Group #18079915 — subgroups

Subgroups — #18079915

Order 4864.

594 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14572659	C₂	1	1	yes	maximal, characteristic
2	#14563627	C₂	1	1	yes	maximal, characteristic
3	#14562320	C₂	1	2	yes	maximal, complemented
4	#14561538	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2542	C₂	1	1	yes	maximal, characteristic
6	D₄×C₁₉⋊C₈	—	2	4	no	—
7	#11926597	C₂²	1	2	yes	—
8	#11926568	C₂²	1	2	yes	—
9	C₂×#10597290	—	2	1	no	—
10	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
11	#11926313	—	2	1	no	—
12	#11926290	—	2	4	no	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#399	C₄	1	4	yes	—
17	C₁₉×#390	—	2	1	no	—
18	C₁₉×#384	—	2	1	no	—
19	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₁₉×C₂²⋊Q₈	—	4	8	no	—
26	C₄×D₄×C₁₉	—	2	2	no	—
27	C₄×D₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
34	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×#64520	—	2	2	no	—
38	C₂²×C₁₉⋊C₈	—	2	4	no	—
39	C₁₉×#95	C₂×C₄	1	2	yes	—
40	#10597290	—	4	2	no	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
46	C₄×C₁₉⋊C₈	—	2	2	no	—
47	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂×Q₈×C₁₉	—	4	4	no	—
49	C₂×Q₈×C₁₉	—	4	1	no	—
50	C₂×Q₈×C₁₉	—	4	1	no	—
51	C₂×D₄×C₁₉	—	2	2	no	—
52	C₂×D₄×C₁₉	—	2	2	no	—
53	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
54	C₂×D₄×C₁₉	Q₁₆	1	2	yes	—
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	4	4	no	—
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₄⋊C₄×C₁₉	—	2	4	no	—
65	C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₄⋊C₄×C₁₉	—	4	8	no	—
68	C₄⋊C₄×C₁₉	—	4	2	no	—
69	C₂²⋊C₄×C₁₉	—	2	4	no	—
70	C₂²⋊C₄×C₁₉	—	4	8	no	—
71	C₄²×C₁₉	—	4	2	no	—
72	C₄²×C₁₉	C₂×D₄	1	2	yes	—
73	C₄²×C₁₉	#41	1	2	yes	—
74	#64520	—	4	2	no	—
75	#64520	—	4	2	no	—
76	C₂×C₁₉⋊C₈	—	2	4	no	—
77	C₂×C₁₉⋊C₈	—	4	2	no	—
78	C₂×C₁₉⋊C₈	—	8	4	no	—
79	#9395	—	19	1	no	maximal, Sylow
80	C₂³×C₁₉	—	2	2	no	—
81	C₂³×C₁₉	—	2	2	no	—
82	C₂³×C₁₉	—	4	2	no	—
83	C₂³×C₁₉	—	4	2	no	—
84	C₂³×C₁₉	#103	1	4	yes	—
85	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	Q₈×C₁₉	—	8	2	no	—
87	Q₈×C₁₉	—	8	2	no	—
88	D₄×C₁₉	—	2	4	no	—
89	D₄×C₁₉	—	2	4	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	4	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	4	4	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	4	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	8	2	no	—
101	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
102	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#121	1	2	yes	—
104	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#135	1	2	yes	—
108	C₁₉⋊C₈	—	4	4	no	—
109	C₁₉⋊C₈	—	8	2	no	—
110	#2972	—	19	1	no	—
111	#2542	D₁₉	1	1	yes	characteristic
112	#1800	—	19	1	no	—
113	#1549	—	19	2	no	—
114	#1303	—	19	2	no	—
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	4	no	—
118	C₂²×C₁₉	—	4	4	no	—
119	C₂²×C₁₉	—	4	2	no	—
120	C₂²×C₁₉	—	4	2	no	—
121	C₂²×C₁₉	—	8	2	no	—
122	C₂²×C₁₉	#386	1	1	yes	characteristic
123	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
124	C₂²×C₁₉	#416	1	1	yes	characteristic
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	2	no	—
127	C₄×C₁₉	—	4	4	no	—
128	C₄×C₁₉	—	4	2	no	—
129	C₄×C₁₉	—	8	2	no	—
130	C₄×C₁₉	#453	1	2	yes	—
131	C₄×C₁₉	#465	1	2	yes	—
132	C₄×C₁₉	#467	1	2	yes	—
133	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
134	C₂×C₂²⋊Q₈	—	2	2	no	—
135	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
136	C₈×D₄	—	38	4	no	—
137	#431	—	19	2	no	—
138	#423	—	19	2	no	—
139	C₂×#100	—	38	1	no	—
140	C₂×C₂²⋊C₈	—	38	2	no	—
141	#399	Dic₁₉	1	4	yes	—
142	#390	—	2	1	no	—
143	#384	—	2	1	no	—
