Group #18077834 — subgroups

Subgroups — #18077834

Order 4864.

738 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 155 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	#14566700	C₂	1	1	yes	maximal, characteristic
2	#14564584	C₂	1	2	yes	maximal, complemented
3	C₂×#11926288	C₂	1	1	yes	maximal, characteristic
4	#14561475	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#492	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×Dic₁₉	—	2	2	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	#11926447	—	2	2	no	—
9	#11926424	—	2	2	no	—
10	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	#11926306	—	2	2	no	—
12	#11926306	—	2	2	no	—
13	#11926288	—	2	2	no	—
14	C₂²×SD₁₆×C₁₉	—	2	2	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
17	C₁₉×#492	—	2	2	no	—
18	C₁₉×#492	C₄	1	4	yes	complemented
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×D₄×C₁₉	D₄	1	2	yes	—
23	C₂³×Dic₁₉	—	2	2	no	—
24	C₂×SD₁₆×C₁₉	—	2	8	no	—
25	C₂×SD₁₆×C₁₉	—	4	4	no	—
26	C₂×SD₁₆×C₁₉	—	4	4	no	—
27	C₂²×C₈×C₁₉	—	2	1	no	—
28	C₁₉×C₄⋊Q₈	—	2	1	no	—
29	C₁₉×C₄⋊Q₈	—	2	2	no	—
30	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
31	C₁₉×#127	—	2	2	no	—
32	C₁₉×#127	C₂×C₄	1	2	yes	—
33	C₁₉×#127	D₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₂²⋊Dic₁₉	—	2	4	no	—
37	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
38	D₄×Dic₁₉	—	4	4	no	—
39	D₄×Dic₁₉	—	4	4	no	—
40	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
41	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
42	C₂×C₄×Dic₁₉	—	2	2	no	—
43	C₂²×C₁₉⋊C₈	—	2	2	no	—
44	C₄×C₈×C₁₉	—	2	1	no	—
45	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	complemented
46	C₁₉⋊#95	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₂⁴×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	—	4	2	no	—
52	C₂×Q₈×C₁₉	—	4	2	no	—
53	C₂×Q₈×C₁₉	—	4	1	no	—
54	C₂×D₄×C₁₉	—	2	4	no	—
55	C₂×D₄×C₁₉	—	2	4	no	—
56	C₂×D₄×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	—	4	2	no	—
58	C₂×D₄×C₁₉	—	4	2	no	—
59	C₂×D₄×C₁₉	—	4	2	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	C₂²⋊C₄	1	4	yes	—
64	C₂²×C₄×C₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×Dic₁₉	—	2	2	no	—
68	C₂²×Dic₁₉	—	2	2	no	—
69	C₂²×Dic₁₉	—	4	8	no	—
70	C₂²×Dic₁₉	—	8	2	no	—
71	SD₁₆×C₁₉	—	4	16	no	—
72	C₂×C₈×C₁₉	—	2	2	no	—
73	C₂×C₈×C₁₉	—	2	2	no	—
74	C₂×C₈×C₁₉	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	2	4	no	—
76	C₄⋊C₄×C₁₉	—	4	2	no	—
77	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	#41	1	2	yes	—
80	C₂²⋊Dic₁₉	—	4	8	no	—
81	C₂²⋊Dic₁₉	—	8	2	no	—
82	C₄⋊Dic₁₉	—	2	2	no	—
83	C₄⋊Dic₁₉	—	2	2	no	—
84	C₄⋊Dic₁₉	—	2	2	no	—
85	C₄⋊Dic₁₉	SD₁₆	1	4	yes	complemented
86	C₄×Dic₁₉	—	4	2	no	—
87	C₄×Dic₁₉	—	4	2	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	C₂×C₁₉⋊C₈	—	4	2	no	—
90	C₂×C₁₉⋊C₈	—	4	2	no	—
91	#9064	—	19	1	no	maximal, Sylow
92	C₂³×C₁₉	—	2	4	no	—
93	C₂³×C₁₉	—	4	4	no	—
