Group #18077829 — subgroups

Subgroups — #18077829

Order 4864.

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

normal subgroups only

This group has 654 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	#14566725	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564563	C₂	1	2	yes	maximal
3	C₂×#11926293	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561475	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#492	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#10597289	—	2	2	no	—
8	C₂×#10597289	—	2	2	no	—
9	#11926451	—	2	2	no	—
10	#11926443	—	2	2	no	—
11	C₄⋊C₄×Dic₁₉	—	2	2	no	—
12	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	#11926293	—	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	D₄	1	2	yes	—
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×D₄×C₁₉	—	2	1	no	—
23	C₂×SD₁₆×C₁₉	—	2	8	no	—
24	C₂×SD₁₆×C₁₉	—	4	4	no	—
25	C₂×SD₁₆×C₁₉	—	4	4	no	—
26	C₂²×C₈×C₁₉	—	2	1	no	—
27	C₁₉×C₄⋊Q₈	—	2	2	no	—
28	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
29	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
30	C₁₉×#127	—	2	1	no	—
31	C₁₉×#127	—	2	2	no	—
32	C₁₉×#127	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₄⋊Dic₁₉	—	2	2	no	—
36	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
37	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
38	C₂×C₄×Dic₁₉	—	2	2	no	—
39	C₂×C₄×Dic₁₉	—	2	2	no	—
40	C₂²×C₁₉⋊C₈	—	2	2	no	—
41	C₄×C₈×C₁₉	—	2	1	no	—
42	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
43	#10597289	—	4	4	no	—
44	#10597289	—	4	4	no	—
45	C₁₉⋊#95	—	2	4	no	—
46	C₁₉⋊#95	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₂⁴×C₁₉	—	4	1	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	C₂²⋊C₄	1	4	yes	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	2	4	no	—
56	C₂×D₄×C₁₉	—	4	2	no	—
57	C₂×D₄×C₁₉	—	4	2	no	—
58	C₂×D₄×C₁₉	—	4	2	no	—
59	C₂×D₄×C₁₉	—	4	1	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	C₂²×C₄×C₁₉	—	2	2	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	SD₁₆×C₁₉	—	4	16	no	—
70	C₂×C₈×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	—	2	2	no	—
72	C₂×C₈×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₉	#41	1	2	yes	—
78	C₄⋊Dic₁₉	—	2	2	no	—
79	C₄⋊Dic₁₉	—	2	2	no	—
80	C₄⋊Dic₁₉	—	2	2	no	—
81	C₄⋊Dic₁₉	—	8	2	no	—
82	C₄⋊Dic₁₉	SD₁₆	1	4	yes	complemented
83	C₄×Dic₁₉	—	4	2	no	—
84	C₄×Dic₁₉	—	4	2	no	—
85	C₄×Dic₁₉	—	8	2	no	—
86	C₂×C₁₉⋊C₈	—	4	2	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	#9063	—	19	1	no	maximal, Sylow
90	C₂³×C₁₉	—	4	2	no	—
91	C₂³×C₁₉	—	8	2	no	—
92	C₂³×C₁₉	—	8	2	no	—
93	C₂³×C₁₉	—	8	1	no	—
94	C₂³×C₁₉	—	8	1	no	—
95	C₂³×C₁₉	#120	1	1	yes	characteristic
96	Q₈×C₁₉	—	4	4	no	—
97	Q₈×C₁₉	—	8	2	no	—
98	D₄×C₁₉	—	4	4	no	—
