Group #18078578 — subgroups

Subgroups — #18078578

Order 4864.

578 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14572273	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562303	C₂	1	2	yes	maximal, complemented
3	#14561949	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561493	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2619	C₂	1	1	yes	maximal, characteristic
6	#11926605	—	2	4	no	—
7	#11926597	C₂²	1	2	yes	—
8	#11926568	C₂²	1	2	yes	—
9	#11926508	—	2	1	no	—
10	C₄×#64520	—	2	1	no	—
11	#11926288	—	2	4	no	—
12	#11926270	—	2	1	no	—
13	#11926268	—	2	1	no	—
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#121	—	2	1	no	—
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₁₉×#394	—	2	1	no	—
18	C₁₉×#394	C₄	1	2	yes	—
19	C₁₉×#392	—	2	1	no	—
20	C₁₉×#392	C₄	1	2	yes	—
21	C₁₉×#390	—	2	1	no	—
22	C₁₉×#382	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₁₉	—	2	2	no	—
24	C₂²×D₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₁₉×#127	—	2	2	no	—
29	C₁₉×#127	—	2	2	no	—
30	C₁₉×#121	—	4	4	no	—
31	C₁₉×#117	—	2	2	no	—
32	C₁₉×#117	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	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	C₂×C₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×#64520	—	2	2	no	—
44	C₁₉×#95	—	2	1	no	—
45	C₁₉×#95	C₂×C₄	1	2	yes	—
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)	D₄	1	4	yes	complemented
51	#10597260	—	2	2	no	—
52	C₄×C₁₉⋊C₈	—	2	2	no	—
53	C₄×C₁₉⋊C₈	—	2	2	no	—
54	C₂⁴×C₁₉	—	2	2	no	—
55	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×D₄×C₁₉	—	2	4	no	—
57	C₂×D₄×C₁₉	—	4	4	no	—
58	C₂×D₄×C₁₉	—	4	1	no	—
59	C₂×D₄×C₁₉	—	4	2	no	—
60	C₂×D₄×C₁₉	—	4	1	no	—
61	C₂×D₄×C₁₉	—	4	2	no	—
62	C₂×D₄×C₁₉	—	4	2	no	—
63	C₂×D₄×C₁₉	—	8	2	no	—
64	C₂×D₄×C₁₉	—	8	2	no	—
65	C₂×D₄×C₁₉	—	8	2	no	—
66	C₂×D₄×C₁₉	—	8	2	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₄⋊C₄×C₁₉	—	4	2	no	—
81	C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂²⋊C₄×C₁₉	—	4	4	no	—
84	C₂²⋊C₄×C₁₉	—	8	2	no	—
85	C₂²⋊C₄×C₁₉	—	8	2	no	—
86	C₄²×C₁₉	—	2	1	no	—
87	C₄²×C₁₉	—	2	1	no	—
88	C₄²×C₁₉	C₂×D₄	1	2	yes	—
89	C₄²×C₁₉	#41	1	2	yes	—
90	#64520	—	4	2	no	—
91	#64520	—	4	2	no	—
92	C₂×C₁₉⋊C₈	—	2	4	no	—
93	C₂×C₁₉⋊C₈	—	4	2	no	—
94	#9198	—	19	1	no	maximal, Sylow
95	C₂³×C₁₉	—	2	1	no	—
96	C₂³×C₁₉	—	2	1	no	—
97	C₂³×C₁₉	—	2	1	no	—
98	C₂³×C₁₉	—	4	1	no	—
99	C₂³×C₁₉	—	4	1	no	—
100	C₂³×C₁₉	—	4	2	no	—
101	C₂³×C₁₉	—	4	2	no	—
102	C₂³×C₁₉	—	4	2	no	—
103	C₂³×C₁₉	—	4	2	no	—
104	C₂³×C₁₉	—	4	2	no	—
105	C₂³×C₁₉	—	4	2	no	—
106	C₂³×C₁₉	—	4	2	no	—
107	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	D₄×C₁₉	—	8	4	no	—
109	D₄×C₁₉	—	8	4	no	—
110	D₄×C₁₉	—	8	8	no	—
111	D₄×C₁₉	—	8	2	no	—
112	D₄×C₁₉	—	8	2	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	—	2	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	1	no	—
