Group #18074659 — subgroups

Subgroups — #18074659

Order 4864.

804 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 171 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×#11927274	C₂	1	1	yes	maximal, characteristic
2	#14563637	C₂	1	2	yes	maximal
3	C₂×#11926293	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926276	C₂	1	2	yes	maximal
5	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic
6	#11927274	—	2	4	no	—
7	#11927274	—	2	2	no	—
8	#11927274	C₄	1	4	yes	complemented
9	C₂×#10597334	—	2	2	no	—
10	C₂×#10597390	—	2	2	no	—
11	C₂×C₄×Dic₃₈	C₂²	1	2	yes	—
12	C₂×#10597333	—	2	2	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
14	C₂×#10597267	—	2	2	no	—
15	#11926306	—	2	2	no	—
16	#11926293	—	2	2	no	—
17	#11926276	—	2	4	no	—
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#103	—	2	2	no	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#384	C₂²	1	1	yes	characteristic
22	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
23	C₂²×Dic₃₈	—	2	2	no	—
24	C₂²×Dic₃₈	D₄	1	2	yes	—
25	C₂²×C₈×C₁₉	—	2	1	no	—
26	C₁₉×C₄⋊Q₈	—	2	2	no	—
27	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
28	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	#10597390	—	2	8	no	—
34	#10597390	—	2	8	no	—
35	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
36	C₂×Dic₁₉⋊C₄	—	2	4	no	—
37	C₂×Dic₁₉⋊C₄	—	2	2	no	—
38	C₂×C₄×Dic₁₉	—	2	2	no	—
39	C₂×C₄×Dic₁₉	—	2	2	no	—
40	C₂²×C₁₉⋊C₈	—	2	2	no	—
41	#10597334	—	2	8	no	—
42	#10597334	—	2	8	no	—
43	#10597333	—	2	8	no	—
44	#10597333	—	2	8	no	—
45	C₄×Dic₃₈	—	2	2	no	—
46	C₄×Dic₃₈	—	2	2	no	—
47	C₄×Dic₃₈	C₂×C₄	1	4	yes	—
48	C₄×Dic₃₈	D₄	1	4	yes	—
49	C₁₉×#103	—	4	4	no	—
50	C₄×C₈×C₁₉	—	2	2	no	—
51	#10597267	—	4	4	no	—
52	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
53	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
54	C₂×Q₈×C₁₉	—	2	2	no	—
55	C₂×Q₈×C₁₉	—	4	2	no	—
56	C₂×Q₈×C₁₉	—	4	2	no	—
57	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	4	1	no	—
60	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×Dic₁₉	—	2	2	no	—
63	C₂²×Dic₁₉	—	2	2	no	—
64	C₂×Dic₃₈	—	2	2	no	—
65	C₂×Dic₃₈	—	2	2	no	—
66	C₂×Dic₃₈	—	2	2	no	—
67	C₂×Dic₃₈	—	2	8	no	—
68	C₂×Dic₃₈	—	8	2	no	—
69	C₂×Dic₃₈	—	8	2	no	—
70	C₂×Dic₃₈	C₂²⋊C₄	1	4	yes	—
71	C₂×Dic₃₈	SD₁₆	1	4	yes	—
72	C₂×Dic₃₈	Q₁₆	1	4	yes	—
73	C₂×C₈×C₁₉	—	2	2	no	—
74	C₂×C₈×C₁₉	—	4	1	no	—
75	C₂×C₈×C₁₉	—	4	1	no	—
76	C₄⋊C₄×C₁₉	—	2	4	no	—
77	C₄⋊C₄×C₁₉	—	2	4	no	—
78	C₄⋊C₄×C₁₉	—	4	2	no	—
79	C₄⋊C₄×C₁₉	—	4	2	no	—
80	C₄⋊C₄×C₁₉	—	4	2	no	—
81	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₁₉	C₂×D₄	1	2	yes	—
84	C₄⋊Dic₁₉	—	2	2	no	—
85	C₄⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
86	Dic₁₉⋊C₄	—	2	16	no	—
87	Dic₁₉⋊C₄	—	2	4	no	—
88	Dic₁₉⋊C₄	—	2	4	no	—
89	C₄×Dic₁₉	—	2	8	no	—
90	C₄×Dic₁₉	—	2	4	no	—
91	C₄×Dic₁₉	—	2	4	no	—