99	D₄×C₁₉	—	4	4	no	—
100	D₄×C₁₉	—	4	4	no	—
101	D₄×C₁₉	—	8	2	no	—
102	D₄×C₁₉	—	8	2	no	—
103	D₄×C₁₉	—	8	2	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	4	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₁₉	#121	1	2	yes	—
112	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
114	C₂×C₄×C₁₉	#135	1	2	yes	—
115	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
116	C₂×C₄×C₁₉	#137	1	2	yes	—
117	C₂×Dic₁₉	—	2	4	no	—
118	C₂×Dic₁₉	—	4	2	no	—
119	C₂×Dic₁₉	—	4	2	no	—
120	C₂×Dic₁₉	—	4	2	no	—
121	C₂×Dic₁₉	—	4	2	no	—
122	C₂×Dic₁₉	—	4	2	no	—
123	C₈×C₁₉	—	2	4	no	—
124	C₁₉⋊C₈	—	8	2	no	—
125	C₂×#492	D₁₉	1	1	yes	characteristic
126	#2369	—	19	1	no	—
127	#1982	—	19	2	no	—
128	C₂×#333	—	19	1	no	—
129	#1279	—	19	2	no	—
130	C₂²×C₁₉	—	8	4	no	—
131	C₂²×C₁₉	—	8	2	no	—
132	C₂²×C₁₉	—	16	2	no	—
133	C₂²×C₁₉	—	16	1	no	—
134	C₂²×C₁₉	—	16	1	no	—
135	C₂²×C₁₉	#386	1	1	yes	characteristic
136	C₂²×C₁₉	#448	1	2	yes	—
137	C₂²×C₁₉	#449	1	2	yes	—
138	C₂²×C₁₉	#453	1	1	yes	characteristic
139	C₂²×C₁₉	#453	1	1	yes	characteristic
140	C₄×C₁₉	—	2	1	no	—
141	C₄×C₁₉	—	2	1	no	—
142	C₄×C₁₉	—	4	4	no	—
143	C₄×C₁₉	C₄×SD₁₆	1	2	yes	—
144	C₄×C₁₉	#440	1	2	yes	—
145	C₄×C₁₉	#460	1	2	yes	—
146	C₄×C₁₉	#464	1	2	yes	—
147	Dic₁₉	—	4	4	no	—
148	Dic₁₉	—	8	2	no	—
149	C₂²×SD₁₆	—	2	2	no	—
150	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
151	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
152	#492	—	2	2	no	—
153	#492	Dic₁₉	1	4	yes	complemented
154	C₂×C₄⋊C₈	—	19	2	no	—
155	C₂×#102	—	38	2	no	—
156	C₂×#102	—	38	2	no	—
157	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
158	#391	—	38	2	no	—
159	#389	—	38	2	no	—
160	C₄×C₄⋊C₄	—	19	2	no	—
161	C₄×C₄⋊C₄	—	38	2	no	—
162	#333	—	38	2	no	—
163	C₂×C₁₉	—	16	2	no	—
164	C₂×C₁₉	#1622	1	2	yes	—
165	C₂×C₁₉	#1623	1	1	yes	characteristic
166	C₂×C₁₉	#1624	1	1	yes	characteristic
167	C₂×C₁₉	#1880	1	2	yes	—
168	C₂×C₁₉	#1887	1	1	yes	characteristic
169	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
170	C₂²×D₄	—	2	2	no	—
171	C₂²×D₄	—	2	1	no	—
172	C₂×SD₁₆	—	2	8	no	—
173	C₂×SD₁₆	—	4	4	no	—
174	C₂×SD₁₆	—	4	4	no	—
175	C₂²×C₈	—	2	1	no	—
176	C₂²×C₈	—	38	2	no	—
177	C₄⋊Q₈	—	2	2	no	—
178	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
179	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
180	#127	—	2	2	no	—
181	#127	—	2	1	no	—
182	#127	C₂×Dic₁₉	1	2	yes	—
183	C₂×C₄⋊C₄	—	2	2	no	—
184	C₂×C₄⋊C₄	—	19	2	no	—
185	C₂×C₄⋊C₄	—	19	2	no	—
186	C₂×C₄⋊C₄	—	38	2	no	—
187	C₂×C₄²	—	38	2	no	—
188	C₂×C₄²	—	38	2	no	—
189	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
190	C₄⋊C₈	—	38	2	no	—
191	C₄⋊C₈	—	38	2	no	—
192	#102	—	76	4	no	—
193	#102	—	76	4	no	—
194	C₄×C₈	—	2	1	no	—
195	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
