Group #18080254 — subgroups

Subgroups — #18080254

Order 4864.

536 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 111 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	#14572720	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562349	C₂	1	2	yes	maximal
3	#14561979	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561491	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2548	C₂	1	1	yes	maximal, characteristic
6	#11926675	—	2	4	no	—
7	#11926601	—	2	1	no	—
8	#11926601	C₂²	1	2	yes	—
9	#11926601	C₂²	1	2	yes	—
10	#11926597	—	2	1	no	—
11	#11926288	—	2	4	no	—
12	#11926270	—	2	1	no	—
13	#11926270	—	2	1	no	—
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#124	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#394	—	2	1	no	—
18	C₁₉×#394	—	2	1	no	—
19	C₁₉×#390	—	2	1	no	—
20	C₁₉×#390	—	2	1	no	—
21	C₁₉×#390	C₄	1	2	yes	—
22	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×D₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₁₉×#127	—	2	2	no	—
28	C₁₉×#127	—	2	2	no	—
29	C₁₉×#124	—	4	4	no	—
30	C₄×Q₈×C₁₉	—	2	2	no	—
31	C₄×Q₈×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
44	C₁₉×#95	—	2	1	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
51	#10597260	—	2	2	no	—
52	#10597260	—	2	2	no	—
53	#10597260	—	2	2	no	—
54	C₄×C₁₉⋊C₈	—	2	2	no	—
55	C₂⁴×C₁₉	—	2	2	no	—
56	C₂×Q₈×C₁₉	—	2	2	no	—
57	C₂×Q₈×C₁₉	—	2	2	no	—
58	C₂×Q₈×C₁₉	—	4	1	no	—
59	C₂×D₄×C₁₉	—	2	4	no	—
60	C₂×D₄×C₁₉	—	4	2	no	—
61	C₂×D₄×C₁₉	—	4	2	no	—
62	C₂×D₄×C₁₉	—	4	2	no	—
63	C₂×D₄×C₁₉	—	4	2	no	—
64	C₂×D₄×C₁₉	—	4	1	no	—
65	C₂×D₄×C₁₉	—	4	2	no	—
66	C₂×D₄×C₁₉	—	4	1	no	—
67	C₂×D₄×C₁₉	—	8	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	4	2	no	—
80	C₂²⋊C₄×C₁₉	—	4	4	no	—
81	C₂²⋊C₄×C₁₉	—	4	4	no	—
82	C₂²⋊C₄×C₁₉	—	8	2	no	—
83	C₂²⋊C₄×C₁₉	—	8	2	no	—
84	C₄²×C₁₉	—	2	1	no	—
85	C₄²×C₁₉	—	2	1	no	—
86	C₄²×C₁₉	—	2	1	no	—
87	C₄²×C₁₉	—	2	1	no	—
88	C₄²×C₁₉	—	4	2	no	—
89	C₄²×C₁₉	C₂×D₄	1	2	yes	—
90	C₄²×C₁₉	#41	1	2	yes	—
91	C₂×C₁₉⋊C₈	—	2	4	no	—
92	C₂×C₁₉⋊C₈	—	4	2	no	—
93	#9458	—	19	1	no	maximal, Sylow
94	C₂³×C₁₉	—	4	2	no	—
95	C₂³×C₁₉	—	4	2	no	—
96	C₂³×C₁₉	—	4	2	no	—
97	C₂³×C₁₉	—	4	2	no	—
98	C₂³×C₁₉	—	4	2	no	—
99	C₂³×C₁₉	—	4	2	no	—
100	C₂³×C₁₉	—	4	2	no	—
101	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	Q₈×C₁₉	—	4	4	no	—
103	D₄×C₁₉	—	8	4	no	—
104	D₄×C₁₉	—	8	2	no	—
105	D₄×C₁₉	—	8	4	no	—
106	D₄×C₁₉	—	8	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	1	no	—
111	C₂×C₄×C₁₉	—	2	2	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	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	2	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	C₄×D₄	1	2	yes	—