92	C₂×C₁₉⋊C₈	—	4	2	no	—
93	C₂×C₁₉⋊C₈	—	4	2	no	—
94	C₂×C₁₉⋊C₈	—	4	2	no	—
95	#8451	—	19	1	no	maximal, Sylow
96	C₂³×C₁₉	#120	1	1	yes	characteristic
97	Q₈×C₁₉	—	4	4	no	—
98	Q₈×C₁₉	—	8	2	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	4	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	8	2	no	—
105	C₂×C₄×C₁₉	—	8	1	no	—
106	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
107	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#120	1	2	yes	—
110	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
111	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
112	C₂×C₄×C₁₉	#137	1	2	yes	—
113	C₂×C₄×C₁₉	#137	1	2	yes	—
114	C₂×Dic₁₉	—	2	4	no	—
115	C₂×Dic₁₉	—	2	4	no	—
116	C₂×Dic₁₉	—	2	4	no	—
117	C₂×Dic₁₉	—	2	4	no	—
118	C₂×Dic₁₉	—	4	2	no	—
119	C₂×Dic₁₉	—	4	2	no	—
120	Dic₃₈	—	2	4	no	—
121	Dic₃₈	—	2	4	no	—
122	Dic₃₈	—	2	4	no	—
123	Dic₃₈	—	8	8	no	—
124	Dic₃₈	#103	1	8	yes	complemented
125	C₈×C₁₉	—	4	2	no	—
126	C₁₉⋊C₈	—	8	2	no	—
127	C₂×Q₈²	—	19	1	no	—
128	#1956	D₁₉	1	1	yes	characteristic
129	#1803	—	19	2	no	—
130	C₂×#333	—	19	1	no	—
131	C₂×Q₈⋊C₈	—	19	2	no	—
132	C₂²×C₁₉	#379	1	1	yes	characteristic
133	C₂²×C₁₉	#448	1	2	yes	—
134	C₂²×C₁₉	#451	1	2	yes	—
135	C₂²×C₁₉	#453	1	1	yes	characteristic
136	C₂²×C₁₉	#455	1	1	yes	characteristic
137	C₄×C₁₉	—	2	1	no	—
138	C₄×C₁₉	—	2	1	no	—
139	C₄×C₁₉	—	4	4	no	—
140	C₄×C₁₉	—	16	1	no	—
141	C₄×C₁₉	C₂×#103	1	2	yes	—
142	C₄×C₁₉	#419	1	2	yes	—
143	C₄×C₁₉	#448	1	2	yes	—
144	C₄×C₁₉	#451	1	2	yes	—
145	Dic₁₉	—	2	8	no	—
146	Dic₁₉	—	4	4	no	—
147	Q₈²	—	19	4	no	—
148	Q₈²	—	38	4	no	—
149	Q₈²	—	38	2	no	—
150	C₂×C₄⋊Q₈	—	38	2	no	—
151	C₂×C₄⋊Q₈	—	38	2	no	—
152	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
153	C₂×C₄×Q₈	—	19	2	no	—
154	C₂×C₄×Q₈	—	38	2	no	—
155	C₂×C₄⋊C₈	—	19	2	no	—
156	C₂×#103	—	2	2	no	—
157	C₂×#103	—	38	2	no	—
158	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
159	#384	C₂×D₁₉	1	1	yes	characteristic
160	#340	—	38	2	no	—
161	#333	—	38	2	no	—
162	Q₈⋊C₈	—	38	4	no	—
163	C₂×C₁₉	#1623	1	1	yes	characteristic
164	C₂×C₁₉	#1633	1	1	yes	characteristic
165	C₂×C₁₉	#1645	1	2	yes	—
166	C₂×C₁₉	#1787	1	2	yes	—
167	C₂×C₁₉	#1792	1	1	yes	characteristic
168	C₂²×Q₈	—	19	2	no	—
169	C₂²×Q₈	—	38	2	no	—
170	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
171	C₂²×C₈	—	2	1	no	—
172	C₂²×C₈	—	38	2	no	—
173	C₄⋊Q₈	—	2	2	no	—
174	C₄⋊Q₈	—	38	8	no	—
175	C₄⋊Q₈	—	38	8	no	—
176	C₄⋊Q₈	—	38	8	no	—
177	C₄⋊Q₈	—	38	8	no	—
178	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
179	C₄⋊Q₈	D₇₆	1	2	yes	—
180	C₄×Q₈	—	19	4	no	—
181	C₄×Q₈	—	19	4	no	—
182	C₄×Q₈	—	38	8	no	—
183	C₄×Q₈	—	38	8	no	—
184	C₄×Q₈	—	38	2	no	—
185	C₄×Q₈	—	38	2	no	—
186	C₂×C₄⋊C₄	—	2	2	no	—
187	C₂×C₄⋊C₄	—	2	2	no	—
188	C₂×C₄⋊C₄	—	2	1	no	—
189	C₂×C₄⋊C₄	—	19	2	no	—
190	C₂×C₄⋊C₄	—	38	4	no	—
191	C₂×C₄⋊C₄	—	38	2	no	—
192	C₂×C₄²	—	38	2	no	—
