Group #18077728 — subgroups

Subgroups — #18077728

Order 4864.

424 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 109 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	#14573674	C₂	1	1	yes	maximal, characteristic
2	#14572575	C₂	1	1	yes	maximal, characteristic
3	#14562293	C₂	1	1	yes	maximal, characteristic
4	#14562064	C₂	1	1	yes	maximal, characteristic
5	#14561532	C₂	1	1	yes	maximal, characteristic
6	#14561480	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	#11926879	C₄	1	2	yes	—
10	#11926839	—	2	1	no	—
11	#11926754	—	2	1	no	—
12	#11926700	C₄	1	2	yes	—
13	#11926672	—	2	2	no	—
14	#11926672	—	2	2	no	—
15	C₄×#64528	—	2	2	no	—
16	#11926597	C₂²	1	1	yes	characteristic
17	#11926597	C₂²	1	1	yes	characteristic
18	#11926570	—	2	1	no	—
19	#11926568	C₂²	1	1	yes	characteristic
20	#11926499	—	2	1	no	—
21	#11926292	—	2	1	no	—
22	#11926289	—	2	1	no	—
23	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
27	C₁₉×#336	—	2	1	no	—
28	C₁₉×#336	—	2	1	no	—
29	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₄×Q₈×C₁₉	—	2	1	no	—
34	C₄×Q₈×C₁₉	—	2	1	no	—
35	C₄×Q₈×C₁₉	—	2	1	no	—
36	C₄×Q₈×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×#64528	—	2	2	no	—
42	#10597372	—	2	1	no	—
43	#10597370	—	2	1	no	—
44	#10597370	C₂×C₄	1	2	yes	—
45	C₂×#64520	—	2	1	no	—
46	#10597316	—	2	1	no	—
47	#10597315	D₄	1	1	yes	characteristic
48	#10597315	D₄	1	1	yes	characteristic
49	C₄×Dic₃₈	—	2	1	no	—
50	C₄×Dic₃₈	D₄	1	2	yes	—
51	C₁₉×C₄⋊C₈	—	2	1	no	—
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×#97	—	2	1	no	—
54	C₁₉×#97	—	2	1	no	—
55	#10597292	—	2	2	no	—
56	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
57	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
58	#10597272	—	2	2	no	—
59	Dic₁₉⋊C₈	—	2	4	no	—
60	C₈×Dic₁₉	—	2	2	no	—
61	#10597267	—	2	2	no	—
62	#10597264	—	2	2	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
67	C₄×C₁₉⋊C₈	—	2	1	no	—
68	C₄×C₁₉⋊C₈	—	2	1	no	—
69	C₂×Q₈×C₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	4	2	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
77	C₂×Dic₃₈	—	2	1	no	—
78	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
79	C₂×C₈×C₁₉	—	2	1	no	—
80	C₂×C₈×C₁₉	—	2	1	no	—
81	C₂×C₈×C₁₉	—	2	1	no	—
82	C₂×C₈×C₁₉	—	2	1	no	—
83	C₂×C₈×C₁₉	—	2	1	no	—
84	C₂×C₈×C₁₉	—	4	1	no	—
85	C₂×C₈×C₁₉	—	4	1	no	—
