Group #18070837 — subgroups

Subgroups — #18070837

Order 4864.

630 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14563703	C₂	1	2	yes	maximal, complemented
2	#14561461	C₂	1	2	yes	maximal, complemented
3	#14561456	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2297	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
6	#11926299	—	2	2	no	—
7	#11926299	C₂²	1	4	yes	—
8	C₂²×#41×C₁₉	C₄	1	1	yes	characteristic
9	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#391	C₄	1	1	yes	characteristic
12	C₁₉×#391	C₂²	1	1	yes	characteristic
13	C₁₉×#390	C₄	1	1	yes	characteristic
14	C₁₉×#390	C₂²	1	1	yes	characteristic
15	C₁₉×#386	—	2	2	no	—
16	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
17	C₂×#41×C₁₉	—	2	2	no	—
18	C₂×#41×C₁₉	—	2	2	no	—
19	C₂×#41×C₁₉	—	4	2	no	—
20	C₂×#41×C₁₉	—	4	2	no	—
21	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₄×C₁₉	—	2	1	no	—
23	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	—	2	1	no	—
25	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	D₄	1	2	yes	—
27	C₁₉×#117	—	4	2	no	—
28	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	—	4	2	no	—
35	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	D₄	1	2	yes	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₁₉⋊C₈	—	2	4	no	—
39	C₁₉×#95	—	2	2	no	—
40	C₁₉×#95	—	2	2	no	—
41	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
42	C₂⁴×C₁₉	—	2	1	no	—
43	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	#41×C₁₉	—	4	8	no	—
45	#41×C₁₉	—	4	8	no	—
46	C₂×Q₈×C₁₉	—	2	1	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂×Q₈×C₁₉	—	4	1	no	—
49	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
50	C₂×D₄×C₁₉	—	2	4	no	—
51	C₂×D₄×C₁₉	—	2	1	no	—
52	C₂×D₄×C₁₉	—	4	1	no	—
53	C₂×D₄×C₁₉	—	4	1	no	—
54	C₂×D₄×C₁₉	—	4	2	no	—
55	C₂×D₄×C₁₉	—	4	2	no	—
56	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	4	no	—
62	C₂²×C₄×C₁₉	—	2	4	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	4	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	—	4	2	no	—
70	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
74	C₄⋊C₄×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	4	1	no	—
76	C₂²⋊C₄×C₁₉	—	4	4	no	—
77	C₂²⋊C₄×C₁₉	—	4	2	no	—
78	C₂²⋊C₄×C₁₉	—	4	4	no	—
79	C₄²×C₁₉	—	4	1	no	—
80	C₄²×C₁₉	—	4	2	no	—
81	C₄²×C₁₉	—	4	1	no	—
82	C₄²×C₁₉	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	4	4	no	—
84	C₂×C₁₉⋊C₈	—	4	4	no	—
85	C₂×C₁₉⋊C₈	—	4	4	no	—
86	#7645	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	—	2	1	no	—
88	C₂³×C₁₉	—	2	1	no	—
89	C₂³×C₁₉	—	2	2	no	—
90	C₂³×C₁₉	—	2	2	no	—
91	C₂³×C₁₉	—	2	2	no	—
92	C₂³×C₁₉	—	4	1	no	—
93	C₂³×C₁₉	—	4	1	no	—
94	C₂³×C₁₉	—	4	2	no	—
95	C₂³×C₁₉	—	4	2	no	—
96	C₂³×C₁₉	#99	1	2	yes	—
97	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	Q₈×C₁₉	—	4	2	no	—
99	Q₈×C₁₉	—	4	2	no	—
100	D₄×C₁₉	—	4	2	no	—
101	D₄×C₁₉	—	4	2	no	—
102	D₄×C₁₉	—	4	8	no	—
103	C₂×C₄×C₁₉	—	2	4	no	—
