Group #18080389 — subgroups

Subgroups — #18080389

Order 4864.

626 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 135 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	#14572659	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563627	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562060	C₂	1	2	yes	maximal, complemented
4	#14561493	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2535	C₂	1	1	yes	maximal, characteristic
6	D₄×C₁₉⋊C₈	—	2	4	no	—
7	#11926597	C₂²	1	2	yes	—
8	#11926568	C₂²	1	2	yes	—
9	C₂×#10597290	—	2	1	no	—
10	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
11	#11926313	—	2	1	no	—
12	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
13	C₂×C₁₉×#121	—	2	1	no	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#397	C₄	1	2	yes	—
17	C₁₉×#392	C₄	1	2	yes	—
18	C₁₉×#386	—	2	2	no	—
19	C₁₉×#382	C₂²	1	1	yes	characteristic
20	C₁₉×#380	—	2	1	no	—
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	—	2	1	no	—
25	C₂³×C₄×C₁₉	D₄	1	2	yes	—
26	C₁₉×#121	—	4	2	no	—
27	C₁₉×#121	—	4	2	no	—
28	C₄×D₄×C₁₉	—	2	2	no	—
29	C₄×D₄×C₁₉	—	2	2	no	—
30	C₄×D₄×C₁₉	—	2	2	no	—
31	C₄×D₄×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×C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×#64520	—	2	2	no	—
41	C₂²×C₁₉⋊C₈	—	2	4	no	—
42	C₁₉×#95	—	2	2	no	—
43	C₁₉×#95	—	2	1	no	—
44	C₁₉×#95	C₂×C₄	1	2	yes	—
45	#10597290	—	4	2	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
47	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄×C₁₉⋊C₈	D₄	1	4	yes	complemented
52	C₂⁴×C₁₉	—	2	1	no	—
53	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	2	2	no	—
56	C₂×D₄×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	—	4	2	no	—
58	C₂×D₄×C₁₉	—	4	4	no	—
59	C₂×D₄×C₁₉	—	4	4	no	—
60	C₂×D₄×C₁₉	—	8	2	no	—
61	C₂×D₄×C₁₉	D₈	1	2	yes	—
62	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	—	4	1	no	—
69	C₂²×C₄×C₁₉	—	4	1	no	—
70	C₂²×C₄×C₁₉	—	4	2	no	—
71	C₂²×C₄×C₁₉	—	8	2	no	—
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
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	—	4	1	no	—
79	C₄⋊C₄×C₁₉	—	4	1	no	—
80	C₂²⋊C₄×C₁₉	—	2	4	no	—
81	C₂²⋊C₄×C₁₉	—	4	4	no	—
82	C₂²⋊C₄×C₁₉	—	4	1	no	—
83	C₂²⋊C₄×C₁₉	—	4	1	no	—
84	C₂²⋊C₄×C₁₉	—	8	2	no	—
85	C₄²×C₁₉	C₂×D₄	1	2	yes	—
86	C₄²×C₁₉	#41	1	2	yes	—
87	#64520	—	4	2	no	—
88	#64520	—	4	2	no	—
89	C₂×C₁₉⋊C₈	—	2	4	no	—
90	C₂×C₁₉⋊C₈	—	4	2	no	—
91	C₂×C₁₉⋊C₈	—	8	4	no	—
92	#9485	—	19	1	no	maximal, Sylow
93	C₂³×C₁₉	—	2	2	no	—
94	C₂³×C₁₉	—	2	2	no	—
95	C₂³×C₁₉	—	2	2	no	—
96	C₂³×C₁₉	—	4	2	no	—
97	C₂³×C₁₉	—	4	2	no	—
98	C₂³×C₁₉	—	4	1	no	—
99	C₂³×C₁₉	—	4	1	no	—
100	C₂³×C₁₉	—	4	1	no	—
101	C₂³×C₁₉	—	4	1	no	—
102	C₂³×C₁₉	—	4	1	no	—
103	C₂³×C₁₉	—	4	1	no	—
104	C₂³×C₁₉	#102	1	4	yes	—
105	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	D₄×C₁₉	—	2	4	no	—
107	D₄×C₁₉	—	2	4	no	—
108	D₄×C₁₉	—	2	4	no	—
109	D₄×C₁₉	—	4	2	no	—
110	D₄×C₁₉	—	8	8	no	—
111	C₂×C₄×C₁₉	—	2	2	no	—
112	C₂×C₄×C₁₉	—	4	1	no	—
113	C₂×C₄×C₁₉	—	4	1	no	—
