Group #18076978 — subgroups

Subgroups — #18076978

Order 4864.

644 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 155 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	#14564442	C₂	1	1	yes	maximal, characteristic
2	#14564398	C₂	1	2	yes	maximal, complemented
3	C₂×#11926288	C₂	1	1	yes	maximal, characteristic
4	#14561476	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2366	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597265	—	2	2	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×#10597289	—	2	2	no	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926414	C₂²	1	1	yes	characteristic
11	#11926306	—	2	2	no	—
12	#11926288	C₄	1	4	yes	complemented
13	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₉	—	2	2	no	—
15	C₁₉×#390	—	2	2	no	—
16	C₁₉×#386	—	2	2	no	—
17	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×D₄×C₁₉	—	2	2	no	—
19	C₂²×D₄×C₁₉	D₄	1	2	yes	—
20	C₂³×C₄×C₁₉	—	2	2	no	—
21	C₁₉×#127	—	2	2	no	—
22	C₁₉×#127	C₂×C₄	1	2	yes	—
23	C₁₉×#127	Q₈	1	2	yes	—
24	C₄×D₄×C₁₉	—	4	4	no	—
25	C₄×D₄×C₁₉	—	4	4	no	—
26	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
27	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
28	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄²×C₁₉	—	2	2	no	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	—	2	2	no	—
34	C₂²×C₁₉⋊C₈	—	2	1	no	—
35	C₂²×C₁₉⋊C₈	—	2	2	no	—
36	C₁₉×#95	—	2	2	no	—
37	#10597289	—	4	4	no	—
38	#10597265	—	4	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	complemented
41	C₄×C₁₉⋊C₈	—	2	2	no	—
42	C₂⁴×C₁₉	—	2	2	no	—
43	C₂×D₄×C₁₉	—	2	4	no	—
44	C₂×D₄×C₁₉	—	2	4	no	—
45	C₂×D₄×C₁₉	—	2	2	no	—
46	C₂×D₄×C₁₉	—	4	2	no	—
47	C₂×D₄×C₁₉	—	4	2	no	—
48	C₂×D₄×C₁₉	—	4	2	no	—
49	C₂×D₄×C₁₉	—	4	2	no	—
50	C₂×D₄×C₁₉	—	4	2	no	—
51	C₂×D₄×C₁₉	—	4	2	no	—
52	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	—	4	8	no	—
56	C₂²×C₄×C₁₉	—	8	2	no	—
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
59	C₂²×Dic₁₉	—	4	1	no	—
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	SD₁₆	1	4	yes	—
64	C₂²⋊C₄×C₁₉	—	4	8	no	—
65	C₂²⋊C₄×C₁₉	—	8	2	no	—
66	C₄²×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	—	4	2	no	—
68	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
70	C₄²×C₁₉	#41	1	2	yes	—
71	C₄⋊Dic₁₉	—	4	2	no	—
72	C₄⋊Dic₁₉	—	4	2	no	—
73	C₄⋊Dic₁₉	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	2	2	no	—
75	C₂×C₁₉⋊C₈	—	2	4	no	—
76	C₂×C₁₉⋊C₈	—	4	1	no	—
77	C₂×C₁₉⋊C₈	—	4	1	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	#8924	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	—	2	4	no	—
82	C₂³×C₁₉	—	4	4	no	—
83	C₂³×C₁₉	—	4	4	no	—
