Group #18075694 — subgroups

Subgroups — #18075694

Order 4864.

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

normal subgroups only

This group has 434 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	C₂×#11926623	C₂	1	1	yes	maximal, characteristic
2	#14563773	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562061	C₂	1	2	yes	maximal
4	#14561531	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#64515	—	2	1	no	—
7	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
8	#11926623	—	2	1	no	—
9	#11926623	—	2	1	no	—
10	#11926623	C₄	1	2	yes	—
11	#11926623	C₄	1	2	yes	—
12	#11926568	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
15	#11926309	—	2	1	no	—
16	#11926309	—	2	1	no	—
17	#11926273	—	2	4	no	—
18	C₁₉×#431	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#335	—	2	1	no	—
21	C₁₉×#334	—	2	1	no	—
22	C₂²×D₇₆	Q₈	1	1	yes	characteristic
23	C₂²×C₄×D₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
28	C₂×C₄⋊Dic₁₉	Q₈	1	1	yes	characteristic
29	C₂×#64520	—	2	2	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	C₂×#64515	—	2	2	no	—
32	C₂×#64515	—	2	2	no	—
33	C₂×#64515	—	4	4	no	—
34	C₄×D₇₆	—	2	1	no	—
35	C₄×D₇₆	—	2	1	no	—
36	C₄×D₇₆	C₂×C₄	1	2	yes	—
37	C₄×D₇₆	D₄	1	2	yes	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×C₂²⋊C₈	—	2	2	no	—
40	C₄×C₈×C₁₉	—	2	2	no	—
41	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	(C₂×D₁₉)⋊C₈	—	2	2	no	—
46	(C₂×D₁₉)⋊C₈	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
51	C₂³×D₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂²×Dic₁₉	—	2	1	no	—
56	C₂×D₇₆	—	2	1	no	—
57	C₂×D₇₆	—	4	2	no	—
58	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
59	C₂×C₄×D₁₉	—	2	2	no	—
60	C₂×C₄×D₁₉	—	2	2	no	—
61	C₂×C₄×D₁₉	—	4	2	no	—
62	C₂×C₄×D₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	(C₂×D₁₉)⋊C₄	—	2	2	no	—
75	(C₂×D₁₉)⋊C₄	—	2	2	no	—
76	C₄⋊Dic₁₉	—	2	1	no	—
77	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
78	#64520	—	4	2	no	—
79	#64520	—	4	2	no	—
80	C₂×C₁₉⋊C₈	—	2	2	no	—
81	C₂×C₁₉⋊C₈	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	#64515	—	4	4	no	—
84	#64515	—	4	4	no	—
85	#8664	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂²×D₁₉	—	2	2	no	—
88	C₂²×D₁₉	—	4	2	no	—
89	C₂²×D₁₉	—	4	2	no	—
90	C₂²×D₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#135	1	2	yes	—
100	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
101	C₂×Dic₁₉	—	2	2	no	—
102	C₂×Dic₁₉	—	4	2	no	—
103	D₇₆	—	2	4	no	—
104	D₇₆	—	4	2	no	—
105	C₄×D₁₉	—	4	2	no	—
106	C₄×D₁₉	—	4	2	no	—
107	C₄×D₁₉	—	4	4	no	—
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	2	1	no	—
112	C₈×C₁₉	—	8	2	no	—
113	C₁₉⋊C₈	—	4	2	no	—
114	C₁₉⋊C₈	—	8	2	no	—
115	C₂×#436	—	19	1	no	—
116	#1837	—	19	1	no	—
117	#1564	D₁₉	1	1	yes	characteristic, complemented
118	#1486	—	19	2	no	—
119	#1301	—	19	2	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	#380	1	1	yes	characteristic
123	C₂²×C₁₉	#478	1	2	yes	—
124	C₂×D₁₉	—	4	2	no	—
125	C₂×D₁₉	—	4	2	no	—
126	C₂×D₁₉	—	4	2	no	—
127	C₂×D₁₉	—	8	4	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	#416	1	1	yes	characteristic
132	C₄×C₁₉	#418	1	1	yes	characteristic
133	C₄×C₁₉	#430	1	2	yes	—
134	C₄×C₁₉	#463	1	2	yes	—
135	Dic₁₉	—	4	2	no	—
136	C₂²×M₁₆	—	38	1	no	—
137	C₂×C₄×D₄	—	19	1	no	—
138	#436	—	19	2	no	—
139	#436	—	19	2	no	—
140	#436	—	38	1	no	—
141	#436	—	38	1	no	—
142	#431	C₂×D₁₉	1	2	yes	—
143	#423	—	19	2	no	—
144	C₂×C₄⋊C₈	—	19	1	no	—
145	C₂×C₂²⋊C₈	—	38	1	no	—
146	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
147	#341	—	38	1	no	—
148	#341	—	38	1	no	—
149	#335	—	2	1	no	—
150	#334	—	2	1	no	—
151	D₄⋊C₈	—	38	4	no	—
