Group #18075490 — subgroups

Subgroups — #18075490

Order 4864.

450 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 111 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×C₈×D₇₆	C₂	1	1	yes	maximal, characteristic
2	#14562398	C₂	1	1	yes	maximal, characteristic, complemented
3	#14561975	C₂	1	2	yes	maximal
4	#14561504	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₁₉	C₄	1	2	yes	—
7	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
8	C₈×D₇₆	—	2	1	no	—
9	C₈×D₇₆	—	2	1	no	—
10	C₈×D₇₆	—	2	1	no	—
11	C₈×D₇₆	—	2	1	no	—
12	#11926601	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₈	C₄	1	2	yes	—
15	#11926297	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926267	—	2	4	no	—
18	C₁₉×#432	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	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×(C₂×D₁₉)⋊C₄	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₁₉	Q₈	1	1	yes	characteristic
29	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
30	C₂×C₈×D₁₉	—	2	2	no	—
31	C₂×C₈×D₁₉	—	2	2	no	—
32	C₂×C₈×D₁₉	—	4	4	no	—
33	C₄×D₇₆	—	2	1	no	—
34	C₄×D₇₆	—	2	1	no	—
35	C₄×D₇₆	—	2	1	no	—
36	C₄×D₇₆	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₂²⋊C₈	—	2	2	no	—
39	C₁₉×#97	—	2	2	no	—
40	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
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	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	#10597260	—	2	2	no	—
51	C₂³×D₁₉	C₄⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
56	C₂×D₇₆	—	2	4	no	—
57	C₂×D₇₆	—	2	1	no	—
58	C₂×D₇₆	—	2	1	no	—
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	—	4	1	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	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	#41	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	—	2	1	no	—
78	C₂×C₁₉⋊C₈	—	2	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	C₂×C₁₉⋊C₈	—	4	2	no	—
81	C₈×D₁₉	—	4	4	no	—
82	C₈×D₁₉	—	4	4	no	—
83	#8622	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂²×D₁₉	—	2	2	no	—
86	C₂²×D₁₉	—	2	2	no	—
87	C₂²×D₁₉	—	4	2	no	—
88	C₂²×D₁₉	—	4	2	no	—
89	C₂²×D₁₉	#108	1	4	yes	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	C₂×C₂²⋊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	C₂²⋊Q₈	1	1	yes	characteristic
100	C₂×Dic₁₉	—	2	2	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	D₇₆	—	2	4	no	—
103	D₇₆	—	2	4	no	—
104	C₄×D₁₉	—	4	4	no	—
105	C₄×D₁₉	—	4	2	no	—
106	C₄×D₁₉	—	4	2	no	—
107	C₈×C₁₉	—	2	1	no	—
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	8	2	no	—
111	C₈×C₁₉	#100	1	2	yes	—
112	C₁₉⋊C₈	—	4	2	no	—
113	C₁₉⋊C₈	—	8	2	no	—
114	C₂×C₈×D₄	—	19	1	no	—
115	#1568	—	19	1	no	—
116	#1568	D₁₉	1	1	yes	characteristic, complemented
117	#1466	—	19	2	no	—
118	#1290	—	19	2	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	#380	1	1	yes	characteristic
122	C₂²×C₁₉	C₂×#108	1	2	yes	—
123	C₂×D₁₉	—	2	4	no	—
124	C₂×D₁₉	—	4	4	no	—
125	C₂×D₁₉	—	4	2	no	—
126	C₂×D₁₉	—	4	2	no	—
127	C₂×D₁₉	—	4	4	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
134	C₄×C₁₉	#413	1	1	yes	characteristic
135	Dic₁₉	—	4	2	no	—
136	C₂³×C₈	—	19	2	no	—
137	C₂×C₄×D₄	—	19	1	no	—
138	C₈×D₄	—	38	1	no	—
139	C₈×D₄	—	38	1	no	—
140	C₈×D₄	—	38	1	no	—
141	C₈×D₄	—	38	1	no	—
142	#432	—	19	2	no	—
143	#432	C₂×D₁₉	1	2	yes	—
144	C₂×C₄⋊C₈	—	19	1	no	—
145	C₂×C₂²⋊C₈	—	19	2	no	—
146	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
147	#335	—	2	1	no	—
148	#335	—	38	1	no	—
149	#334	—	2	1	no	—
