Group #18079186 — subgroups

Subgroups — #18079186

Order 4864.

410 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14574786	C₂	1	1	yes	maximal, characteristic
2	#14572572	C₂	1	1	yes	maximal, characteristic
3	#14564609	C₂	1	1	yes	maximal, characteristic
4	#14562200	C₂	1	1	yes	maximal, characteristic
5	#14561495	C₂	1	1	yes	maximal, characteristic
6	#14561465	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	#11926947	C₄	1	2	yes	complemented
10	#11926896	C₄	1	2	yes	complemented
11	#11926879	—	2	2	no	—
12	#11926836	—	2	2	no	—
13	#11926673	—	2	2	no	—
14	#11926673	—	2	2	no	—
15	#11926597	C₂²	1	1	yes	characteristic
16	#11926572	—	2	1	no	—
17	#11926502	—	2	1	no	—
18	C₂×#10597260	C₂²	1	1	yes	characteristic
19	#11926410	C₂²	1	1	yes	characteristic
20	#11926306	—	2	1	no	—
21	#11926306	—	2	1	no	—
22	#11926282	—	2	2	no	—
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#431	C₂²	1	1	yes	characteristic
25	C₁₉×#423	C₂²	1	1	yes	characteristic
26	C₁₉×#333	—	2	2	no	—
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₁₉×C₄⋊Q₈	—	2	1	no	—
30	C₁₉×C₄⋊Q₈	—	2	1	no	—
31	C₁₉×C₄⋊Q₈	—	2	1	no	—
32	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	#10597372	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	#10597370	—	2	1	no	—
39	#10597370	D₄	1	2	yes	—
40	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
41	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
42	#10597316	—	2	1	no	—
43	#10597315	C₂×C₄	1	1	yes	characteristic
44	#10597315	C₂×C₄	1	1	yes	characteristic
45	C₄×Dic₃₈	—	2	1	no	—
46	C₄×Dic₃₈	D₄	1	2	yes	—
47	C₁₉×C₄⋊C₈	—	2	1	no	—
48	C₁₉×C₄⋊C₈	—	2	1	no	—
49	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
50	C₁₉×C₂²⋊C₈	—	2	1	no	—
51	C₄×C₈×C₁₉	—	2	1	no	—
52	C₁₉⋊#95	—	2	1	no	—
53	C₁₉⋊#95	—	2	1	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
55	#10597272	—	2	2	no	—
56	Dic₁₉⋊C₈	—	2	4	no	—
57	C₈×Dic₁₉	—	2	2	no	—
58	#10597267	—	2	4	no	—
59	#10597264	—	2	4	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
61	#10597260	—	2	1	no	—
62	#10597260	—	2	1	no	—
63	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
64	C₂×Q₈×C₁₉	—	2	2	no	—
65	C₂×Q₈×C₁₉	—	4	1	no	—
66	C₂×Q₈×C₁₉	—	8	2	no	—
67	C₂²×C₄×C₁₉	—	4	1	no	—
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
71	C₂²×Dic₁₉	—	4	1	no	—
72	C₂×Dic₃₈	—	2	1	no	—
73	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
74	M₁₆×C₁₉	—	4	1	no	—
75	M₁₆×C₁₉	—	4	1	no	—
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	—	4	1	no	—
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₄⋊C₄×C₁₉	—	4	1	no	—
81	C₄⋊C₄×C₁₉	—	4	1	no	—
82	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₁₉	#41	1	1	yes	characteristic
86	C₂²⋊Dic₁₉	—	2	2	no	—
87	C₄⋊Dic₁₉	—	2	1	no	—
88	C₄⋊Dic₁₉	—	2	1	no	—
89	C₄⋊Dic₁₉	—	2	1	no	—
90	C₄⋊Dic₁₉	—	4	1	no	—
91	C₄⋊Dic₁₉	—	4	1	no	—
92	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
93	Dic₁₉⋊C₄	—	2	2	no	—
94	Dic₁₉⋊C₄	—	2	2	no	—
95	C₄×Dic₁₉	—	2	2	no	—
96	C₂×C₁₉⋊C₈	—	2	1	no	—
97	C₂×C₁₉⋊C₈	—	2	1	no	—