193	C₂×C₄²	—	38	2	no	—
194	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
195	C₄⋊C₈	—	38	2	no	—
196	C₄⋊C₈	—	38	2	no	—
197	#103	—	4	4	no	—
198	#103	—	76	4	no	—
199	C₄×C₈	—	2	2	no	—
200	C₁₉	#8451	1	1	yes	characteristic, complemented, Sylow
201	C₂×Q₈	—	2	2	no	—
202	C₂×Q₈	—	4	2	no	—
203	C₂×Q₈	—	4	2	no	—
204	C₂×Q₈	—	19	4	no	—
205	C₂×Q₈	—	19	4	no	—
206	C₂×Q₈	—	19	4	no	—
207	C₂×Q₈	—	38	8	no	—
208	C₂×Q₈	—	38	2	no	—
209	C₂×Q₈	—	38	2	no	—
210	C₂×Q₈	—	38	2	no	—
211	C₂×Q₈	—	152	2	no	—
212	C₂×Q₈	—	152	2	no	—
213	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
214	C₂²×C₄	—	2	2	no	—
215	C₂²×C₄	—	4	1	no	—
216	C₂²×C₄	—	38	2	no	—
217	C₂²×C₄	—	38	2	no	—
218	C₂²×C₄	D₄×D₁₉	1	2	yes	—
219	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
220	C₂×C₈	—	2	2	no	—
221	C₂×C₈	—	4	1	no	—
222	C₂×C₈	—	4	1	no	—
223	C₂×C₈	—	76	2	no	—
224	C₂×C₈	—	76	2	no	—
225	C₂×C₈	—	76	2	no	—
226	C₄⋊C₄	—	2	4	no	—
227	C₄⋊C₄	—	2	4	no	—
228	C₄⋊C₄	—	4	2	no	—
229	C₄⋊C₄	—	4	2	no	—
230	C₄⋊C₄	—	4	2	no	—
231	C₄⋊C₄	—	19	4	no	—
232	C₄⋊C₄	—	38	16	no	—
233	C₄⋊C₄	—	38	4	no	—
234	C₄⋊C₄	—	38	2	no	—
235	C₄⋊C₄	—	38	4	no	—
236	C₄²	—	38	8	no	—
237	C₄²	—	38	4	no	—
238	C₄²	—	38	4	no	—
239	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
240	C₄²	C₂×D₇₆	1	1	yes	characteristic
241	C₄²	D₄×D₁₉	1	2	yes	—
242	C₂³	#10597383	1	1	yes	characteristic
243	Q₈	—	4	4	no	—
244	Q₈	—	8	2	no	—
245	Q₈	—	19	8	no	—
246	Q₈	—	38	4	no	—
247	Q₈	—	38	4	no	—
248	Q₈	—	38	4	no	—
249	Q₈	—	152	8	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	1	no	—
252	C₂×C₄	—	2	4	no	—
253	C₂×C₄	—	4	2	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	—	8	2	no	—
256	C₂×C₄	—	8	1	no	—
257	C₂×C₄	—	38	4	no	—
258	C₂×C₄	—	38	4	no	—
259	C₂×C₄	—	38	4	no	—
260	C₂×C₄	—	38	4	no	—
261	C₂×C₄	—	76	2	no	—
262	C₂×C₄	—	76	2	no	—
263	C₂×C₄	C₂²⋊C₄×D₁₉	1	2	yes	—
264	C₂×C₄	#10597328	1	2	yes	—
265	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
266	C₂×C₄	#10597361	1	2	yes	—
267	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
268	C₂×C₄	#10597364	1	2	yes	—
269	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
270	C₂×C₄	#10597383	1	1	yes	characteristic
271	C₈	—	4	2	no	—
272	C₈	—	152	2	no	—
273	C₂²	#11926399	1	1	yes	characteristic
274	C₂²	#11926681	1	2	yes	—
275	C₂²	#11926698	1	2	yes	—
276	C₂²	#11926711	1	1	yes	characteristic
277	C₂²	#11926721	1	1	yes	characteristic
278	C₄	—	2	1	no	—
279	C₄	—	2	1	no	—
280	C₄	—	4	4	no	—
281	C₄	—	16	1	no	—
282	C₄	—	38	8	no	—
283	C₄	—	76	4	no	—
284	C₄	#103×D₁₉	1	2	yes	—
285	C₄	#11926551	1	2	yes	—
286	C₄	#11926684	1	2	yes	—
287	C₄	#11926701	1	2	yes	—
288	C₂	#14562711	1	1	yes	characteristic
289	C₂	#14562773	1	1	yes	characteristic
290	C₂	#14562853	1	2	yes	—
291	C₂	#14563568	1	2	yes	—
292	C₂	#14563588	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11927274

