Group #18069667 — subgroups

Subgroups — #18069667

Order 4864.

328 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14563374	C₂	1	1	yes	maximal, characteristic
2	#14561949	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1798	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	—	2	1	no	—
5	#11926597	—	2	1	no	—
6	#11926313	—	2	1	no	—
7	#11926313	C₄	1	2	yes	—
8	#11926270	—	2	1	no	—
9	#11926268	C₄	1	2	yes	—
10	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
13	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
14	C₁₉×#336	—	2	1	no	—
15	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	—	2	1	no	—
17	C₂²×C₈×C₁₉	—	2	1	no	—
18	C₁₉×#117	—	4	1	no	—
19	C₁₉×#117	—	4	1	no	—
20	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×#64520	—	2	2	no	—
27	C₂×#64520	—	2	2	no	—
28	C₂×#64520	—	2	2	no	—
29	C₂×#64520	—	4	1	no	—
30	C₂×#64520	—	4	1	no	—
31	C₂×#64520	—	4	1	no	—
32	C₂²×C₁₉⋊C₈	—	4	1	no	—
33	C₁₉×C₄⋊C₈	—	4	1	no	—
34	C₁₉×C₄⋊C₈	—	4	1	no	—
35	C₁₉×C₂²⋊C₈	—	4	1	no	—
36	C₁₉×C₂²⋊C₈	—	4	1	no	—
37	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
39	C₄×C₁₉⋊C₈	—	4	1	no	—
40	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	—	2	1	no	—
42	C₂²×C₄×C₁₉	—	2	1	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
55	C₂×C₈×C₁₉	—	4	1	no	—
56	C₂×C₈×C₁₉	—	4	1	no	—
57	C₂×C₈×C₁₉	—	4	1	no	—
58	C₂×C₈×C₁₉	—	4	1	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₂×C₈×C₁₉	—	4	1	no	—
61	C₄⋊C₄×C₁₉	—	4	1	no	—
62	C₄⋊C₄×C₁₉	—	4	1	no	—
63	C₂²⋊C₄×C₁₉	—	4	1	no	—
64	C₂²⋊C₄×C₁₉	—	4	1	no	—
65	C₄²×C₁₉	—	2	1	no	—
66	C₄²×C₁₉	—	2	1	no	—
67	C₄²×C₁₉	—	2	1	no	—
68	C₄²×C₁₉	—	2	1	no	—
69	#64520	—	2	4	no	—
70	#64520	—	4	2	no	—
71	#64520	—	4	2	no	—
72	#64520	—	4	2	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	#7253	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	—	2	1	no	—
79	C₂³×C₁₉	—	2	1	no	—
80	C₂³×C₁₉	—	4	1	no	—
81	C₂³×C₁₉	—	4	1	no	—
82	C₂³×C₁₉	#95	1	1	yes	characteristic
83	C₂³×C₁₉	#106	1	1	yes	characteristic
84	C₂³×C₁₉	#107	1	1	yes	characteristic
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
110	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
111	C₈×C₁₉	—	8	1	no	—
112	C₈×C₁₉	—	8	1	no	—
113	C₁₉⋊C₈	—	4	4	no	—
114	C₁₉⋊C₈	—	8	2	no	—
115	#1798	D₁₉	1	1	yes	characteristic
116	#1742	—	19	1	no	—