123	C₂×C₄×C₁₉	—	4	1	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	4	2	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
128	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
129	C₂×C₄×C₁₉	#121	1	2	yes	—
130	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#135	1	2	yes	—
132	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
133	C₁₉⋊C₈	—	4	4	no	—
134	C₁₉⋊C₈	—	8	2	no	—
135	#2921	—	19	1	no	—
136	#2619	D₁₉	1	1	yes	characteristic
137	#1545	—	19	2	no	—
138	#1458	—	19	1	no	—
139	#1286	—	19	2	no	—
140	C₂²×C₁₉	—	2	1	no	—
141	C₂²×C₁₉	—	2	1	no	—
142	C₂²×C₁₉	—	4	2	no	—
143	C₂²×C₁₉	—	4	1	no	—
144	C₂²×C₁₉	—	4	1	no	—
145	C₂²×C₁₉	—	4	1	no	—
146	C₂²×C₁₉	—	8	1	no	—
147	C₂²×C₁₉	—	8	2	no	—
148	C₂²×C₁₉	—	8	2	no	—
149	C₂²×C₁₉	—	8	2	no	—
150	C₂²×C₁₉	—	8	2	no	—
151	C₂²×C₁₉	—	8	2	no	—
152	C₂²×C₁₉	—	8	2	no	—
153	C₂²×C₁₉	—	8	2	no	—
154	C₂²×C₁₉	#386	1	1	yes	characteristic
155	C₂²×C₁₉	#416	1	1	yes	characteristic
156	C₂²×C₁₉	#418	1	1	yes	characteristic
157	C₄×C₁₉	—	2	2	no	—
158	C₄×C₁₉	—	2	2	no	—
159	C₄×C₁₉	—	4	1	no	—
160	C₄×C₁₉	—	4	1	no	—
161	C₄×C₁₉	—	4	1	no	—
162	C₄×C₁₉	—	8	2	no	—
163	C₄×C₁₉	#449	1	2	yes	—
164	C₄×C₁₉	#482	1	2	yes	—
165	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
166	C₂×#121	—	2	1	no	—
167	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
168	#433	—	38	4	no	—
169	#431	—	19	2	no	—
170	#423	—	19	2	no	—
171	#407	—	38	1	no	—
172	C₄×M₁₆	—	38	1	no	—
173	#394	—	2	1	no	—
174	#394	Dic₁₉	1	2	yes	—
175	#392	—	2	1	no	—
176	#392	Dic₁₉	1	2	yes	—
177	#390	—	2	1	no	—
178	#382	C₂×D₁₉	1	1	yes	characteristic
179	#331	—	38	4	no	—
180	#324	—	38	1	no	—
181	#323	—	38	1	no	—
182	C₂×C₁₉	—	2	1	no	—
183	C₂×C₁₉	—	2	1	no	—
184	C₂×C₁₉	—	8	1	no	—
185	C₂×C₁₉	—	16	2	no	—
186	C₂×C₁₉	#1875	1	1	yes	characteristic
187	C₂×C₁₉	#1910	1	1	yes	characteristic
188	C₂×C₁₉	#1914	1	1	yes	characteristic
189	C₂²×D₄	—	2	2	no	—
190	C₂²×D₄	—	2	1	no	—
191	C₂²×D₄	—	2	1	no	—
192	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
193	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
194	C₂×M₁₆	—	38	2	no	—
195	#127	—	2	2	no	—
196	#127	—	2	2	no	—
197	#121	—	4	4	no	—
198	#117	—	2	2	no	—
199	#117	—	2	2	no	—
200	C₂×C₄⋊C₄	—	2	1	no	—
201	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
202	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
203	C₂×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
208	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
209	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
210	C₄⋊C₈	—	19	4	no	—
211	C₄⋊C₈	—	38	2	no	—
212	C₄⋊C₈	—	38	2	no	—
213	C₂²⋊C₈	—	38	4	no	—
214	C₂²⋊C₈	—	38	2	no	—
215	#97	—	38	2	no	—
216	C₄×C₈	—	38	2	no	—
217	C₄×C₈	—	38	2	no	—
218	#95	—	2	1	no	—
219	#95	C₂×Dic₁₉	1	2	yes	—
220	C₁₉	#9198	1	1	yes	characteristic, complemented, Sylow