125	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
126	C₂×C₄×C₁₉	#121	1	2	yes	—
127	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
128	C₁₉⋊C₈	—	4	4	no	—
129	C₁₉⋊C₈	—	8	2	no	—
130	#2983	—	19	1	no	—
131	#2548	D₁₉	1	1	yes	characteristic
132	#1555	—	19	2	no	—
133	#1467	—	19	1	no	—
134	#1285	—	19	2	no	—
135	C₂²×C₁₉	—	2	1	no	—
136	C₂²×C₁₉	—	2	1	no	—
137	C₂²×C₁₉	—	8	2	no	—
138	C₂²×C₁₉	—	8	2	no	—
139	C₂²×C₁₉	—	8	2	no	—
140	C₂²×C₁₉	—	8	2	no	—
141	C₂²×C₁₉	—	8	2	no	—
142	C₂²×C₁₉	—	8	2	no	—
143	C₂²×C₁₉	—	8	2	no	—
144	C₂²×C₁₉	#386	1	1	yes	characteristic
145	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
146	C₂²×C₁₉	#413	1	1	yes	characteristic
147	C₄×C₁₉	—	2	1	no	—
148	C₄×C₁₉	—	2	2	no	—
149	C₄×C₁₉	—	2	2	no	—
150	C₄×C₁₉	—	2	2	no	—
151	C₄×C₁₉	—	4	1	no	—
152	C₄×C₁₉	—	4	1	no	—
153	C₄×C₁₉	—	4	1	no	—
154	C₄×C₁₉	—	8	2	no	—
155	C₄×C₁₉	#454	1	2	yes	—
156	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
157	C₂×#124	Dic₁₉	1	2	yes	—
158	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
159	#446	—	38	4	no	—
160	#432	—	19	2	no	—
161	#432	—	19	2	no	—
162	#432	—	38	1	no	—
163	#431	—	38	1	no	—
164	#394	—	2	1	no	—
165	#394	—	2	1	no	—
166	#390	—	2	1	no	—
167	#390	—	2	1	no	—
168	#390	Dic₁₉	1	2	yes	—
169	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
170	#331	—	38	4	no	—
171	#324	—	38	1	no	—
172	#324	—	38	1	no	—
173	C₂×C₁₉	—	2	1	no	—
174	C₂×C₁₉	—	2	1	no	—
175	C₂×C₁₉	—	16	2	no	—
176	C₂×C₁₉	#1888	1	1	yes	characteristic
177	C₂×C₁₉	#1900	1	1	yes	characteristic
178	C₂×C₁₉	#1910	1	1	yes	characteristic
179	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
180	C₂²×D₄	—	2	1	no	—
181	C₂²×D₄	—	2	1	no	—
182	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
183	#127	—	2	2	no	—
184	#127	—	2	2	no	—
185	#124	—	4	4	no	—
186	C₄×Q₈	—	2	2	no	—
187	C₄×Q₈	—	2	2	no	—
188	C₂×C₄⋊C₄	—	2	1	no	—
189	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
190	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
191	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
192	C₂×C₂²⋊C₄	—	2	2	no	—
193	C₂×C₂²⋊C₄	—	2	2	no	—
194	C₂×C₂²⋊C₄	—	2	2	no	—
195	C₂×C₂²⋊C₄	—	2	2	no	—
196	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
197	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
198	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
199	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
200	C₄⋊C₈	—	19	4	no	—
201	C₄⋊C₈	—	38	2	no	—
202	C₄⋊C₈	—	38	2	no	—
203	C₄⋊C₈	—	38	2	no	—