117	#1458	—	19	1	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	4	1	no	—
123	C₂²×C₁₉	—	4	1	no	—
124	C₂²×C₁₉	—	4	1	no	—
125	C₂²×C₁₉	—	4	1	no	—
126	C₂²×C₁₉	—	8	1	no	—
127	C₂²×C₁₉	#339	1	1	yes	characteristic
128	C₂²×C₁₉	#340	1	1	yes	characteristic
129	C₂²×C₁₉	#342	1	1	yes	characteristic
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	4	1	no	—
133	C₄×C₁₉	—	4	1	no	—
134	C₄×C₁₉	—	4	1	no	—
135	C₄×C₁₉	—	4	1	no	—
136	C₄×C₁₉	#327	1	1	yes	characteristic
137	C₄×C₁₉	#327	1	1	yes	characteristic
138	C₄×C₁₉	#328	1	1	yes	characteristic
139	C₄×C₁₉	#328	1	1	yes	characteristic
140	C₂²×M₁₆	—	38	1	no	—
141	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
142	#431	—	38	1	no	—
143	C₂×C₄⋊C₈	Dic₁₉	1	1	yes	characteristic
144	C₂×C₄⋊C₈	Dic₁₉	1	1	yes	characteristic
145	C₂×C₂²⋊C₈	—	2	1	no	—
146	#343	—	19	2	no	—
147	#343	—	38	1	no	—
148	#336	—	2	1	no	—
149	#324	—	38	1	no	—
150	#323	—	19	2	no	—
151	C₂×C₁₉	—	2	1	no	—
152	C₂×C₁₉	—	2	1	no	—
153	C₂×C₁₉	—	4	1	no	—
154	C₂×C₁₉	—	4	1	no	—
155	C₂×C₁₉	#1294	1	1	yes	characteristic
156	C₂×C₁₉	#1392	1	1	yes	characteristic
157	C₂×C₁₉	#1395	1	1	yes	characteristic
158	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
159	C₂×M₁₆	—	38	2	no	—
160	C₂×M₁₆	—	38	2	no	—
161	C₂×M₁₆	—	38	2	no	—
162	C₂×M₁₆	—	76	1	no	—
163	C₂×M₁₆	—	76	1	no	—
164	C₂×M₁₆	—	76	1	no	—
165	C₂²×C₈	—	2	1	no	—
166	C₂²×C₈	—	2	1	no	—
167	C₂²×C₈	—	76	1	no	—
168	#117	—	4	1	no	—
169	#117	—	4	1	no	—
170	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
171	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
172	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	C₄×D₁₉	1	1	yes	characteristic
174	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
175	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
176	C₄⋊C₈	—	4	1	no	—
177	C₄⋊C₈	—	4	1	no	—
178	C₄⋊C₈	—	76	1	no	—
179	C₂²⋊C₈	—	4	1	no	—
180	C₂²⋊C₈	—	4	1	no	—
181	C₂²⋊C₈	—	38	2	no	—
182	C₄×C₈	—	76	1	no	—
183	C₁₉	#7253	1	1	yes	characteristic, complemented, Sylow
184	C₂⁴	Dic₁₉⋊C₄	1	1	yes	characteristic
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
190	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
191	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
192	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