94	C₂³×C₁₉	—	4	4	no	—
95	C₂³×C₁₉	—	4	2	no	—
96	C₂³×C₁₉	—	4	2	no	—
97	C₂³×C₁₉	#120	1	1	yes	characteristic
98	Q₈×C₁₉	—	4	4	no	—
99	Q₈×C₁₉	—	8	2	no	—
100	D₄×C₁₉	—	4	4	no	—
101	D₄×C₁₉	—	4	4	no	—
102	D₄×C₁₉	—	4	4	no	—
103	D₄×C₁₉	—	4	4	no	—
104	D₄×C₁₉	—	4	4	no	—
105	D₄×C₁₉	—	8	2	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	—	8	1	no	—
110	C₂×C₄×C₁₉	—	8	1	no	—
111	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
113	C₂×C₄×C₁₉	#121	1	2	yes	—
114	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
115	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
116	C₂×C₄×C₁₉	#135	1	2	yes	—
117	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
118	C₂×C₄×C₁₉	#137	1	2	yes	—
119	C₂×Dic₁₉	—	2	4	no	—
120	C₂×Dic₁₉	—	4	2	no	—
121	C₂×Dic₁₉	—	4	2	no	—
122	C₂×Dic₁₉	—	4	2	no	—
123	C₂×Dic₁₉	—	4	2	no	—
124	C₂×Dic₁₉	—	4	2	no	—
125	C₂×Dic₁₉	—	8	8	no	—
126	C₈×C₁₉	—	2	4	no	—
127	C₁₉⋊C₈	—	8	2	no	—
128	C₂×#492	D₁₉	1	1	yes	characteristic
129	#2366	—	19	1	no	—
130	#1987	—	19	2	no	—
131	C₂×#331	—	19	1	no	—
132	#1279	—	19	2	no	—
133	C₂²×C₁₉	—	4	8	no	—
134	C₂²×C₁₉	—	4	4	no	—
135	C₂²×C₁₉	—	8	2	no	—
136	C₂²×C₁₉	—	8	2	no	—
137	C₂²×C₁₉	—	8	4	no	—
138	C₂²×C₁₉	#386	1	1	yes	characteristic
139	C₂²×C₁₉	#450	1	2	yes	—
140	C₂²×C₁₉	#452	1	2	yes	—
141	C₂²×C₁₉	#453	1	1	yes	characteristic
142	C₂²×C₁₉	#453	1	1	yes	characteristic
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	8	2	no	—
146	C₄×C₁₉	C₄×SD₁₆	1	2	yes	—
147	C₄×C₁₉	#440	1	2	yes	—
148	C₄×C₁₉	#461	1	2	yes	—
149	C₄×C₁₉	#463	1	2	yes	—
150	Dic₁₉	—	4	4	no	—
151	Dic₁₉	—	8	2	no	—
152	C₂²×SD₁₆	—	2	2	no	—
153	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
154	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
155	C₂×C₄×D₄	—	38	2	no	—
156	#492	—	2	2	no	—
157	#492	Dic₁₉	1	4	yes	complemented
158	C₂×C₄⋊C₈	—	19	2	no	—
159	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
160	#390	—	38	2	no	—
161	#386	—	38	2	no	—
162	C₄×C₄⋊C₄	—	19	2	no	—
163	#340	—	38	2	no	—
164	#340	—	38	2	no	—
165	#331	—	38	2	no	—
166	C₂×C₁₉	—	8	4	no	—
167	C₂×C₁₉	#1629	1	1	yes	characteristic
168	C₂×C₁₉	#1630	1	1	yes	characteristic
169	C₂×C₁₉	#1631	1	2	yes	—
170	C₂×C₁₉	#1877	1	2	yes	—
171	C₂×C₁₉	#1887	1	1	yes	characteristic
172	C₂²×Q₈	—	2	1	no	—
173	C₂²×D₄	—	2	2	no	—
174	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
175	C₂³×C₄	—	38	2	no	—
176	C₂×SD₁₆	—	2	8	no	—
177	C₂×SD₁₆	—	4	4	no	—
178	C₂×SD₁₆	—	4	4	no	—
179	C₂²×C₈	—	2	1	no	—
180	C₂²×C₈	—	38	2	no	—
181	C₄⋊Q₈	—	2	2	no	—
182	C₄⋊Q₈	—	2	1	no	—
183	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	complemented
184	#127	—	2	2	no	—
185	#127	C₂×Dic₁₉	1	2	yes	—
186	#127	C₂²⋊D₁₉	1	2	yes	—
187	C₄×D₄	—	76	4	no	—
188	C₄×D₄	—	76	4	no	—
189	C₂×C₄⋊C₄	—	2	2	no	—
190	C₂×C₄⋊C₄	—	19	2	no	—
191	C₂×C₄⋊C₄	—	19	2	no	—
192	C₂×C₂²⋊C₄	—	38	4	no	—
193	C₂×C₂²⋊C₄	—	38	2	no	—
194	C₂×C₄²	—	38	2	no	—
195	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