104	C₂×C₄×C₁₉	—	2	4	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	2	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	2	no	—
111	C₂×C₄×C₁₉	—	2	2	no	—
112	C₂×C₄×C₁₉	—	2	2	no	—
113	C₂×C₄×C₁₉	—	2	2	no	—
114	C₂×C₄×C₁₉	—	2	2	no	—
115	C₂×C₄×C₁₉	—	4	8	no	—
116	C₂×C₄×C₁₉	—	4	8	no	—
117	C₂×C₄×C₁₉	—	4	1	no	—
118	C₂×C₄×C₁₉	—	4	1	no	—
119	C₂×C₄×C₁₉	—	4	1	no	—
120	C₂×C₄×C₁₉	—	4	1	no	—
121	C₂×C₄×C₁₉	—	4	2	no	—
122	C₂×C₄×C₁₉	—	4	2	no	—
123	C₂×C₄×C₁₉	#100	1	2	yes	—
124	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
125	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
126	C₂×C₄×C₁₉	#135	1	4	yes	—
127	C₁₉⋊C₈	—	8	4	no	—
128	#2297	D₁₉	1	1	yes	characteristic
129	#1817	—	19	2	no	—
130	#1272	—	19	2	no	—
131	#1270	—	19	2	no	—
132	C₂²×C₁₉	—	2	2	no	—
133	C₂²×C₁₉	—	2	4	no	—
134	C₂²×C₁₉	—	4	1	no	—
135	C₂²×C₁₉	—	4	1	no	—
136	C₂²×C₁₉	—	4	2	no	—
137	C₂²×C₁₉	—	4	2	no	—
138	C₂²×C₁₉	—	4	4	no	—
139	C₂²×C₁₉	—	8	1	no	—
140	C₂²×C₁₉	—	8	1	no	—
141	C₂²×C₁₉	—	8	2	no	—
142	C₂²×C₁₉	#407	1	1	yes	characteristic
143	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
144	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
145	C₂²×C₁₉	#416	1	2	yes	—
146	C₂²×C₁₉	#421	1	2	yes	—
147	C₄×C₁₉	—	2	2	no	—
148	C₄×C₁₉	—	2	1	no	—
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	—	2	4	no	—
151	C₄×C₁₉	—	4	2	no	—
152	C₄×C₁₉	—	4	2	no	—
153	C₄×C₁₉	—	8	1	no	—
154	C₄×C₁₉	—	8	1	no	—
155	C₂²×#41	Dic₁₉	1	1	yes	characteristic
156	C₂×#117	Dic₁₉	1	1	yes	characteristic
157	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
158	C₂×C₂²⋊C₈	—	38	2	no	—
159	#391	Dic₁₉	1	1	yes	characteristic
160	#391	C₂×D₁₉	1	1	yes	characteristic
161	#390	Dic₁₉	1	1	yes	characteristic
162	#390	C₂×D₁₉	1	1	yes	characteristic
163	#386	—	2	2	no	—
164	C₄×C₂²⋊C₄	—	2	2	no	—
165	#336	—	19	4	no	—
166	#336	—	38	2	no	—
167	C₂×C₁₉	—	4	2	no	—
168	C₂×C₁₉	—	8	2	no	—
169	C₂×C₁₉	#1462	1	1	yes	characteristic
170	C₂×C₁₉	#1488	1	2	yes	—
171	C₂×C₁₉	#1516	1	2	yes	—
172	C₂×C₁₉	#1536	1	1	yes	characteristic
173	C₂×C₁₉	#1543	1	1	yes	characteristic
174	C₂×#41	—	2	2	no	—
175	C₂×#41	—	2	2	no	—
176	C₂×#41	—	4	2	no	—
177	C₂×#41	—	4	2	no	—
178	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
179	C₂²×D₄	—	2	1	no	—
180	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
181	C₂³×C₄	—	2	1	no	—
182	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
183	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
184	C₂²×C₈	—	38	4	no	—
185	#117	—	4	2	no	—
186	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
187	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
188	C₂×C₂²⋊C₄	—	2	1	no	—
189	C₂×C₂²⋊C₄	—	2	2	no	—
190	C₂×C₂²⋊C₄	—	2	2	no	—
191	C₂×C₄²	—	2	1	no	—
192	C₂×C₄²	—	4	2	no	—
193	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
194	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
195	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
