×C₁₉	—	8	1	no	—
118	C₂²×C₁₉	—	8	1	no	—
119	C₂²×C₁₉	—	8	2	no	—
120	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
122	C₂²×C₁₉	#413	1	1	yes	characteristic
123	C₂²×C₁₉	#421	1	2	yes	—
124	C₂²×C₁₉	#421	1	2	yes	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	2	4	no	—
128	C₄×C₁₉	—	2	2	no	—
129	C₄×C₁₉	—	4	1	no	—
130	C₄×C₁₉	—	4	2	no	—
131	C₄×C₁₉	—	4	2	no	—
132	C₄×C₁₉	—	8	1	no	—
133	C₄×C₁₉	—	8	1	no	—
134	C₂×#124	C₂×D₁₉	1	1	yes	characteristic
135	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic
136	C₂×C₄×D₄	Dic₁₉	1	1	yes	characteristic
137	C₂×#97	—	19	4	no	—
138	#391	Dic₁₉	1	1	yes	characteristic
139	#390	Dic₁₉	1	1	yes	characteristic
140	#388	—	2	2	no	—
141	#382	C₂×D₁₉	1	1	yes	characteristic
142	C₄×C₂²⋊C₄	—	2	2	no	—
143	C₄³	C₂×D₁₉	1	1	yes	characteristic
144	#336	—	38	2	no	—
145	#336	—	38	2	no	—
146	#329	—	19	8	no	—
147	C₂×C₁₉	—	8	2	no	—
148	C₂×C₁₉	#1533	1	1	yes	characteristic
149	C₂×C₁₉	#1535	1	2	yes	—
150	C₂×C₁₉	#1536	1	1	yes	characteristic
151	C₂×C₁₉	C₄×#100	1	1	yes	characteristic
152	C₂×C₁₉	#1759	1	2	yes	—
153	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
154	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
155	C₂³×C₄	—	2	1	no	—
156	C₂²×C₈	—	38	4	no	—
157	#124	—	2	2	no	—
158	#124	C₄×D₁₉	1	4	yes	—
159	C₄×Q₈	—	4	2	no	—
160	C₄×D₄	—	4	2	no	—
161	C₂×C₄⋊C₄	—	2	1	no	—
162	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
163	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
164	C₂×C₂²⋊C₄	—	2	2	no	—
165	C₂×C₂²⋊C₄	—	2	1	no	—
166	C₂×C₂²⋊C₄	—	2	2	no	—
167	C₂×C₄²	—	2	1	no	—
168	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
169	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
170	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
171	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
172	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	#97	—	19	8	no	—
174	#97	—	38	4	no	—
175	#95	—	2	2	no	—
176	#95	—	2	2	no	—
177	C₁₉	#8224	1	1	yes	characteristic, complemented, Sylow
178	C₂⁴	—	2	1	no	—
179	C₂×Q₈	—	2	1	no	—
180	C₂×Q₈	—	4	1	no	—
181	C₂×Q₈	—	4	1	no	—
182	C₂×Q₈	C₄×Dic₁₉	1	2	yes	—
183	C₂×D₄	—	2	1	no	—
184	C₂×D₄	—	4	1	no	—
185	C₂×D₄	—	4	1	no	—
186	C₂×D₄	C₄×Dic₁₉	1	2	yes	—
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	—	2	1	no	—
190	C₂²×C₄	—	4	4	no	—
191	C₂²×C₄	—	4	2	no	—
192	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
193	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
194	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
195	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
196	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
197	C₂×C₈	—	38	8	no	—
198	C₂×C₈	—	76	4	no	—
199	C₂×C₈	—	76	4	no	—
200	C₄⋊C₄	—	4	1	no	—
201	C₄⋊C₄	—	4	1	no	—
202	C₄⋊C₄	—	4	2	no	—
203	C₂²⋊C₄	—	2	8	no	—
204	C₂²⋊C₄	—	4	4	no	—
205	C₂²⋊C₄	—	4	2	no	—
206	C₄²	—	2	2	no	—
207	C₄²	—	4	1	no	—
208	C₄²	—	4	2	no	—
209	C₄²	—	4	2	no	—
210	C₄²	—	4	2	no	—
211	C₄²	C₂×C₄×D₁₉	1	2	yes	—
212	C₄²	#64541	1	2	yes	—
213	C₂³	—	2	2	no	—
214	C₂³	—	4	1	no	—
215	C₂³	—	4	2	no	—
216	C₂³	—	4	2	no	—
217	C₂³	—	4	1	no	—
218	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
219	Q₈	—	4	2	no	—
220	Q₈	—	4	2	no	—
221	D₄	—	4	2	no	—
222	D₄	—	4	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	—	2	1	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	4	1	no	—
235	C₂×C₄	—	4	1	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	4	1	no	—
240	C₂×C₄	—	8	4	no	—
241	C₂×C₄	#10597290	1	2	yes	—
242	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
243	C₂×C₄	#10597372	1	1	yes	characteristic
244	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
245	C₈	—	76	8	no	—
246	C₂²	—	4	2	no	—
247	C₂²	—	4	4	no	—
248	C₂²	—	8	1	no	—
249	C₂²	—	8	2	no	—
250	C₂²	—	8	1	no	—
251	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
252	C₂²	C₂×#10597290	1	1	yes	characteristic
253	C₂²	#11926528	1	1	yes	characteristic
254	C₂²	#11926561	1	2	yes	—
255	C₂²	#11926561	1	2	yes	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	4	no	—
259	C₄	—	2	2	no	—
260	C₄	—	4	2	no	—
261	C₄	—	4	2	no	—
262	C₄	—	4	1	no	—
263	C₄	—	8	1	no	—
264	C₄	—	8	1	no	—
265	C₂	—	8	2	no	—
266	C₂	#14562259	1	1	yes	characteristic
267	C₂	#14562266	1	2	yes	—
268	C₂	#14562270	1	1	yes	characteristic
269	C₂	C₄×#10597290	1	1	yes	characteristic
270	C₂	#14563445	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563384