C₂

yes

maximal, characteristic

#14563637

C₂

yes

maximal

C₂×#11926293

C₂

yes

maximal, characteristic

C₂×#11926276

C₂

yes

maximal

C₁₉×#1956

C₂

yes

maximal, characteristic

#11927274

—

#11927274

—

#11927274

C₄

yes

complemented

C₂×#10597334

—

C₂×#10597390

—

C₂×C₄×Dic₃₈

C₂²

yes

—

C₂×#10597333

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

—

C₂²×Dic₃₈

—

C₂²×Dic₃₈

D₄

yes

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597390

—

#10597390

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂×C₄

yes

—

C₄×Dic₃₈

D₄

yes

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

#10597267

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂²⋊C₄

yes

—

C₂×Dic₃₈

SD₁₆

yes

—

C₂×Dic₃₈

Q₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂²⋊C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

107

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

108

C₂×C₄×C₁₉

#120

yes

characteristic

109

C₂×C₄×C₁₉

#120

yes

—

110

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

111

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

112

C₂×C₄×C₁₉

#137

yes

—

113

C₂×C₄×C₁₉

#137

yes

—

114

C₂×Dic₁₉

—

115

C₂×Dic₁₉

—

116

C₂×Dic₁₉

—

117

C₂×Dic₁₉

—

118

C₂×Dic₁₉

—

119

C₂×Dic₁₉

—

120

Dic₃₈

—

121

Dic₃₈

—

122

Dic₃₈

—

123

Dic₃₈

—

124

Dic₃₈

#103

yes

complemented

125

C₈×C₁₉

—

126

C₁₉⋊C₈

—

127

C₂×Q₈²

—

128

#1956

D₁₉

yes

characteristic

129

#1803

—

130

C₂×#333

—

131

C₂×Q₈⋊C₈

—

132

C₂²×C₁₉

#379

yes

characteristic

133

C₂²×C₁₉

#448

yes

—

134

C₂²×C₁₉

#451

yes

—

135

C₂²×C₁₉

#453

yes

characteristic

136

C₂²×C₁₉

#455

yes

characteristic

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

C₂×#103

yes

—

142

C₄×C₁₉

#419

yes

—

143

C₄×C₁₉

#448

yes

—

144

C₄×C₁₉

#451

yes

—

145

Dic₁₉

—

146

Dic₁₉

—

147

Q₈²

—

148

Q₈²

—

149

Q₈²

—

150

C₂×C₄⋊Q₈

—

151

C₂×C₄⋊Q₈

—

152

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

153

C₂×C₄×Q₈

—

154

C₂×C₄×Q₈

—

155

C₂×C₄⋊C₈

—

156

C₂×#103

—

157

C₂×#103

—

158

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

159

#384

C₂×D₁₉

yes

characteristic

160

#340

—

161

#333

—

162

Q₈⋊C₈

—

163

C₂×C₁₉

#1623

yes

characteristic

164

C₂×C₁₉

#1633

yes

characteristic

165

C₂×C₁₉

#1645

yes

—

166

C₂×C₁₉

#1787

yes

—

167

C₂×C₁₉

#1792

yes

characteristic

168

C₂²×Q₈

—

169

C₂²×Q₈

—

170

C₂²×Q₈

C₂²⋊D₁₉

yes

—

171

C₂²×C₈

—

172

C₂²×C₈

—

173

C₄⋊Q₈

—

174

C₄⋊Q₈

—

175

C₄⋊Q₈

—

176

C₄⋊Q₈

—

177

C₄⋊Q₈

—

178

C₄⋊Q₈

C₄×D₁₉

yes

—

179

C₄⋊Q₈

D₇₆

yes

—

180

C₄×Q₈

—

181

C₄×Q₈

—

182

C₄×Q₈

—

183

C₄×Q₈

—

184

C₄×Q₈

—

185

C₄×Q₈

—

186

C₂×C₄⋊C₄

—