114	C₂×C₄×C₁₉	—	4	4	no	—
115	C₂×C₄×C₁₉	—	4	2	no	—
116	C₂×C₄×C₁₉	—	4	2	no	—
117	C₂×C₄×C₁₉	—	4	2	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	1	no	—
122	C₂×C₄×C₁₉	—	8	2	no	—
123	C₂×C₄×C₁₉	—	8	2	no	—
124	C₂×C₄×C₁₉	—	8	2	no	—
125	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
126	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
127	C₂×C₄×C₁₉	#121	1	2	yes	—
128	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
129	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#135	1	2	yes	—
132	C₁₉⋊C₈	—	4	4	no	—
133	C₁₉⋊C₈	—	8	2	no	—
134	#2972	—	19	1	no	—
135	#2535	D₁₉	1	1	yes	characteristic
136	#1800	—	19	1	no	—
137	#1486	—	19	2	no	—
138	#1286	—	19	2	no	—
139	C₂²×C₁₉	—	2	1	no	—
140	C₂²×C₁₉	—	2	1	no	—
141	C₂²×C₁₉	—	2	4	no	—
142	C₂²×C₁₉	—	4	4	no	—
143	C₂²×C₁₉	—	4	2	no	—
144	C₂²×C₁₉	—	4	2	no	—
145	C₂²×C₁₉	—	4	2	no	—
146	C₂²×C₁₉	—	4	2	no	—
147	C₂²×C₁₉	—	4	2	no	—
148	C₂²×C₁₉	—	8	2	no	—
149	C₂²×C₁₉	—	8	1	no	—
150	C₂²×C₁₉	—	8	1	no	—
151	C₂²×C₁₉	—	8	1	no	—
152	C₂²×C₁₉	—	8	1	no	—
153	C₂²×C₁₉	#386	1	1	yes	characteristic
154	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
155	C₂²×C₁₉	#416	1	1	yes	characteristic
156	C₄×C₁₉	—	2	2	no	—
157	C₄×C₁₉	—	2	1	no	—
158	C₄×C₁₉	—	2	1	no	—
159	C₄×C₁₉	—	4	2	no	—
160	C₄×C₁₉	—	8	2	no	—
161	C₄×C₁₉	—	8	1	no	—
162	C₄×C₁₉	#465	1	2	yes	—
163	C₄×C₁₉	#466	1	2	yes	—
164	C₂×#121	—	2	1	no	—
165	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
166	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
167	C₈×D₄	—	38	4	no	—
168	#431	—	19	2	no	—
169	#423	—	19	2	no	—
170	C₂×#100	—	38	1	no	—
171	C₂×C₂²⋊C₈	—	38	2	no	—
172	#397	Dic₁₉	1	2	yes	—
173	#392	Dic₁₉	1	2	yes	—
174	#386	—	2	2	no	—
175	#382	C₂×D₁₉	1	1	yes	characteristic
176	#380	—	2	1	no	—
177	#343	—	38	1	no	—
178	D₄⋊C₈	—	38	4	no	—
179	C₂×C₁₉	—	2	1	no	—
180	C₂×C₁₉	—	2	1	no	—
181	C₂×C₁₉	—	4	4	no	—
182	C₂×C₁₉	—	8	2	no	—
183	C₂×C₁₉	#1891	1	1	yes	characteristic
184	C₂×C₁₉	#1893	1	1	yes	characteristic
185	C₂×C₁₉	#1911	1	1	yes	characteristic
186	C₂²×D₄	—	2	2	no	—
187	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
188	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
189	C₂³×C₄	—	2	1	no	—
190	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
191	C₂×M₁₆	—	38	2	no	—
192	C₂²×C₈	—	38	4	no	—
193	#121	—	4	2	no	—
194	#121	—	4	2	no	—
195	C₄×D₄	—	2	2	no	—
196	C₄×D₄	—	2	2	no	—
197	C₄×D₄	—	2	2	no	—
198	C₄×D₄	—	2	2	no	—
199	C₂×C₄⋊C₄	—	2	1	no	—
200	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
202	C₂×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₂²⋊C₄	—	2	1	no	—
204	C₂×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
206	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
207	C₄⋊C₈	—	38	2	no	—
208	C₄⋊C₈	—	38	2	no	—
209	C₄⋊C₈	—	38	2	no	—
210	#100	—	76	2	no	—
211	C₂²⋊C₈	—	38	4	no	—
212	C₂²⋊C₈	—	38	2	no	—
213	C₄×C₈	—	19	4	no	—
214	#95	—	2	2	no	—
215	#95	—	2	1	no	—
216	#95	C₂×Dic₁₉	1	2	yes	—
217	C₁₉	#9485	1	1	yes	characteristic, complemented, Sylow
