Group #18074785 — subgroups

Subgroups — #18074785

Order 4864.

682 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14564625	C₂	1	2	yes	maximal, complemented
2	#14562373	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562230	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562074	C₂	1	2	yes	maximal
5	C₁₉×#3509	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	2	yes	—
7	C₄×#64520	C₂²	1	2	yes	—
8	#11926313	—	2	4	no	—
9	#11926290	—	2	2	no	—
10	#11926286	—	2	2	no	—
11	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
12	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
13	C₁₉×#557	—	2	2	no	—
14	C₁₉×#556	—	2	2	no	—
15	C₁₉×#552	—	2	4	no	—
16	C₁₉×#541	—	2	2	no	—
17	C₁₉×#536	C₄	1	2	yes	—
18	C₁₉×#533	—	2	2	no	—
19	C₁₉×#533	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₉×#519	C₄	1	2	yes	—
22	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₁₉×C₄⋊Q₈	—	2	2	no	—
26	C₁₉×C₄⋊Q₈	—	2	1	no	—
27	C₁₉×C₄⋊Q₈	—	2	1	no	—
28	C₁₉×C₄⋊Q₈	—	2	2	no	—
29	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
30	C₁₉×#126	—	2	8	no	—
31	C₁₉×#125	—	2	4	no	—
32	C₁₉×#125	—	2	8	no	—
33	C₁₉×#125	D₄	1	2	yes	—
34	C₁₉×#124	—	2	2	no	—
35	C₁₉×#123	—	2	4	no	—
36	C₁₉×C₂²⋊Q₈	—	2	4	no	—
37	C₁₉×C₂²⋊Q₈	—	2	2	no	—
38	C₁₉×C₂²⋊Q₈	—	2	4	no	—
39	C₄×Q₈×C₁₉	—	2	4	no	—
40	C₄×Q₈×C₁₉	—	2	4	no	—
41	C₄×Q₈×C₁₉	—	2	4	no	—
42	C₄×Q₈×C₁₉	—	2	2	no	—
43	C₄×Q₈×C₁₉	D₄	1	2	yes	—
44	C₄×D₄×C₁₉	—	2	2	no	—
45	C₄×D₄×C₁₉	D₄	1	2	yes	—
46	C₁₉×#117	—	2	4	no	—
47	C₁₉×#117	—	2	4	no	—
48	C₁₉×#117	—	2	1	no	—
49	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
50	C₁₉×#117	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×#64520	—	2	2	no	—
55	C₂×#64520	—	2	2	no	—
56	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	#10597260	—	2	2	no	—
59	C₄×C₁₉⋊C₈	—	2	2	no	—
60	#41×C₁₉	—	4	2	no	—
61	C₂×Q₈×C₁₉	—	2	2	no	—
62	C₂×Q₈×C₁₉	—	2	2	no	—
63	C₂×Q₈×C₁₉	—	2	2	no	—
64	C₂×Q₈×C₁₉	—	4	4	no	—
65	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×D₄×C₁₉	—	2	1	no	—
67	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
71	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
73	C₄⋊C₄×C₁₉	—	2	8	no	—
74	C₄⋊C₄×C₁₉	—	2	8	no	—
75	C₄⋊C₄×C₁₉	—	2	4	no	—
76	C₄⋊C₄×C₁₉	—	2	4	no	—
77	C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	2	4	no	—
80	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
81	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
82	C₂²⋊C₄×C₁₉	—	2	8	no	—
83	C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₄²×C₁₉	—	2	8	no	—
87	C₄²×C₁₉	—	2	1	no	—
88	C₄²×C₁₉	—	2	2	no	—
89	C₄²×C₁₉	—	2	2	no	—
90	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₄²×C₁₉	C₂×D₄	1	2	yes	—
