Group #18074097 — subgroups

Subgroups — #18074097

Order 4864.

774 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 167 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	#14564430	C₂	1	1	yes	maximal, characteristic
2	#14563627	C₂	1	1	yes	maximal, characteristic
3	#14562325	C₂	1	2	yes	maximal, complemented
4	#14562090	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×#10597290	—	2	1	no	—
9	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	#11926313	—	2	1	no	—
12	#11926293	—	2	2	no	—
13	#11926290	—	2	2	no	—
14	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
15	C₁₉×#554	—	2	2	no	—
16	C₁₉×#554	—	2	4	no	—
17	D₄×Q₈×C₁₉	—	2	2	no	—
18	C₁₉×#544	—	2	1	no	—
19	C₁₉×#543	C₄	1	4	yes	—
20	C₁₉×#533	C₂²	1	2	yes	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
22	C₁₉×#518	—	2	1	no	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×Q₈×C₁₉	—	2	2	no	—
25	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	D₄	1	2	yes	—
27	C₁₉×C₄⋊Q₈	—	2	4	no	—
28	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
29	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
30	C₁₉×#125	—	2	4	no	—
31	C₁₉×#125	—	2	2	no	—
32	C₁₉×C₂²⋊Q₈	—	2	4	no	—
33	C₁₉×C₂²⋊Q₈	—	2	4	no	—
34	C₁₉×C₂²⋊Q₈	—	2	8	no	—
35	C₁₉×C₂²⋊Q₈	—	2	4	no	—
36	C₁₉×C₂²⋊Q₈	—	2	2	no	—
37	C₁₉×C₂²⋊Q₈	—	2	8	no	—
38	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
39	C₄×Q₈×C₁₉	—	2	2	no	—
40	C₄×Q₈×C₁₉	D₄	1	4	yes	—
41	C₄×D₄×C₁₉	—	2	4	no	—
42	C₄×D₄×C₁₉	—	2	4	no	—
43	C₄×D₄×C₁₉	—	2	2	no	—
44	C₄×D₄×C₁₉	—	2	2	no	—
45	C₁₉×#117	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×#64520	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	2	1	no	—
55	#10597290	—	4	2	no	—
56	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
60	C₄×C₁₉⋊C₈	—	2	2	no	—
61	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
62	C₂×Q₈×C₁₉	—	2	4	no	—
63	C₂×Q₈×C₁₉	—	2	2	no	—
64	C₂×Q₈×C₁₉	—	8	2	no	—
65	C₂×Q₈×C₁₉	—	8	2	no	—
66	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
67	C₂×D₄×C₁₉	—	2	2	no	—
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
70	C₂×D₄×C₁₉	Q₁₆	1	2	yes	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	2	4	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	4	2	no	—
76	C₂²×C₄×C₁₉	—	4	2	no	—
77	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₄⋊C₄×C₁₉	—	2	4	no	—
82	C₄⋊C₄×C₁₉	—	2	8	no	—
83	C₄⋊C₄×C₁₉	—	2	4	no	—
84	C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₄⋊C₄×C₁₉	—	2	4	no	—
86	C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
90	C₂²⋊C₄×C₁₉	—	2	8	no	—
91	C₂²⋊C₄×C₁₉	—	2	4	no	—
92	C₂²⋊C₄×C₁₉	—	2	4	no	—
93	C₄²×C₁₉	—	2	4	no	—
94	C₄²×C₁₉	C₂×D₄	1	2	yes	—
95	C₄²×C₁₉	C₂×D₄	1	2	yes	—
96	#64520	—	4	2	no	—
97	#64520	—	4	2	no	—
98	C₂×C₁₉⋊C₈	—	2	2	no	—
99	C₂×C₁₉⋊C₈	—	4	1	no	—
100	C₂×C₁₉⋊C₈	—	4	1	no	—
101	C₂×C₁₉⋊C₈	—	4	2	no	—
102	C₂×C₁₉⋊C₈	—	4	1	no	—
103	C₂×C₁₉⋊C₈	—	4	2	no	—
104	#8355	—	19	1	no	maximal, Sylow
105	C₂³×C₁₉	—	2	2	no	—
106	C₂³×C₁₉	—	2	2	no	—