196	C₄⋊C₈	—	38	2	no	—
197	C₄⋊C₈	—	38	2	no	—
198	C₄×C₈	—	2	1	no	—
199	C₄×C₈	C₂×Dic₁₉	1	2	yes	complemented
200	#95	—	38	2	no	—
201	C₁₉	#9064	1	1	yes	characteristic, complemented, Sylow
202	C₂⁴	—	2	2	no	—
203	C₂×Q₈	—	2	2	no	—
204	C₂×Q₈	—	4	2	no	—
205	C₂×Q₈	—	4	2	no	—
206	C₂×Q₈	—	4	1	no	—
207	C₂×D₄	—	2	4	no	—
208	C₂×D₄	—	2	2	no	—
209	C₂×D₄	—	2	4	no	—
210	C₂×D₄	—	4	2	no	—
211	C₂×D₄	—	4	2	no	—
212	C₂×D₄	—	4	2	no	—
213	C₂×D₄	—	4	2	no	—
214	C₂×D₄	—	4	2	no	—
215	C₂×D₄	—	4	2	no	—
216	C₂×D₄	C₂²⋊Dic₁₉	1	4	yes	—
217	C₂²×C₄	—	4	1	no	—
218	C₂²×C₄	—	38	2	no	—
219	C₂²×C₄	—	38	2	no	—
220	C₂²×C₄	—	76	8	no	—
221	C₂²×C₄	—	152	2	no	—
222	C₂²×C₄	D₄×D₁₉	1	2	yes	—
223	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
224	SD₁₆	—	4	16	no	—
225	C₂×C₈	—	2	2	no	—
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	76	2	no	—
229	C₂×C₈	—	76	2	no	—
230	C₂×C₈	—	76	2	no	—
231	C₄⋊C₄	—	2	4	no	—
232	C₄⋊C₄	—	4	2	no	—
233	C₄⋊C₄	—	19	4	no	—
234	C₄⋊C₄	—	38	2	no	—
235	C₄⋊C₄	—	38	2	no	—
236	C₄⋊C₄	—	38	2	no	—
237	C₂²⋊C₄	—	76	8	no	—
238	C₂²⋊C₄	—	152	2	no	—
239	C₄²	—	76	2	no	—
240	C₄²	—	76	2	no	—
241	C₄²	#64543	1	2	yes	—
242	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
243	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
244	C₂³	—	2	4	no	—
245	C₂³	—	4	4	no	—
246	C₂³	—	4	4	no	—
247	C₂³	—	4	2	no	—
248	C₂³	—	4	2	no	—
249	C₂³	#10597383	1	1	yes	characteristic
250	Q₈	—	4	4	no	—
251	Q₈	—	8	2	no	—
252	D₄	—	4	4	no	—
253	D₄	—	4	4	no	—
254	D₄	—	4	4	no	—
255	D₄	—	4	4	no	—
256	D₄	—	4	4	no	—
257	D₄	—	8	2	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	8	1	no	—
262	C₂×C₄	—	8	1	no	—
263	C₂×C₄	—	38	4	no	—
264	C₂×C₄	—	76	2	no	—
265	C₂×C₄	—	76	2	no	—
266	C₂×C₄	—	76	2	no	—
267	C₂×C₄	—	76	2	no	—
268	C₂×C₄	—	76	2	no	—
269	C₂×C₄	—	152	8	no	—
270	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
271	C₂×C₄	#10597360	1	2	yes	—
272	C₂×C₄	#10597361	1	2	yes	—
273	C₂×C₄	#10597362	1	2	yes	—
274	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
275	C₂×C₄	#10597381	1	1	yes	characteristic
276	C₂×C₄	#10597385	1	2	yes	—
277	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
278	C₈	—	2	4	no	—
279	C₈	—	152	2	no	—
280	C₂²	—	4	8	no	—
281	C₂²	—	4	4	no	—
282	C₂²	—	8	2	no	—
283	C₂²	—	8	2	no	—
284	C₂²	—	8	4	no	—
285	C₂²	#11926424	1	1	yes	characteristic
286	C₂²	#11926693	1	2	yes	—
287	C₂²	#11926703	1	2	yes	—
288	C₂²	#11926711	1	1	yes	characteristic
289	C₂²	#11926711	1	1	yes	characteristic
290	C₄	—	2	1	no	—
291	C₄	—	2	1	no	—
292	C₄	—	8	2	no	—
293	C₄	—	76	4	no	—
294	C₄	—	152	2	no	—
295	C₄	SD₁₆×Dic₁₉	1	2	yes	—
296	C₄	#11926645	1	2	yes	—
297	C₄	#11926747	1	2	yes	—
298	C₄	#11926761	1	2	yes	—
299	C₂	—	8	4	no	—
300	C₂	#14562749	1	1	yes	characteristic
301	C₂	#14562754	1	1	yes	characteristic
302	C₂	#14562759	1	2	yes	—
303	C₂	#14563971	1	2	yes	—
304	C₂	#14564034	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14566700