C₂

yes

maximal, complemented

C₂×#11926284

C₂

yes

maximal

#14561516

C₂

yes

maximal, complemented

C₄×C₁₉×#124

C₂

yes

maximal, characteristic

C₂×#10597260

C₂²

yes

—

#11926299

—

#11926299

—

#11926284

C₄

yes

complemented

C₂×C₁₉×#124

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₄×D₄×C₁₉

C₄

yes

characteristic

C₁₉×#391

C₄

yes

characteristic

C₁₉×#390

C₄

yes

characteristic

C₁₉×#388

—

C₁₉×#382

C₂²

yes

characteristic

C₄×C₂²⋊C₄×C₁₉

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₁₉×#124

—

C₁₉×#124

C₂×C₄

yes

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

#10597260

—

#10597260

C₂×C₄

yes

complemented

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₄²

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄²

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8224

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×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

—

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

#100

yes

—

107

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

108

C₂×C₄×C₁₉

#117

yes

characteristic

109

C₂×C₄×C₁₉

C₄×D₄

yes

—

110

C₁₉⋊C₈

—

111

C₄×#124

D₁₉

yes

characteristic

112

#1745

—

113

C₂×#329

—

114

#1295

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

121

C₂²×C₁₉

C₂×#100

yes

characteristic

122

C₂²×C₁₉

#413

yes

characteristic

123

C₂²×C₁₉

#421

yes

—

124

C₂²×C₁₉

#421

yes

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₂×#124

C₂×D₁₉

yes

characteristic

135

C₂×C₄×Q₈

Dic₁₉

yes

characteristic

136

C₂×C₄×D₄

Dic₁₉

yes

characteristic

137

C₂×#97

—

138

#391

Dic₁₉

yes

characteristic

139

#390

Dic₁₉

yes

characteristic

140

#388

—

141

#382

C₂×D₁₉

yes

characteristic

142

C₄×C₂²⋊C₄

—

143

C₄³

C₂×D₁₉

yes

characteristic

144

#336

—

145

#336

—

146

#329

—

147

C₂×C₁₉

—

148

C₂×C₁₉

#1533

yes

characteristic

149

C₂×C₁₉

#1535

yes

—

150

C₂×C₁₉

#1536

yes

characteristic

151

C₂×C₁₉

C₄×#100

yes

characteristic

152

C₂×C₁₉

#1759

yes

—

153

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

154

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

155

C₂³×C₄

—

156

C₂²×C₈

—

157

#124

—

158

#124

C₄×D₁₉

yes

—

159

C₄×Q₈

—

160

C₄×D₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

163

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

164

C₂×C₂²⋊C₄

—

165

C₂×C₂²⋊C₄

—

166

C₂×C₂²⋊C₄

—

167

C₂×C₄²

—

168

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

169

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

170

C₂×C₄²

C₂²⋊D₁₉

yes

—

171

C₂×C₄²

C₂²⋊D₁₉

yes

—

172

C₂×C₄²

C₂²×D₁₉

yes

characteristic

173

#97

—

174

#97

—

175

#95

—

176

#95

—

177

C₁₉

#8224

yes

characteristic, complemented, Sylow

178

C₂⁴

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

C₄×Dic₁₉

yes

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

C₄×Dic₁₉

yes

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

193

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

194

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

195

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

196

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₄²

—

211

C₄²

C₂×C₄×D₁₉

yes

—

212

C₄²

#64541

yes

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

219

Q₈

—

220

Q₈

—

221

D₄

—

222

D₄

—

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

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

#10597290

yes

—

242

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

243

C₂×C₄

#10597372

yes

characteristic

244

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

245

C₈

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

C₄×C₂²⋊Dic₁₉

yes

characteristic

252

C₂²

C₂×#10597290

yes

characteristic

253

C₂²

#11926528

yes

characteristic

254

C₂²

#11926561

yes

—

255

C₂²

#11926561

yes

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₂

—

266

C₂

#14562259

yes

characteristic

267

C₂

#14562266

yes

—

268

C₂

#14562270

yes

characteristic

269

C₂

C₄×#10597290

yes

characteristic

270

C₂

#14563445

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#124	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#124	D₁₉
hypocenter	C₁₉	#8224
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#124

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#124

N	H ≅ G/N	type
1. #14563384	C₂	semidirect
3. #14561516	C₂	semidirect
8. #11926284	C₄	semidirect
41. #10597260	C₂×C₄	semidirect
177. C₁₉	#8224	semidirect

H ≅ G/N

type

1. #14563384

C₂

semidirect

3. #14561516

C₂

semidirect

8. #11926284

C₄

semidirect

41. #10597260

C₂×C₄

semidirect

177. C₁₉

#8224

semidirect

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

subgroup	index
#14563384	2
C₂×#11926284	2
#14561516	2
C₄×C₁₉×#124	2
#8224	19

subgroup

index

C₄×C₁₉×#124

Subgroups — #18073461

Conjugacy classes of subgroups

Complements

Maximal subgroups