84	C₂³×C₁₉	—	4	2	no	—
85	C₂³×C₁₉	—	4	2	no	—
86	C₂³×C₁₉	#120	1	1	yes	characteristic
87	D₄×C₁₉	—	4	4	no	—
88	D₄×C₁₉	—	4	4	no	—
89	D₄×C₁₉	—	4	4	no	—
90	D₄×C₁₉	—	4	4	no	—
91	D₄×C₁₉	—	4	4	no	—
92	D₄×C₁₉	—	8	2	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	4	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	8	8	no	—
102	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
104	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
105	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
107	C₂×C₄×C₁₉	#135	1	2	yes	—
108	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
109	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
110	C₂×Dic₁₉	—	8	2	no	—
111	C₂×Dic₁₉	—	8	1	no	—
112	C₁₉⋊C₈	—	4	2	no	—
113	C₁₉⋊C₈	—	4	4	no	—
114	#2366	D₁₉	1	1	yes	characteristic
115	#1957	—	19	1	no	—
116	#1948	—	19	2	no	—
117	C₂×#331	—	19	1	no	—
118	#1279	—	19	2	no	—
119	C₂²×C₁₉	—	4	4	no	—
120	C₂²×C₁₉	—	4	8	no	—
121	C₂²×C₁₉	—	8	2	no	—
122	C₂²×C₁₉	—	8	2	no	—
123	C₂²×C₁₉	—	8	4	no	—
124	C₂²×C₁₉	#385	1	1	yes	characteristic
125	C₂²×C₁₉	#449	1	2	yes	—
126	C₂²×C₁₉	#450	1	2	yes	—
127	C₂²×C₁₉	#453	1	1	yes	characteristic
128	C₂²×C₁₉	#455	1	1	yes	characteristic
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	4	4	no	—
132	C₄×C₁₉	—	8	2	no	—
133	C₄×C₁₉	C₄×SD₁₆	1	2	yes	—
134	C₄×C₁₉	#442	1	2	yes	—
135	C₄×C₁₉	#476	1	2	yes	—
136	C₄×C₁₉	#478	1	2	yes	—
137	Dic₁₉	—	16	1	no	—
138	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
139	C₂×C₄×D₄	—	2	2	no	—
140	C₂×#106	—	38	2	no	—
141	C₂×C₄⋊C₈	—	19	2	no	—
142	C₂×#102	—	38	2	no	—
143	C₂×C₄×C₈	—	19	1	no	—
144	#390	—	2	2	no	—
145	#386	—	2	2	no	—
146	#384	—	19	1	no	—
147	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
148	#340	—	38	2	no	—
149	#331	—	19	4	no	—
150	C₂×C₁₉	—	8	4	no	—
151	C₂×C₁₉	#1620	1	1	yes	characteristic
152	C₂×C₁₉	#1629	1	1	yes	characteristic
153	C₂×C₁₉	#1642	1	2	yes	—
154	C₂×C₁₉	#1856	1	1	yes	characteristic
155	C₂×C₁₉	#1864	1	2	yes	—
156	C₂²×D₄	—	2	2	no	—
157	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
158	C₂³×C₄	—	2	2	no	—
159	C₂²×C₈	—	38	2	no	—
160	C₂²×C₈	—	38	1	no	—
161	#127	—	2	2	no	—
162	#127	Dic₃₈	1	2	yes	—
163	#127	C₄×D₁₉	1	2	yes	—
164	C₄×D₄	—	4	4	no	—
165	C₄×D₄	—	4	4	no	—
166	C₂×C₄⋊C₄	—	38	2	no	—
167	C₂×C₄⋊C₄	—	38	1	no	—
168	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
169	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
170	C₂×C₂²⋊C₄	—	2	4	no	—
171	C₂×C₂²⋊C₄	—	2	2	no	—
172	C₂×C₄²	—	2	2	no	—
173	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
174	#106	—	76	4	no	—
175	C₄⋊C₈	—	19	4	no	—
176	C₄⋊C₈	—	38	2	no	—
177	#102	—	76	4	no	—
