Group #18070659 — subgroups

Subgroups — #18070659

Order 4864.

608 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₄×#10597320	C₂	1	1	yes	maximal, characteristic
2	#14563778	C₂	1	1	yes	maximal, characteristic, complemented
3	#14561455	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1839	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597320	C₄	1	1	yes	characteristic
6	C₂×C₄×D₇₆	—	2	1	no	—
7	C₂×C₄×D₇₆	—	2	1	no	—
8	C₂×C₄×D₇₆	C₄	1	2	yes	—
9	#11926446	—	2	1	no	—
10	#11926446	—	2	1	no	—
11	#11926446	C₂²	1	2	yes	—
12	#11926414	C₄	1	1	yes	characteristic
13	#11926299	—	2	1	no	—
14	#11926299	—	2	1	no	—
15	#11926299	C₂²	1	2	yes	—
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#336	—	2	1	no	—
18	C₁₉×#336	—	2	1	no	—
19	C₁₉×#336	C₂²	1	2	yes	—
20	C₂²×D₇₆	—	2	1	no	—
21	C₂²×D₇₆	—	2	1	no	—
22	C₂²×D₇₆	C₂×C₄	1	2	yes	—
23	C₂²×C₄×D₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
33	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
34	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
35	C₂×C₄⋊Dic₁₉	—	2	1	no	—
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	#10597320	—	2	2	no	—
40	#10597320	C₈	1	4	yes	complemented
41	C₄×D₇₆	—	4	4	no	—
42	C₄×D₇₆	—	4	4	no	—
43	C₄×D₇₆	—	4	4	no	—
44	C₂³×D₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₁₉	—	2	2	no	—
53	C₂×D₇₆	—	2	4	no	—
54	C₂×D₇₆	—	2	4	no	—
55	C₂×D₇₆	—	2	2	no	—
56	C₂×D₇₆	—	4	2	no	—
57	C₂×D₇₆	—	4	2	no	—
58	C₂×D₇₆	—	4	2	no	—
59	C₂×D₇₆	—	4	2	no	—
60	C₂×D₇₆	—	4	2	no	—
61	C₂×D₇₆	—	4	2	no	—
62	C₂×D₇₆	C₂×C₈	1	4	yes	—
63	C₂×C₄×D₁₉	—	4	4	no	—
64	C₂×C₄×D₁₉	—	4	4	no	—
65	C₂×C₄×D₁₉	—	4	4	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	—	4	2	no	—
69	C₄²×C₁₉	—	2	2	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄²×C₁₉	—	4	1	no	—
74	C₄²×C₁₉	—	4	1	no	—
75	C₄²×C₁₉	C₂×C₈	1	2	yes	—
76	C₄²×C₁₉	M₁₆	1	2	yes	—
77	(C₂×D₁₉)⋊C₄	—	4	4	no	—
78	(C₂×D₁₉)⋊C₄	—	4	4	no	—
79	(C₂×D₁₉)⋊C₄	—	4	4	no	—
80	C₄⋊Dic₁₉	—	4	2	no	—
81	C₄⋊Dic₁₉	—	4	2	no	—
82	C₄⋊Dic₁₉	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	4	2	no	—
84	C₂×C₁₉⋊C₈	—	4	2	no	—
85	C₂×C₁₉⋊C₈	—	4	2	no	—
86	#7603	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×D₁₉	—	2	4	no	—
89	C₂²×D₁₉	—	4	2	no	—
90	C₂²×D₁₉	—	4	2	no	—
91	C₂²×D₁₉	—	4	2	no	—
92	C₂²×D₁₉	—	4	2	no	—
93	C₂²×D₁₉	—	4	2	no	—
94	C₂²×D₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	1	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	C₂²⋊C₈	1	2	yes	—
111	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
112	C₂×C₄×C₁₉	#100	1	2	yes	—
113	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
115	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
116	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
117	C₂×Dic₁₉	—	4	2	no	—