204	C₂²⋊C₈	—	38	2	no	—
205	C₂²⋊C₈	—	38	2	no	—
206	#97	—	38	2	no	—
207	#97	—	38	2	no	—
208	#97	—	38	2	no	—
209	C₄×C₈	—	38	2	no	—
210	#95	—	2	1	no	—
211	C₁₉	#9458	1	1	yes	characteristic, complemented, Sylow
212	C₂⁴	—	2	2	no	—
213	C₂×Q₈	—	2	2	no	—
214	C₂×Q₈	—	2	2	no	—
215	C₂×Q₈	—	4	1	no	—
216	C₂×D₄	—	2	4	no	—
217	C₂×D₄	—	4	2	no	—
218	C₂×D₄	—	4	2	no	—
219	C₂×D₄	—	4	2	no	—
220	C₂×D₄	—	4	2	no	—
221	C₂×D₄	—	4	1	no	—
222	C₂×D₄	—	4	1	no	—
223	C₂×D₄	—	4	2	no	—
224	C₂×D₄	—	8	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
227	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
228	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
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	1	yes	characteristic
232	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
233	C₂×C₈	—	38	4	no	—
234	C₂×C₈	—	76	2	no	—
235	C₄⋊C₄	—	2	2	no	—
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	—	2	2	no	—
238	C₄⋊C₄	—	4	2	no	—
239	C₂²⋊C₄	—	4	4	no	—
240	C₂²⋊C₄	—	4	4	no	—
241	C₂²⋊C₄	—	8	2	no	—
242	C₂²⋊C₄	—	8	2	no	—
243	C₄²	—	2	1	no	—
244	C₄²	—	2	1	no	—
245	C₄²	—	2	1	no	—
246	C₄²	—	2	1	no	—
247	C₄²	—	4	2	no	—
248	C₄²	D₄×D₁₉	1	2	yes	—
249	C₄²	#64543	1	2	yes	—
250	C₂³	—	4	2	no	—
251	C₂³	—	4	2	no	—
252	C₂³	—	4	2	no	—
253	C₂³	—	4	2	no	—
254	C₂³	—	4	2	no	—
255	C₂³	—	4	2	no	—
256	C₂³	—	4	2	no	—
257	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
258	Q₈	—	4	4	no	—
259	D₄	—	8	4	no	—
260	D₄	—	8	2	no	—
261	D₄	—	8	4	no	—
262	D₄	—	8	2	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	4	1	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	2	no	—
279	C₂×C₄	#10597290	1	2	yes	—
280	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
281	C₂×C₄	#10597381	1	1	yes	characteristic
282	C₂×C₄	#10597383	1	1	yes	characteristic
283	C₂×C₄	#10597385	1	2	yes	—
284	C₈	—	76	4	no	—
285	C₈	—	152	2	no	—
286	C₂²	—	2	1	no	—
287	C₂²	—	2	1	no	—
288	C₂²	—	8	2	no	—
289	C₂²	—	8	2	no	—
290	C₂²	—	8	2	no	—
291	C₂²	—	8	2	no	—
292	C₂²	—	8	2	no	—
293	C₂²	—	8	2	no	—
294	C₂²	—	8	2	no	—
295	C₂²	#11926424	1	1	yes	characteristic
296	C₂²	C₂×#10597290	1	1	yes	characteristic
297	C₂²	#11926528	1	1	yes	characteristic
298	C₄	—	2	2	no	—
299	C₄	—	2	2	no	—
300	C₄	—	2	2	no	—
301	C₄	—	2	1	no	—
302	C₄	—	4	1	no	—
303	C₄	—	4	1	no	—
304	C₄	—	4	1	no	—
305	C₄	—	8	2	no	—
306	C₄	#11926716	1	2	yes	—
307	C₂	—	2	1	no	—
308	C₂	—	2	1	no	—
309	C₂	—	16	2	no	—
310	C₂	#14564039	1	1	yes	characteristic
311	C₂	#14564099	1	1	yes	characteristic
312	C₂	#14564163	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572720