98	C₂×C₁₉⋊C₈	—	2	2	no	—
99	C₂×C₁₉⋊C₈	—	2	1	no	—
100	C₂×C₁₉⋊C₈	—	2	1	no	—
101	C₂×C₁₉⋊C₈	—	2	1	no	—
102	C₂×C₁₉⋊C₈	Q₁₆	1	2	yes	—
103	#9288	—	19	1	no	maximal, Sylow
104	C₂³×C₁₉	#121	1	1	yes	characteristic
105	Q₈×C₁₉	—	8	2	no	—
106	Q₈×C₁₉	—	8	2	no	—
107	C₂×C₄×C₁₉	—	4	1	no	—
108	C₂×C₄×C₁₉	—	4	1	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	—	8	2	no	—
111	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
115	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
116	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
118	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
120	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
121	C₂×Dic₁₉	—	2	2	no	—
122	C₂×Dic₁₉	—	2	2	no	—
123	C₂×Dic₁₉	—	8	1	no	—
124	C₂×Dic₁₉	—	8	1	no	—
125	C₂×Dic₁₉	—	8	1	no	—
126	Dic₃₈	—	4	2	no	—
127	Dic₃₈	—	8	1	no	—
128	C₈×C₁₉	—	4	2	no	—
129	C₈×C₁₉	—	8	1	no	—
130	C₁₉⋊C₈	—	2	2	no	—
131	C₁₉⋊C₈	—	4	2	no	—
132	C₁₉⋊C₈	—	4	1	no	—
133	#3230	—	19	1	no	—
134	#2961	—	19	1	no	—
135	#1993	—	19	1	no	—
136	#1548	D₁₉	1	1	yes	characteristic
137	#1518	—	19	1	no	—
138	#1286	—	19	1	no	—
139	#1275	—	19	1	no	—
140	C₂²×C₁₉	—	2	1	no	—
141	C₂²×C₁₉	—	2	1	no	—
142	C₂²×C₁₉	#386	1	1	yes	characteristic
143	C₂²×C₁₉	#462	1	1	yes	characteristic
144	C₂²×C₁₉	#464	1	1	yes	characteristic
145	C₄×C₁₉	—	2	1	no	—
146	C₄×C₁₉	—	2	1	no	—
147	C₄×C₁₉	—	2	1	no	—
148	C₄×C₁₉	—	2	1	no	—
149	C₄×C₁₉	—	8	2	no	—
150	C₄×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
151	C₄×C₁₉	#441	1	1	yes	characteristic
152	C₄×C₁₉	#451	1	1	yes	characteristic
153	C₄×C₁₉	#452	1	1	yes	characteristic
154	Dic₁₉	—	4	2	no	—
155	Dic₁₉	—	4	2	no	—
156	Dic₁₉	—	16	1	no	—
157	#533	—	19	1	no	—
158	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
159	#500	—	19	2	no	—
160	#487	—	19	2	no	—
161	#484	—	38	2	no	—
162	#477	—	38	2	no	—
163	#446	—	38	2	no	—
164	#446	—	38	2	no	—
165	#431	—	19	1	no	—
166	#431	C₂×D₁₉	1	1	yes	characteristic
167	#424	—	38	1	no	—
168	#423	C₂×D₁₉	1	1	yes	characteristic
169	#405	—	38	1	no	—
170	C₂×#97	—	19	1	no	—
171	#382	—	19	1	no	—
172	#340	—	38	1	no	—
173	#340	—	38	1	no	—
174	#333	—	2	2	no	—
175	#328	—	38	2	no	—
176	C₂×C₁₉	—	2	1	no	—
177	C₂×C₁₉	—	2	1	no	—
178	C₂×C₁₉	#1878	1	1	yes	characteristic
179	C₂×C₁₉	#1903	1	1	yes	characteristic
180	C₂×C₁₉	#1909	1	1	yes	characteristic
181	C₂²×Q₈	—	2	1	no	—
182	C₂×M₁₆	—	2	1	no	—
183	C₂²×C₈	—	19	1	no	—
184	C₂²×C₈	—	19	1	no	—
185	C₄⋊Q₈	—	2	1	no	—
186	C₄⋊Q₈	—	2	1	no	—
187	C₄⋊Q₈	—	2	1	no	—
188	C₄⋊Q₈	—	19	1	no	—
189	C₄⋊Q₈	—	19	1	no	—
190	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
191	#125	—	38	1	no	—
192	C₂²⋊Q₈	—	19	2	no	—
193	C₂²⋊Q₈	—	38	1	no	—
194	C₄×Q₈	—	19	2	no	—
195	C₄×Q₈	—	38	1	no	—
196	#117	—	38	1	no	—
197	C₂×C₄⋊C₄	—	2	1	no	—
198	C₂×C₄⋊C₄	—	2	1	no	—
199	C₂×C₄⋊C₄	—	38	1	no	—
200	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
201	#107	—	38	4	no	—
202	C₄⋊C₈	—	2	1	no	—
203	C₄⋊C₈	—	2	1	no	—
204	C₄⋊C₈	—	38	4	no	—
205	C₄⋊C₈	—	38	1	no	—
206	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