193	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
194	C₂²×C₄	#64525	1	1	yes	characteristic
195	C₂²×C₄	#64526	1	1	yes	characteristic
196	C₂²×C₄	#64527	1	1	yes	characteristic
197	C₂²×C₄	#64528	1	1	yes	characteristic
198	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
199	M₁₆	—	38	4	no	—
200	M₁₆	—	76	2	no	—
201	M₁₆	—	76	2	no	—
202	M₁₆	—	76	2	no	—
203	C₂×C₈	—	4	1	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	4	1	no	—
206	C₂×C₈	—	4	1	no	—
207	C₂×C₈	—	4	1	no	—
208	C₂×C₈	—	4	1	no	—
209	C₂×C₈	—	76	2	no	—
210	C₂×C₈	—	76	2	no	—
211	C₂×C₈	—	76	2	no	—
212	C₂×C₈	—	76	2	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₄⋊C₄	—	4	1	no	—
215	C₂²⋊C₄	—	4	1	no	—
216	C₂²⋊C₄	—	4	1	no	—
217	C₄²	—	2	1	no	—
218	C₄²	—	2	1	no	—
219	C₄²	—	2	1	no	—
220	C₄²	—	2	1	no	—
221	C₂³	—	2	1	no	—
222	C₂³	—	2	1	no	—
223	C₂³	—	4	1	no	—
224	C₂³	—	4	1	no	—
225	C₂³	#10597264	1	1	yes	characteristic
226	C₂³	#10597265	1	1	yes	characteristic
227	C₂³	C₁₉⋊#95	1	1	yes	characteristic
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	#10597266	1	1	yes	characteristic
247	C₂×C₄	#10597267	1	1	yes	characteristic
248	C₂×C₄	#10597289	1	1	yes	characteristic
249	C₂×C₄	#10597291	1	1	yes	characteristic
250	C₂×C₄	#10597291	1	1	yes	characteristic
251	C₂×C₄	#10597292	1	1	yes	characteristic
252	C₂×C₄	#10597294	1	1	yes	characteristic
253	C₂×C₄	#10597294	1	1	yes	characteristic
254	C₈	—	8	1	no	—
255	C₈	—	8	1	no	—
256	C₈	—	76	4	no	—
257	C₈	—	152	2	no	—
258	C₂²	—	2	1	no	—
259	C₂²	—	2	1	no	—
260	C₂²	—	2	1	no	—
261	C₂²	—	2	1	no	—
262	C₂²	—	4	1	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	4	1	no	—
265	C₂²	—	4	1	no	—
266	C₂²	—	8	1	no	—
267	C₂²	#11926303	1	1	yes	characteristic
268	C₂²	#11926306	1	1	yes	characteristic
269	C₂²	#11926311	1	1	yes	characteristic
270	C₄	—	2	1	no	—
271	C₄	—	2	1	no	—
272	C₄	—	4	1	no	—
273	C₄	—	4	1	no	—
274	C₄	—	4	1	no	—
275	C₄	—	4	1	no	—
276	C₄	#11926278	1	1	yes	characteristic
277	C₄	#11926278	1	1	yes	characteristic
278	C₄	#11926281	1	1	yes	characteristic
279	C₄	#11926281	1	1	yes	characteristic
280	C₂	—	2	1	no	—
281	C₂	—	2	1	no	—
282	C₂	—	4	1	no	—
283	C₂	—	4	1	no	—
284	C₂	#14561513	1	1	yes	characteristic
285	C₂	#14561758	1	1	yes	characteristic
286	C₂	#14561764	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563374

