Group #18070854 — subgroups

Subgroups — #18070854

Order 4864.

468 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14563778	C₂	1	2	yes	maximal, complemented
2	#14561461	C₂	1	2	yes	maximal, complemented
3	#14561456	C₂	1	2	yes	maximal
4	C₄×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
5	#11926299	—	2	2	no	—
6	#11926299	—	2	2	no	—
7	#11926299	C₂²	1	4	yes	—
8	C₂×C₁₉×#124	C₄	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
11	C₁₉×#391	C₂²	1	1	yes	characteristic
12	C₁₉×#390	C₂²	1	1	yes	characteristic
13	C₁₉×#388	—	2	2	no	—
14	C₁₉×#382	C₄	1	1	yes	characteristic
15	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	—	2	1	no	—
20	C₁₉×#124	—	2	2	no	—
21	C₁₉×#124	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	4	2	no	—
23	C₄×D₄×C₁₉	—	4	2	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄²×C₁₉	—	2	1	no	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	D₄	1	2	yes	—
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₁₉⋊C₈	—	2	4	no	—
37	C₁₉×#95	—	2	2	no	—
38	C₁₉×#95	—	2	2	no	—
39	C₂⁴×C₁₉	—	2	1	no	—
40	C₂×Q₈×C₁₉	—	2	1	no	—
41	C₂×Q₈×C₁₉	—	4	1	no	—
42	C₂×Q₈×C₁₉	—	4	1	no	—
43	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
44	C₂×D₄×C₁₉	—	2	1	no	—
45	C₂×D₄×C₁₉	—	4	1	no	—
46	C₂×D₄×C₁₉	—	4	1	no	—
47	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
48	C₂²×C₄×C₁₉	—	2	1	no	—
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	—	4	4	no	—
52	C₂²×C₄×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₄⋊C₄×C₁₉	—	4	1	no	—
59	C₄⋊C₄×C₁₉	—	4	1	no	—
60	C₄⋊C₄×C₁₉	—	4	2	no	—
61	C₂²⋊C₄×C₁₉	—	2	8	no	—
62	C₂²⋊C₄×C₁₉	—	4	2	no	—
63	C₂²⋊C₄×C₁₉	—	4	4	no	—
64	C₄²×C₁₉	—	2	2	no	—
65	C₄²×C₁₉	—	2	1	no	—
66	C₄²×C₁₉	—	2	1	no	—
67	C₄²×C₁₉	—	2	4	no	—
68	C₄²×C₁₉	—	4	2	no	—
69	C₄²×C₁₉	—	4	1	no	—
70	C₄²×C₁₉	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	4	no	—
72	C₂×C₁₉⋊C₈	—	4	4	no	—
73	C₂×C₁₉⋊C₈	—	4	4	no	—
74	#7649	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	—	2	2	no	—
76	C₂³×C₁₉	—	4	1	no	—
77	C₂³×C₁₉	—	4	1	no	—
78	C₂³×C₁₉	—	4	2	no	—
79	C₂³×C₁₉	—	4	2	no	—
80	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	Q₈×C₁₉	—	4	2	no	—
82	Q₈×C₁₉	—	4	2	no	—
83	D₄×C₁₉	—	4	2	no	—
84	D₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	2	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	1	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	4	1	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	2	no	—
101	C₂×C₄×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	8	4	no	—
103	C₂×C₄×C₁₉	#100	1	2	yes	—
104	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#135	1	4	yes	—
107	C₁₉⋊C₈	—	8	4	no	—
108	C₄×#124	D₁₉	1	1	yes	characteristic
109	#1839	—	19	2	no	—
110	#1272	—	19	2	no	—
111	#1270	—	19	2	no	—
112	C₂²×C₁₉	—	4	2	no	—
113	C₂²×C₁₉	—	4	4	no	—
114	C₂²×C₁₉	—	8	1	no	—
115	C₂²×C₁₉	—	8	2	no	—
116	C₂²×C₁₉	—	8	1	no	—
117	C₂²×C₁₉	#407	1	1	yes	characteristic
118	C₂²×C₁₉	#410	1	1	yes	characteristic
119	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
120	C₂²×C₁₉	#416	1	2	yes	—
121	C₂²×C₁₉	#421	1	2	yes	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	4	no	—
125	C₄×C₁₉	—	2	2	no	—
126	C₄×C₁₉	—	4	1	no	—
127	C₄×C₁₉	—	4	2	no	—
128	C₄×C₁₉	—	4	2	no	—
129	C₄×C₁₉	—	8	1	no	—
130	C₄×C₁₉	—	8	1	no	—
131	C₂×#124	Dic₁₉	1	1	yes	characteristic
132	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic
133	C₂×C₄×D₄	Dic₁₉	1	1	yes	characteristic
134	#391	C₂×D₁₉	1	1	yes	characteristic
135	#390	C₂×D₁₉	1	1	yes	characteristic
136	#388	—	2	2	no	—