196	#95	—	38	4	no	—
197	#95	—	38	2	no	—
198	C₁₉	#9063	1	1	yes	characteristic, complemented, Sylow
199	C₂⁴	—	4	1	no	—
200	C₂×Q₈	—	2	2	no	—
201	C₂×Q₈	—	4	2	no	—
202	C₂×Q₈	—	4	2	no	—
203	C₂×Q₈	C₂²⋊Dic₁₉	1	4	yes	—
204	C₂×D₄	—	2	4	no	—
205	C₂×D₄	—	2	2	no	—
206	C₂×D₄	—	4	2	no	—
207	C₂×D₄	—	4	2	no	—
208	C₂×D₄	—	4	1	no	—
209	C₂×D₄	—	4	2	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	C₂²×C₄	—	2	2	no	—
215	C₂²×C₄	—	38	2	no	—
216	C₂²×C₄	—	38	2	no	—
217	C₂²×C₄	D₄×D₁₉	1	2	yes	—
218	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
219	SD₁₆	—	4	16	no	—
220	C₂×C₈	—	2	2	no	—
221	C₂×C₈	—	2	2	no	—
222	C₂×C₈	—	2	2	no	—
223	C₂×C₈	—	76	2	no	—
224	C₂×C₈	—	76	2	no	—
225	C₂×C₈	—	76	2	no	—
226	C₄⋊C₄	—	2	4	no	—
227	C₄⋊C₄	—	2	4	no	—
228	C₄⋊C₄	—	19	4	no	—
229	C₄⋊C₄	—	38	2	no	—
230	C₄⋊C₄	—	38	2	no	—
231	C₄⋊C₄	—	38	2	no	—
232	C₄⋊C₄	—	152	2	no	—
233	C₄²	—	76	2	no	—
234	C₄²	—	76	2	no	—
235	C₄²	—	152	2	no	—
236	C₄²	#64543	1	2	yes	—
237	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
238	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
239	C₂³	—	4	2	no	—
240	C₂³	—	8	2	no	—
241	C₂³	—	8	2	no	—
242	C₂³	—	8	1	no	—
243	C₂³	—	8	1	no	—
244	C₂³	#10597383	1	1	yes	characteristic
245	Q₈	—	4	4	no	—
246	Q₈	—	8	2	no	—
247	D₄	—	4	4	no	—
248	D₄	—	4	4	no	—
249	D₄	—	4	4	no	—
250	D₄	—	8	2	no	—
251	D₄	—	8	2	no	—
252	D₄	—	8	2	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	4	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	38	4	no	—
259	C₂×C₄	—	76	2	no	—
260	C₂×C₄	—	76	2	no	—
261	C₂×C₄	—	76	2	no	—
262	C₂×C₄	—	76	2	no	—
263	C₂×C₄	—	76	2	no	—
264	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
265	C₂×C₄	#10597360	1	2	yes	—
266	C₂×C₄	#10597361	1	2	yes	—
267	C₂×C₄	#10597362	1	2	yes	—
268	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
269	C₂×C₄	#10597381	1	1	yes	characteristic
270	C₂×C₄	#10597385	1	2	yes	—
271	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
272	C₈	—	2	4	no	—
273	C₈	—	152	2	no	—
274	C₂²	—	8	4	no	—
275	C₂²	—	8	2	no	—
276	C₂²	—	16	2	no	—
277	C₂²	—	16	1	no	—
278	C₂²	—	16	1	no	—
279	C₂²	#11926424	1	1	yes	characteristic
280	C₂²	#11926681	1	2	yes	—
281	C₂²	#11926688	1	2	yes	—
282	C₂²	#11926711	1	1	yes	characteristic
283	C₂²	#11926711	1	1	yes	characteristic
284	C₄	—	2	1	no	—
285	C₄	—	2	1	no	—
286	C₄	—	4	4	no	—
287	C₄	—	76	4	no	—
288	C₄	—	152	2	no	—
289	C₄	SD₁₆×Dic₁₉	1	2	yes	—
290	C₄	#11926645	1	2	yes	—
291	C₄	#11926742	1	2	yes	—
292	C₄	#11926764	1	2	yes	—
293	C₂	—	16	2	no	—
294	C₂	#14562704	1	2	yes	—
295	C₂	#14562711	1	1	yes	characteristic
296	C₂	#14562716	1	1	yes	characteristic
297	C₂	#14563992	1	2	yes	—
298	C₂	#14564034	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14566725