150	#334	—	38	1	no	—
151	#323	—	38	4	no	—
152	C₂×C₁₉	—	2	2	no	—
153	C₂×C₁₉	#1800	1	1	yes	characteristic
154	C₂×C₁₉	#1810	1	1	yes	characteristic
155	C₂×C₁₉	#1812	1	1	yes	characteristic
156	D₁₉	—	4	4	no	—
157	C₂²×D₄	—	19	1	no	—
158	C₂³×C₄	—	19	2	no	—
159	C₂²×C₈	—	19	2	no	—
160	C₂²×C₈	—	38	2	no	—
161	C₂²×C₈	—	38	2	no	—
162	C₂²×C₈	—	76	4	no	—
163	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
164	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
165	C₄×D₄	—	38	1	no	—
166	C₄×D₄	—	38	1	no	—
167	C₄×D₄	—	38	1	no	—
168	C₄×D₄	—	38	1	no	—
169	C₂×C₄⋊C₄	—	19	1	no	—
170	C₂×C₂²⋊C₄	—	19	2	no	—
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	C₄⋊C₈	—	2	2	no	—
173	C₄⋊C₈	—	38	1	no	—
174	C₄⋊C₈	—	38	2	no	—
175	C₄⋊C₈	—	38	1	no	—
176	C₂²⋊C₈	—	2	2	no	—
177	C₂²⋊C₈	—	38	2	no	—
178	C₂²⋊C₈	—	38	2	no	—
179	C₂²⋊C₈	—	38	2	no	—
180	#97	—	2	2	no	—
181	#97	—	38	2	no	—
182	C₄×C₈	D₇₆	1	1	yes	characteristic
183	C₄×C₈	D₇₆	1	1	yes	characteristic
184	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
185	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
186	C₁₉	#8622	1	1	yes	characteristic, complemented, Sylow
187	C₂⁴	—	19	2	no	—
188	C₂×D₄	—	38	4	no	—
189	C₂×D₄	—	38	1	no	—
190	C₂×D₄	—	38	1	no	—
191	C₂²×C₄	—	19	2	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×C₄×D₁₉	1	1	yes	characteristic
197	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
198	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	4	2	no	—
202	C₂×C₈	—	38	2	no	—
203	C₂×C₈	—	76	4	no	—
204	C₂×C₈	—	76	4	no	—
205	C₂×C₈	—	76	2	no	—
206	C₂×C₈	—	76	2	no	—
207	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
208	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
209	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
210	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
211	C₄⋊C₄	—	38	1	no	—
212	C₄⋊C₄	—	38	1	no	—
213	C₂²⋊C₄	—	38	2	no	—
214	C₂²⋊C₄	—	38	2	no	—
215	C₄²	C₂×D₇₆	1	1	yes	characteristic
216	C₄²	#64543	1	1	yes	characteristic
217	C₄²	#64545	1	1	yes	characteristic
218	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
219	C₂³	—	19	4	no	—
220	C₂³	—	38	2	no	—
221	C₂³	—	38	2	no	—
222	C₂³	—	76	2	no	—
223	C₂³	—	76	2	no	—
224	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
225	D₄	—	38	4	no	—
226	D₄	—	38	4	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	38	2	no	—
232	C₂×C₄	—	76	4	no	—
233	C₂×C₄	—	76	2	no	—
234	C₂×C₄	—	76	2	no	—
235	C₂×C₄	—	76	2	no	—
236	C₂×C₄	#10597338	1	1	yes	characteristic
237	C₂×C₄	#10597341	1	1	yes	characteristic
238	C₂×C₄	#10597343	1	1	yes	characteristic
239	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
240	C₂×C₄	#10597384	1	1	yes	characteristic
241	C₂×C₄	#10597392	1	1	yes	characteristic
242	C₈	—	2	1	no	—
243	C₈	—	2	1	no	—
244	C₈	—	2	1	no	—
245	C₈	—	8	2	no	—
246	C₈	—	76	2	no	—
247	C₈	—	152	2	no	—
248	C₈	#10597280	1	2	yes	—
249	C₂²	—	2	1	no	—
250	C₂²	—	2	1	no	—
251	C₂²	—	38	4	no	—
252	C₂²	—	76	4	no	—
253	C₂²	—	76	4	no	—
254	C₂²	—	76	2	no	—
255	C₂²	—	76	2	no	—
256	C₂²	#11926401	1	1	yes	characteristic
257	C₂²	#108×D₁₉	1	2	yes	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	2	1	no	—
263	C₄	—	76	2	no	—
264	C₄	C₂×#10597280	1	1	yes	characteristic
265	C₄	#11926526	1	1	yes	characteristic
266	C₂	—	2	2	no	—
267	C₂	—	76	4	no	—
268	C₂	#14563624	1	1	yes	characteristic
269	C₂	#14563670	1	1	yes	characteristic
270	C₂	#14563678	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×D₇₆