137	#382	Dic₁₉	1	1	yes	characteristic
138	C₄×C₂²⋊C₄	—	2	2	no	—
139	C₄³	C₂×D₁₉	1	1	yes	characteristic
140	#336	—	19	4	no	—
141	#336	—	38	2	no	—
142	#336	—	38	2	no	—
143	C₂×C₁₉	—	8	2	no	—
144	C₂×C₁₉	#1466	1	1	yes	characteristic
145	C₂×C₁₉	#1488	1	2	yes	—
146	C₂×C₁₉	#1521	1	2	yes	—
147	C₂×C₁₉	#1533	1	1	yes	characteristic
148	C₂×C₁₉	#1543	1	1	yes	characteristic
149	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
150	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
151	C₂³×C₄	—	2	1	no	—
152	C₂²×C₈	—	38	4	no	—
153	#124	—	2	2	no	—
154	#124	—	2	2	no	—
155	C₄×Q₈	—	4	2	no	—
156	C₄×D₄	—	4	2	no	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
159	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
160	C₂×C₂²⋊C₄	—	2	2	no	—
161	C₂×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₂²⋊C₄	—	2	2	no	—
163	C₂×C₄²	—	2	1	no	—
164	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
165	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
166	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
167	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
168	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
169	#95	—	2	2	no	—
170	#95	—	2	2	no	—
171	C₁₉	#7649	1	1	yes	characteristic, complemented, Sylow
172	C₂⁴	—	2	1	no	—
173	C₂×Q₈	—	2	1	no	—
174	C₂×Q₈	—	4	1	no	—
175	C₂×Q₈	—	4	1	no	—
176	C₂×Q₈	#64520	1	2	yes	—
177	C₂×D₄	—	2	1	no	—
178	C₂×D₄	—	4	1	no	—
179	C₂×D₄	—	4	1	no	—
180	C₂×D₄	#64520	1	2	yes	—
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	4	4	no	—
185	C₂²×C₄	—	4	2	no	—
186	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
187	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
188	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
189	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
190	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
191	C₂×C₈	—	76	4	no	—
192	C₂×C₈	—	76	4	no	—
193	C₂×C₈	—	76	4	no	—
194	C₄⋊C₄	—	4	1	no	—
195	C₄⋊C₄	—	4	1	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₂²⋊C₄	—	2	8	no	—
198	C₂²⋊C₄	—	4	2	no	—
199	C₂²⋊C₄	—	4	4	no	—
200	C₄²	—	2	4	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	1	no	—
203	C₄²	—	2	1	no	—
204	C₄²	—	4	2	no	—
205	C₄²	—	4	1	no	—
206	C₄²	—	4	2	no	—
207	C₂³	—	2	2	no	—
208	C₂³	—	4	2	no	—
209	C₂³	—	4	2	no	—
210	C₂³	—	4	1	no	—
211	C₂³	—	4	1	no	—
212	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
213	Q₈	—	4	2	no	—
214	Q₈	—	4	2	no	—
215	D₄	—	4	2	no	—
216	D₄	—	4	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	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	—	4	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	8	4	no	—
235	C₂×C₄	#10597290	1	2	yes	—
236	C₂×C₄	C₂×#64520	1	1	yes	characteristic
237	C₂×C₄	C₂×#64520	1	1	yes	characteristic
238	C₂×C₄	#10597396	1	4	yes	—
239	C₈	—	152	4	no	—
240	C₂²	—	4	4	no	—
241	C₂²	—	4	2	no	—
242	C₂²	—	8	2	no	—
243	C₂²	—	8	1	no	—
244	C₂²	—	8	1	no	—
245	C₂²	#11926508	1	1	yes	characteristic
246	C₂²	#11926518	1	1	yes	characteristic
247	C₂²	C₂×#10597290	1	1	yes	characteristic
248	C₂²	#11926540	1	2	yes	—
249	C₂²	#11926561	1	2	yes	—
250	C₄	—	2	4	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	2	2	no	—
254	C₄	—	4	2	no	—
255	C₄	—	4	2	no	—
256	C₄	—	4	1	no	—
257	C₄	—	8	1	no	—
258	C₄	—	8	1	no	—
259	C₂	—	8	2	no	—
260	C₂	#14561976	1	1	yes	characteristic
261	C₂	#14562069	1	2	yes	—
262	C₂	#14562212	1	2	yes	—
263	C₂	#14562259	1	1	yes	characteristic
264	C₂	#14562297	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563778