93	#64520	—	2	4	no	—
94	#64520	—	4	2	no	—
95	#64520	—	4	4	no	—
96	C₂×C₁₉⋊C₈	—	4	2	no	—
97	C₂×C₁₉⋊C₈	—	4	2	no	—
98	#8474	—	19	1	no	maximal, Sylow
99	C₂³×C₁₉	—	2	1	no	—
100	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	Q₈×C₁₉	—	2	2	no	—
102	Q₈×C₁₉	—	4	4	no	—
103	Q₈×C₁₉	—	4	4	no	—
104	Q₈×C₁₉	—	4	2	no	—
105	Q₈×C₁₉	—	4	2	no	—
106	D₄×C₁₉	—	2	2	no	—
107	D₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	2	2	no	—
110	C₂×C₄×C₁₉	—	2	2	no	—
111	C₂×C₄×C₁₉	—	2	2	no	—
112	C₂×C₄×C₁₉	—	2	4	no	—
113	C₂×C₄×C₁₉	—	2	4	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	4	2	no	—
116	C₂×C₄×C₁₉	—	4	2	no	—
117	C₂×C₄×C₁₉	—	4	2	no	—
118	C₂×C₄×C₁₉	—	4	4	no	—
119	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₉	#120	1	2	yes	—
122	C₂×C₄×C₁₉	#120	1	2	yes	—
123	C₁₉⋊C₈	—	4	4	no	—
124	C₁₉⋊C₈	—	8	2	no	—
125	#3509	D₁₉	1	1	yes	characteristic
126	#1997	—	19	2	no	—
127	#1561	—	19	1	no	—
128	#1526	—	19	1	no	—
129	#1489	—	19	2	no	—
130	C₂²×C₁₉	—	2	2	no	—
131	C₂²×C₁₉	—	2	1	no	—
132	C₂²×C₁₉	—	4	2	no	—
133	C₂²×C₁₉	—	4	1	no	—
134	C₂²×C₁₉	#379	1	1	yes	characteristic
135	C₄×C₁₉	—	2	2	no	—
136	C₄×C₁₉	—	2	1	no	—
137	C₄×C₁₉	—	4	2	no	—
138	C₄×C₁₉	—	4	4	no	—
139	C₄×C₁₉	—	4	1	no	—
140	C₄×C₁₉	—	4	4	no	—
141	C₄×C₁₉	#413	1	2	yes	—
142	C₄×C₁₉	#454	1	2	yes	—
143	C₄×C₁₉	#456	1	2	yes	—
144	#557	—	2	2	no	—
145	#556	—	2	2	no	—
146	#552	—	2	4	no	—
147	#541	—	2	2	no	—
148	#536	Dic₁₉	1	2	yes	—
149	#533	—	2	2	no	—
150	#533	C₂×D₁₉	1	1	yes	characteristic
151	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
152	#519	Dic₁₉	1	2	yes	—
153	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
154	#423	—	19	2	no	—
155	C₄×M₁₆	—	19	2	no	—
156	#343	—	38	4	no	—
157	#332	—	38	2	no	—
158	#330	—	38	2	no	—
159	Q₈⋊C₈	—	38	2	no	—
160	D₄⋊C₈	—	38	2	no	—
161	C₂×C₁₉	—	4	1	no	—
162	C₂×C₁₉	—	8	1	no	—
163	C₂×C₁₉	#1785	1	1	yes	characteristic
164	C₂×C₁₉	#1793	1	2	yes	—
165	C₂×#41	C₂×Dic₁₉	1	1	yes	characteristic
166	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
167	C₂×M₁₆	—	38	2	no	—
168	C₂×M₁₆	—	38	2	no	—
169	C₄⋊Q₈	—	2	2	no	—
170	C₄⋊Q₈	—	2	1	no	—
171	C₄⋊Q₈	—	2	1	no	—
172	C₄⋊Q₈	—	2	2	no	—
173	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
174	#126	—	2	8	no	—
175	#125	—	2	4	no	—
176	#125	—	2	8	no	—
177	#125	C₂²⋊D₁₉	1	2	yes	—
178	#124	—	2	2	no	—
179	#123	—	2	4	no	—
180	C₂²⋊Q₈	—	2	4	no	—
181	C₂²⋊Q₈	—	2	2	no	—
182	C₂²⋊Q₈	—	2	4	no	—
183	C₄×Q₈	—	2	4	no	—
184	C₄×Q₈	—	2	4	no	—
185	C₄×Q₈	—	2	4	no	—
186	C₄×Q₈	—	2	2	no	—
187	C₄×Q₈	C₂²⋊D₁₉	1	2	yes	—
188	C₄×D₄	—	2	2	no	—
189	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
190	#117	—	2	4	no	—
191	#117	—	2	4	no	—