107	C₂³×C₁₉	—	4	2	no	—
108	C₂³×C₁₉	—	4	2	no	—
109	C₂³×C₁₉	#103	1	4	yes	—
110	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	Q₈×C₁₉	—	4	4	no	—
112	Q₈×C₁₉	—	4	2	no	—
113	Q₈×C₁₉	—	4	2	no	—
114	Q₈×C₁₉	—	8	4	no	—
115	D₄×C₁₉	—	2	4	no	—
116	D₄×C₁₉	—	2	4	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	4	no	—
120	C₂×C₄×C₁₉	—	2	4	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	4	1	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	4	2	no	—
126	C₂×C₄×C₁₉	—	8	2	no	—
127	C₂×C₄×C₁₉	—	8	4	no	—
128	C₂×C₄×C₁₉	—	8	4	no	—
129	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#120	1	2	yes	—
132	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
133	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#137	1	2	yes	—
136	C₁₉⋊C₈	—	4	2	no	—
137	C₁₉⋊C₈	—	8	2	no	—
138	C₁₉⋊C₈	—	8	1	no	—
139	#3501	D₁₉	1	1	yes	characteristic
140	#1954	—	19	1	no	—
141	#1800	—	19	1	no	—
142	#1550	—	19	2	no	—
143	#1493	—	19	2	no	—
144	C₂²×C₁₉	—	2	1	no	—
145	C₂²×C₁₉	—	2	1	no	—
146	C₂²×C₁₉	—	2	4	no	—
147	C₂²×C₁₉	—	4	4	no	—
148	C₂²×C₁₉	—	4	2	no	—
149	C₂²×C₁₉	—	4	2	no	—
150	C₂²×C₁₉	—	8	2	no	—
151	C₂²×C₁₉	#379	1	1	yes	characteristic
152	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
153	C₂²×C₁₉	#419	1	1	yes	characteristic
154	C₄×C₁₉	—	2	1	no	—
155	C₄×C₁₉	—	2	2	no	—
156	C₄×C₁₉	—	4	2	no	—
157	C₄×C₁₉	—	4	4	no	—
158	C₄×C₁₉	—	4	4	no	—
159	C₄×C₁₉	#448	1	2	yes	—
160	C₄×C₁₉	#451	1	2	yes	—
161	C₄×C₁₉	#453	1	1	yes	characteristic
162	C₄×C₁₉	#455	1	1	yes	characteristic
163	#554	—	2	2	no	—
164	#554	—	2	4	no	—
165	D₄×Q₈	—	2	2	no	—
166	#544	—	2	1	no	—
167	#543	Dic₁₉	1	4	yes	—
168	#533	C₂×D₁₉	1	2	yes	—
169	C₂×C₂²⋊Q₈	—	2	2	no	—
170	#518	—	2	1	no	—
171	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
172	#423	—	19	2	no	—
173	C₂×C₄⋊C₈	—	19	1	no	—
174	C₂×#100	—	38	1	no	—
175	C₂×C₂²⋊C₈	—	38	2	no	—
176	C₂×C₄×C₈	—	19	1	no	—
177	#343	—	38	1	no	—
178	#333	—	38	2	no	—
179	#332	—	38	2	no	—
180	Q₈⋊C₈	—	38	4	no	—
181	C₂×C₁₉	—	2	1	no	—
182	C₂×C₁₉	—	2	1	no	—
183	C₂×C₁₉	—	4	4	no	—
184	C₂×C₁₉	#1787	1	1	yes	characteristic
185	C₂×C₁₉	#1791	1	1	yes	characteristic
186	C₂×C₁₉	#1792	1	1	yes	characteristic
187	C₂²×Q₈	—	2	2	no	—
188	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
189	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
190	C₂×M₁₆	—	38	2	no	—
191	C₂²×C₈	—	38	1	no	—
192	C₂²×C₈	—	38	1	no	—
193	C₄⋊Q₈	—	2	4	no	—
194	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
195	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
196	#125	—	2	4	no	—
197	#125	—	2	2	no	—
198	C₂²⋊Q₈	—	2	4	no	—
199	C₂²⋊Q₈	—	2	4	no	—
200	C₂²⋊Q₈	—	2	8	no	—
201	C₂²⋊Q₈	—	2	4	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	8	no	—
204	C₂²⋊Q₈	C₂×Dic₁₉	1	4	yes	—
205	C₄×Q₈	—	2	2	no	—
206	C₄×Q₈	C₂²⋊D₁₉	1	4	yes	—
207	C₄×D₄	—	2	4	no	—
208	C₄×D₄	—	2	4	no	—
209	C₄×D₄	—	2	2	no	—
210	C₄×D₄	—	2	2	no	—
211	#117	—	2	2	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	—	2	4	no	—