86	C₂×C₈×C₁₉	—	4	1	no	—
87	C₂×C₈×C₁₉	Q₁₆	1	2	yes	complemented
88	C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₄⋊C₄×C₁₉	—	4	1	no	—
91	C₄⋊C₄×C₁₉	—	4	1	no	—
92	C₄²×C₁₉	—	4	1	no	—
93	C₄²×C₁₉	—	4	1	no	—
94	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₄²×C₁₉	#41	1	1	yes	characteristic
98	C₂²⋊Dic₁₉	—	2	2	no	—
99	#64528	—	4	4	no	—
100	C₄⋊Dic₁₉	—	2	1	no	—
101	C₄⋊Dic₁₉	—	2	1	no	—
102	C₄⋊Dic₁₉	—	2	1	no	—
103	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
104	Dic₁₉⋊C₄	—	2	2	no	—
105	Dic₁₉⋊C₄	—	2	2	no	—
106	C₄×Dic₁₉	—	2	2	no	—
107	#64520	—	4	1	no	—
108	#64520	—	4	1	no	—
109	C₂×C₁₉⋊C₈	—	2	2	no	—
110	C₂×C₁₉⋊C₈	—	2	2	no	—
111	C₂×C₁₉⋊C₈	—	4	1	no	—
112	#9048	—	19	1	no	maximal, Sylow
113	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
114	Q₈×C₁₉	—	2	2	no	—
115	Q₈×C₁₉	—	2	2	no	—
116	Q₈×C₁₉	—	4	1	no	—
117	Q₈×C₁₉	—	4	1	no	—
118	C₂×C₄×C₁₉	—	2	2	no	—
119	C₂×C₄×C₁₉	—	4	1	no	—
120	C₂×C₄×C₁₉	—	4	1	no	—
121	C₂×C₄×C₁₉	—	4	1	no	—
122	C₂×C₄×C₁₉	—	4	1	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
127	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
128	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
129	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
130	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
131	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
133	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
135	C₂×Dic₁₉	—	2	2	no	—
136	C₂×Dic₁₉	—	2	2	no	—
137	Dic₃₈	—	4	2	no	—
138	Dic₃₈	—	8	1	no	—
139	C₈×C₁₉	—	2	2	no	—
140	C₈×C₁₉	—	4	1	no	—
141	C₈×C₁₉	—	8	1	no	—
142	C₁₉⋊C₈	—	4	2	no	—
143	C₁₉⋊C₈	—	4	2	no	—
144	C₁₉⋊C₈	—	8	1	no	—
145	#3104	—	19	1	no	—
146	#2961	—	19	1	no	—
147	#1985	D₁₉	1	1	yes	characteristic
148	#1542	—	19	1	no	—
149	#1487	—	19	1	no	—
150	#1301	—	19	1	no	—
151	#1281	—	19	1	no	—
152	C₂²×C₁₉	—	2	1	no	—
153	C₂²×C₁₉	—	2	1	no	—
154	C₂²×C₁₉	#386	1	1	yes	characteristic
155	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
156	C₂²×C₁₉	#441	1	1	yes	characteristic
157	C₄×C₁₉	—	2	1	no	—
158	C₄×C₁₉	—	2	1	no	—
159	C₄×C₁₉	—	2	1	no	—
160	C₄×C₁₉	—	2	1	no	—
161	C₄×C₁₉	—	4	2	no	—
162	C₄×C₁₉	—	8	1	no	—
163	C₄×C₁₉	#451	1	1	yes	characteristic
164	C₄×C₁₉	#452	1	1	yes	characteristic
165	C₄×C₁₉	#462	1	1	yes	characteristic
166	C₄×C₁₉	#464	1	1	yes	characteristic
167	Dic₁₉	—	4	2	no	—
168	Dic₁₉	—	4	2	no	—