221	C₂⁴	—	2	2	no	—
222	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
223	C₂×D₄	—	2	4	no	—
224	C₂×D₄	—	4	4	no	—
225	C₂×D₄	—	4	2	no	—
226	C₂×D₄	—	4	1	no	—
227	C₂×D₄	—	4	1	no	—
228	C₂×D₄	—	4	2	no	—
229	C₂×D₄	—	4	2	no	—
230	C₂×D₄	—	8	2	no	—
231	C₂×D₄	—	8	2	no	—
232	C₂×D₄	—	8	2	no	—
233	C₂×D₄	—	8	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	1	no	—
236	C₂²×C₄	—	2	1	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
240	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
241	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
242	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
243	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
244	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
245	M₁₆	—	76	2	no	—
246	M₁₆	—	76	2	no	—
247	C₂×C₈	—	38	4	no	—
248	C₂×C₈	—	76	2	no	—
249	C₄⋊C₄	—	2	2	no	—
250	C₄⋊C₄	—	2	2	no	—
251	C₄⋊C₄	—	4	2	no	—
252	C₂²⋊C₄	—	2	2	no	—
253	C₂²⋊C₄	—	2	2	no	—
254	C₂²⋊C₄	—	4	4	no	—
255	C₂²⋊C₄	—	8	2	no	—
256	C₂²⋊C₄	—	8	2	no	—
257	C₄²	—	2	1	no	—
258	C₄²	—	2	1	no	—
259	C₄²	D₄×D₁₉	1	2	yes	—
260	C₄²	#64543	1	2	yes	—
261	C₂³	—	2	1	no	—
262	C₂³	—	2	1	no	—
263	C₂³	—	2	1	no	—
264	C₂³	—	4	1	no	—
265	C₂³	—	4	1	no	—
266	C₂³	—	4	2	no	—
267	C₂³	—	4	2	no	—
268	C₂³	—	4	2	no	—
269	C₂³	—	4	2	no	—
270	C₂³	—	4	2	no	—
271	C₂³	—	4	2	no	—
272	C₂³	—	4	2	no	—
273	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
274	D₄	—	8	4	no	—
275	D₄	—	8	4	no	—
276	D₄	—	8	8	no	—
277	D₄	—	8	2	no	—
278	D₄	—	8	2	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	4	1	no	—
285	C₂×C₄	—	4	1	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	1	no	—
289	C₂×C₄	—	4	1	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	4	2	no	—
293	C₂×C₄	#10597378	1	2	yes	—
294	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
295	C₂×C₄	#10597381	1	1	yes	characteristic
296	C₂×C₄	#10597383	1	1	yes	characteristic
297	C₂×C₄	#10597385	1	2	yes	—
298	C₂×C₄	#10597396	1	2	yes	—
299	C₈	—	76	4	no	—
300	C₈	—	152	2	no	—
301	C₂²	—	2	1	no	—
302	C₂²	—	2	1	no	—
303	C₂²	—	4	2	no	—
304	C₂²	—	4	1	no	—
305	C₂²	—	4	1	no	—
306	C₂²	—	4	1	no	—
307	C₂²	—	8	1	no	—
308	C₂²	—	8	2	no	—
309	C₂²	—	8	2	no	—
310	C₂²	—	8	2	no	—
311	C₂²	—	8	2	no	—
312	C₂²	—	8	2	no	—
313	C₂²	—	8	2	no	—
314	C₂²	—	8	2	no	—
315	C₂²	#11926424	1	1	yes	characteristic
316	C₂²	#11926540	1	1	yes	characteristic
317	C₂²	#11926549	1	1	yes	characteristic
318	C₄	—	2	2	no	—
319	C₄	—	2	2	no	—
320	C₄	—	4	1	no	—
321	C₄	—	4	1	no	—
322	C₄	—	4	1	no	—
323	C₄	—	8	2	no	—
324	C₄	#11926687	1	2	yes	—
325	C₄	#11926865	1	2	yes	—
326	C₂	—	2	1	no	—
327	C₂	—	2	1	no	—
328	C₂	—	8	1	no	—
329	C₂	—	16	2	no	—
330	C₂	#14563958	1	1	yes	characteristic
331	C₂	#14564163	1	1	yes	characteristic
332	C₂	#14564183	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572273