C₂

yes

maximal, characteristic

#14564584

C₂

yes

maximal, complemented

C₂×#11926288

C₂

yes

maximal, characteristic

#14561475

C₂

yes

maximal, complemented

C₂×C₁₉×#492

C₂

yes

maximal, characteristic

C₂×D₄×Dic₁₉

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926447

—

#11926424

—

C₄×C₄⋊Dic₁₉

C₂²

yes

—

#11926306

—

#11926306

—

#11926288

—

C₂²×SD₁₆×C₁₉

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#127

C₂²

yes

characteristic

C₁₉×#492

—

C₁₉×#492

C₄

yes

complemented

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂³×Dic₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

complemented

C₁₉×#127

—

C₁₉×#127

C₂×C₄

yes

—

C₁₉×#127

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

D₄×Dic₁₉

—

D₄×Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

complemented

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂×Q₈×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

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

SD₁₆

yes

complemented

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9064

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

100

D₄×C₁₉

—

101

D₄×C₁₉

—

102

D₄×C₁₉

—

103

D₄×C₁₉

—

104

D₄×C₁₉

—

105

D₄×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

C₂×C₂²⋊C₄

yes

characteristic

112

C₂×C₄×C₁₉

C₄×D₄

yes

—

113

C₂×C₄×C₁₉

#121

yes

—

114

C₂×C₄×C₁₉

#123

yes

characteristic

115

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

116

C₂×C₄×C₁₉

#135

yes

—

117

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

118

C₂×C₄×C₁₉

#137

yes

—

119

C₂×Dic₁₉

—

120

C₂×Dic₁₉

—

121

C₂×Dic₁₉

—

122

C₂×Dic₁₉

—

123

C₂×Dic₁₉

—

124

C₂×Dic₁₉

—

125

C₂×Dic₁₉

—

126

C₈×C₁₉

—

127

C₁₉⋊C₈

—

128

C₂×#492

D₁₉

yes

characteristic

129

#2366

—

130

#1987

—

131

C₂×#331

—

132

#1279

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

#386

yes

characteristic

139

C₂²×C₁₉

#450

yes

—

140

C₂²×C₁₉

#452

yes

—

141

C₂²×C₁₉

#453

yes

characteristic

142

C₂²×C₁₉

#453

yes

characteristic

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

C₄×SD₁₆

yes

—

147

C₄×C₁₉

#440

yes

—

148

C₄×C₁₉

#461

yes

—

149

C₄×C₁₉

#463

yes

—

150

Dic₁₉

—

151

Dic₁₉

—

152

C₂²×SD₁₆

—

153

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

154

C₂×#127

C₂×D₁₉

yes

characteristic

155

C₂×C₄×D₄

—

156

#492

—

157

#492

Dic₁₉

yes

complemented

158

C₂×C₄⋊C₈

—

159

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

160

#390

—

161

#386

—

162

C₄×C₄⋊C₄

—

163

#340

—

164

#340

—

165

#331

—

166

C₂×C₁₉

—

167

C₂×C₁₉

#1629

yes

characteristic

168

C₂×C₁₉

#1630

yes

characteristic

169

C₂×C₁₉

#1631

yes

—

170

C₂×C₁₉

#1877

yes

—

171

C₂×C₁₉

#1887

yes

characteristic

172

C₂²×Q₈

—

173

C₂²×D₄

—

174

C₂²×D₄

C₂²⋊D₁₉

yes

—

175

C₂³×C₄

—

176

C₂×SD₁₆

—

177

C₂×SD₁₆

—

178

C₂×SD₁₆

—

179

C₂²×C₈

—

180

C₂²×C₈

—

181

C₄⋊Q₈

—

182

C₄⋊Q₈

—

183

C₄⋊Q₈

C₂×Dic₁₉

yes

complemented

184

#127

—

185

#127

C₂×Dic₁₉

yes

—

186

#127

C₂²⋊D₁₉

yes

—

187

C₄×D₄

—

188

C₄×D₄

—

189

C₂×C₄⋊C₄

—

190

C₂×C₄⋊C₄

—

191

C₂×C₄⋊C₄

—

192

C₂×C₂²⋊C₄

—

193

C₂×C₂²⋊C₄

—

194

C₂×C₄²

—

195

C₂×C₄²

C₂²×D₁₉

yes

characteristic

196