192	#117	—	2	1	no	—
193	#117	C₂×Dic₁₉	1	1	yes	characteristic
194	#117	C₂×Dic₁₉	1	2	yes	—
195	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	4	yes	—
196	C₂×C₄²	—	2	1	no	—
197	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
198	C₄⋊C₈	—	38	2	no	—
199	C₄⋊C₈	—	38	2	no	—
200	#97	—	38	2	no	—
201	C₄×C₈	—	38	2	no	—
202	C₁₉	#8474	1	1	yes	characteristic, complemented, Sylow
203	#41	—	4	2	no	—
204	C₂×Q₈	—	2	2	no	—
205	C₂×Q₈	—	2	2	no	—
206	C₂×Q₈	—	2	2	no	—
207	C₂×Q₈	—	4	4	no	—
208	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
209	C₂×D₄	—	2	1	no	—
210	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
211	C₂²×C₄	—	2	1	no	—
212	C₂²×C₄	—	2	2	no	—
213	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
214	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
215	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
216	M₁₆	—	38	4	no	—
217	M₁₆	—	76	2	no	—
218	M₁₆	—	76	4	no	—
219	C₂×C₈	—	76	2	no	—
220	C₂×C₈	—	76	2	no	—
221	C₄⋊C₄	—	2	8	no	—
222	C₄⋊C₄	—	2	8	no	—
223	C₄⋊C₄	—	2	4	no	—
224	C₄⋊C₄	—	2	4	no	—
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	—	2	2	no	—
227	C₄⋊C₄	—	2	4	no	—
228	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
229	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
230	C₂²⋊C₄	—	2	8	no	—
231	C₂²⋊C₄	—	2	1	no	—
232	C₂²⋊C₄	—	2	2	no	—
233	C₂²⋊C₄	—	2	2	no	—
234	C₄²	—	2	8	no	—
235	C₄²	—	2	1	no	—
236	C₄²	—	2	2	no	—
237	C₄²	—	2	2	no	—
238	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
239	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
240	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
241	C₂³	—	2	1	no	—
242	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
243	Q₈	—	2	2	no	—
244	Q₈	—	4	4	no	—
245	Q₈	—	4	4	no	—
246	Q₈	—	4	2	no	—
247	Q₈	—	4	2	no	—
248	D₄	—	2	2	no	—
249	D₄	—	4	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	4	no	—
255	C₂×C₄	—	2	4	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	4	no	—
261	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
262	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
263	C₂×C₄	#10597399	1	2	yes	—
264	C₂×C₄	#10597399	1	2	yes	—
265	C₈	—	76	4	no	—
266	C₈	—	152	2	no	—
267	C₂²	—	2	2	no	—
268	C₂²	—	2	1	no	—
269	C₂²	—	4	2	no	—
270	C₂²	—	4	1	no	—
271	C₂²	#11926400	1	1	yes	characteristic
272	C₄	—	2	2	no	—
273	C₄	—	2	1	no	—
274	C₄	—	4	2	no	—
275	C₄	—	4	4	no	—
276	C₄	—	4	1	no	—
277	C₄	—	4	4	no	—
278	C₄	#11926528	1	2	yes	—
279	C₄	#11926717	1	2	yes	—
280	C₄	#11926727	1	2	yes	—
281	C₂	—	4	1	no	—
282	C₂	—	8	1	no	—
283	C₂	#14563563	1	1	yes	characteristic
284	C₂	#14563594	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564625