C₂

yes

maximal, complemented

#14561461

C₂

yes

maximal, complemented

#14561456

C₂

yes

maximal

C₄×C₁₉×#124

C₂

yes

maximal, characteristic

#11926299

—

#11926299

—

#11926299

C₂²

yes

—

C₂×C₁₉×#124

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₄×D₄×C₁₉

C₄

yes

characteristic

C₁₉×#391

C₂²

yes

characteristic

C₁₉×#390

C₂²

yes

characteristic

C₁₉×#388

—

C₁₉×#382

C₄

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

—

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

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

M₁₆

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

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7649

—

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

—

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

#100

yes

—

104

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

105

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

106

C₂×C₄×C₁₉

#135

yes

—

107

C₁₉⋊C₈

—

108

C₄×#124

D₁₉

yes

characteristic

109

#1839

—

110

#1272

—

111

#1270

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

#407

yes

characteristic

118

C₂²×C₁₉

#410

yes

characteristic

119

C₂²×C₁₉

C₂×#100

yes

characteristic

120

C₂²×C₁₉

#416

yes

—

121

C₂²×C₁₉

#421

yes

—

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

—

131

C₂×#124

Dic₁₉

yes

characteristic

132

C₂×C₄×Q₈

Dic₁₉

yes

characteristic

133

C₂×C₄×D₄

Dic₁₉

yes

characteristic

134

#391

C₂×D₁₉

yes

characteristic

135

#390

C₂×D₁₉

yes

characteristic

136

#388

—

137

#382

Dic₁₉

yes

characteristic

138

C₄×C₂²⋊C₄

—

139

C₄³

C₂×D₁₉

yes

characteristic

140

#336

—

141

#336

—

142

#336

—

143

C₂×C₁₉

—

144

C₂×C₁₉

#1466

yes

characteristic

145

C₂×C₁₉

#1488

yes

—

146

C₂×C₁₉

#1521

yes

—

147

C₂×C₁₉

#1533

yes

characteristic

148

C₂×C₁₉

#1543

yes

characteristic

149

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

150

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

151

C₂³×C₄

—

152

C₂²×C₈

—

153

#124

—

154

#124

—

155

C₄×Q₈

—

156

C₄×D₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

159

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

160

C₂×C₂²⋊C₄

—

161

C₂×C₂²⋊C₄

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₄²

—

164

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

165

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

166

C₂×C₄²

C₂²⋊D₁₉

yes

—

167

C₂×C₄²

C₂²⋊D₁₉

yes

—

168

C₂×C₄²

C₂²×D₁₉

yes

characteristic

169

#95

—

170

#95

—

171

C₁₉

#7649

yes

characteristic, complemented, Sylow

172

C₂⁴

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

#64520

yes

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

#64520

yes

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

187

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

188

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

189

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

190

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₂²⋊C₄

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

213

Q₈

—

214

Q₈

—

215

D₄

—

216

D₄

—

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

#10597290

yes

—

236

C₂×C₄

C₂×#64520

yes

characteristic

237

C₂×C₄

C₂×#64520

yes

characteristic

238

C₂×C₄

#10597396

yes

—

239

C₈

—

152

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

#11926508

yes

characteristic

246

C₂²

#11926518

yes

characteristic

247

C₂²

C₂×#10597290

yes

characteristic

248

C₂²

#11926540

yes

—

249

C₂²

#11926561

yes

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₂

—

260

C₂

#14561976

yes

characteristic

261

C₂

#14562069

yes

—

262

C₂

#14562212

yes

—

263

C₂

#14562259

yes

characteristic

264

C₂

#14562297

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
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	#7649
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

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 ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#124

N	H ≅ G/N	type
1. #14563778	C₂	semidirect
2. #14561461	C₂	semidirect
171. C₁₉	#7649	semidirect

H ≅ G/N

type

1. #14563778

C₂

semidirect

2. #14561461

C₂

semidirect

171. C₁₉

#7649

semidirect

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

subgroup	index
#14563778	2
#14561461	2
#14561456	2
C₄×C₁₉×#124	2
#7649	19

subgroup

index

C₄×C₁₉×#124

Subgroups — #18070854

Conjugacy classes of subgroups

Complements

Maximal subgroups