152	C₂×C₁₉	—	2	2	no	—
153	C₂×C₁₉	#1804	1	1	yes	characteristic
154	C₂×C₁₉	#1811	1	1	yes	characteristic
155	C₂×C₁₉	#1814	1	1	yes	characteristic
156	D₁₉	—	8	2	no	—
157	C₂²×D₄	—	19	1	no	—
158	C₂³×C₄	—	38	1	no	—
159	C₂×M₁₆	—	38	2	no	—
160	C₂×M₁₆	—	38	2	no	—
161	C₂×M₁₆	—	38	2	no	—
162	C₂×M₁₆	—	76	4	no	—
163	C₂²×C₈	—	38	1	no	—
164	C₂²×C₈	D₇₆	1	1	yes	characteristic
165	C₂²×C₈	D₇₆	1	1	yes	characteristic
166	C₄×D₄	—	19	2	no	—
167	C₄×D₄	—	19	2	no	—
168	C₄×D₄	—	38	1	no	—
169	C₄×D₄	—	38	1	no	—
170	C₂×C₄⋊C₄	—	19	1	no	—
171	C₂×C₂²⋊C₄	—	38	1	no	—
172	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	19	2	no	—
175	C₄⋊C₈	—	38	2	no	—
176	C₄⋊C₈	—	38	2	no	—
177	C₄⋊C₈	—	38	1	no	—
178	C₂²⋊C₈	—	2	2	no	—
179	C₂²⋊C₈	—	38	2	no	—
180	C₂²⋊C₈	—	38	2	no	—
181	C₄×C₈	—	2	2	no	—
182	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
183	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
184	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
185	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
186	C₁₉	#8664	1	1	yes	characteristic, complemented, Sylow
187	C₂⁴	—	38	1	no	—
188	C₂×D₄	—	19	2	no	—
189	C₂×D₄	—	38	1	no	—
190	C₂×D₄	—	76	2	no	—
191	C₂²×C₄	—	38	1	no	—
192	C₂²×C₄	—	38	2	no	—
193	C₂²×C₄	—	38	2	no	—
194	C₂²×C₄	—	76	2	no	—
195	C₂²×C₄	—	76	2	no	—
196	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
197	C₂²×C₄	#64543	1	1	yes	characteristic
198	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
199	M₁₆	—	76	4	no	—
200	M₁₆	—	76	4	no	—
201	M₁₆	—	76	2	no	—
202	M₁₆	—	76	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	4	2	no	—
206	C₂×C₈	—	38	2	no	—
207	C₂×C₈	—	76	2	no	—
208	C₂×C₈	—	76	2	no	—
209	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
210	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
211	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
212	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
213	C₄⋊C₄	—	19	2	no	—
214	C₄⋊C₄	—	38	1	no	—
215	C₂²⋊C₄	—	38	2	no	—
216	C₂²⋊C₄	—	38	2	no	—
217	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
218	C₄²	D₄×D₁₉	1	1	yes	characteristic
219	C₄²	#64545	1	1	yes	characteristic
220	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
221	C₂³	—	38	2	no	—
222	C₂³	—	76	2	no	—
223	C₂³	—	76	2	no	—
224	C₂³	—	76	2	no	—
225	C₂³	#10597343	1	1	yes	characteristic
226	D₄	—	38	4	no	—
227	D₄	—	76	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	38	2	no	—
231	C₂×C₄	—	76	2	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	—	76	2	no	—
234	C₂×C₄	—	76	4	no	—
235	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
236	C₂×C₄	#10597338	1	1	yes	characteristic
237	C₂×C₄	#10597341	1	1	yes	characteristic
238	C₂×C₄	#10597350	1	2	yes	—
239	C₂×C₄	#10597354	1	2	yes	—
240	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
241	C₂×C₄	#10597384	1	1	yes	characteristic
242	C₂×C₄	#10597392	1	1	yes	characteristic
243	C₈	—	2	1	no	—
244	C₈	—	2	1	no	—
245	C₈	—	2	1	no	—
246	C₈	—	2	1	no	—
247	C₈	—	8	2	no	—
248	C₈	—	76	2	no	—
249	C₈	—	152	2	no	—
250	C₂²	—	2	1	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	76	2	no	—
253	C₂²	—	76	2	no	—
254	C₂²	—	76	2	no	—
255	C₂²	—	152	4	no	—
256	C₂²	#11926401	1	1	yes	characteristic
257	C₂²	#11926845	1	2	yes	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	76	2	no	—
262	C₄	#11926541	1	1	yes	characteristic
263	C₄	#11926550	1	1	yes	characteristic
264	C₄	#11926591	1	2	yes	—
265	C₄	#11926760	1	2	yes	—
266	C₂	—	2	2	no	—
267	C₂	—	152	2	no	—
268	C₂	#14563646	1	1	yes	characteristic
269	C₂	#14563674	1	1	yes	characteristic
270	C₂	#14563686	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926623