207	#103	—	38	4	no	—
208	C₂²⋊C₈	—	2	1	no	—
209	C₂²⋊C₈	—	38	1	no	—
210	#97	—	38	2	no	—
211	#97	—	38	1	no	—
212	#97	—	38	1	no	—
213	C₄×C₈	—	2	1	no	—
214	C₄×C₈	—	19	2	no	—
215	C₄×C₈	—	38	2	no	—
216	#95	—	38	1	no	—
217	#95	—	38	1	no	—
218	C₁₉	#9288	1	1	yes	characteristic, complemented, Sylow
219	C₂×Q₈	—	2	2	no	—
220	C₂×Q₈	—	4	1	no	—
221	C₂×Q₈	—	8	2	no	—
222	C₂×Q₈	—	19	2	no	—
223	C₂×Q₈	—	38	1	no	—
224	C₂²×C₄	—	4	1	no	—
225	C₂²×C₄	—	76	1	no	—
226	C₂²×C₄	#64541	1	1	yes	characteristic
227	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
228	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
229	M₁₆	—	4	1	no	—
230	M₁₆	—	4	1	no	—
231	C₂×C₈	—	2	2	no	—
232	C₂×C₈	—	4	1	no	—
233	C₂×C₈	—	19	2	no	—
234	C₂×C₈	—	38	1	no	—
235	C₂×C₈	—	38	1	no	—
236	C₂×C₈	—	38	1	no	—
237	C₂×C₈	—	38	2	no	—
238	C₂×C₈	—	38	1	no	—
239	C₂×C₈	—	38	1	no	—
240	C₄⋊C₄	—	2	2	no	—
241	C₄⋊C₄	—	2	2	no	—
242	C₄⋊C₄	—	4	1	no	—
243	C₄⋊C₄	—	4	1	no	—
244	C₄⋊C₄	—	19	2	no	—
245	C₄⋊C₄	—	38	2	no	—
246	C₄⋊C₄	—	38	1	no	—
247	C₄⋊C₄	—	38	1	no	—
248	C₄⋊C₄	—	38	2	no	—
249	C₄⋊C₄	—	38	1	no	—
250	C₄⋊C₄	—	76	1	no	—
251	C₄⋊C₄	—	76	1	no	—
252	C₂²⋊C₄	—	38	2	no	—
253	C₄²	—	38	2	no	—
254	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
255	C₄²	D₄×D₁₉	1	1	yes	characteristic
256	C₄²	#64543	1	1	yes	characteristic
257	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
258	C₂³	#10597330	1	1	yes	characteristic
259	Q₈	—	8	2	no	—
260	Q₈	—	8	2	no	—
261	Q₈	—	76	2	no	—
262	Q₈	—	152	1	no	—
263	C₂×C₄	—	4	1	no	—
264	C₂×C₄	—	4	1	no	—
265	C₂×C₄	—	4	2	no	—
266	C₂×C₄	—	8	2	no	—
267	C₂×C₄	—	38	2	no	—
268	C₂×C₄	—	38	2	no	—
269	C₂×C₄	—	152	1	no	—
270	C₂×C₄	—	152	1	no	—
271	C₂×C₄	—	152	1	no	—
272	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
273	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
274	C₂×C₄	#10597329	1	1	yes	characteristic
275	C₂×C₄	#10597361	1	1	yes	characteristic
276	C₂×C₄	#10597362	1	1	yes	characteristic
277	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
278	C₂×C₄	#10597364	1	1	yes	characteristic
279	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
280	C₂×C₄	#10597383	1	1	yes	characteristic
281	C₂×C₄	#10597384	1	1	yes	characteristic
282	C₈	—	4	2	no	—
283	C₈	—	8	1	no	—
284	C₈	—	38	2	no	—
285	C₈	—	76	2	no	—
286	C₈	—	76	1	no	—
287	C₂²	—	2	1	no	—
288	C₂²	—	2	1	no	—
289	C₂²	#11926420	1	1	yes	characteristic
290	C₂²	#11926753	1	1	yes	characteristic
291	C₂²	#11926769	1	1	yes	characteristic
292	C₄	—	2	1	no	—
293	C₄	—	2	1	no	—
294	C₄	—	2	1	no	—
295	C₄	—	2	1	no	—
296	C₄	—	8	2	no	—
297	C₄	—	304	1	no	—
298	C₄	—	76	2	no	—
299	C₄	—	76	2	no	—
300	C₄	#11926636	1	1	yes	characteristic
301	C₄	#11926648	1	1	yes	characteristic
302	C₄	#11926698	1	1	yes	characteristic
303	C₄	#11926703	1	1	yes	characteristic
304	C₂	—	2	1	no	—
305	C₂	—	2	1	no	—
306	C₂	#14563973	1	1	yes	characteristic
307	C₂	#14564118	1	1	yes	characteristic
308	C₂	#14564154	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574786

