Group #18075457 — subgroups

Subgroups — #18075457

Order 4864.

486 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 137 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×D₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#14563627	C₂	1	1	yes	maximal, characteristic
3	#14562390	C₂	1	2	yes	maximal, complemented
4	#14561509	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₄	1	2	yes	—
7	D₄×C₁₉⋊C₈	—	2	2	no	—
8	D₄×C₁₉⋊C₈	—	2	2	no	—
9	#11926568	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597290	—	2	1	no	—
12	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926313	—	2	1	no	—
15	#11926294	—	2	2	no	—
16	#11926294	—	2	2	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#423	C₂²	1	2	yes	—
19	C₂×C₁₉×#100	—	2	1	no	—
20	C₁₉×#343	—	2	1	no	—
21	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₄×D₄×C₁₉	—	2	2	no	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×#64520	—	2	2	no	—
30	C₂²×C₁₉⋊C₈	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	C₂²×C₁₉⋊C₈	—	4	4	no	—
33	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
35	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×#100	—	4	2	no	—
39	#10597290	—	4	2	no	—
40	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
45	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
46	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
47	C₂×D₄×C₁₉	—	2	2	no	—
48	C₂×D₄×C₁₉	—	2	2	no	—
49	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
50	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
59	M₁₆×C₁₉	—	4	2	no	—
60	M₁₆×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	—	4	2	no	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₄²×C₁₉	C₂×D₄	1	2	yes	—
65	C₄²×C₁₉	#41	1	2	yes	—
66	#64520	—	4	2	no	—
67	#64520	—	4	2	no	—
68	C₂×C₁₉⋊C₈	—	2	2	no	—
69	C₂×C₁₉⋊C₈	—	2	2	no	—
70	C₂×C₁₉⋊C₈	—	4	1	no	—
71	C₂×C₁₉⋊C₈	—	4	4	no	—
72	C₂×C₁₉⋊C₈	—	4	4	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
76	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
78	#8614	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	—	2	2	no	—
80	C₂³×C₁₉	—	2	2	no	—
81	C₂³×C₁₉	—	4	2	no	—
82	C₂³×C₁₉	—	4	2	no	—
83	C₂³×C₁₉	#106	1	4	yes	—
84	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
85	D₄×C₁₉	—	2	4	no	—
86	D₄×C₁₉	—	2	4	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	—	4	4	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#121	1	2	yes	—
98	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
99	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#135	1	2	yes	—
102	C₈×C₁₉	—	8	2	no	—
103	C₁₉⋊C₈	—	2	1	no	—
104	C₁₉⋊C₈	—	2	2	no	—
105	C₁₉⋊C₈	—	4	2	no	—
106	C₁₉⋊C₈	—	8	2	no	—
107	C₁₉⋊C₈	#100	1	2	yes	complemented
108	C₂×C₈×D₄	—	19	1	no	—
109	#1800	—	19	1	no	—
110	#1800	D₁₉	1	1	yes	characteristic
111	#1566	—	19	2	no	—
112	#1292	—	19	2	no	—
113	C₂²×C₁₉	—	2	1	no	—
114	C₂²×C₁₉	—	2	1	no	—
115	C₂²×C₁₉	—	2	4	no	—
116	C₂²×C₁₉	—	4	4	no	—
117	C₂²×C₁₉	—	4	4	no	—
118	C₂²×C₁₉	—	4	2	no	—
119	C₂²×C₁₉	—	4	2	no	—
120	C₂²×C₁₉	#380	1	1	yes	characteristic
121	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
122	C₂²×C₁₉	#427	1	1	yes	characteristic
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	2	no	—
125	C₄×C₁₉	—	4	2	no	—
126	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
127	C₄×C₁₉	#413	1	1	yes	characteristic
128	C₄×C₁₉	#465	1	2	yes	—
129	C₄×C₁₉	#465	1	2	yes	—
130	C₂³×C₈	—	19	2	no	—
131	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