118	C₂×Dic₁₉	—	4	2	no	—
119	C₂×Dic₁₉	—	4	2	no	—
120	D₇₆	—	4	4	no	—
121	D₇₆	—	4	4	no	—
122	D₇₆	—	4	8	no	—
123	D₇₆	—	4	8	no	—
124	C₄×D₁₉	—	8	8	no	—
125	C₈×C₁₉	—	8	2	no	—
126	C₁₉⋊C₈	—	8	2	no	—
127	C₄×#127	—	19	1	no	—
128	#1839	—	19	1	no	—
129	#1839	D₁₉	1	1	yes	characteristic, complemented
130	#1270	—	19	4	no	—
131	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
132	C₂²×C₁₉	#410	1	1	yes	characteristic
133	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
134	C₂²×C₁₉	#418	1	1	yes	characteristic
135	C₂²×C₁₉	#418	1	1	yes	characteristic
136	C₂²×C₁₉	#421	1	1	yes	characteristic
137	C₂²×C₁₉	#421	1	1	yes	characteristic
138	C₂×D₁₉	—	4	4	no	—
139	C₂×D₁₉	—	4	4	no	—
140	C₂×D₁₉	—	4	4	no	—
141	C₂×D₁₉	—	8	2	no	—
142	C₂×D₁₉	—	8	2	no	—
143	C₂×D₁₉	—	8	2	no	—
144	C₂×D₁₉	—	8	2	no	—
145	C₄×C₁₉	—	2	2	no	—
146	C₄×C₁₉	—	2	1	no	—
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	—	2	2	no	—
152	C₄×C₁₉	—	4	1	no	—
153	Dic₁₉	—	8	2	no	—
154	C₂×#127	—	19	1	no	—
155	C₂×C₄×D₄	—	19	2	no	—
156	C₂×C₄×D₄	—	38	1	no	—
157	C₂×C₄×D₄	—	38	1	no	—
158	#390	—	19	2	no	—
159	#390	—	38	1	no	—
160	#390	—	38	1	no	—
161	#384	—	19	1	no	—
162	C₄³	C₂×D₁₉	1	1	yes	characteristic
163	#336	—	2	1	no	—
164	#336	—	2	1	no	—
165	#336	—	19	2	no	—
166	#336	—	38	1	no	—
167	#336	—	38	1	no	—
168	#336	C₂×D₁₉	1	2	yes	—
169	C₂×C₁₉	#1460	1	1	yes	characteristic
170	C₂×C₁₉	#1478	1	1	yes	characteristic
171	C₂×C₁₉	#1478	1	1	yes	characteristic
172	C₂×C₁₉	#1514	1	1	yes	characteristic
173	C₂×C₁₉	#1514	1	1	yes	characteristic
174	C₂×C₁₉	#1536	1	1	yes	characteristic
175	C₂×C₁₉	#1555	1	1	yes	characteristic
176	D₁₉	—	8	4	no	—
177	C₂²×D₄	—	19	2	no	—
178	C₂²×D₄	—	38	1	no	—
179	C₂²×D₄	—	38	1	no	—
180	C₂³×C₄	—	38	2	no	—
181	C₂²×C₈	—	2	2	no	—
182	C₂²×C₈	—	38	2	no	—
183	#127	—	19	4	no	—
184	#127	—	38	2	no	—
185	C₄×D₄	—	76	4	no	—
186	C₄×D₄	—	76	4	no	—
187	C₄×D₄	—	76	4	no	—
188	C₂×C₄⋊C₄	—	19	2	no	—
189	C₂×C₄⋊C₄	—	38	1	no	—
190	C₂×C₄⋊C₄	—	38	1	no	—
191	C₂×C₂²⋊C₄	—	38	2	no	—
192	C₂×C₂²⋊C₄	—	38	2	no	—
193	C₂×C₂²⋊C₄	—	38	2	no	—
194	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
195	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
196	C₂×C₄²	D₇₆	1	1	yes	characteristic
197	C₂×C₄²	D₇₆	1	1	yes	characteristic
198	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
199	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
200	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
201	C₁₉	#7603	1	1	yes	characteristic, complemented, Sylow
202	C₂⁴	—	38	2	no	—
203	C₂×D₄	—	19	4	no	—
204	C₂×D₄	—	38	4	no	—
205	C₂×D₄	—	38	4	no	—
206	C₂×D₄	—	38	2	no	—
207	C₂×D₄	—	76	2	no	—
208	C₂×D₄	—	76	2	no	—
209	C₂×D₄	—	76	2	no	—
210	C₂×D₄	—	76	2	no	—
211	C₂×D₄	—	76	2	no	—
212	C₂×D₄	—	76	2	no	—