C₂

yes

maximal, characteristic

#14562398

C₂

yes

maximal, characteristic, complemented

#14561975

C₂

yes

maximal

#14561504

C₂

yes

maximal, complemented

C₁₉×#1568

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₁₉

C₄

yes

—

C₂×C₄×D₇₆

C₂²

yes

characteristic

C₈×D₇₆

—

C₈×D₇₆

—

C₈×D₇₆

—

C₈×D₇₆

—

#11926601

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₈

C₄

yes

—

#11926297

—

#11926295

—

#11926267

—

C₁₉×#432

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂²×D₇₆

Q₈

yes

characteristic

C₂²×C₄×D₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

D₄

yes

—

C₂×C₄⋊Dic₁₉

Q₈

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₈×D₁₉

—

C₂×C₈×D₁₉

—

C₂×C₈×D₁₉

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

(C₂×D₁₉)⋊C₈

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂³×D₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

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

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₈×D₁₉

—

C₈×D₁₉

—

#8622

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

#108

yes

—

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

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

D₇₆

—

103

D₇₆

—

104

C₄×D₁₉

—

105

C₄×D₁₉

—

106

C₄×D₁₉

—

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

#100

yes

—

112

C₁₉⋊C₈

—

113

C₁₉⋊C₈

—

114

C₂×C₈×D₄

—

115

#1568

—

116

#1568

D₁₉

yes

characteristic, complemented

117

#1466

—

118

#1290

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#380

yes

characteristic

122

C₂²×C₁₉

C₂×#108

yes

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₂×D₁₉

—

127

C₂×D₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

C₂×#100

yes

characteristic

134

C₄×C₁₉

#413

yes

characteristic

135

Dic₁₉

—

136

C₂³×C₈

—

137

C₂×C₄×D₄

—

138

C₈×D₄

—

139

C₈×D₄

—

140

C₈×D₄

—

141

C₈×D₄

—

142

#432

—

143

#432

C₂×D₁₉

yes

—

144

C₂×C₄⋊C₈

—

145

C₂×C₂²⋊C₈

—

146

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

147

#335

—

148

#335

—

149

#334

—

150

#334

—

151

#323

—

152

C₂×C₁₉

—

153

C₂×C₁₉

#1800

yes

characteristic

154

C₂×C₁₉

#1810

yes

characteristic

155

C₂×C₁₉

#1812

yes

characteristic

156

D₁₉

—

157

C₂²×D₄

—

158

C₂³×C₄

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

C₂²×C₈

—

162

C₂²×C₈

—

163

C₂²×C₈

C₄×D₁₉

yes

characteristic

164

C₂²×C₈

C₄×D₁₉

yes

characteristic

165

C₄×D₄

—

166

C₄×D₄

—

167

C₄×D₄

—

168

C₄×D₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₂²⋊C₄

—

171

C₂×C₄²

C₂²×D₁₉

yes

characteristic

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

C₂²⋊C₈

—

179

C₂²⋊C₈

—

180

#97

—

181

#97

—

182

C₄×C₈

D₇₆

yes

characteristic

183

C₄×C₈

D₇₆

yes

characteristic

184

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

185

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

186

C₁₉

#8622

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×C₄×D₁₉

yes

characteristic

197

C₂²×C₄

D₄×D₁₉

yes

characteristic

198

C₂²×C₄

Q₈×D₁₉

yes

characteristic

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

208

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

209

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

210

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₂²⋊C₄

—

214

C₂²⋊C₄

—

215

C₄²

C₂×D₇₆

yes

characteristic

216

C₄²

#64543

yes

characteristic

217

C₄²

#64545

yes

characteristic

218

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

C₄⋊C₄×D₁₉

yes

characteristic

225

D₄

—

226

D₄

—

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

—

236

C₂×C₄

#10597338

yes

characteristic

237

C₂×C₄

#10597341

yes

characteristic

238

C₂×C₄

#10597343

yes

characteristic

239

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

240

C₂×C₄

#10597384

yes

characteristic

241

C₂×C₄

#10597392

yes

characteristic

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

—

246

C₈

—

247

C₈

—

152

—

248

C₈

#10597280

yes

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

#11926401

yes

characteristic

257

C₂²

#108×D₁₉

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

C₂×#10597280

yes

characteristic

265

C₄

#11926526

yes

characteristic

266

C₂

—

267

C₂

—

268

C₂

#14563624

yes

characteristic

269

C₂

#14563670

yes

characteristic

270

C₂

#14563678

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1568	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₇₆	Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1568	D₁₉
hypocenter	C₁₉	#8622
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#11926401

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1568

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂²×D₇₆

Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
2. #14562398	C₂	semidirect
4. #14561504	C₂	semidirect
5. C₁₉×#1568	C₂	semidirect
116. #1568	D₁₉	semidirect
186. C₁₉	#8622	semidirect

H ≅ G/N

type

2. #14562398

C₂

semidirect

4. #14561504

C₂

semidirect

5. C₁₉×#1568

C₂

semidirect

116. #1568

D₁₉

semidirect

186. C₁₉

#8622

semidirect

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

subgroup	index
C₂×C₈×D₇₆	2
#14562398	2
#14561975	2
#14561504	2
C₁₉×#1568	2
#8622	19

subgroup

index

C₂×C₈×D₇₆

C₁₉×#1568

Subgroups — #18075490

Conjugacy classes of subgroups

Complements

Maximal subgroups