144	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
145	#343	—	38	1	no	—
146	#332	—	38	4	no	—
147	C₂×C₁₉	—	2	1	no	—
148	C₂×C₁₉	—	2	1	no	—
149	C₂×C₁₉	—	4	4	no	—
150	C₂×C₁₉	#1887	1	1	yes	characteristic
151	C₂×C₁₉	#1892	1	1	yes	characteristic
152	C₂×C₁₉	#1915	1	1	yes	characteristic
153	C₂²×Q₈	—	2	1	no	—
154	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
155	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
156	C₂×M₁₆	—	38	2	no	—
157	C₂²×C₈	—	38	4	no	—
158	C₄⋊Q₈	—	2	2	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₂²⋊Q₈	—	4	8	no	—
161	C₄×D₄	—	2	2	no	—
162	C₄×D₄	—	2	2	no	—
163	C₂×C₄⋊C₄	—	2	1	no	—
164	C₂×C₄⋊C₄	—	2	4	no	—
165	C₂×C₄⋊C₄	—	2	1	no	—
166	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
167	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
168	C₂×C₂²⋊C₄	—	2	4	no	—
169	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
170	C₂×C₄²	—	2	1	no	—
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	C₄⋊C₈	—	19	4	no	—
173	C₄⋊C₈	—	38	2	no	—
174	C₄⋊C₈	—	38	2	no	—
175	#100	—	76	2	no	—
176	C₂²⋊C₈	—	38	4	no	—
177	C₂²⋊C₈	—	38	2	no	—
178	C₄×C₈	—	38	2	no	—
179	#95	C₂×Dic₁₉	1	2	yes	—
180	C₁₉	#9395	1	1	yes	characteristic, complemented, Sylow
181	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
182	C₂×Q₈	—	4	4	no	—
183	C₂×Q₈	—	4	1	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×D₄	—	2	2	no	—
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	#64527	1	2	yes	—
188	C₂×D₄	#64528	1	2	yes	—
189	C₂²×C₄	—	2	2	no	—
190	C₂²×C₄	—	2	2	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	4	4	no	—
194	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
195	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
196	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
197	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
198	M₁₆	—	76	2	no	—
199	M₁₆	—	76	2	no	—
200	C₂×C₈	—	38	4	no	—
201	C₂×C₈	—	76	2	no	—
202	C₂×C₈	—	152	4	no	—
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	2	4	no	—
206	C₄⋊C₄	—	4	8	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₂²⋊C₄	—	2	4	no	—
209	C₂²⋊C₄	—	4	8	no	—
210	C₄²	—	4	2	no	—
211	C₄²	D₄×D₁₉	1	2	yes	—
212	C₄²	#64543	1	2	yes	—
213	C₂³	—	2	2	no	—
214	C₂³	—	2	2	no	—
215	C₂³	—	4	2	no	—
216	C₂³	—	4	2	no	—
217	C₂³	#10597292	1	4	yes	—
218	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
219	Q₈	—	8	2	no	—
220	Q₈	—	8	2	no	—
221	D₄	—	2	4	no	—
222	D₄	—	2	4	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	4	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	4	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	4	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	8	2	no	—
234	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
235	C₂×C₄	#10597381	1	1	yes	characteristic
236	C₂×C₄	#10597383	1	1	yes	characteristic
237	C₂×C₄	#10597385	1	2	yes	—
238	C₂×C₄	C₂×#64527	1	1	yes	characteristic
239	C₂×C₄	C₂×#64528	1	1	yes	characteristic
240	C₂×C₄	#10597396	1	2	yes	—
241	C₈	—	76	4	no	—
242	C₈	—	152	2	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	—	2	4	no	—
246	C₂²	—	4	4	no	—
247	C₂²	—	4	2	no	—
248	C₂²	—	4	2	no	—
249	C₂²	—	8	2	no	—
250	C₂²	#11926424	1	1	yes	characteristic
251	C₂²	C₂×#10597292	1	1	yes	characteristic
252	C₂²	#11926540	1	1	yes	characteristic
253	C₄	—	2	2	no	—
254	C₄	—	2	1	no	—
255	C₄	—	4	4	no	—
256	C₄	—	4	2	no	—
257	C₄	—	8	2	no	—
258	C₄	#11926711	1	2	yes	—
259	C₄	#11926775	1	2	yes	—
260	C₄	#11926783	1	2	yes	—
261	C₂	—	2	1	no	—
262	C₂	—	2	1	no	—
263	C₂	—	4	4	no	—
264	C₂	#14564034	1	1	yes	characteristic
265	C₂	#14564059	1	1	yes	characteristic
266	C₂	#14564188	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572659