218	C₂⁴	—	2	1	no	—
219	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
220	C₂×D₄	—	2	2	no	—
221	C₂×D₄	—	2	2	no	—
222	C₂×D₄	—	2	2	no	—
223	C₂×D₄	—	4	2	no	—
224	C₂×D₄	—	4	4	no	—
225	C₂×D₄	—	4	4	no	—
226	C₂×D₄	—	8	2	no	—
227	C₂×D₄	#64525	1	2	yes	—
228	C₂×D₄	#64526	1	2	yes	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	1	no	—
233	C₂²×C₄	—	4	1	no	—
234	C₂²×C₄	—	4	1	no	—
235	C₂²×C₄	—	4	2	no	—
236	C₂²×C₄	—	4	2	no	—
237	C₂²×C₄	—	8	2	no	—
238	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
239	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
240	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
241	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
242	M₁₆	—	76	2	no	—
243	M₁₆	—	76	2	no	—
244	C₂×C₈	—	38	4	no	—
245	C₂×C₈	—	76	2	no	—
246	C₂×C₈	—	152	4	no	—
247	C₄⋊C₄	—	2	2	no	—
248	C₄⋊C₄	—	2	2	no	—
249	C₄⋊C₄	—	4	1	no	—
250	C₄⋊C₄	—	4	1	no	—
251	C₂²⋊C₄	—	2	4	no	—
252	C₂²⋊C₄	—	4	4	no	—
253	C₂²⋊C₄	—	4	1	no	—
254	C₂²⋊C₄	—	4	1	no	—
255	C₂²⋊C₄	—	8	2	no	—
256	C₄²	D₄×D₁₉	1	2	yes	—
257	C₄²	#64543	1	2	yes	—
258	C₂³	—	2	2	no	—
259	C₂³	—	2	2	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	4	2	no	—
262	C₂³	—	4	2	no	—
263	C₂³	—	4	1	no	—
264	C₂³	—	4	1	no	—
265	C₂³	—	4	1	no	—
266	C₂³	—	4	1	no	—
267	C₂³	—	4	1	no	—
268	C₂³	—	4	1	no	—
269	C₂³	#10597289	1	4	yes	—
270	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
271	D₄	—	2	4	no	—
272	D₄	—	2	4	no	—
273	D₄	—	2	4	no	—
274	D₄	—	4	2	no	—
275	D₄	—	8	8	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	4	1	no	—
278	C₂×C₄	—	4	1	no	—
279	C₂×C₄	—	4	4	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	4	1	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	1	no	—
286	C₂×C₄	—	4	1	no	—
287	C₂×C₄	—	8	2	no	—
288	C₂×C₄	—	8	2	no	—
289	C₂×C₄	—	8	2	no	—
290	C₂×C₄	C₂×#64525	1	1	yes	characteristic
291	C₂×C₄	C₂×#64526	1	1	yes	characteristic
292	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
293	C₂×C₄	#10597381	1	1	yes	characteristic
294	C₂×C₄	#10597383	1	1	yes	characteristic
295	C₂×C₄	#10597385	1	2	yes	—
296	C₂×C₄	#10597396	1	2	yes	—
297	C₈	—	76	4	no	—
298	C₈	—	152	2	no	—
299	C₂²	—	2	1	no	—
300	C₂²	—	2	1	no	—
301	C₂²	—	2	4	no	—
302	C₂²	—	4	4	no	—
303	C₂²	—	4	2	no	—
304	C₂²	—	4	2	no	—
305	C₂²	—	4	2	no	—
306	C₂²	—	4	2	no	—
307	C₂²	—	4	2	no	—
308	C₂²	—	8	2	no	—
309	C₂²	—	8	1	no	—
310	C₂²	—	8	1	no	—
311	C₂²	—	8	1	no	—
312	C₂²	—	8	1	no	—
313	C₂²	#11926424	1	1	yes	characteristic
314	C₂²	C₂×#10597289	1	1	yes	characteristic
315	C₂²	#11926540	1	1	yes	characteristic
316	C₄	—	2	1	no	—
317	C₄	—	2	1	no	—
318	C₄	—	2	2	no	—
319	C₄	—	4	2	no	—
320	C₄	—	8	2	no	—
321	C₄	—	8	1	no	—
322	C₄	#11926771	1	2	yes	—
323	C₄	#11926778	1	2	yes	—
324	C₂	—	2	1	no	—
325	C₂	—	2	1	no	—
326	C₂	—	4	4	no	—
327	C₂	—	8	2	no	—
328	C₂	#14564054	1	1	yes	characteristic
329	C₂	#14564064	1	1	yes	characteristic
330	C₂	#14564168	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572659