178	C₄×C₈	—	38	2	no	—
179	#95	—	2	2	no	—
180	C₁₉	#8924	1	1	yes	characteristic, complemented, Sylow
181	C₂⁴	—	2	2	no	—
182	C₂×D₄	—	2	4	no	—
183	C₂×D₄	—	2	4	no	—
184	C₂×D₄	—	2	2	no	—
185	C₂×D₄	—	4	2	no	—
186	C₂×D₄	—	4	2	no	—
187	C₂×D₄	—	4	2	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂×D₄	—	4	2	no	—
190	C₂×D₄	—	4	2	no	—
191	C₂×D₄	Dic₁₉⋊C₄	1	4	yes	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	4	8	no	—
195	C₂²×C₄	—	8	2	no	—
196	C₂²×C₄	—	76	1	no	—
197	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
198	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
199	C₂×C₈	—	38	2	no	—
200	C₂×C₈	—	38	4	no	—
201	C₂×C₈	—	76	1	no	—
202	C₂×C₈	—	76	2	no	—
203	C₂×C₈	—	76	2	no	—
204	C₂×C₈	—	76	1	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	2	2	no	—
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	76	2	no	—
209	C₄⋊C₄	—	76	2	no	—
210	C₄⋊C₄	—	76	2	no	—
211	C₄⋊C₄	#64526	1	4	yes	—
212	C₂²⋊C₄	—	4	8	no	—
213	C₂²⋊C₄	—	8	2	no	—
214	C₄²	—	4	2	no	—
215	C₄²	—	4	2	no	—
216	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
217	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
218	C₄²	#64541	1	2	yes	—
219	C₂³	—	2	4	no	—
220	C₂³	—	4	4	no	—
221	C₂³	—	4	4	no	—
222	C₂³	—	4	2	no	—
223	C₂³	—	4	2	no	—
224	C₂³	#10597399	1	1	yes	characteristic
225	D₄	—	4	4	no	—
226	D₄	—	4	4	no	—
227	D₄	—	4	4	no	—
228	D₄	—	4	4	no	—
229	D₄	—	4	4	no	—
230	D₄	—	8	2	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	8	8	no	—
240	C₂×C₄	—	152	2	no	—
241	C₂×C₄	—	152	1	no	—
242	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
243	C₂×C₄	#10597370	1	2	yes	—
244	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
245	C₂×C₄	#10597375	1	1	yes	characteristic
246	C₂×C₄	#10597378	1	2	yes	—
247	C₂×C₄	C₂×#64526	1	2	yes	—
248	C₂×C₄	#10597395	1	2	yes	—
249	C₂×C₄	#10597396	1	2	yes	—
250	C₈	—	76	2	no	—
251	C₈	—	76	4	no	—
252	C₂²	—	4	4	no	—
253	C₂²	—	4	8	no	—
254	C₂²	—	8	4	no	—
255	C₂²	—	8	2	no	—
256	C₂²	—	8	2	no	—
257	C₂²	#11926417	1	1	yes	characteristic
258	C₂²	#11926689	1	2	yes	—
259	C₂²	#11926695	1	2	yes	—
260	C₂²	#11926712	1	1	yes	characteristic
261	C₂²	#11926722	1	1	yes	characteristic
262	C₄	—	2	1	no	—
263	C₄	—	2	1	no	—
264	C₄	—	4	4	no	—
265	C₄	—	8	2	no	—
266	C₄	—	304	1	no	—
267	C₄	C₄×#64526	1	2	yes	—
268	C₄	#11926654	1	2	yes	—
269	C₄	#11926834	1	2	yes	—
270	C₄	#11926844	1	2	yes	—
271	C₂	—	8	4	no	—
272	C₂	#14562694	1	1	yes	characteristic
273	C₂	#14562751	1	1	yes	characteristic
274	C₂	#14562835	1	2	yes	—
275	C₂	#14563845	1	1	yes	characteristic
276	C₂	#14563896	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564442