C₂

yes

maximal, characteristic

#14561949

C₂

yes

maximal, characteristic

C₁₉×#1798

C₂

yes

maximal, characteristic

C₂²×#64520

—

#11926597

—

#11926313

—

#11926313

C₄

yes

—

#11926270

—

#11926268

C₄

yes

—

C₂×C₁₉×#117

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₁₉×#336

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

—

—

—

—

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7253

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂³×C₁₉

yes

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×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

—

103

C₂×C₄×C₁₉

#99

yes

characteristic

104

C₂×C₄×C₁₉

#99

yes

characteristic

105

C₂×C₄×C₁₉

#102

yes

characteristic

106

C₂×C₄×C₁₉

#102

yes

characteristic

107

C₂×C₄×C₁₉

#103

yes

characteristic

108

C₂×C₄×C₁₉

#103

yes

characteristic

109

C₂×C₄×C₁₉

#104

yes

characteristic

110

C₂×C₄×C₁₉

#104

yes

characteristic

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

#1798

D₁₉

yes

characteristic

116

#1742

—

117

#1458

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

#339

yes

characteristic

128

C₂²×C₁₉

#340

yes

characteristic

129

C₂²×C₁₉

#342

yes

characteristic

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

#327

yes

characteristic

137

C₄×C₁₉

#327

yes

characteristic

138

C₄×C₁₉

#328

yes

characteristic

139

C₄×C₁₉

#328

yes

characteristic

140

C₂²×M₁₆

—

141

C₂×#117

C₂×D₁₉

yes

characteristic

142

#431

—

143

C₂×C₄⋊C₈

Dic₁₉

yes

characteristic

144

C₂×C₄⋊C₈

Dic₁₉

yes

characteristic

145

C₂×C₂²⋊C₈

—

146

#343

—

147

#343

—

148

#336

—

149

#324

—

150

#323

—

151

C₂×C₁₉

—

152

C₂×C₁₉

—

153

C₂×C₁₉

—

154

C₂×C₁₉

—

155

C₂×C₁₉

#1294

yes

characteristic

156

C₂×C₁₉

#1392

yes

characteristic

157

C₂×C₁₉

#1395

yes

characteristic

158

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

159

C₂×M₁₆

—

160

C₂×M₁₆

—

161

C₂×M₁₆

—

162

C₂×M₁₆

—

163

C₂×M₁₆

—

164

C₂×M₁₆

—

165

C₂²×C₈

—

166

C₂²×C₈

—

167

C₂²×C₈

—

168

#117

—

169

#117

—

170

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

171

C₂×C₄⋊C₄

D₇₆

yes

characteristic

172

C₂×C₂²⋊C₄

Dic₃₈

yes

characteristic

173

C₂×C₂²⋊C₄

C₄×D₁₉

yes

characteristic

174

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

175

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₂²⋊C₈

—

180

C₂²⋊C₈

—

181

C₂²⋊C₈

—

182

C₄×C₈

—

183

C₁₉

#7253

yes

characteristic, complemented, Sylow

184

C₂⁴

Dic₁₉⋊C₄

yes

characteristic

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

190

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

191

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

192

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

193

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

194

C₂²×C₄

#64525

yes

characteristic

195

C₂²×C₄

#64526

yes

characteristic

196

C₂²×C₄

#64527

yes

characteristic

197

C₂²×C₄

#64528

yes

characteristic

198

C₂²×C₄

C₂²⋊Dic₁₉

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

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₂²⋊C₄

—

216

C₂²⋊C₄

—

217

C₄²

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

#10597264

yes

characteristic

226

C₂³

#10597265

yes

characteristic

227

C₂³

C₁₉⋊#95

yes

characteristic

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

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

#10597266

yes

characteristic

247

C₂×C₄

#10597267

yes

characteristic

248

C₂×C₄

#10597289

yes

characteristic

249

C₂×C₄

#10597291

yes

characteristic

250

C₂×C₄

#10597291

yes

characteristic

251

C₂×C₄

#10597292

yes

characteristic

252

C₂×C₄

#10597294

yes

characteristic

253

C₂×C₄

#10597294

yes

characteristic

254

C₈

—

255

C₈

—

256

C₈

—

257

C₈

—

152

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

#11926303

yes

characteristic

268

C₂²

#11926306

yes

characteristic

269

C₂²

#11926311

yes

characteristic

270

C₄

—

271

C₄

—

272

C₄

—

273

C₄

—

274

C₄

—

275

C₄

—

276

C₄

#11926278

yes

characteristic

277

C₄

#11926278

yes

characteristic

278

C₄

#11926281

yes

characteristic

279

C₄

#11926281

yes

characteristic

280

C₂

—

281

C₂

—

282

C₂

—

283

C₂

—

284

C₂

#14561513

yes

characteristic

285

C₂

#14561758

yes

characteristic

286

C₂

#14561764

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597291
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂×#117	C₂×D₁₉
Fitting	C₁₉×#1798	C₂
socle	C₂²×C₁₉	#342
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₁₉×#117	C₂²
hypercenter	#1798	D₁₉
hypocenter	C₁₉	#7253
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1798

subgroup

G/H

center

C₂×C₄

#10597291

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂×#117

C₂×D₁₉

Fitting

C₁₉×#1798

C₂

socle

C₂²×C₁₉

#342

prime radical

C₂⁴×C₁₉

C₄⋊C₄

cosocle

C₂×C₁₉×#117

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1798

N	H ≅ G/N	type
183. C₁₉	#7253	semidirect

H ≅ G/N

type

183. C₁₉

#7253

semidirect

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

subgroup	index
#14563374	2
#14561949	2
C₁₉×#1798	2
#7253	19

subgroup

index

#14563374

#14561949

C₁₉×#1798

#7253

Subgroups — #18069667

Conjugacy classes of subgroups

Complements

Maximal subgroups