C₂

yes

maximal, characteristic, complemented

#14562303

C₂

yes

maximal, complemented

#14561949

C₂

yes

maximal, characteristic, complemented

#14561493

C₂

yes

maximal, complemented

C₁₉×#2619

C₂

yes

maximal, characteristic

#11926605

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

—

—

—

—

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×#121

—

C₂×C₁₉×#117

C₂²

yes

characteristic

C₁₉×#394

—

C₁₉×#394

C₄

yes

—

C₁₉×#392

—

C₁₉×#392

C₄

yes

—

C₁₉×#390

—

C₁₉×#382

C₂²

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#121

—

C₁₉×#117

—

C₁₉×#117

—

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

characteristic

C₂×C₂²⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×#95

—

C₁₉×#95

C₂×C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

complemented

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

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

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×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

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

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

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9198

—

maximal, Sylow

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

—

105

C₂³×C₁₉

—

106

C₂³×C₁₉

—

107

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

108

D₄×C₁₉

—

109

D₄×C₁₉

—

110

D₄×C₁₉

—

111

D₄×C₁₉

—

112

D₄×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

—

126

C₂×C₄×C₁₉

—

127

C₂×C₄×C₁₉

C₄×D₄

yes

—

128

C₂×C₄×C₁₉

#120

yes

characteristic

129

C₂×C₄×C₁₉

#121

yes

—

130

C₂×C₄×C₁₉

#123

yes

characteristic

131

C₂×C₄×C₁₉

#135

yes

—

132

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

133

C₁₉⋊C₈

—

134

C₁₉⋊C₈

—

135

#2921

—

136

#2619

D₁₉

yes

characteristic

137

#1545

—

138

#1458

—

139

#1286

—

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

—

154

C₂²×C₁₉

#386

yes

characteristic

155

C₂²×C₁₉

#416

yes

characteristic

156

C₂²×C₁₉

#418

yes

characteristic

157

C₄×C₁₉

—

158

C₄×C₁₉

—

159

C₄×C₁₉

—

160

C₄×C₁₉

—

161

C₄×C₁₉

—

162

C₄×C₁₉

—

163

C₄×C₁₉

#449

yes

—

164

C₄×C₁₉

#482

yes

—

165

C₂×#127

C₂×D₁₉

yes

characteristic

166

C₂×#121

—

167

C₂×#117

C₂×D₁₉

yes

characteristic

168

#433

—

169

#431

—

170

#423

—

171

#407

—

172

C₄×M₁₆

—

173

#394

—

174

#394

Dic₁₉

yes

—

175

#392

—

176

#392

Dic₁₉

yes

—

177

#390

—

178

#382

C₂×D₁₉

yes

characteristic

179

#331

—

180

#324

—

181

#323

—

182

C₂×C₁₉

—

183

C₂×C₁₉

—

184

C₂×C₁₉

—

185

C₂×C₁₉

—

186

C₂×C₁₉

#1875

yes

characteristic

187

C₂×C₁₉

#1910

yes

characteristic

188

C₂×C₁₉

#1914

yes

characteristic

189

C₂²×D₄

—

190

C₂²×D₄

—

191

C₂²×D₄

—

192

C₂²×D₄

C₂×Dic₁₉

yes

—

193

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

194

C₂×M₁₆

—

195

#127

—

196

#127

—

197

#121

—

198

#117

—

199

#117

—

200

C₂×C₄⋊C₄

—

201

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

202

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

203

C₂×C₂²⋊C₄

—

204

C₂×C₂²⋊C₄

—

205

C₂×C₂²⋊C₄

—

206

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

characteristic

207

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

characteristic