132	C₈×D₄	—	38	2	no	—
133	C₈×D₄	—	38	2	no	—
134	#423	—	19	2	no	—
135	#423	C₂×D₁₉	1	2	yes	—
136	C₂×C₄⋊C₈	—	19	1	no	—
137	C₂×#100	—	2	1	no	—
138	C₂×#100	—	38	1	no	—
139	C₂×C₂²⋊C₈	—	19	2	no	—
140	C₂×C₄×C₈	—	19	1	no	—
141	#343	—	2	1	no	—
142	#343	—	38	1	no	—
143	#334	—	38	2	no	—
144	#334	—	38	2	no	—
145	C₂×C₁₉	—	2	1	no	—
146	C₂×C₁₉	—	2	1	no	—
147	C₂×C₁₉	—	4	4	no	—
148	C₂×C₁₉	#1800	1	1	yes	characteristic
149	C₂×C₁₉	#1807	1	1	yes	characteristic
150	C₂×C₁₉	#1813	1	1	yes	characteristic
151	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
152	C₂³×C₄	C₄×D₁₉	1	2	yes	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	38	2	no	—
155	C₂²×C₈	—	19	1	no	—
156	C₂²×C₈	—	19	1	no	—
157	C₂²×C₈	—	19	2	no	—
158	C₂²×C₈	—	38	2	no	—
159	C₂²×C₈	—	38	2	no	—
160	C₂²×C₈	—	76	4	no	—
161	C₄×D₄	—	2	2	no	—
162	C₄×D₄	—	2	2	no	—
163	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
164	C₂×C₂²⋊C₄	Dic₃₈	1	2	yes	—
165	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
166	C₄⋊C₈	—	2	2	no	—
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	—	38	2	no	—
169	C₄⋊C₈	—	38	2	no	—
170	C₄⋊C₈	—	38	2	no	—
171	#100	—	4	2	no	—
172	#100	—	76	2	no	—
173	C₂²⋊C₈	—	38	4	no	—
174	C₄×C₈	—	19	2	no	—
175	C₄×C₈	—	19	2	no	—
176	C₁₉	#8614	1	1	yes	characteristic, complemented, Sylow
177	C₂⁴	Dic₁₉⋊C₄	1	2	yes	—
178	C₂×D₄	—	2	2	no	—
179	C₂×D₄	—	2	2	no	—
180	C₂×D₄	#64526	1	2	yes	—
181	C₂×D₄	#64527	1	2	yes	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	—	4	2	no	—
186	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
187	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
190	M₁₆	—	4	2	no	—
191	M₁₆	—	4	2	no	—
192	M₁₆	—	76	2	no	—
193	M₁₆	—	76	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	19	1	no	—
196	C₂×C₈	—	19	2	no	—
197	C₂×C₈	—	19	1	no	—
198	C₂×C₈	—	38	2	no	—
199	C₂×C₈	—	38	2	no	—
200	C₂×C₈	—	76	4	no	—
201	C₂×C₈	—	76	1	no	—
202	C₂×C₈	—	76	4	no	—
203	C₂×C₈	—	76	2	no	—
204	C₂×C₈	—	76	2	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₂²⋊C₄	—	2	4	no	—
207	C₄²	D₄×D₁₉	1	2	yes	—
208	C₄²	#64543	1	2	yes	—
209	C₂³	—	2	2	no	—
210	C₂³	—	2	2	no	—
211	C₂³	—	4	2	no	—
212	C₂³	—	4	2	no	—
213	C₂³	#10597265	1	4	yes	—
214	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
215	D₄	—	2	4	no	—
216	D₄	—	2	4	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	1	no	—
221	C₂×C₄	—	4	4	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	#10597323	1	1	yes	characteristic
226	C₂×C₄	#10597324	1	2	yes	—
227	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
228	C₂×C₄	C₂×#64526	1	1	yes	characteristic
229	C₂×C₄	#10597385	1	2	yes	—
230	C₂×C₄	C₂×#64527	1	1	yes	characteristic
231	C₂×C₄	#10597396	1	2	yes	—
232	C₈	—	8	2	no	—
233	C₈	—	19	2	no	—
234	C₈	—	38	1	no	—
235	C₈	—	38	2	no	—
236	C₈	—	76	2	no	—
237	C₈	—	152	2	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	4	no	—
241	C₂²	—	4	4	no	—
242	C₂²	—	4	4	no	—
243	C₂²	—	4	2	no	—
244	C₂²	—	4	2	no	—
245	C₂²	#11926402	1	1	yes	characteristic
246	C₂²	C₂×#10597265	1	1	yes	characteristic
247	C₂²	#11926580	1	1	yes	characteristic
248	C₄	—	2	1	no	—
249	C₄	—	2	2	no	—
250	C₄	—	4	2	no	—
251	C₄	#100×D₁₉	1	1	yes	characteristic
252	C₄	#11926525	1	1	yes	characteristic
253	C₄	#11926771	1	2	yes	—
254	C₄	#11926775	1	2	yes	—
255	C₂	—	2	1	no	—
256	C₂	—	2	1	no	—
257	C₂	—	4	4	no	—
258	C₂	#14563625	1	1	yes	characteristic
259	C₂	#14563658	1	1	yes	characteristic
260	C₂	#14563683	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×C₁₉⋊C₈