C₂

yes

maximal, characteristic, complemented

#14562349

C₂

yes

maximal

#14561979

C₂

yes

maximal, characteristic, complemented

#14561491

C₂

yes

maximal, complemented

C₁₉×#2548

C₂

yes

maximal, characteristic

#11926675

—

#11926601

—

#11926601

C₂²

yes

—

#11926601

C₂²

yes

—

—

—

—

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×#124

C₄

yes

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#394

—

C₁₉×#394

—

C₁₉×#390

—

C₁₉×#390

—

C₁₉×#390

C₄

yes

—

C₄×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#124

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

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

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9458

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

100

C₂³×C₁₉

—

101

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

102

Q₈×C₁₉

—

103

D₄×C₁₉

—

104

D₄×C₁₉

—

105

D₄×C₁₉

—

106

D₄×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

C₄×D₄

yes

—

125

C₂×C₄×C₁₉

#120

yes

characteristic

126

C₂×C₄×C₁₉

#121

yes

—

127

C₂×C₄×C₁₉

#123

yes

characteristic

128

C₁₉⋊C₈

—

129

C₁₉⋊C₈

—

130

#2983

—

131

#2548

D₁₉

yes

characteristic

132

#1555

—

133

#1467

—

134

#1285

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

—

139

C₂²×C₁₉

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

—

142

C₂²×C₁₉

—

143

C₂²×C₁₉

—

144

C₂²×C₁₉

#386

yes

characteristic

145

C₂²×C₁₉

C₂×#100

yes

characteristic

146

C₂²×C₁₉

#413

yes

characteristic

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

C₄×C₁₉

#454

yes

—

156

C₂×#127

C₂×D₁₉

yes

characteristic

157

C₂×#124

Dic₁₉

yes

—

158

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

159

#446

—

160

#432

—

161

#432

—

162

#432

—

163

#431

—

164

#394

—

165

#394

—

166

#390

—

167

#390

—

168

#390

Dic₁₉

yes

—

169

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

170

#331

—

171

#324

—

172

#324

—

173

C₂×C₁₉

—

174

C₂×C₁₉

—

175

C₂×C₁₉

—

176

C₂×C₁₉

#1888

yes

characteristic

177

C₂×C₁₉

#1900

yes

characteristic

178

C₂×C₁₉

#1910

yes

characteristic

179

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

180

C₂²×D₄

—

181

C₂²×D₄

—

182

C₂²×D₄

C₂×Dic₁₉

yes

—

183

#127

—

184

#127

—

185

#124

—

186

C₄×Q₈

—

187

C₄×Q₈

—

188

C₂×C₄⋊C₄

—

189

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

190

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

191

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

192

C₂×C₂²⋊C₄

—

193

C₂×C₂²⋊C₄

—

194

C₂×C₂²⋊C₄

—

195

C₂×C₂²⋊C₄

—

196

C₂×C₄²

C₂×Dic₁₉

yes

—

197

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

198

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

199

C₂×C₄²

C₂²×D₁₉

yes

characteristic

200

C₄⋊C₈

—

201

C₄⋊C₈

—

202

C₄⋊C₈

—

203

C₄⋊C₈

—

204

C₂²⋊C₈

—

205

C₂²⋊C₈

—

206

#97

—

207

#97

—

208

#97

—

209

C₄×C₈

—

210

#95

—

211

C₁₉

#9458

yes

characteristic, complemented, Sylow

212

C₂⁴

—

213

C₂×Q₈

—

214

C₂×Q₈

—

215

C₂×Q₈

—

216

C₂×D₄

—

217

C₂×D₄

—

218

C₂×D₄

—

219

C₂×D₄

—

220

C₂×D₄

—

221

C₂×D₄

—

222

C₂×D₄

—

223

C₂×D₄

—

224

C₂×D₄

—

225

C₂²×C₄

—

226

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

227

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

228

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

229

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

230

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

231

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

232

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

233

C₂×C₈

—

234

C₂×C₈

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₄⋊C₄

—

239

C₂²⋊C₄

—

240

C₂²⋊C₄

—

241

C₂²⋊C₄

—

242

C₂²⋊C₄

—

243

C₄²

—

244

C₄²

—

245

C₄²

—

246

C₄²

—

247

C₄²

—

248

C₄²

D₄×D₁₉

yes

—

249

C₄²

#64543

yes

—

250

C₂³

—

251

C₂³

—

252

C₂³

—

253

C₂³

—

254

C₂³

—

255

C₂³

—

256

C₂³

—

257

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

258

Q₈

—

259

D₄

—

260

D₄

—

261

D₄

—

262

D₄

—

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

#10597290

yes

—

280

C₂×C₄

D₄×Dic₁₉

yes

—

281

C₂×C₄

#10597381

yes

characteristic

282

C₂×C₄

#10597383

yes

characteristic

283

C₂×C₄

#10597385

yes

—

284

C₈

—

285

C₈

—

152

—

286

C₂²

—

287

C₂²

—

288

C₂²

—

289

C₂²

—

290

C₂²

—

291

C₂²

—

292

C₂²

—

293

C₂²

—

294

C₂²

—

295

C₂²

#11926424

yes

characteristic

296

C₂²

C₂×#10597290

yes

characteristic

297

C₂²

#11926528

yes

characteristic

298

C₄

—

299

C₄

—

300

C₄

—

301

C₄

—

302

C₄

—

303

C₄

—

304

C₄

—

305

C₄

—

306

C₄

#11926716

yes

—

307

C₂

—

308

C₂

—

309

C₂

—

310

C₂

#14564039

yes

characteristic

311

C₂

#14564099

yes

characteristic

312

C₂

#14564163

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2548	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2548	D₁₉
hypocenter	C₁₉	#9458
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2548

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2548

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂×C₁₉×#127

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2548

N	H ≅ G/N	type
1. #14572720	C₂	semidirect
3. #14561979	C₂	semidirect
4. #14561491	C₂	semidirect
211. C₁₉	#9458	semidirect

H ≅ G/N

type

1. #14572720

C₂

semidirect

3. #14561979

C₂

semidirect

4. #14561491

C₂

semidirect

211. C₁₉

#9458

semidirect

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

subgroup	index
#14572720	2
#14562349	2
#14561979	2
#14561491	2
C₁₉×#2548	2
#9458	19

subgroup

index

C₁₉×#2548

Subgroups — #18080254

Conjugacy classes of subgroups

Complements

Maximal subgroups