208

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

209

C₂×C₄²

C₂²×D₁₉

yes

characteristic

210

C₄⋊C₈

—

211

C₄⋊C₈

—

212

C₄⋊C₈

—

213

C₂²⋊C₈

—

214

C₂²⋊C₈

—

215

#97

—

216

C₄×C₈

—

217

C₄×C₈

—

218

#95

—

219

#95

C₂×Dic₁₉

yes

—

220

C₁₉

#9198

yes

characteristic, complemented, Sylow

221

C₂⁴

—

222

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

223

C₂×D₄

—

224

C₂×D₄

—

225

C₂×D₄

—

226

C₂×D₄

—

227

C₂×D₄

—

228

C₂×D₄

—

229

C₂×D₄

—

230

C₂×D₄

—

231

C₂×D₄

—

232

C₂×D₄

—

233

C₂×D₄

—

234

C₂²×C₄

—

235

C₂²×C₄

—

236

C₂²×C₄

—

237

C₂²×C₄

—

238

C₂²×C₄

—

239

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

240

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

241

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

242

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

243

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

244

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

245

M₁₆

—

246

M₁₆

—

247

C₂×C₈

—

248

C₂×C₈

—

249

C₄⋊C₄

—

250

C₄⋊C₄

—

251

C₄⋊C₄

—

252

C₂²⋊C₄

—

253

C₂²⋊C₄

—

254

C₂²⋊C₄

—

255

C₂²⋊C₄

—

256

C₂²⋊C₄

—

257

C₄²

—

258

C₄²

—

259

C₄²

D₄×D₁₉

yes

—

260

C₄²

#64543

yes

—

261

C₂³

—

262

C₂³

—

263

C₂³

—

264

C₂³

—

265

C₂³

—

266

C₂³

—

267

C₂³

—

268

C₂³

—

269

C₂³

—

270

C₂³

—

271

C₂³

—

272

C₂³

—

273

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

274

D₄

—

275

D₄

—

276

D₄

—

277

D₄

—

278

D₄

—

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

—

291

C₂×C₄

—

292

C₂×C₄

—

293

C₂×C₄

#10597378

yes

—

294

C₂×C₄

D₄×Dic₁₉

yes

—

295

C₂×C₄

#10597381

yes

characteristic

296

C₂×C₄

#10597383

yes

characteristic

297

C₂×C₄

#10597385

yes

—

298

C₂×C₄

#10597396

yes

—

299

C₈

—

300

C₈

—

152

—

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

—

314

C₂²

—

315

C₂²

#11926424

yes

characteristic

316

C₂²

#11926540

yes

characteristic

317

C₂²

#11926549

yes

characteristic

318

C₄

—

319

C₄

—

320

C₄

—

321

C₄

—

322

C₄

—

323

C₄

—

324

C₄

#11926687

yes

—

325

C₄

#11926865

yes

—

326

C₂

—

327

C₂

—

328

C₂

—

329

C₂

—

330

C₂

#14563958

yes

characteristic

331

C₂

#14564163

yes

characteristic

332

C₂

#14564183

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#2619	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2619	D₁₉
hypocenter	C₁₉	#9198
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2619

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#2619

C₂

socle

C₂²×C₁₉

#386

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2619

N	H ≅ G/N	type
1. #14572273	C₂	semidirect
2. #14562303	C₂	semidirect
3. #14561949	C₂	semidirect
4. #14561493	C₂	semidirect
50. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
220. C₁₉	#9198	semidirect

H ≅ G/N

type

1. #14572273

C₂

semidirect

2. #14562303

C₂

semidirect

3. #14561949

C₂

semidirect

4. #14561493

C₂

semidirect

50. C₄⋊(C₁₉⋊C₈)

D₄

semidirect

220. C₁₉

#9198

semidirect

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

subgroup	index
#14572273	2
#14562303	2
#14561949	2
#14561493	2
C₁₉×#2619	2
#9198	19

subgroup

index

C₁₉×#2619

Subgroups — #18078578

Conjugacy classes of subgroups

Complements

Maximal subgroups