169	#533	—	19	1	no	—
170	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
171	#484	—	19	2	no	—
172	#477	—	38	1	no	—
173	#462	—	38	1	no	—
174	#451	—	19	2	no	—
175	#446	—	38	2	no	—
176	#446	—	38	2	no	—
177	C₄×Q₁₆	—	38	2	no	—
178	#431	—	19	1	no	—
179	#431	—	19	1	no	—
180	#424	—	38	1	no	—
181	#423	—	19	1	no	—
182	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
183	#405	—	38	1	no	—
184	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
185	#336	—	2	1	no	—
186	#336	—	2	1	no	—
187	#333	—	38	1	no	—
188	#332	—	38	1	no	—
189	Q₈⋊C₈	—	38	2	no	—
190	C₂×C₁₉	—	2	1	no	—
191	C₂×C₁₉	—	2	1	no	—
192	C₂×C₁₉	#1878	1	1	yes	characteristic
193	C₂×C₁₉	#1881	1	1	yes	characteristic
194	C₂×C₁₉	#1891	1	1	yes	characteristic
195	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
196	C₂×Q₁₆	—	38	2	no	—
197	C₂×M₁₆	—	38	1	no	—
198	C₂²×C₈	—	2	1	no	—
199	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
200	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
201	C₄⋊Q₈	—	19	1	no	—
202	C₄⋊Q₈	—	19	1	no	—
203	#125	—	38	1	no	—
204	C₂²⋊Q₈	—	19	2	no	—
205	C₂²⋊Q₈	—	38	1	no	—
206	C₄×Q₈	—	2	1	no	—
207	C₄×Q₈	—	2	1	no	—
208	C₄×Q₈	—	2	1	no	—
209	C₄×Q₈	—	2	1	no	—
210	C₄×Q₈	—	19	2	no	—
211	C₄×Q₈	—	38	1	no	—
212	#117	—	38	1	no	—
213	C₂×C₄⋊C₄	—	2	1	no	—
214	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
215	C₂×C₄²	—	2	1	no	—
216	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
217	#107	—	38	2	no	—
218	C₄⋊C₈	—	2	1	no	—
219	C₄⋊C₈	—	2	1	no	—
220	C₄⋊C₈	—	19	2	no	—
221	C₄⋊C₈	—	38	4	no	—
222	C₄⋊C₈	—	38	1	no	—
223	C₄⋊C₈	—	38	1	no	—
224	C₄⋊C₈	—	38	1	no	—
225	#103	—	38	2	no	—
226	#103	—	38	2	no	—
227	C₂²⋊C₈	—	19	2	no	—
228	C₂²⋊C₈	—	38	1	no	—
229	#97	—	2	1	no	—
230	#97	—	2	1	no	—
231	#97	—	38	2	no	—
232	C₄×C₈	—	38	2	no	—
233	C₄×C₈	—	38	1	no	—
234	C₄×C₈	—	38	1	no	—
235	C₁₉	#9048	1	1	yes	characteristic, complemented, Sylow
236	C₂×Q₈	—	2	1	no	—
237	C₂×Q₈	—	2	1	no	—
238	C₂×Q₈	—	4	2	no	—
239	C₂×Q₈	—	19	2	no	—
240	C₂×Q₈	—	38	1	no	—
241	C₂²×C₄	—	2	1	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
244	C₂²×C₄	#64541	1	1	yes	characteristic
245	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
246	Q₁₆	—	76	4	no	—
247	M₁₆	—	76	1	no	—
248	M₁₆	—	76	1	no	—
249	C₂×C₈	—	2	1	no	—
250	C₂×C₈	—	2	1	no	—
251	C₂×C₈	—	2	1	no	—
252	C₂×C₈	—	2	1	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	4	1	no	—