213	C₂²×C₄	—	38	2	no	—
214	C₂²×C₄	—	76	4	no	—
215	C₂²×C₄	—	76	4	no	—
216	C₂²×C₄	—	76	4	no	—
217	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
218	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
219	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
220	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
221	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
222	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
223	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
224	C₂×C₈	—	4	2	no	—
225	C₂×C₈	—	4	2	no	—
226	C₂×C₈	—	4	2	no	—
227	C₂×C₈	—	76	2	no	—
228	C₂×C₈	—	76	2	no	—
229	C₂×C₈	—	76	2	no	—
230	C₄⋊C₄	—	76	2	no	—
231	C₄⋊C₄	—	76	2	no	—
232	C₄⋊C₄	—	76	2	no	—
233	C₂²⋊C₄	—	76	4	no	—
234	C₂²⋊C₄	—	76	4	no	—
235	C₂²⋊C₄	—	76	4	no	—
236	C₄²	—	2	2	no	—
237	C₄²	—	2	2	no	—
238	C₄²	—	2	2	no	—
239	C₄²	—	4	1	no	—
240	C₄²	—	4	1	no	—
241	C₄²	—	4	1	no	—
242	C₄²	C₈×D₁₉	1	2	yes	—
243	C₄²	#64515	1	2	yes	—
244	C₂³	—	38	4	no	—
245	C₂³	—	76	2	no	—
246	C₂³	—	76	2	no	—
247	C₂³	—	76	2	no	—
248	C₂³	—	76	2	no	—
249	C₂³	—	76	2	no	—
250	C₂³	—	76	2	no	—
251	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
252	D₄	—	76	4	no	—
253	D₄	—	76	4	no	—
254	D₄	—	76	8	no	—
255	D₄	—	76	8	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	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	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	76	2	no	—
272	C₂×C₄	—	76	2	no	—
273	C₂×C₄	—	76	2	no	—
274	C₂×C₄	—	152	8	no	—
275	C₂×C₄	(C₂×D₁₉)⋊C₈	1	2	yes	—
276	C₂×C₄	(C₂×D₁₉)⋊C₈	1	2	yes	—
277	C₂×C₄	#10597280	1	2	yes	—
278	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
279	C₂×C₄	C₂×#64515	1	1	yes	characteristic
280	C₂×C₄	#10597354	1	2	yes	—
281	C₂×C₄	#10597395	1	2	yes	—
282	C₈	—	8	2	no	—
283	C₈	—	152	2	no	—
284	C₂²	—	76	4	no	—
285	C₂²	—	76	4	no	—
286	C₂²	—	76	4	no	—
287	C₂²	—	152	2	no	—
288	C₂²	—	152	2	no	—
289	C₂²	—	152	2	no	—
290	C₂²	—	152	2	no	—
291	C₂²	C₂×(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
292	C₂²	#11926517	1	1	yes	characteristic
293	C₂²	C₂×#10597280	1	1	yes	characteristic
294	C₂²	#11926548	1	1	yes	characteristic
295	C₂²	#11926550	1	1	yes	characteristic
296	C₂²	#11926560	1	1	yes	characteristic
297	C₂²	#11926562	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	—	2	1	no	—
303	C₄	—	2	2	no	—
304	C₄	—	2	2	no	—
305	C₄	—	4	1	no	—
306	C₄	—	152	2	no	—
307	C₂	—	152	4	no	—
308	C₂	#14561955	1	1	yes	characteristic
309	C₂	#14562025	1	1	yes	characteristic
310	C₂	#14562027	1	1	yes	characteristic
311	C₂	#14562181	1	1	yes	characteristic
312	C₂	#14562183	1	1	yes	characteristic
313	C₂	#14562269	1	1	yes	characteristic
314	C₂	#14562348	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597320