C₂

yes

maximal, characteristic, complemented

#14563627

C₂

yes

maximal, characteristic, complemented

#14562060

C₂

yes

maximal, complemented

#14561493

C₂

yes

maximal, complemented

C₁₉×#2535

C₂

yes

maximal, characteristic

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597290

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926313

—

D₄⋊(C₁₉⋊C₈)

—

C₂×C₁₉×#121

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#397

C₄

yes

—

C₁₉×#392

C₄

yes

—

C₁₉×#386

—

C₁₉×#382

C₂²

yes

characteristic

C₁₉×#380

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

D₄

yes

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

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×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

C₂×C₄

yes

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

complemented

C₂⁴×C₁₉

—

C₂⁴×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

D₈

yes

—

C₂×D₄×C₁₉

SD₁₆

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

yes

—

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

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9485

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

100

C₂³×C₁₉

—

101

C₂³×C₁₉

—

102

C₂³×C₁₉

—

103

C₂³×C₁₉

—

104

C₂³×C₁₉

#102

yes

—

105

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

106

D₄×C₁₉

—

107

D₄×C₁₉

—

108

D₄×C₁₉

—

109

D₄×C₁₉

—

110

D₄×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

—

124

C₂×C₄×C₁₉

—

125

C₂×C₄×C₁₉

C₄×D₄

yes

—

126

C₂×C₄×C₁₉

#120

yes

characteristic

127

C₂×C₄×C₁₉

#121

yes

—

128

C₂×C₄×C₁₉

#123

yes

characteristic

129

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

130

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

131

C₂×C₄×C₁₉

#135

yes

—

132

C₁₉⋊C₈

—

133

C₁₉⋊C₈

—

134

#2972

—

135

#2535

D₁₉

yes

characteristic

136

#1800

—

137

#1486

—

138

#1286

—

139

C₂²×C₁₉

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

—

142

C₂²×C₁₉

—

143

C₂²×C₁₉

—

144

C₂²×C₁₉

—

145

C₂²×C₁₉

—

146

C₂²×C₁₉

—

147

C₂²×C₁₉

—

148

C₂²×C₁₉

—

149

C₂²×C₁₉

—

150

C₂²×C₁₉

—

151

C₂²×C₁₉

—

152

C₂²×C₁₉

—

153

C₂²×C₁₉

#386

yes

characteristic

154

C₂²×C₁₉

C₂×#102

yes

characteristic

155

C₂²×C₁₉

#416

yes

characteristic

156

C₄×C₁₉

—

157

C₄×C₁₉

—

158

C₄×C₁₉

—

159

C₄×C₁₉

—

160

C₄×C₁₉

—

161

C₄×C₁₉

—

162

C₄×C₁₉

#465

yes

—

163

C₄×C₁₉

#466

yes

—

164

C₂×#121

—

165

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

166

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

167

C₈×D₄

—

168

#431

—

169

#423

—

170

C₂×#100

—

171

C₂×C₂²⋊C₈

—

172

#397

Dic₁₉

yes

—

173

#392

Dic₁₉

yes

—

174

#386

—

175

#382

C₂×D₁₉

yes

characteristic

176

#380

—

177

#343

—

178

D₄⋊C₈

—

179

C₂×C₁₉

—

180

C₂×C₁₉

—

181

C₂×C₁₉

—

182

C₂×C₁₉

—

183

C₂×C₁₉

#1891

yes

characteristic

184

C₂×C₁₉

#1893

yes

characteristic

185

C₂×C₁₉

#1911

yes

characteristic

186

C₂²×D₄

—

187

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

188

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

189

C₂³×C₄

—

190

C₂³×C₄

C₂²⋊D₁₉

yes

—

191

C₂×M₁₆

—

192

C₂²×C₈

—

193

#121

—

194

#121

—

195

C₄×D₄

—

196

C₄×D₄

—

197

C₄×D₄

—

198

C₄×D₄

—

199

C₂×C₄⋊C₄

—

200

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

201

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

202

C₂×C₂²⋊C₄

—

203

C₂×C₂²⋊C₄

—

204

C₂×C₂²⋊C₄

—

205