255	C₂×C₈	—	4	1	no	—
256	C₂×C₈	—	4	1	no	—
257	C₂×C₈	—	38	2	no	—
258	C₂×C₈	—	38	2	no	—
259	C₂×C₈	—	76	1	no	—
260	C₂×C₈	#64528	1	2	yes	complemented
261	C₄⋊C₄	—	2	1	no	—
262	C₄⋊C₄	—	2	1	no	—
263	C₄⋊C₄	—	4	1	no	—
264	C₄⋊C₄	—	4	1	no	—
265	C₄⋊C₄	—	19	2	no	—
266	C₄⋊C₄	—	38	1	no	—
267	C₄⋊C₄	—	38	1	no	—
268	C₄⋊C₄	—	38	2	no	—
269	C₄⋊C₄	—	38	2	no	—
270	C₄⋊C₄	—	38	1	no	—
271	C₂²⋊C₄	—	38	2	no	—
272	C₄²	—	4	1	no	—
273	C₄²	—	4	1	no	—
274	C₄²	—	38	2	no	—
275	C₄²	D₄×D₁₉	1	1	yes	characteristic
276	C₄²	D₄×D₁₉	1	1	yes	characteristic
277	C₄²	D₄×D₁₉	1	1	yes	characteristic
278	C₄²	#64543	1	1	yes	characteristic
279	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
280	Q₈	—	2	2	no	—
281	Q₈	—	2	2	no	—
282	Q₈	—	4	1	no	—
283	Q₈	—	4	1	no	—
284	Q₈	—	76	2	no	—
285	Q₈	—	152	1	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	4	1	no	—
288	C₂×C₄	—	4	1	no	—
289	C₂×C₄	—	4	1	no	—
290	C₂×C₄	—	4	1	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	4	1	no	—
293	C₂×C₄	—	38	2	no	—
294	C₂×C₄	—	38	2	no	—
295	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
296	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
297	C₂×C₄	#10597329	1	1	yes	characteristic
298	C₂×C₄	#10597330	1	1	yes	characteristic
299	C₂×C₄	#10597383	1	1	yes	characteristic
300	C₂×C₄	#10597384	1	1	yes	characteristic
301	C₂×C₄	#10597388	1	1	yes	characteristic
302	C₂×C₄	C₂×#64528	1	1	yes	characteristic
303	C₂×C₄	#10597396	1	1	yes	characteristic
304	C₂×C₄	#10597397	1	1	yes	characteristic
305	C₈	—	2	2	no	—
306	C₈	—	4	1	no	—
307	C₈	—	8	1	no	—
308	C₈	—	76	2	no	—
309	C₈	—	76	2	no	—
310	C₈	—	152	1	no	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	1	no	—
313	C₂²	#11926420	1	1	yes	characteristic
314	C₂²	C₄×#64528	1	1	yes	characteristic
315	C₂²	#11926649	1	1	yes	characteristic
316	C₄	—	2	1	no	—
317	C₄	—	2	1	no	—
318	C₄	—	2	1	no	—
319	C₄	—	2	1	no	—
320	C₄	—	4	2	no	—
321	C₄	—	8	1	no	—
322	C₄	—	76	2	no	—
323	C₄	—	76	2	no	—
324	C₄	#11926699	1	1	yes	characteristic
325	C₄	#11926704	1	1	yes	characteristic
326	C₄	#11926751	1	1	yes	characteristic
327	C₄	#11926763	1	1	yes	characteristic
328	C₂	—	2	1	no	—
329	C₂	—	2	1	no	—
330	C₂	#14563979	1	1	yes	characteristic
331	C₂	#14564000	1	1	yes	characteristic
332	C₂	#14564050	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14573674