C₂

yes

maximal, complemented

#14562373

C₂

yes

maximal, characteristic, complemented

#14562230

C₂

yes

maximal, characteristic, complemented

#14562074

C₂

yes

maximal

C₁₉×#3509

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

C₄×#64520

C₂²

yes

—

#11926313

—

#11926290

—

#11926286

—

Q₈⋊(C₁₉⋊C₈)

—

D₄⋊(C₁₉⋊C₈)

—

C₁₉×#557

—

C₁₉×#556

—

C₁₉×#552

—

C₁₉×#541

—

C₁₉×#536

C₄

yes

—

C₁₉×#533

—

C₁₉×#533

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#519

C₄

yes

—

C₄×#41×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

C₂×C₄

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#126

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

D₄

yes

—

C₁₉×#124

—

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

D₄

yes

—

C₁₉×#117

—

C₁₉×#117

—

C₁₉×#117

—

C₁₉×#117

C₂×C₄

yes

characteristic

C₁₉×#117

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂×#64520

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

#64520

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8474

—

maximal, Sylow

C₂³×C₁₉

—

100

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

101

Q₈×C₁₉

—

102

Q₈×C₁₉

—

103

Q₈×C₁₉

—

104

Q₈×C₁₉

—

105

Q₈×C₁₉

—

106

D₄×C₁₉

—

107

D₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

—

111

C₂×C₄×C₁₉

—

112

C₂×C₄×C₁₉

—

113

C₂×C₄×C₁₉

—

114

C₂×C₄×C₁₉

—

115

C₂×C₄×C₁₉

—

116

C₂×C₄×C₁₉

—

117

C₂×C₄×C₁₉

—

118

C₂×C₄×C₁₉

—

119

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

120

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

121

C₂×C₄×C₁₉

#120

yes

—

122

C₂×C₄×C₁₉

#120

yes

—

123

C₁₉⋊C₈

—

124

C₁₉⋊C₈

—

125

#3509

D₁₉

yes

characteristic

126

#1997

—

127

#1561

—

128

#1526

—

129

#1489

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

#379

yes

characteristic

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

#413

yes

—

142

C₄×C₁₉

#454

yes

—

143

C₄×C₁₉

#456

yes

—

144

#557

—

145

#556

—

146

#552

—

147

#541

—

148

#536

Dic₁₉

yes

—

149

#533

—

150

#533

C₂×D₁₉

yes

characteristic

151

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

152

#519

Dic₁₉

yes

—

153

C₄×#41

C₂×D₁₉

yes

characteristic

154

#423

—

155

C₄×M₁₆

—

156

#343

—

157

#332

—

158

#330

—

159

Q₈⋊C₈

—

160

D₄⋊C₈

—

161

C₂×C₁₉

—

162

C₂×C₁₉

—

163

C₂×C₁₉

#1785

yes

characteristic

164

C₂×C₁₉

#1793

yes

—

165

C₂×#41

C₂×Dic₁₉

yes

characteristic

166

C₂²×Q₈

C₂×Dic₁₉

yes

—

167

C₂×M₁₆

—

168

C₂×M₁₆

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

174

#126

—

175

#125

—

176

#125

—

177

#125

C₂²⋊D₁₉

yes

—

178

#124

—

179

#123

—

180

C₂²⋊Q₈

—

181

C₂²⋊Q₈

—

182

C₂²⋊Q₈

—

183

C₄×Q₈

—

184

C₄×Q₈

—

185

C₄×Q₈

—

186

C₄×Q₈

—

187

C₄×Q₈

C₂²⋊D₁₉

yes

—

188

C₄×D₄

—

189

C₄×D₄

C₂²⋊D₁₉

yes

—

190

#117

—

191

#117

—

192

#117

—

193

#117

C₂×Dic₁₉

yes

characteristic

194

#117

C₂×Dic₁₉

yes

—

195

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

196

C₂×C₄²

—

197

C₂×C₄²

C₂²×D₁₉

yes

characteristic

198

C₄⋊C₈

—

199

C₄⋊C₈

—

200

#97

—

201

C₄×C₈

—

202

C₁₉

#8474

yes

characteristic, complemented, Sylow

203

#41

—

204

C₂×Q₈

—

205

C₂×Q₈

—

206

C₂×Q₈

—

207

C₂×Q₈

—

208

C₂×Q₈

C₂²⋊Dic₁₉

yes

characteristic

209

C₂×D₄

—

210

C₂×D₄

C₂²⋊Dic₁₉

yes

characteristic

211

C₂²×C₄

—

212

C₂²×C₄

—

213

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

214

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

215

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

216

M₁₆

—

217

M₁₆

—

218

M₁₆

—

219

C₂×C₈

—

220

C₂×C₈

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

229

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

230

C₂²⋊C₄

—

231

C₂²⋊C₄

—

232

C₂²⋊C₄

—

233

C₂²⋊C₄

—

234

C₄²

—

235

C₄²

—

236

C₄²

—

237

C₄²

—

238

C₄²

C₂×C₂²⋊D₁₉

yes

—

239

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

240

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

241

C₂³

—

242

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

243

Q₈

—

244

Q₈

—

245

Q₈

—

246

Q₈

—

247

Q₈

—

248

D₄

—

249

D₄

—

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

C₂×C₂²⋊Dic₁₉

yes

characteristic

262

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

263

C₂×C₄

#10597399

yes

—

264

C₂×C₄

#10597399

yes

—

265

C₈

—

266

C₈

—

152

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

#11926400

yes

characteristic

272

C₄

—

273

C₄

—

274

C₄

—

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

#11926528

yes

—

279

C₄

#11926717

yes

—

280

C₄

#11926727

yes

—

281

C₂

—

282

C₂

—

283

C₂

#14563563

yes

characteristic

284

C₂

#14563594

yes

—

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3509	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂×#41×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3509	D₁₉
hypocenter	C₁₉	#8474
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3509

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3509

C₂

socle

C₂²×C₁₉

#379

prime radical

C₂×#41×C₁₉

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3509

N	H ≅ G/N	type
1. #14564625	C₂	semidirect
2. #14562373	C₂	semidirect
3. #14562230	C₂	semidirect
202. C₁₉	#8474	semidirect

H ≅ G/N

type

1. #14564625

C₂

semidirect

2. #14562373

C₂

semidirect

3. #14562230

C₂

semidirect

202. C₁₉

#8474

semidirect

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

subgroup	index
#14564625	2
#14562373	2
#14562230	2
#14562074	2
C₁₉×#3509	2
#8474	19

subgroup

index

C₁₉×#3509

Subgroups — #18074785

Conjugacy classes of subgroups

Complements

Maximal subgroups