214	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	—	2	4	no	—
216	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
217	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
218	C₄⋊C₈	—	38	2	no	—
219	C₄⋊C₈	—	38	2	no	—
220	C₄⋊C₈	—	38	2	no	—
221	#100	—	76	2	no	—
222	C₂²⋊C₈	—	76	4	no	—
223	C₄×C₈	—	38	2	no	—
224	C₁₉	#8355	1	1	yes	characteristic, complemented, Sylow
225	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
226	C₂×Q₈	—	2	4	no	—
227	C₂×Q₈	—	2	2	no	—
228	C₂×Q₈	—	8	2	no	—
229	C₂×Q₈	—	8	2	no	—
230	C₂×Q₈	C₂²⋊Dic₁₉	1	4	yes	—
231	C₂×D₄	—	2	2	no	—
232	C₂×D₄	—	2	2	no	—
233	C₂×D₄	#64527	1	2	yes	—
234	C₂×D₄	#64528	1	2	yes	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	2	no	—
241	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
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	2	no	—
248	C₂×C₈	—	76	1	no	—
249	C₂×C₈	—	76	1	no	—
250	C₂×C₈	—	76	2	no	—
251	C₂×C₈	—	76	1	no	—
252	C₂×C₈	—	76	2	no	—
253	C₄⋊C₄	—	2	4	no	—
254	C₄⋊C₄	—	2	8	no	—
255	C₄⋊C₄	—	2	4	no	—
256	C₄⋊C₄	—	2	2	no	—
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	2	2	no	—
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	—	2	2	no	—
261	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
262	C₂²⋊C₄	—	2	8	no	—
263	C₂²⋊C₄	—	2	4	no	—
264	C₂²⋊C₄	—	2	4	no	—
265	C₄²	—	2	4	no	—
266	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
267	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
268	C₂³	—	2	2	no	—
269	C₂³	—	2	2	no	—
270	C₂³	—	4	2	no	—
271	C₂³	—	4	2	no	—
272	C₂³	#10597292	1	4	yes	—
273	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
274	Q₈	—	4	4	no	—
275	Q₈	—	4	2	no	—
276	Q₈	—	4	2	no	—
277	Q₈	—	8	4	no	—
278	D₄	—	2	4	no	—
279	D₄	—	2	4	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	4	1	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	—	8	2	no	—
290	C₂×C₄	—	8	4	no	—
291	C₂×C₄	—	8	4	no	—
292	C₂×C₄	C₂×#64527	1	1	yes	characteristic
293	C₂×C₄	#10597388	1	2	yes	—
294	C₂×C₄	C₂×#64528	1	1	yes	characteristic
295	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
296	C₂×C₄	#10597399	1	1	yes	characteristic
297	C₂×C₄	#10597399	1	2	yes	—
298	C₂×C₄	#10597399	1	1	yes	characteristic
299	C₈	—	76	2	no	—
300	C₈	—	152	2	no	—
301	C₈	—	152	1	no	—
302	C₂²	—	2	1	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	2	4	no	—
305	C₂²	—	4	4	no	—
306	C₂²	—	4	2	no	—
307	C₂²	—	4	2	no	—
308	C₂²	—	8	2	no	—
309	C₂²	#11926400	1	1	yes	characteristic
310	C₂²	C₂×#10597292	1	1	yes	characteristic
311	C₂²	#11926553	1	1	yes	characteristic
312	C₄	—	2	2	no	—
313	C₄	—	2	1	no	—
314	C₄	—	4	4	no	—
315	C₄	—	4	2	no	—
316	C₄	—	4	4	no	—
317	C₄	#11926683	1	2	yes	—
318	C₄	#11926700	1	2	yes	—
319	C₄	#11926712	1	1	yes	characteristic
320	C₄	#11926722	1	1	yes	characteristic
321	C₂	—	2	1	no	—
322	C₂	—	2	1	no	—
323	C₂	—	4	4	no	—
324	C₂	#14563570	1	1	yes	characteristic
325	C₂	#14563586	1	1	yes	characteristic
326	C₂	#14563589	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564430