C₂

yes

maximal, characteristic

#14572575

C₂

yes

maximal, characteristic

#14562293

C₂

yes

maximal, characteristic

#14562064

C₂

yes

maximal, characteristic

#14561532

C₂

yes

maximal, characteristic

#14561480

C₂

yes

maximal, characteristic

C₁₉×#1985

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926879

C₄

yes

—

#11926839

—

#11926754

—

#11926700

C₄

yes

—

—

—

—

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

#11926570

—

#11926568

C₂²

yes

—

—

—

Q₈⋊(C₁₉⋊C₈)

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×#336

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×C₄

yes

—

C₂×#64520

—

#10597316

—

#10597315

D₄

yes

characteristic

#10597315

D₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₁₉×#97

—

#10597292

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

#10597272

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

#10597267

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

Q₁₆

yes

complemented

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

#64528

—

100

C₄⋊Dic₁₉

—

101

C₄⋊Dic₁₉

—

102

C₄⋊Dic₁₉

—

103

C₄⋊Dic₁₉

C₂²⋊C₄

yes

—

104

Dic₁₉⋊C₄

—

105

Dic₁₉⋊C₄

—

106

C₄×Dic₁₉

—

107

#64520

—

108

#64520

—

109

C₂×C₁₉⋊C₈

—

110

C₂×C₁₉⋊C₈

—

111

C₂×C₁₉⋊C₈

—

112

#9048

—

maximal, Sylow

113

C₂³×C₁₉

C₄×D₄

yes

characteristic

114

Q₈×C₁₉

—

115

Q₈×C₁₉

—

116

Q₈×C₁₉

—

117

Q₈×C₁₉

—

118

C₂×C₄×C₁₉

—

119

C₂×C₄×C₁₉

—

120

C₂×C₄×C₁₉

—

121

C₂×C₄×C₁₉

—

122

C₂×C₄×C₁₉

—

123

C₂×C₄×C₁₉

—

124

C₂×C₄×C₁₉

—

125

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

126

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

127

C₂×C₄×C₁₉

#120

yes

characteristic

128

C₂×C₄×C₁₉

#121

yes

characteristic

129

C₂×C₄×C₁₉

#121

yes

characteristic

130

C₂×C₄×C₁₉

#123

yes

characteristic

131

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

132

C₂×C₄×C₁₉

#135

yes

characteristic

133

C₂×C₄×C₁₉

#137

yes

characteristic

134

C₂×C₄×C₁₉

#137

yes

characteristic

135

C₂×Dic₁₉

—

136

C₂×Dic₁₉

—

137

Dic₃₈

—

138

Dic₃₈

—

139

C₈×C₁₉

—

140

C₈×C₁₉

—

141

C₈×C₁₉

—

142

C₁₉⋊C₈

—

143

C₁₉⋊C₈

—

144

C₁₉⋊C₈

—

145

#3104

—

146

#2961

—

147

#1985

D₁₉

yes

characteristic

148

#1542

—

149

#1487

—

150

#1301

—

151

#1281

—

152

C₂²×C₁₉

—

153

C₂²×C₁₉

—

154

C₂²×C₁₉

#386

yes

characteristic

155

C₂²×C₁₉

C₄×Q₁₆

yes

characteristic

156

C₂²×C₁₉

#441

yes

characteristic

157

C₄×C₁₉

—

158

C₄×C₁₉

—

159

C₄×C₁₉

—

160

C₄×C₁₉

—

161

C₄×C₁₉

—

162

C₄×C₁₉

—

163

C₄×C₁₉

#451

yes

characteristic

164

C₄×C₁₉

#452

yes

characteristic

165

C₄×C₁₉

#462

yes

characteristic

166

C₄×C₁₉

#464

yes

characteristic

167

Dic₁₉

—

168

Dic₁₉

—

169

#533

—

170

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

171

#484

—

172

#477

—

173

#462

—

174

#451

—

175

#446

—

176

#446

—

177

C₄×Q₁₆

—

178

#431

—

179

#431

—

180

#424

—

181

#423

—

182

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

183

#405

—

184

C₂×#97

C₂×D₁₉

yes

characteristic

185

#336

—

186

#336

—

187

#333

—

188

#332

—

189

Q₈⋊C₈

—

190

C₂×C₁₉

—

191

C₂×C₁₉

—

192

C₂×C₁₉

#1878

yes

characteristic

193

C₂×C₁₉

#1881

yes

characteristic

194

C₂×C₁₉

#1891

yes

characteristic

195

C₂²×Q₈

C₄×D₁₉

yes

characteristic

196

C₂×Q₁₆

—

197

C₂×M₁₆

—

198

C₂²×C₈

—

199

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

200

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

201

C₄⋊Q₈

—

202

C₄⋊Q₈

—

203

#125

—

204

C₂²⋊Q₈

—

205

C₂²⋊Q₈

—

206

C₄×Q₈

—

207

C₄×Q₈