C₂

yes

maximal, characteristic

#14563773

C₂

yes

maximal, characteristic, complemented

#14562061

C₂

yes

maximal

#14561531

C₂

yes

maximal, complemented

C₁₉×#1564

C₂

yes

maximal, characteristic, complemented

C₂²×#64515

—

C₂×C₄×D₇₆

C₂²

yes

—

—

C₄

yes

—

#11926623

C₄

yes

—

#11926568

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₈

—

#11926309

—

#11926309

—

#11926273

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂²×D₇₆

Q₈

yes

characteristic

C₂²×C₄×D₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

Q₈

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂×#64515

—

C₂×#64515

—

C₂×#64515

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

C₂×C₄

yes

—

C₄×D₇₆

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

(C₂×D₁₉)⋊C₈

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₄⋊C₄

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

—

—

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

100

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

D₇₆

—

104

D₇₆

—

105

C₄×D₁₉

—

106

C₄×D₁₉

—

107

C₄×D₁₉

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

C₂×#436

—

116

#1837

—

117

#1564

D₁₉

yes

characteristic, complemented

118

#1486

—

119

#1301

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

#380

yes

characteristic

123

C₂²×C₁₉

#478

yes

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₂×D₁₉

—

127

C₂×D₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

#416

yes

characteristic

132

C₄×C₁₉

#418

yes

characteristic

133

C₄×C₁₉

#430

yes

—

134

C₄×C₁₉

#463

yes

—

135

Dic₁₉

—

136

C₂²×M₁₆

—

137

C₂×C₄×D₄

—

138

#436

—

139

#436

—

140

#436

—

141

#436

—

142

#431

C₂×D₁₉

yes

—

143

#423

—

144

C₂×C₄⋊C₈

—

145

C₂×C₂²⋊C₈

—

146

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

147

#341

—

148

#341

—

149

#335

—

150

#334

—

151

D₄⋊C₈

—

152

C₂×C₁₉

—

153

C₂×C₁₉

#1804

yes

characteristic

154

C₂×C₁₉

#1811

yes

characteristic

155

C₂×C₁₉

#1814

yes

characteristic

156

D₁₉

—

157

C₂²×D₄

—

158

C₂³×C₄

—

159

C₂×M₁₆

—

160

C₂×M₁₆

—

161

C₂×M₁₆

—

162

C₂×M₁₆

—

163

C₂²×C₈

—

164

C₂²×C₈

D₇₆

yes

characteristic

165

C₂²×C₈

D₇₆

yes

characteristic

166

C₄×D₄

—

167

C₄×D₄

—

168

C₄×D₄

—

169

C₄×D₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₂²⋊C₄

—

172

C₂×C₄²

C₂²×D₁₉

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₂²⋊C₈

—

179

C₂²⋊C₈

—

180

C₂²⋊C₈

—

181

C₄×C₈

—

182

C₄×C₈

C₄×D₁₉

yes

characteristic

183

C₄×C₈

C₄×D₁₉

yes

characteristic

184

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

185

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

186

C₁₉

#8664

yes

characteristic, complemented, Sylow

187

C₂⁴

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂×D₇₆

yes

characteristic

197

C₂²×C₄

#64543

yes

characteristic

198

C₂²×C₄

Q₈×D₁₉

yes

characteristic

199

M₁₆

—

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

210

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

211

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

212

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₂²⋊C₄

—

216

C₂²⋊C₄

—

217

C₄²

C₂×C₄×D₁₉

yes

characteristic

218

C₄²

D₄×D₁₉

yes

characteristic

219

C₄²

#64545

yes

characteristic

220

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

#10597343

yes

characteristic

226

D₄

—

227

D₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

236

C₂×C₄

#10597338

yes

characteristic

237

C₂×C₄

#10597341

yes

characteristic

238

C₂×C₄

#10597350

yes

—

239

C₂×C₄

#10597354

yes

—

240

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

241

C₂×C₄

#10597384

yes

characteristic

242

C₂×C₄

#10597392

yes

characteristic

243

C₈

—

244

C₈

—

245

C₈

—

246

C₈

—

247

C₈

—

248

C₈

—

249

C₈

—

152

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

152

—

256

C₂²

#11926401

yes

characteristic

257

C₂²

#11926845

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

#11926541

yes

characteristic

263

C₄

#11926550

yes

characteristic

264

C₄

#11926591

yes

—

265

C₄

#11926760

yes

—

266

C₂

—

267

C₂

—

152

—

268

C₂

#14563646

yes

characteristic

269

C₂

#14563674

yes

characteristic

270

C₂

#14563686

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597341
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1564	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₇₆	Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1564	D₁₉
hypocenter	C₁₉	#8664
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂×C₄

#10597341

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1564

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂²×D₇₆

Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
2. #14563773	C₂	semidirect
4. #14561531	C₂	semidirect
5. C₁₉×#1564	C₂	semidirect
117. #1564	D₁₉	semidirect
186. C₁₉	#8664	semidirect

H ≅ G/N

type

2. #14563773

C₂

semidirect

4. #14561531

C₂

semidirect

5. C₁₉×#1564

C₂

semidirect

117. #1564

D₁₉

semidirect

186. C₁₉

#8664

semidirect

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

subgroup	index
C₂×#11926623	2
#14563773	2
#14562061	2
#14561531	2
C₁₉×#1564	2
#8664	19

subgroup

index

C₁₉×#1564

Subgroups — #18075694

Conjugacy classes of subgroups

Complements

Maximal subgroups