196	C₂²⋊C₈	—	76	4	no	—
197	#95	—	2	2	no	—
198	#95	—	2	2	no	—
199	C₁₉	#7645	1	1	yes	characteristic, complemented, Sylow
200	C₂⁴	—	2	1	no	—
201	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
202	#41	—	4	8	no	—
203	#41	—	4	8	no	—
204	C₂×Q₈	—	2	1	no	—
205	C₂×Q₈	—	4	1	no	—
206	C₂×Q₈	—	4	1	no	—
207	C₂×Q₈	#64520	1	2	yes	—
208	C₂×D₄	—	2	4	no	—
209	C₂×D₄	—	2	1	no	—
210	C₂×D₄	—	4	1	no	—
211	C₂×D₄	—	4	1	no	—
212	C₂×D₄	—	4	2	no	—
213	C₂×D₄	—	4	2	no	—
214	C₂×D₄	#64520	1	2	yes	—
215	C₂²×C₄	—	2	2	no	—
216	C₂²×C₄	—	2	2	no	—
217	C₂²×C₄	—	2	1	no	—
218	C₂²×C₄	—	2	1	no	—
219	C₂²×C₄	—	2	4	no	—
220	C₂²×C₄	—	2	1	no	—
221	C₂²×C₄	—	2	4	no	—
222	C₂²×C₄	—	2	4	no	—
223	C₂²×C₄	—	2	1	no	—
224	C₂²×C₄	—	2	1	no	—
225	C₂²×C₄	—	4	2	no	—
226	C₂²×C₄	—	4	2	no	—
227	C₂²×C₄	—	4	2	no	—
228	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
229	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
230	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
231	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
232	C₂×C₈	—	76	4	no	—
233	C₂×C₈	—	76	4	no	—
234	C₂×C₈	—	76	4	no	—
235	C₄⋊C₄	—	4	1	no	—
236	C₄⋊C₄	—	4	1	no	—
237	C₂²⋊C₄	—	4	4	no	—
238	C₂²⋊C₄	—	4	2	no	—
239	C₂²⋊C₄	—	4	4	no	—
240	C₄²	—	4	1	no	—
241	C₄²	—	4	2	no	—
242	C₄²	—	4	1	no	—
243	C₄²	—	4	2	no	—
244	C₂³	—	2	2	no	—
245	C₂³	—	2	2	no	—
246	C₂³	—	2	1	no	—
247	C₂³	—	2	1	no	—
248	C₂³	—	2	2	no	—
249	C₂³	—	4	2	no	—
250	C₂³	—	4	2	no	—
251	C₂³	—	4	1	no	—
252	C₂³	—	4	1	no	—
253	C₂³	#10597291	1	2	yes	—
254	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
255	Q₈	—	4	2	no	—
256	Q₈	—	4	2	no	—
257	D₄	—	4	2	no	—
258	D₄	—	4	2	no	—
259	D₄	—	4	8	no	—
260	C₂×C₄	—	2	4	no	—
261	C₂×C₄	—	2	4	no	—
262	C₂×C₄	—	2	2	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	4	8	no	—
273	C₂×C₄	—	4	8	no	—
274	C₂×C₄	—	4	1	no	—
275	C₂×C₄	—	4	1	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	1	no	—
279	C₂×C₄	—	4	1	no	—
280	C₂×C₄	#10597290	1	2	yes	—
281	C₂×C₄	C₂×#64520	1	1	yes	characteristic
282	C₂×C₄	C₂×#64520	1	1	yes	characteristic
283	C₂×C₄	#10597396	1	4	yes	—
284	C₈	—	152	4	no	—
285	C₂²	—	2	4	no	—
286	C₂²	—	2	2	no	—
287	C₂²	—	4	2	no	—
288	C₂²	—	4	1	no	—
289	C₂²	—	4	1	no	—
290	C₂²	—	4	4	no	—
291	C₂²	—	4	2	no	—
292	C₂²	—	8	2	no	—
293	C₂²	—	8	1	no	—
294	C₂²	—	8	1	no	—
295	C₂²	#11926508	1	1	yes	characteristic
296	C₂²	C₂×#10597291	1	1	yes	characteristic
297	C₂²	C₂×#10597290	1	1	yes	characteristic
298	C₂²	#11926540	1	2	yes	—
299	C₂²	#11926561	1	2	yes	—
300	C₄	—	2	4	no	—
301	C₄	—	2	2	no	—
302	C₄	—	2	1	no	—
303	C₄	—	2	1	no	—
304	C₄	—	4	2	no	—
305	C₄	—	4	2	no	—
306	C₄	—	8	1	no	—
307	C₄	—	8	1	no	—
308	C₂	—	4	2	no	—
309	C₂	—	8	2	no	—
310	C₂	#14561962	1	1	yes	characteristic
311	C₂	#14562069	1	2	yes	—
312	C₂	#14562191	1	2	yes	—
313	C₂	#14562270	1	1	yes	characteristic
314	C₂	#14562297	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563703