C₂

yes

maximal, characteristic

#14563627

C₂

yes

maximal, characteristic

#14562325

C₂

yes

maximal, complemented

#14562090

C₂

yes

maximal, complemented

C₁₉×#3501

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597290

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

Q₈⋊(C₁₉⋊C₈)

—

C₁₉×#554

—

C₁₉×#554

—

D₄×Q₈×C₁₉

—

C₁₉×#544

—

C₁₉×#543

C₄

yes

—

C₁₉×#533

C₂²

yes

—

C₂×C₁₉×C₂²⋊Q₈

—

C₁₉×#518

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

C₂×C₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂×Q₈×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

SD₁₆

yes

—

C₂×D₄×C₁₉

Q₁₆

yes

—

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

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

100

C₂×C₁₉⋊C₈

—

101

C₂×C₁₉⋊C₈

—

102

C₂×C₁₉⋊C₈

—

103

C₂×C₁₉⋊C₈

—

104

#8355

—

maximal, Sylow

105

C₂³×C₁₉

—

106

C₂³×C₁₉

—

107

C₂³×C₁₉

—

108

C₂³×C₁₉

—

109

C₂³×C₁₉

#103

yes

—

110

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

111

Q₈×C₁₉

—

112

Q₈×C₁₉

—

113

Q₈×C₁₉

—

114

Q₈×C₁₉

—

115

D₄×C₁₉

—

116

D₄×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

—

128

C₂×C₄×C₁₉

—

129

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

130

C₂×C₄×C₁₉

#120

yes

characteristic

131

C₂×C₄×C₁₉

#120

yes

—

132

C₂×C₄×C₁₉

#120

yes

characteristic

133

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

134

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

135

C₂×C₄×C₁₉

#137

yes

—

136

C₁₉⋊C₈

—

137

C₁₉⋊C₈

—

138

C₁₉⋊C₈

—

139

#3501

D₁₉

yes

characteristic

140

#1954

—

141

#1800

—

142

#1550

—

143

#1493

—

144

C₂²×C₁₉

—

145

C₂²×C₁₉

—

146

C₂²×C₁₉

—

147

C₂²×C₁₉

—

148

C₂²×C₁₉

—

149

C₂²×C₁₉

—

150

C₂²×C₁₉

—

151

C₂²×C₁₉

#379

yes

characteristic

152

C₂²×C₁₉

C₂×#103

yes

characteristic

153

C₂²×C₁₉

#419

yes

characteristic

154

C₄×C₁₉

—

155

C₄×C₁₉

—

156

C₄×C₁₉

—

157

C₄×C₁₉

—

158

C₄×C₁₉

—

159

C₄×C₁₉

#448

yes

—

160

C₄×C₁₉

#451

yes

—

161

C₄×C₁₉

#453

yes

characteristic

162

C₄×C₁₉

#455

yes

characteristic

163

#554

—

164

#554

—

165

D₄×Q₈

—

166

#544

—

167

#543

Dic₁₉

yes

—

168

#533

C₂×D₁₉

yes

—

169

C₂×C₂²⋊Q₈

—

170

#518

—

171

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

172

#423

—

173

C₂×C₄⋊C₈

—

174

C₂×#100

—

175

C₂×C₂²⋊C₈

—

176

C₂×C₄×C₈

—

177

#343

—

178

#333

—

179

#332

—

180

Q₈⋊C₈

—

181

C₂×C₁₉

—

182

C₂×C₁₉

—

183

C₂×C₁₉

—

184

C₂×C₁₉

#1787

yes

characteristic

185

C₂×C₁₉

#1791

yes

characteristic

186

C₂×C₁₉

#1792

yes

characteristic

187

C₂²×Q₈

—

188

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

189

C₂³×C₄

C₂²⋊D₁₉

yes

—

190

C₂×M₁₆

—

191

C₂²×C₈

—

192

C₂²×C₈

—

193

C₄⋊Q₈

—

194

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