C₂

yes

maximal, characteristic

#14563627

C₂

yes

maximal, characteristic

#14562320

C₂

yes

maximal, complemented

#14561538

C₂

yes

maximal, complemented

C₁₉×#2542

C₂

yes

maximal, characteristic

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597290

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926313

—

#11926290

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊Q₈

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#399

C₄

yes

—

C₁₉×#390

—

C₁₉×#384

—

C₄×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

C₂×C₄

yes

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

SD₁₆

yes

—

C₂×D₄×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

—

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

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

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9395

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#103

yes

—

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

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

C₄×D₄

yes

—

102

C₂×C₄×C₁₉

#120

yes

characteristic

103

C₂×C₄×C₁₉

#121

yes

—

104

C₂×C₄×C₁₉

#123

yes

characteristic

105

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

106

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

107

C₂×C₄×C₁₉

#135

yes

—

108

C₁₉⋊C₈

—

109

C₁₉⋊C₈

—

110

#2972

—

111

#2542

D₁₉

yes

characteristic

112

#1800

—

113

#1549

—

114

#1303

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

#386

yes

characteristic

123

C₂²×C₁₉

C₂×#103

yes

characteristic

124

C₂²×C₁₉

#416

yes

characteristic

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

#453

yes

—

131

C₄×C₁₉

#465

yes

—

132

C₄×C₁₉

#467

yes

—

133

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

134

C₂×C₂²⋊Q₈

—

135

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

136

C₈×D₄

—

137

#431

—

138

#423

—

139

C₂×#100

—

140

C₂×C₂²⋊C₈

—

141

#399

Dic₁₉

yes

—

142

#390

—

143

#384

—

144

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

145

#343

—

146

#332

—

147

C₂×C₁₉

—

148

C₂×C₁₉

—

149

C₂×C₁₉

—

150

C₂×C₁₉

#1887

yes

characteristic

151

C₂×C₁₉

#1892

yes

characteristic

152

C₂×C₁₉

#1915

yes

characteristic

153

C₂²×Q₈

—

154

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

155

C₂³×C₄

C₂²⋊D₁₉

yes

—

156

C₂×M₁₆

—

157

C₂²×C₈

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

—

160

C₂²⋊Q₈

—

161

C₄×D₄

—

162

C₄×D₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

167

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

168

C₂×C₂²⋊C₄

—

169

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

—

170

C₂×C₄²

—

171

C₂×C₄²

C₂²×D₁₉

yes

characteristic

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

#100

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

C₄×C₈

—

179

#95

C₂×Dic₁₉

yes

—

180

C₁₉

#9395

yes

characteristic, complemented, Sylow

181

C₂⁴

C₂²⋊Dic₁₉

yes

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

#64527

yes

—

188

C₂×D₄

#64528

yes

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

195

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

196

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

197

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

198

M₁₆

—

199

M₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

152

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₂²⋊C₄

—

210

C₄²

—

211

C₄²

D₄×D₁₉

yes

—

212

C₄²

#64543

yes

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

#10597292

yes

—

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

D₄×Dic₁₉

yes

—

235

C₂×C₄

#10597381

yes

characteristic

236

C₂×C₄

#10597383

yes

characteristic

237

C₂×C₄

#10597385

yes

—

238

C₂×C₄

C₂×#64527

yes

characteristic

239

C₂×C₄

C₂×#64528

yes

characteristic

240

C₂×C₄

#10597396

yes

—

241

C₈

—

242

C₈

—

152

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

#11926424

yes

characteristic

251

C₂²

C₂×#10597292

yes

characteristic

252

C₂²

#11926540

yes

characteristic

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

#11926711

yes

—

259

C₄

#11926775

yes

—

260

C₄

#11926783

yes

—

261

C₂

—

262

C₂

—

263

C₂

—

264

C₂

#14564034

yes

characteristic

265

C₂

#14564059

yes

characteristic

266

C₂

#14564188

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2542	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2542	D₁₉
hypocenter	C₁₉	#9395
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2542

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2542

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂²×D₄×C₁₉

D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2542

N	H ≅ G/N	type
3. #14562320	C₂	semidirect
4. #14561538	C₂	semidirect
180. C₁₉	#9395	semidirect

H ≅ G/N

type

3. #14562320

C₂

semidirect

4. #14561538

C₂

semidirect

180. C₁₉

#9395

semidirect

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

subgroup	index
#14572659	2
#14563627	2
#14562320	2
#14561538	2
C₁₉×#2542	2
#9395	19

subgroup

index

C₁₉×#2542

Subgroups — #18079915

Conjugacy classes of subgroups

Complements

Maximal subgroups