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

—

206

C₂×C₄²

C₂²×D₁₉

yes

characteristic

207

C₄⋊C₈

—

208

C₄⋊C₈

—

209

C₄⋊C₈

—

210

#100

—

211

C₂²⋊C₈

—

212

C₂²⋊C₈

—

213

C₄×C₈

—

214

#95

—

215

#95

—

216

#95

C₂×Dic₁₉

yes

—

217

C₁₉

#9485

yes

characteristic, complemented, Sylow

218

C₂⁴

—

219

C₂⁴

C₂²⋊Dic₁₉

yes

—

220

C₂×D₄

—

221

C₂×D₄

—

222

C₂×D₄

—

223

C₂×D₄

—

224

C₂×D₄

—

225

C₂×D₄

—

226

C₂×D₄

—

227

C₂×D₄

#64525

yes

—

228

C₂×D₄

#64526

yes

—

229

C₂²×C₄

—

230

C₂²×C₄

—

231

C₂²×C₄

—

232

C₂²×C₄

—

233

C₂²×C₄

—

234

C₂²×C₄

—

235

C₂²×C₄

—

236

C₂²×C₄

—

237

C₂²×C₄

—

238

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

239

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

240

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

241

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

242

M₁₆

—

243

M₁₆

—

244

C₂×C₈

—

245

C₂×C₈

—

246

C₂×C₈

—

152

—

247

C₄⋊C₄

—

248

C₄⋊C₄

—

249

C₄⋊C₄

—

250

C₄⋊C₄

—

251

C₂²⋊C₄

—

252

C₂²⋊C₄

—

253

C₂²⋊C₄

—

254

C₂²⋊C₄

—

255

C₂²⋊C₄

—

256

C₄²

D₄×D₁₉

yes

—

257

C₄²

#64543

yes

—

258

C₂³

—

259

C₂³

—

260

C₂³

—

261

C₂³

—

262

C₂³

—

263

C₂³

—

264

C₂³

—

265

C₂³

—

266

C₂³

—

267

C₂³

—

268

C₂³

—

269

C₂³

#10597289

yes

—

270

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

271

D₄

—

272

D₄

—

273

D₄

—

274

D₄

—

275

D₄

—

276

C₂×C₄

—

277

C₂×C₄

—

278

C₂×C₄

—

279

C₂×C₄

—

280

C₂×C₄

—

281

C₂×C₄

—

282

C₂×C₄

—

283

C₂×C₄

—

284

C₂×C₄

—

285

C₂×C₄

—

286

C₂×C₄

—

287

C₂×C₄

—

288

C₂×C₄

—

289

C₂×C₄

—

290

C₂×C₄

C₂×#64525

yes

characteristic

291

C₂×C₄

C₂×#64526

yes

characteristic

292

C₂×C₄

D₄×Dic₁₉

yes

—

293

C₂×C₄

#10597381

yes

characteristic

294

C₂×C₄

#10597383

yes

characteristic

295

C₂×C₄

#10597385

yes

—

296

C₂×C₄

#10597396

yes

—

297

C₈

—

298

C₈

—

152

—

299

C₂²

—

300

C₂²

—

301

C₂²

—

302

C₂²

—

303

C₂²

—

304

C₂²

—

305

C₂²

—

306

C₂²

—

307

C₂²

—

308

C₂²

—

309

C₂²

—

310

C₂²

—

311

C₂²

—

312

C₂²

—

313

C₂²

#11926424

yes

characteristic

314

C₂²

C₂×#10597289

yes

characteristic

315

C₂²

#11926540

yes

characteristic

316

C₄

—

317

C₄

—

318

C₄

—

319

C₄

—

320

C₄

—

321

C₄

—

322

C₄

#11926771

yes

—

323

C₄

#11926778

yes

—

324

C₂

—

325

C₂

—

326

C₂

—

327

C₂

—

328

C₂

#14564054

yes

characteristic

329

C₂

#14564064

yes

characteristic

330

C₂

#14564168

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#2535	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2535	D₁₉
hypocenter	C₁₉	#9485
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2535

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#2535

C₂

socle

C₂²×C₁₉

#386

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2535

N	H ≅ G/N	type
1. #14572659	C₂	semidirect
2. #14563627	C₂	semidirect
3. #14562060	C₂	semidirect
4. #14561493	C₂	semidirect
51. C₄×C₁₉⋊C₈	D₄	semidirect
217. C₁₉	#9485	semidirect

H ≅ G/N

type

1. #14572659

C₂

semidirect

2. #14563627

C₂

semidirect

3. #14562060

C₂

semidirect

4. #14561493

C₂

semidirect

51. C₄×C₁₉⋊C₈

D₄

semidirect

217. C₁₉

#9485

semidirect

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

subgroup	index
#14572659	2
#14563627	2
#14562060	2
#14561493	2
C₁₉×#2535	2
#9485	19

subgroup

index

C₁₉×#2535

Subgroups — #18080389

Conjugacy classes of subgroups

Complements

Maximal subgroups