187

C₂×C₄⋊C₄

—

188

C₂×C₄⋊C₄

—

189

C₂×C₄⋊C₄

—

190

C₂×C₄⋊C₄

—

191

C₂×C₄⋊C₄

—

192

C₂×C₄²

—

193

C₂×C₄²

—

194

C₂×C₄²

C₂²×D₁₉

yes

characteristic

195

C₄⋊C₈

—

196

C₄⋊C₈

—

197

#103

—

198

#103

—

199

C₄×C₈

—

200

C₁₉

#8451

yes

characteristic, complemented, Sylow

201

C₂×Q₈

—

202

C₂×Q₈

—

203

C₂×Q₈

—

204

C₂×Q₈

—

205

C₂×Q₈

—

206

C₂×Q₈

—

207

C₂×Q₈

—

208

C₂×Q₈

—

209

C₂×Q₈

—

210

C₂×Q₈

—

211

C₂×Q₈

—

152

—

212

C₂×Q₈

—

152

—

213

C₂×Q₈

(C₂×D₁₉)⋊C₄

yes

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

—

218

C₂²×C₄

D₄×D₁₉

yes

—

219

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

220

C₂×C₈

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄²

—

237

C₄²

—

238

C₄²

—

239

C₄²

C₂×C₄×D₁₉

yes

characteristic

240

C₄²

C₂×D₇₆

yes

characteristic

241

C₄²

D₄×D₁₉

yes

—

242

C₂³

#10597383

yes

characteristic

243

Q₈

—

244

Q₈

—

245

Q₈

—

246

Q₈

—

247

Q₈

—

248

Q₈

—

249

Q₈

—

152

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

C₂²⋊C₄×D₁₉

yes

—

264

C₂×C₄

#10597328

yes

—

265

C₂×C₄

SD₁₆×D₁₉

yes

—

266

C₂×C₄

#10597361

yes

—

267

C₂×C₄

Q₁₆×D₁₉

yes

—

268

C₂×C₄

#10597364

yes

—

269

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

270

C₂×C₄

#10597383

yes

characteristic

271

C₈

—

272

C₈

—

152

—

273

C₂²

#11926399

yes

characteristic

274

C₂²

#11926681

yes

—

275

C₂²

#11926698

yes

—

276

C₂²

#11926711

yes

characteristic

277

C₂²

#11926721

yes

characteristic

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

282

C₄

—

283

C₄

—

284

C₄

#103×D₁₉

yes

—

285

C₄

#11926551

yes

—

286

C₄

#11926684

yes

—

287

C₄

#11926701

yes

—

288

C₂

#14562711

yes

characteristic

289

C₂

#14562773

yes

characteristic

290

C₂

#14562853

yes

—

291

C₂

#14563568

yes

—

292

C₂

#14563588

yes

characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1956	C₂
socle, prime radical	C₂³×C₁₉	#120
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1956	D₁₉
hypocenter	C₁₉	#8451
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#10597383

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1956

C₂

socle, prime radical

C₂³×C₁₉

#120

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
8. #11927274	C₄	semidirect
124. Dic₃₈	#103	semidirect
200. C₁₉	#8451	semidirect

H ≅ G/N

type

8. #11927274

C₄

semidirect

124. Dic₃₈

#103

semidirect

200. C₁₉

#8451

semidirect

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

subgroup	index
C₂×#11927274	2
#14563637	2
C₂×#11926293	2
C₂×#11926276	2
C₁₉×#1956	2
#8451	19

subgroup

index

C₁₉×#1956

Subgroups — #18074659

Conjugacy classes of subgroups

Complements

Maximal subgroups