C₂

yes

maximal, complemented

#14561461

C₂

yes

maximal, complemented

#14561456

C₂

yes

maximal, complemented

C₁₉×#2297

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926299

—

#11926299

C₂²

yes

—

C₂²×#41×C₁₉

C₄

yes

characteristic

C₂×C₁₉×#117

C₄

yes

characteristic

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#391

C₄

yes

characteristic

C₁₉×#391

C₂²

yes

characteristic

C₁₉×#390

C₄

yes

characteristic

C₁₉×#390

C₂²

yes

characteristic

C₁₉×#386

—

C₄×C₂²⋊C₄×C₁₉

—

C₂×#41×C₁₉

—

C₂×#41×C₁₉

—

C₂×#41×C₁₉

—

C₂×#41×C₁₉

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊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

—

#7645

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#99

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

100

D₄×C₁₉

—

101

D₄×C₁₉

—

102

D₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×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

—

120

C₂×C₄×C₁₉

—

121

C₂×C₄×C₁₉

—

122

C₂×C₄×C₁₉

—

123

C₂×C₄×C₁₉

#100

yes

—

124

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

125

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

126

C₂×C₄×C₁₉

#135

yes

—

127

C₁₉⋊C₈

—

128

#2297

D₁₉

yes

characteristic

129

#1817

—

130

#1272

—

131

#1270

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

—

139

C₂²×C₁₉

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

—

142

C₂²×C₁₉

#407

yes

characteristic

143

C₂²×C₁₉

C₂×#99

yes

characteristic

144

C₂²×C₁₉

C₂×#100

yes

characteristic

145

C₂²×C₁₉

#416

yes

—

146

C₂²×C₁₉

#421

yes

—

147

C₄×C₁₉

—

148

C₄×C₁₉

—

149

C₄×C₁₉

—

150

C₄×C₁₉

—

151

C₄×C₁₉

—

152

C₄×C₁₉

—

153

C₄×C₁₉

—

154

C₄×C₁₉

—

155

C₂²×#41

Dic₁₉

yes

characteristic

156

C₂×#117

Dic₁₉

yes

characteristic

157

C₂²×C₄²

C₂×D₁₉

yes

characteristic

158

C₂×C₂²⋊C₈

—

159

#391

Dic₁₉

yes

characteristic

160

#391

C₂×D₁₉

yes

characteristic

161

#390

Dic₁₉

yes

characteristic

162

#390

C₂×D₁₉

yes

characteristic

163

#386

—

164

C₄×C₂²⋊C₄

—

165

#336

—

166

#336

—

167

C₂×C₁₉

—

168

C₂×C₁₉

—

169

C₂×C₁₉

#1462

yes

characteristic

170

C₂×C₁₉

#1488

yes

—

171

C₂×C₁₉

#1516

yes

—

172

C₂×C₁₉

#1536

yes

characteristic

173

C₂×C₁₉

#1543

yes

characteristic

174

C₂×#41

—

175

C₂×#41

—

176

C₂×#41

—

177

C₂×#41

—

178

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

179

C₂²×D₄

—

180

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

181

C₂³×C₄

—

182

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

183

C₂³×C₄

C₂²⋊D₁₉

yes

—

184

C₂²×C₈

—

185

#117

—

186

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

187

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

188

C₂×C₂²⋊C₄

—

189

C₂×C₂²⋊C₄

—

190

C₂×C₂²⋊C₄

—

191

C₂×C₄²

—

192

C₂×C₄²

—

193

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

194

C₂×C₄²

C₂²⋊D₁₉

yes

—

195

C₂×C₄²

C₂²×D₁₉

yes

characteristic

196

C₂²⋊C₈

—

197

#95

—

198

#95

—

199

C₁₉

#7645

yes

characteristic, complemented, Sylow

200

C₂⁴

—