C₂

yes

maximal, characteristic

#14572572

C₂

yes

maximal, characteristic

#14564609

C₂

yes

maximal, characteristic

#14562200

C₂

yes

maximal, characteristic

#14561495

C₂

yes

maximal, characteristic

#14561465

C₂

yes

maximal, characteristic

C₁₉×#1548

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926947

C₄

yes

complemented

#11926896

C₄

yes

—

—

—

—

C₂²

yes

—

—

C₂²

yes

characteristic

#11926410

C₂²

yes

—

—

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#333

—

C₂²×Q₈×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

—

#10597370

—

#10597370

D₄

yes

—

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

#10597316

—

#10597315

C₂×C₄

yes

characteristic

#10597315

C₂×C₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597272

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

#10597267

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂²⋊C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×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

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂²⋊C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

100

C₂×C₁₉⋊C₈

—

101

C₂×C₁₉⋊C₈

—

102

C₂×C₁₉⋊C₈

Q₁₆

yes

—

103

#9288

—

maximal, Sylow

104

C₂³×C₁₉

#121

yes

characteristic

105

Q₈×C₁₉

—

106

Q₈×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

—

111

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

112

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

113

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

114

C₂×C₄×C₁₉

#120

yes

characteristic

115

C₂×C₄×C₁₉

#121

yes

characteristic

116

C₂×C₄×C₁₉

#123

yes

characteristic

117

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

118

C₂×C₄×C₁₉

#135

yes

characteristic

119

C₂×C₄×C₁₉

#137

yes

characteristic

120

C₂×C₄×C₁₉

#137

yes

characteristic

121

C₂×Dic₁₉

—

122

C₂×Dic₁₉

—

123

C₂×Dic₁₉

—

124

C₂×Dic₁₉

—

125

C₂×Dic₁₉

—

126

Dic₃₈

—

127

Dic₃₈

—

128

C₈×C₁₉

—

129

C₈×C₁₉

—

130

C₁₉⋊C₈

—

131

C₁₉⋊C₈

—

132

C₁₉⋊C₈

—

133

#3230

—

134

#2961

—

135

#1993

—

136

#1548

D₁₉

yes

characteristic

137

#1518

—

138

#1286

—

139

#1275

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

—

142

C₂²×C₁₉

#386

yes

characteristic

143

C₂²×C₁₉

#462

yes

characteristic

144

C₂²×C₁₉

#464

yes

characteristic

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₄×C₁₉

—

149

C₄×C₁₉

—

150

C₄×C₁₉

C₄×Q₁₆

yes

characteristic

151

C₄×C₁₉

#441

yes

characteristic

152

C₄×C₁₉

#451

yes

characteristic

153

C₄×C₁₉

#452

yes

characteristic

154

Dic₁₉

—

155

Dic₁₉

—

156

Dic₁₉

—

157

#533

—

158

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

159

#500

—

160

#487

—

161

#484

—

162

#477

—

163

#446

—

164

#446

—

165

#431

—

166

#431

C₂×D₁₉

yes

characteristic

167

#424

—

168

#423

C₂×D₁₉

yes

characteristic

169

#405

—

170

C₂×#97

—

171

#382

—

172

#340

—

173

#340

—

174

#333

—

175

#328

—

176

C₂×C₁₉

—

177

C₂×C₁₉

—

178

C₂×C₁₉

#1878

yes

characteristic

179

C₂×C₁₉

#1903

yes

characteristic

180

C₂×C₁₉

#1909

yes

characteristic

181

C₂²×Q₈

—

182

C₂×M₁₆

—

183

C₂²×C₈

—

184

C₂²×C₈

—

185

C₄⋊Q₈

—

186

C₄⋊Q₈

—

187

C₄⋊Q₈

—

188

C₄⋊Q₈

—

189

C₄⋊Q₈

—

190

C₄⋊Q₈

C₄×D₁₉

yes

—

191

#125

—

192

C₂²⋊Q₈

—

193

C₂²⋊Q₈

—

194

C₄×Q₈

—

195

C₄×Q₈

—

196

#117