C₄⋊C₈

—

197

C₄⋊C₈

—

198

C₄×C₈

—

199

C₄×C₈

C₂×Dic₁₉

yes

complemented

200

#95

—

201

C₁₉

#9064

yes

characteristic, complemented, Sylow

202

C₂⁴

—

203

C₂×Q₈

—

204

C₂×Q₈

—

205

C₂×Q₈

—

206

C₂×Q₈

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂×D₄

—

215

C₂×D₄

—

216

C₂×D₄

C₂²⋊Dic₁₉

yes

—

217

C₂²×C₄

—

218

C₂²×C₄

—

219

C₂²×C₄

—

220

C₂²×C₄

—

221

C₂²×C₄

—

152

—

222

C₂²×C₄

D₄×D₁₉

yes

—

223

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

224

SD₁₆

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

—

230

C₂×C₈

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₂²⋊C₄

—

238

C₂²⋊C₄

—

152

—

239

C₄²

—

240

C₄²

—

241

C₄²

#64543

yes

—

242

C₄²

C₂²×Dic₁₉

yes

characteristic

243

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

—

248

C₂³

—

249

C₂³

#10597383

yes

characteristic

250

Q₈

—

251

Q₈

—

252

D₄

—

253

D₄

—

254

D₄

—

255

D₄

—

256

D₄

—

257

D₄

—

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

—

152

—

270

C₂×C₄

SD₁₆×D₁₉

yes

—

271

C₂×C₄

#10597360

yes

—

272

C₂×C₄

#10597361

yes

—

273

C₂×C₄

#10597362

yes

—

274

C₂×C₄

D₄×Dic₁₉

yes

—

275

C₂×C₄

#10597381

yes

characteristic

276

C₂×C₄

#10597385

yes

—

277

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

278

C₈

—

279

C₈

—

152

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

—

285

C₂²

#11926424

yes

characteristic

286

C₂²

#11926693

yes

—

287

C₂²

#11926703

yes

—

288

C₂²

#11926711

yes

characteristic

289

C₂²

#11926711

yes

characteristic

290

C₄

—

291

C₄

—

292

C₄

—

293

C₄

—

294

C₄

—

152

—

295

C₄

SD₁₆×Dic₁₉

yes

—

296

C₄

#11926645

yes

—

297

C₄

#11926747

yes

—

298

C₄

#11926761

yes

—

299

C₂

—

300

C₂

#14562749

yes

characteristic

301

C₂

#14562754

yes

characteristic

302

C₂

#14562759

yes

—

303

C₂

#14563971

yes

—

304

C₂

#14564034

yes

characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#492	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#492	D₁₉
hypocenter	C₁₉	#9064
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#492

subgroup

G/H

center

C₂³

#10597383

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#492

C₂

socle

C₂³×C₁₉

#120

prime radical

C₂×C₁₉×#127

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#492

N	H ≅ G/N	type
2. #14564584	C₂	semidirect
4. #14561475	C₂	semidirect
18. C₁₉×#492	C₄	semidirect
30. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
45. C₄×C₈×C₁₉	C₂×C₄	semidirect
85. C₄⋊Dic₁₉	SD₁₆	semidirect
157. #492	Dic₁₉	semidirect
183. C₄⋊Q₈	C₂×Dic₁₉	semidirect
199. C₄×C₈	C₂×Dic₁₉	semidirect
201. C₁₉	#9064	semidirect

H ≅ G/N

type

2. #14564584

C₂

semidirect

4. #14561475

C₂

semidirect

18. C₁₉×#492

C₄

semidirect

30. C₁₉×C₄⋊Q₈

C₂×C₄

semidirect

45. C₄×C₈×C₁₉

C₂×C₄

semidirect

85. C₄⋊Dic₁₉

SD₁₆

semidirect

157. #492

Dic₁₉

semidirect

183. C₄⋊Q₈

C₂×Dic₁₉

semidirect

199. C₄×C₈

C₂×Dic₁₉

semidirect

201. C₁₉

#9064

semidirect

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

subgroup	index
#14566700	2
#14564584	2
C₂×#11926288	2
#14561475	2
C₂×C₁₉×#492	2
#9064	19

subgroup

index

C₂×C₁₉×#492

Subgroups — #18077834

Conjugacy classes of subgroups

Complements

Maximal subgroups