C₂

yes

maximal, characteristic, complemented

#14564563

C₂

yes

maximal

C₂×#11926293

C₂

yes

maximal, characteristic, complemented

#14561475

C₂

yes

maximal, complemented

C₂×C₁₉×#492

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

—

C₄⋊C₄×Dic₁₉

—

C₄×C₄⋊Dic₁₉

C₂²

yes

—

#11926293

—

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

D₄

yes

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

#10597289

—

#10597289

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

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×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

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

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

SD₁₆

yes

complemented

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9063

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

100

D₄×C₁₉

—

101

D₄×C₁₉

—

102

D₄×C₁₉

—

103

D₄×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

C₂×C₂²⋊C₄

yes

characteristic

110

C₂×C₄×C₁₉

C₄×D₄

yes

—

111

C₂×C₄×C₁₉

#121

yes

—

112

C₂×C₄×C₁₉

#123

yes

characteristic

113

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

114

C₂×C₄×C₁₉

#135

yes

—

115

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

116

C₂×C₄×C₁₉

#137

yes

—

117

C₂×Dic₁₉

—

118

C₂×Dic₁₉

—

119

C₂×Dic₁₉

—

120

C₂×Dic₁₉

—

121

C₂×Dic₁₉

—

122

C₂×Dic₁₉

—

123

C₈×C₁₉

—

124

C₁₉⋊C₈

—

125

C₂×#492

D₁₉

yes

characteristic

126

#2369

—

127

#1982

—

128

C₂×#333

—

129

#1279

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

#386

yes

characteristic

136

C₂²×C₁₉

#448

yes

—

137

C₂²×C₁₉

#449

yes

—

138

C₂²×C₁₉

#453

yes

characteristic

139

C₂²×C₁₉

#453

yes

characteristic

140

C₄×C₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

C₄×SD₁₆

yes

—

144

C₄×C₁₉

#440

yes

—

145

C₄×C₁₉

#460

yes

—

146

C₄×C₁₉

#464

yes

—

147

Dic₁₉

—

148

Dic₁₉

—

149

C₂²×SD₁₆

—

150

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

151

C₂×#127

C₂×D₁₉

yes

characteristic

152

#492

—

153

#492

Dic₁₉

yes

complemented

154

C₂×C₄⋊C₈

—

155

C₂×#102

—

156

C₂×#102

—

157

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

158

#391

—

159

#389

—

160

C₄×C₄⋊C₄

—

161

C₄×C₄⋊C₄

—

162

#333

—

163

C₂×C₁₉

—

164

C₂×C₁₉

#1622

yes

—

165

C₂×C₁₉

#1623

yes

characteristic

166

C₂×C₁₉

#1624

yes

characteristic

167

C₂×C₁₉

#1880

yes

—

168

C₂×C₁₉

#1887

yes

characteristic

169

C₂²×Q₈

C₂²⋊D₁₉

yes

—

170

C₂²×D₄

—

171

C₂²×D₄

—

172

C₂×SD₁₆

—

173

C₂×SD₁₆

—

174

C₂×SD₁₆

—

175

C₂²×C₈

—

176

C₂²×C₈

—

177

C₄⋊Q₈

—

178

C₄⋊Q₈

C₂×Dic₁₉

yes

—

179

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

180

#127

—

181

#127

—

182

#127

C₂×Dic₁₉

yes

—

183

C₂×C₄⋊C₄

—

184

C₂×C₄⋊C₄

—

185

C₂×C₄⋊C₄

—

186

C₂×C₄⋊C₄

—

187

C₂×C₄²

—

188

C₂×C₄²

—

189

C₂×C₄²

C₂²×D₁₉

yes

characteristic

190

C₄⋊C₈

—

191

C₄⋊C₈

—

192

#102

—

193

#102

—

194

C₄×C₈

—

195

C₄×C₈

C₂×Dic₁₉

yes

—

196

#95

—

197

#95

—

198

C₁₉

#9063

yes

characteristic, complemented, Sylow

199

C₂⁴

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

203

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

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

C₂×D₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

D₄×D₁₉

yes

—

218

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

219

SD₁₆

—

220

C₂×C₈

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

152

—

233

C₄²

—

234

C₄²

—

235

C₄²

—

152

—

236

C₄²

#64543

yes

—

237

C₄²

C₂²×Dic₁₉

yes

characteristic

238

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

239

C₂³

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

#10597383

yes

characteristic

245

Q₈

—

246

Q₈

—

247

D₄

—

248

D₄

—

249

D₄

—

250

D₄

—

251

D₄

—

252

D₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

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

SD₁₆×D₁₉

yes

—

265

C₂×C₄

#10597360

yes

—

266

C₂×C₄

#10597361

yes

—

267

C₂×C₄

#10597362

yes

—

268

C₂×C₄

D₄×Dic₁₉

yes

—

269

C₂×C₄

#10597381

yes

characteristic

270

C₂×C₄

#10597385

yes

—

271

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

272

C₈

—

273

C₈

—

152

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

#11926424

yes

characteristic

280

C₂²

#11926681

yes

—

281

C₂²

#11926688

yes

—

282

C₂²

#11926711

yes

characteristic

283

C₂²

#11926711

yes

characteristic

284

C₄

—

285

C₄

—

286

C₄

—

287

C₄

—

288

C₄

—

152

—

289

C₄

SD₁₆×Dic₁₉

yes

—

290

C₄

#11926645

yes

—

291

C₄

#11926742

yes

—

292

C₄

#11926764

yes

—

293

C₂

—

294

C₂

#14562704

yes

—

295

C₂

#14562711

yes

characteristic

296

C₂

#14562716

yes

characteristic

297

C₂

#14563992

yes

—

298

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	#9063
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
1. #14566725	C₂	semidirect
3. C₂×#11926293	C₂	semidirect
4. #14561475	C₂	semidirect
18. C₁₉×#492	C₄	semidirect
82. C₄⋊Dic₁₉	SD₁₆	semidirect
153. #492	Dic₁₉	semidirect
198. C₁₉	#9063	semidirect

H ≅ G/N

type

1. #14566725

C₂

semidirect

3. C₂×#11926293

C₂

semidirect

4. #14561475

C₂

semidirect

18. C₁₉×#492

C₄

semidirect

82. C₄⋊Dic₁₉

SD₁₆

semidirect

153. #492

Dic₁₉

semidirect

198. C₁₉

#9063

semidirect

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

subgroup	index
#14566725	2
#14564563	2
C₂×#11926293	2
#14561475	2
C₂×C₁₉×#492	2
#9063	19

subgroup

index

C₂×C₁₉×#492

Subgroups — #18077829

Conjugacy classes of subgroups

Complements

Maximal subgroups