—

197

C₂×C₄⋊C₄

—

198

C₂×C₄⋊C₄

—

199

C₂×C₄⋊C₄

—

200

C₂×C₄²

C₂²×D₁₉

yes

characteristic

201

#107

—

202

C₄⋊C₈

—

203

C₄⋊C₈

—

204

C₄⋊C₈

—

205

C₄⋊C₈

—

206

C₄⋊C₈

C₂²⋊D₁₉

yes

—

207

#103

—

208

C₂²⋊C₈

—

209

C₂²⋊C₈

—

210

#97

—

211

#97

—

212

#97

—

213

C₄×C₈

—

214

C₄×C₈

—

215

C₄×C₈

—

216

#95

—

217

#95

—

218

C₁₉

#9288

yes

characteristic, complemented, Sylow

219

C₂×Q₈

—

220

C₂×Q₈

—

221

C₂×Q₈

—

222

C₂×Q₈

—

223

C₂×Q₈

—

224

C₂²×C₄

—

225

C₂²×C₄

—

226

C₂²×C₄

#64541

yes

characteristic

227

C₂²×C₄

D₄×D₁₉

yes

characteristic

228

C₂²×C₄

D₄×D₁₉

yes

characteristic

229

M₁₆

—

230

M₁₆

—

231

C₂×C₈

—

232

C₂×C₈

—

233

C₂×C₈

—

234

C₂×C₈

—

235

C₂×C₈

—

236

C₂×C₈

—

237

C₂×C₈

—

238

C₂×C₈

—

239

C₂×C₈

—

240

C₄⋊C₄

—

241

C₄⋊C₄

—

242

C₄⋊C₄

—

243

C₄⋊C₄

—

244

C₄⋊C₄

—

245

C₄⋊C₄

—

246

C₄⋊C₄

—

247

C₄⋊C₄

—

248

C₄⋊C₄

—

249

C₄⋊C₄

—

250

C₄⋊C₄

—

251

C₄⋊C₄

—

252

C₂²⋊C₄

—

253

C₄²

—

254

C₄²

C₂×C₄×D₁₉

yes

characteristic

255

C₄²

D₄×D₁₉

yes

characteristic

256

C₄²

#64543

yes

characteristic

257

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

258

C₂³

#10597330

yes

characteristic

259

Q₈

—

260

Q₈

—

261

Q₈

—

262

Q₈

—

152

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

—

267

C₂×C₄

—

268

C₂×C₄

—

269

C₂×C₄

—

152

—

270

C₂×C₄

—

152

—

271

C₂×C₄

—

152

—

272

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

273

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

274

C₂×C₄

#10597329

yes

characteristic

275

C₂×C₄

#10597361

yes

characteristic

276

C₂×C₄

#10597362

yes

characteristic

277

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

278

C₂×C₄

#10597364

yes

characteristic

279

C₂×C₄

C₄×C₂²⋊D₁₉

yes

characteristic

280

C₂×C₄

#10597383

yes

characteristic

281

C₂×C₄

#10597384

yes

characteristic

282

C₈

—

283

C₈

—

284

C₈

—

285

C₈

—

286

C₈

—

287

C₂²

—

288

C₂²

—

289

C₂²

#11926420

yes

characteristic

290

C₂²

#11926753

yes

characteristic

291

C₂²

#11926769

yes

characteristic

292

C₄

—

293

C₄

—

294

C₄

—

295

C₄

—

296

C₄

—

297

C₄

—

304

—

298

C₄

—

299

C₄

—

300

C₄

#11926636

yes

characteristic

301

C₄

#11926648

yes

characteristic

302

C₄

#11926698

yes

characteristic

303

C₄

#11926703

yes

characteristic

304

C₂

—

305

C₂

—

306

C₂

#14563973

yes

characteristic

307

C₂

#14564118

yes

characteristic

308

C₂

#14564154

yes

characteristic

	subgroup	G/H
center	C₂²	#11926420
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1548	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1548	D₁₉
hypocenter	C₁₉	#9288
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

subgroup

G/H

center

C₂²

#11926420

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1548

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

N	H ≅ G/N	type
9. #11926947	C₄	semidirect
10. #11926896	C₄	semidirect
218. C₁₉	#9288	semidirect

H ≅ G/N

type

9. #11926947

C₄

semidirect

10. #11926896

C₄

semidirect

218. C₁₉

#9288

semidirect

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

subgroup	index
#14574786	2
#14572572	2
#14564609	2
#14562200	2
#14561495	2
#14561465	2
C₁₉×#1548	2
#9288	19

subgroup

index

C₁₉×#1548

Subgroups — #18079186

Conjugacy classes of subgroups

Complements

Maximal subgroups