C₂

yes

maximal, characteristic

#14563778

C₂

yes

maximal, characteristic, complemented

#14561455

C₂

yes

maximal, complemented

C₁₉×#1839

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₄

yes

characteristic

C₂×C₄×D₇₆

—

C₂×C₄×D₇₆

—

C₂×C₄×D₇₆

C₄

yes

—

#11926446

—

#11926446

—

#11926446

C₂²

yes

—

#11926414

C₄

yes

—

—

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×#336

—

C₁₉×#336

C₂²

yes

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×D₇₆

C₂×C₄

yes

—

C₂²×C₄×D₁₉

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

#10597320

—

#10597320

C₈

yes

complemented

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₂³×D₁₉

—

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

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₈

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

—

C₄²×C₁₉

M₁₆

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7603

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×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

C₂²⋊C₈

yes

—

111

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

112

C₂×C₄×C₁₉

#100

yes

—

113

C₂×C₄×C₁₉

C₂²×C₈

yes

characteristic

114

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

115

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

116

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

117

C₂×Dic₁₉

—

118

C₂×Dic₁₉

—

119

C₂×Dic₁₉

—

120

D₇₆

—

121

D₇₆

—

122

D₇₆

—

123

D₇₆

—

124

C₄×D₁₉

—

125

C₈×C₁₉

—

126

C₁₉⋊C₈

—

127

C₄×#127

—

128

#1839

—

129

#1839

D₁₉

yes

characteristic, complemented

130

#1270

—

131

C₂²×C₁₉

C₂×C₂²⋊C₈

yes

characteristic

132

C₂²×C₁₉

#410

yes

characteristic

133

C₂²×C₁₉

C₂×#100

yes

characteristic

134

C₂²×C₁₉

#418

yes

characteristic

135

C₂²×C₁₉

#418

yes

characteristic

136

C₂²×C₁₉

#421

yes

characteristic

137

C₂²×C₁₉

#421

yes

characteristic

138

C₂×D₁₉

—

139

C₂×D₁₉

—

140

C₂×D₁₉

—

141

C₂×D₁₉

—

142

C₂×D₁₉

—

143

C₂×D₁₉

—

144

C₂×D₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₄×C₁₉

—

149

C₄×C₁₉

—

150

C₄×C₁₉

—

151

C₄×C₁₉

—

152

C₄×C₁₉

—

153

Dic₁₉

—

154

C₂×#127

—

155

C₂×C₄×D₄

—

156

C₂×C₄×D₄

—

157

C₂×C₄×D₄

—

158

#390

—

159

#390

—

160

#390

—

161

#384

—

162

C₄³

C₂×D₁₉

yes

characteristic

163

#336

—

164

#336

—

165

#336

—

166

#336

—

167

#336

—

168

#336

C₂×D₁₉

yes

—

169

C₂×C₁₉

#1460

yes

characteristic

170

C₂×C₁₉

#1478

yes

characteristic

171

C₂×C₁₉

#1478

yes

characteristic

172

C₂×C₁₉

#1514

yes

characteristic

173

C₂×C₁₉

#1514

yes

characteristic

174

C₂×C₁₉

#1536

yes

characteristic

175

C₂×C₁₉

#1555

yes

characteristic

176

D₁₉

—

177

C₂²×D₄

—

178

C₂²×D₄

—

179

C₂²×D₄

—

180

C₂³×C₄

—

181

C₂²×C₈

—

182

C₂²×C₈

—

183

#127

—

184

#127

—

185

C₄×D₄

—

186

C₄×D₄

—

187

C₄×D₄

—

188

C₂×C₄⋊C₄

—

189

C₂×C₄⋊C₄

—

190

C₂×C₄⋊C₄

—

191

C₂×C₂²⋊C₄

—

192

C₂×C₂²⋊C₄

—

193

C₂×C₂²⋊C₄

—

194

C₂×C₄²

C₄×D₁₉

yes

characteristic

195

C₂×C₄²

C₄×D₁₉

yes

characteristic

196

C₂×C₄²

D₇₆

yes

characteristic

197

C₂×C₄²

D₇₆

yes

characteristic

198

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

199