C₂

yes

maximal, characteristic

#14563627

C₂

yes

maximal, characteristic

#14562390

C₂

yes

maximal, complemented

#14561509

C₂

yes

maximal, complemented

C₁₉×#1800

C₂

yes

maximal, characteristic

C₂³×C₁₉⋊C₈

C₄

yes

—

D₄×C₁₉⋊C₈

—

D₄×C₁₉⋊C₈

—

#11926568

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597290

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#100

—

C₁₉×#343

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#100

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂⁴×C₁₉

C₄⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

SD₁₆

yes

—

C₂×D₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

#8614

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#106

yes

—

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

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×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

100

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

101

C₂×C₄×C₁₉

#135

yes

—

102

C₈×C₁₉

—

103

C₁₉⋊C₈

—

104

C₁₉⋊C₈

—

105

C₁₉⋊C₈

—

106

C₁₉⋊C₈

—

107

C₁₉⋊C₈

#100

yes

complemented

108

C₂×C₈×D₄

—

109

#1800

—

110

#1800

D₁₉

yes

characteristic

111

#1566

—

112

#1292

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

#380

yes

characteristic

121

C₂²×C₁₉

C₂×#106

yes

characteristic

122

C₂²×C₁₉

#427

yes

characteristic

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

C₂×#100

yes

characteristic

127

C₄×C₁₉

#413

yes

characteristic

128

C₄×C₁₉

#465

yes

—

129

C₄×C₁₉

#465

yes

—

130

C₂³×C₈

—

131

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

132

C₈×D₄

—

133

C₈×D₄

—

134

#423

—

135

#423

C₂×D₁₉

yes

—

136

C₂×C₄⋊C₈

—

137

C₂×#100

—

138

C₂×#100

—

139

C₂×C₂²⋊C₈

—

140

C₂×C₄×C₈

—

141

#343

—

142

#343

—

143

#334

—

144

#334

—

145

C₂×C₁₉

—

146

C₂×C₁₉

—

147

C₂×C₁₉

—

148

C₂×C₁₉

#1800

yes

characteristic

149

C₂×C₁₉

#1807

yes

characteristic

150

C₂×C₁₉

#1813

yes

characteristic

151

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

152

C₂³×C₄

C₄×D₁₉

yes

—

153

C₂×M₁₆

—

154

C₂×M₁₆

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

C₄×D₄

—

162

C₄×D₄

—

163

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

164

C₂×C₂²⋊C₄

Dic₃₈

yes

—

165

C₂×C₄²

C₂²×D₁₉

yes

characteristic

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

#100

—

172

#100

—

173

C₂²⋊C₈

—

174

C₄×C₈

—

175

C₄×C₈

—

176

C₁₉

#8614

yes

characteristic, complemented, Sylow

177

C₂⁴

Dic₁₉⋊C₄

yes

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

#64526

yes

—

181

C₂×D₄

#64527

yes

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

Dic₁₉⋊C₄

yes

—

187

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

188

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

189

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

190

M₁₆

—

191

M₁₆

—

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₄⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

D₄×D₁₉

yes

—

208

C₄²

#64543

yes

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

#10597265

yes

—

214

C₂³

C₂×Dic₁₉⋊C₄

yes

characteristic

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

#10597323

yes

characteristic

226

C₂×C₄

#10597324

yes

—

227

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

228

C₂×C₄

C₂×#64526

yes

characteristic

229

C₂×C₄

#10597385

yes

—

230

C₂×C₄

C₂×#64527

yes

characteristic

231

C₂×C₄

#10597396

yes

—

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

236

C₈

—

237

C₈

—

152

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

#11926402

yes

characteristic

246

C₂²

C₂×#10597265

yes

characteristic

247

C₂²

#11926580

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

#100×D₁₉

yes

characteristic

252

C₄

#11926525

yes

characteristic

253

C₄

#11926771

yes

—

254

C₄

#11926775

yes

—

255

C₂

—

256

C₂

—

257

C₂

—

258

C₂

#14563625

yes

characteristic

259

C₂

#14563658

yes

characteristic

260

C₂

#14563683

yes

characteristic

	subgroup	G/H
center	C₂²	#11926402
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1800	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1800	D₁₉
hypocenter	C₁₉	#8614
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

subgroup

G/H

center

C₂²

#11926402

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1800

C₂

socle

C₂²×C₁₉

#380

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 ◁ #1800

N	H ≅ G/N	type
3. #14562390	C₂	semidirect
4. #14561509	C₂	semidirect
107. C₁₉⋊C₈	#100	semidirect
176. C₁₉	#8614	semidirect

H ≅ G/N

type

3. #14562390

C₂

semidirect

4. #14561509

C₂

semidirect

107. C₁₉⋊C₈

#100

semidirect

176. C₁₉

#8614

semidirect

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

subgroup	index
C₂×D₄×C₁₉⋊C₈	2
#14563627	2
#14562390	2
#14561509	2
C₁₉×#1800	2
#8614	19

subgroup

index

C₂×D₄×C₁₉⋊C₈

C₁₉×#1800

Subgroups — #18075457

Conjugacy classes of subgroups

Complements

Maximal subgroups