201

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

202

#41

—

203

#41

—

204

C₂×Q₈

—

205

C₂×Q₈

—

206

C₂×Q₈

—

207

C₂×Q₈

#64520

yes

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂×D₄

#64520

yes

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

—

218

C₂²×C₄

—

219

C₂²×C₄

—

220

C₂²×C₄

—

221

C₂²×C₄

—

222

C₂²×C₄

—

223

C₂²×C₄

—

224

C₂²×C₄

—

225

C₂²×C₄

—

226

C₂²×C₄

—

227

C₂²×C₄

—

228

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

229

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

230

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

231

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

232

C₂×C₈

—

233

C₂×C₈

—

234

C₂×C₈

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₂²⋊C₄

—

238

C₂²⋊C₄

—

239

C₂²⋊C₄

—

240

C₄²

—

241

C₄²

—

242

C₄²

—

243

C₄²

—

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

—

248

C₂³

—

249

C₂³

—

250

C₂³

—

251

C₂³

—

252

C₂³

—

253

C₂³

#10597291

yes

—

254

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

255

Q₈

—

256

Q₈

—

257

D₄

—

258

D₄

—

259

D₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

—

267

C₂×C₄

—

268

C₂×C₄

—

269

C₂×C₄

—

270

C₂×C₄

—

271

C₂×C₄

—

272

C₂×C₄

—

273

C₂×C₄

—

274

C₂×C₄

—

275

C₂×C₄

—

276

C₂×C₄

—

277

C₂×C₄

—

278

C₂×C₄

—

279

C₂×C₄

—

280

C₂×C₄

#10597290

yes

—

281

C₂×C₄

C₂×#64520

yes

characteristic

282

C₂×C₄

C₂×#64520

yes

characteristic

283

C₂×C₄

#10597396

yes

—

284

C₈

—

152

—

285

C₂²

—

286

C₂²

—

287

C₂²

—

288

C₂²

—

289

C₂²

—

290

C₂²

—

291

C₂²

—

292

C₂²

—

293

C₂²

—

294

C₂²

—

295

C₂²

#11926508

yes

characteristic

296

C₂²

C₂×#10597291

yes

characteristic

297

C₂²

C₂×#10597290

yes

characteristic

298

C₂²

#11926540

yes

—

299

C₂²

#11926561

yes

—

300

C₄

—

301

C₄

—

302

C₄

—

303

C₄

—

304

C₄

—

305

C₄

—

306

C₄

—

307

C₄

—

308

C₂

—

309

C₂

—

310

C₂

#14561962

yes

characteristic

311

C₂

#14562069

yes

—

312

C₂

#14562191

yes

—

313

C₂

#14562270

yes

characteristic

314

C₂

#14562297

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2297	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₁₉	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2297	D₁₉
hypocenter	C₁₉	#7645
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2297

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2297

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂²×#41×C₁₉

C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2297

N	H ≅ G/N	type
1. #14563703	C₂	semidirect
2. #14561461	C₂	semidirect
3. #14561456	C₂	semidirect
199. C₁₉	#7645	semidirect

H ≅ G/N

type

1. #14563703

C₂

semidirect

2. #14561461

C₂

semidirect

3. #14561456

C₂

semidirect

199. C₁₉

#7645

semidirect

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

subgroup	index
#14563703	2
#14561461	2
#14561456	2
C₁₉×#2297	2
#7645	19

subgroup

index

C₁₉×#2297

Subgroups — #18070837

Conjugacy classes of subgroups

Complements

Maximal subgroups