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

200

C₂×C₄²

C₂²×D₁₉

yes

characteristic

201

C₁₉

#7603

yes

characteristic, complemented, Sylow

202

C₂⁴

—

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂×D₄

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

218

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

219

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

220

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

221

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

222

C₂²×C₄

C₂×D₇₆

yes

characteristic

223

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₂²⋊C₄

—

234

C₂²⋊C₄

—

235

C₂²⋊C₄

—

236

C₄²

—

237

C₄²

—

238

C₄²

—

239

C₄²

—

240

C₄²

—

241

C₄²

—

242

C₄²

C₈×D₁₉

yes

—

243

C₄²

#64515

yes

—

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

—

248

C₂³

—

249

C₂³

—

250

C₂³

—

251

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

252

D₄

—

253

D₄

—

254

D₄

—

255

D₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

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

—

152

—

275

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

—

276

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

—

277

C₂×C₄

#10597280

yes

—

278

C₂×C₄

C₂×C₈×D₁₉

yes

characteristic

279

C₂×C₄

C₂×#64515

yes

characteristic

280

C₂×C₄

#10597354

yes

—

281

C₂×C₄

#10597395

yes

—

282

C₈

—

283

C₈

—

152

—

284

C₂²

—

285

C₂²

—

286

C₂²

—

287

C₂²

—

152

—

288

C₂²

—

152

—

289

C₂²

—

152

—

290

C₂²

—

152

—

291

C₂²

C₂×(C₂×D₁₉)⋊C₈

yes

characteristic

292

C₂²

#11926517

yes

characteristic

293

C₂²

C₂×#10597280

yes

characteristic

294

C₂²

#11926548

yes

characteristic

295

C₂²

#11926550

yes

characteristic

296

C₂²

#11926560

yes

characteristic

297

C₂²

#11926562

yes

characteristic

298

C₄

—

299

C₄

—

300

C₄

—

301

C₄

—

302

C₄

—

303

C₄

—

304

C₄

—

305

C₄

—

306

C₄

—

152

—

307

C₂

—

152

—

308

C₂

#14561955

yes

characteristic

309

C₂

#14562025

yes

characteristic

310

C₂

#14562027

yes

characteristic

311

C₂

#14562181

yes

characteristic

312

C₂

#14562183

yes

characteristic

313

C₂

#14562269

yes

characteristic

314

C₂

#14562348

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1839	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×#10597320	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1839	D₁₉
hypocenter	C₁₉	#7603
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1839

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂×#10597320

C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

N	H ≅ G/N	type
2. #14563778	C₂	semidirect
3. #14561455	C₂	semidirect
4. C₁₉×#1839	C₂	semidirect
40. #10597320	C₈	semidirect
129. #1839	D₁₉	semidirect
201. C₁₉	#7603	semidirect

H ≅ G/N

type

2. #14563778

C₂

semidirect

3. #14561455

C₂

semidirect

4. C₁₉×#1839

C₂

semidirect

40. #10597320

C₈

semidirect

129. #1839

D₁₉

semidirect

201. C₁₉

#7603

semidirect

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

subgroup	index
C₄×#10597320	2
#14563778	2
#14561455	2
C₁₉×#1839	2
#7603	19

subgroup

index

C₁₉×#1839

Subgroups — #18070659

Conjugacy classes of subgroups

Complements

Maximal subgroups