C₂

yes

maximal, characteristic

#14564398

C₂

yes

maximal, complemented

C₂×#11926288

C₂

yes

maximal, characteristic

#14561476

C₂

yes

maximal, complemented

C₁₉×#2366

C₂

yes

maximal, characteristic

C₂×#10597265

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597289

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926414

C₂²

yes

characteristic

#11926306

—

#11926288

C₄

yes

complemented

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

—

C₁₉×#390

—

C₁₉×#386

—

C₄×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

—

C₁₉×#127

—

C₁₉×#127

C₂×C₄

yes

—

C₁₉×#127

Q₈

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

#10597289

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

complemented

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

SD₁₆

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8924

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

103

C₂×C₄×C₁₉

C₄×D₄

yes

—

104

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

105

C₂×C₄×C₁₉

#123

yes

characteristic

106

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

107

C₂×C₄×C₁₉

#135

yes

—

108

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

109

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

110

C₂×Dic₁₉

—

111

C₂×Dic₁₉

—

112

C₁₉⋊C₈

—

113

C₁₉⋊C₈

—

114

#2366

D₁₉

yes

characteristic

115

#1957

—

116

#1948

—

117

C₂×#331

—

118

#1279

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

#385

yes

characteristic

125

C₂²×C₁₉

#449

yes

—

126

C₂²×C₁₉

#450

yes

—

127

C₂²×C₁₉

#453

yes

characteristic

128

C₂²×C₁₉

#455

yes

characteristic

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

C₄×SD₁₆

yes

—

134

C₄×C₁₉

#442

yes

—

135

C₄×C₁₉

#476

yes

—

136

C₄×C₁₉

#478

yes

—

137

Dic₁₉

—

138

C₂×#127

C₂×D₁₉

yes

characteristic

139

C₂×C₄×D₄

—

140

C₂×#106

—

141

C₂×C₄⋊C₈

—

142

C₂×#102

—

143

C₂×C₄×C₈

—

144

#390

—

145

#386

—

146

#384

—

147

C₄×C₄⋊C₄

C₂×D₁₉

yes

—

148

#340

—

149

#331

—

150

C₂×C₁₉

—

151

C₂×C₁₉

#1620

yes

characteristic

152

C₂×C₁₉

#1629

yes

characteristic

153

C₂×C₁₉

#1642

yes

—

154

C₂×C₁₉

#1856

yes

characteristic

155

C₂×C₁₉

#1864

yes

—

156

C₂²×D₄

—

157

C₂²×D₄

C₂²⋊D₁₉

yes

—

158

C₂³×C₄

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

#127

—

162

#127

Dic₃₈

yes

—

163

#127

C₄×D₁₉

yes

—

164

C₄×D₄

—

165

C₄×D₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

169

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

170

C₂×C₂²⋊C₄

—

171

C₂×C₂²⋊C₄

—

172

C₂×C₄²

—

173

C₂×C₄²

C₂²×D₁₉

yes

characteristic

174

#106

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

#102

—

178

C₄×C₈

—

179

#95

—

180

C₁₉

#8924

yes

characteristic, complemented, Sylow

181

C₂⁴

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

Dic₁₉⋊C₄

yes

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

198

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

#64526

yes

—

212

C₂²⋊C₄

—

213

C₂²⋊C₄

—

214

C₄²

—

215

C₄²

—

216

C₄²

C₂×Dic₃₈

yes

characteristic

217

C₄²

C₂×C₄×D₁₉

yes

characteristic

218

C₄²

#64541

yes

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

#10597399

yes

characteristic

225

D₄

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

230

D₄

—

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

—

152

—

241

C₂×C₄

—

152

—

242

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

243

C₂×C₄

#10597370

yes

—

244

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

245

C₂×C₄

#10597375

yes

characteristic

246

C₂×C₄

#10597378

yes

—

247

C₂×C₄

C₂×#64526

yes

—

248

C₂×C₄

#10597395

yes

—

249

C₂×C₄

#10597396

yes

—

250

C₈

—

251

C₈

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

#11926417

yes

characteristic

258

C₂²

#11926689

yes

—

259

C₂²

#11926695

yes

—

260

C₂²

#11926712

yes

characteristic

261

C₂²

#11926722

yes

characteristic

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

—

304

—

267

C₄

C₄×#64526

yes

—

268

C₄

#11926654

yes

—

269

C₄

#11926834

yes

—

270

C₄

#11926844

yes

—

271

C₂

—

272

C₂

#14562694

yes

characteristic

273

C₂

#14562751

yes

characteristic

274

C₂

#14562835

yes

—

275

C₂

#14563845

yes

characteristic

276

C₂

#14563896

yes

—

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2366	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2366	D₁₉
hypocenter	C₁₉	#8924
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2366

subgroup

G/H

center

C₂³

#10597399

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2366

C₂

socle

C₂³×C₁₉

#120

prime radical

C₂×C₁₉×#127

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2366

N	H ≅ G/N	type
2. #14564398	C₂	semidirect
4. #14561476	C₂	semidirect
12. #11926288	C₄	semidirect
40. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
180. C₁₉	#8924	semidirect

H ≅ G/N

type

2. #14564398

C₂

semidirect

4. #14561476

C₂

semidirect

12. #11926288

C₄

semidirect

40. C₄⋊(C₁₉⋊C₈)

C₂×C₄

semidirect

180. C₁₉

#8924

semidirect

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

subgroup	index
#14564442	2
#14564398	2
C₂×#11926288	2
#14561476	2
C₁₉×#2366	2
#8924	19

subgroup

index

C₁₉×#2366

Subgroups — #18076978

Conjugacy classes of subgroups

Complements

Maximal subgroups