—

208

C₄×Q₈

—

209

C₄×Q₈

—

210

C₄×Q₈

—

211

C₄×Q₈

—

212

#117

—

213

C₂×C₄⋊C₄

—

214

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

215

C₂×C₄²

—

216

C₂×C₄²

C₂²×D₁₉

yes

characteristic

217

#107

—

218

C₄⋊C₈

—

219

C₄⋊C₈

—

220

C₄⋊C₈

—

221

C₄⋊C₈

—

222

C₄⋊C₈

—

223

C₄⋊C₈

—

224

C₄⋊C₈

—

225

#103

—

226

#103

—

227

C₂²⋊C₈

—

228

C₂²⋊C₈

—

229

#97

—

230

#97

—

231

#97

—

232

C₄×C₈

—

233

C₄×C₈

—

234

C₄×C₈

—

235

C₁₉

#9048

yes

characteristic, complemented, Sylow

236

C₂×Q₈

—

237

C₂×Q₈

—

238

C₂×Q₈

—

239

C₂×Q₈

—

240

C₂×Q₈

—

241

C₂²×C₄

—

242

C₂²×C₄

—

243

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

244

C₂²×C₄

#64541

yes

characteristic

245

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

246

Q₁₆

—

247

M₁₆

—

248

M₁₆

—

249

C₂×C₈

—

250

C₂×C₈

—

251

C₂×C₈

—

252

C₂×C₈

—

253

C₂×C₈

—

254

C₂×C₈

—

255

C₂×C₈

—

256

C₂×C₈

—

257

C₂×C₈

—

258

C₂×C₈

—

259

C₂×C₈

—

260

C₂×C₈

#64528

yes

complemented

261

C₄⋊C₄

—

262

C₄⋊C₄

—

263

C₄⋊C₄

—

264

C₄⋊C₄

—

265

C₄⋊C₄

—

266

C₄⋊C₄

—

267

C₄⋊C₄

—

268

C₄⋊C₄

—

269

C₄⋊C₄

—

270

C₄⋊C₄

—

271

C₂²⋊C₄

—

272

C₄²

—

273

C₄²

—

274

C₄²

—

275

C₄²

D₄×D₁₉

yes

characteristic

276

C₄²

D₄×D₁₉

yes

characteristic

277

C₄²

D₄×D₁₉

yes

characteristic

278

C₄²

#64543

yes

characteristic

279

C₂³

C₄×C₂²⋊D₁₉

yes

characteristic

280

Q₈

—

281

Q₈

—

282

Q₈

—

283

Q₈

—

284

Q₈

—

285

Q₈

—

152

—

286

C₂×C₄

—

287

C₂×C₄

—

288

C₂×C₄

—

289

C₂×C₄

—

290

C₂×C₄

—

291

C₂×C₄

—

292

C₂×C₄

—

293

C₂×C₄

—

294

C₂×C₄

—

295

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

296

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

297

C₂×C₄

#10597329

yes

characteristic

298

C₂×C₄

#10597330

yes

characteristic

299

C₂×C₄

#10597383

yes

characteristic

300

C₂×C₄

#10597384

yes

characteristic

301

C₂×C₄

#10597388

yes

characteristic

302

C₂×C₄

C₂×#64528

yes

characteristic

303

C₂×C₄

#10597396

yes

characteristic

304

C₂×C₄

#10597397

yes

characteristic

305

C₈

—

306

C₈

—

307

C₈

—

308

C₈

—

309

C₈

—

310

C₈

—

152

—

311

C₂²

—

312

C₂²

—

313

C₂²

#11926420

yes

characteristic

314

C₂²

C₄×#64528

yes

characteristic

315

C₂²

#11926649

yes

characteristic

316

C₄

—

317

C₄

—

318

C₄

—

319

C₄

—

320

C₄

—

321

C₄

—

322

C₄

—

323

C₄

—

324

C₄

#11926699

yes

characteristic

325

C₄

#11926704

yes

characteristic

326

C₄

#11926751

yes

characteristic

327

C₄

#11926763

yes

characteristic

328

C₂

—

329

C₂

—

330

C₂

#14563979

yes

characteristic

331

C₂

#14564000

yes

characteristic

332

C₂

#14564050

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1985	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1985	D₁₉
hypocenter	C₁₉	#9048
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1985

subgroup

G/H

center

C₂×C₄

#10597383

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1985

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂³×C₁₉

C₄×D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1985

N	H ≅ G/N	type
87. C₂×C₈×C₁₉	Q₁₆	semidirect
235. C₁₉	#9048	semidirect
260. C₂×C₈	#64528	semidirect

H ≅ G/N

type

87. C₂×C₈×C₁₉

Q₁₆

semidirect

235. C₁₉

#9048

semidirect

260. C₂×C₈

#64528

semidirect

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

subgroup	index
#14573674	2
#14572575	2
#14562293	2
#14562064	2
#14561532	2
#14561480	2
C₁₉×#1985	2
#9048	19

subgroup

index

C₁₉×#1985

Subgroups — #18077728

Conjugacy classes of subgroups

Complements

Maximal subgroups