195

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

196

#125

—

197

#125

—

198

C₂²⋊Q₈

—

199

C₂²⋊Q₈

—

200

C₂²⋊Q₈

—

201

C₂²⋊Q₈

—

202

C₂²⋊Q₈

—

203

C₂²⋊Q₈

—

204

C₂²⋊Q₈

C₂×Dic₁₉

yes

—

205

C₄×Q₈

—

206

C₄×Q₈

C₂²⋊D₁₉

yes

—

207

C₄×D₄

—

208

C₄×D₄

—

209

C₄×D₄

—

210

C₄×D₄

—

211

#117

—

212

C₂×C₄⋊C₄

—

213

C₂×C₄⋊C₄

—

214

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

215

C₂×C₂²⋊C₄

—

216

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

—

217

C₂×C₄²

C₂²×D₁₉

yes

characteristic

218

C₄⋊C₈

—

219

C₄⋊C₈

—

220

C₄⋊C₈

—

221

#100

—

222

C₂²⋊C₈

—

223

C₄×C₈

—

224

C₁₉

#8355

yes

characteristic, complemented, Sylow

225

C₂⁴

C₂²⋊Dic₁₉

yes

—

226

C₂×Q₈

—

227

C₂×Q₈

—

228

C₂×Q₈

—

229

C₂×Q₈

—

230

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

231

C₂×D₄

—

232

C₂×D₄

—

233

C₂×D₄

#64527

yes

—

234

C₂×D₄

#64528

yes

—

235

C₂²×C₄

—

236

C₂²×C₄

—

237

C₂²×C₄

—

238

C₂²×C₄

—

239

C₂²×C₄

—

240

C₂²×C₄

—

241

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

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

C₂×C₈

—

250

C₂×C₈

—

251

C₂×C₈

—

252

C₂×C₈

—

253

C₄⋊C₄

—

254

C₄⋊C₄

—

255

C₄⋊C₄

—

256

C₄⋊C₄

—

257

C₄⋊C₄

—

258

C₄⋊C₄

—

259

C₄⋊C₄

—

260

C₄⋊C₄

—

261

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

262

C₂²⋊C₄

—

263

C₂²⋊C₄

—

264

C₂²⋊C₄

—

265

C₄²

—

266

C₄²

C₂×C₂²⋊D₁₉

yes

—

267

C₄²

C₂×C₂²⋊D₁₉

yes

—

268

C₂³

—

269

C₂³

—

270

C₂³

—

271

C₂³

—

272

C₂³

#10597292

yes

—

273

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

274

Q₈

—

275

Q₈

—

276

Q₈

—

277

Q₈

—

278

D₄

—

279

D₄

—

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

C₂×#64527

yes

characteristic

293

C₂×C₄

#10597388

yes

—

294

C₂×C₄

C₂×#64528

yes

characteristic

295

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

—

296

C₂×C₄

#10597399

yes

characteristic

297

C₂×C₄

#10597399

yes

—

298

C₂×C₄

#10597399

yes

characteristic

299

C₈

—

300

C₈

—

152

—

301

C₈

—

152

—

302

C₂²

—

303

C₂²

—

304

C₂²

—

305

C₂²

—

306

C₂²

—

307

C₂²

—

308

C₂²

—

309

C₂²

#11926400

yes

characteristic

310

C₂²

C₂×#10597292

yes

characteristic

311

C₂²

#11926553

yes

characteristic

312

C₄

—

313

C₄

—

314

C₄

—

315

C₄

—

316

C₄

—

317

C₄

#11926683

yes

—

318

C₄

#11926700

yes

—

319

C₄

#11926712

yes

characteristic

320

C₄

#11926722

yes

characteristic

321

C₂

—

322

C₂

—

323

C₂

—

324

C₂

#14563570

yes

characteristic

325

C₂

#14563586

yes

characteristic

326

C₂

#14563589

yes

characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3501	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3501	D₁₉
hypocenter	C₁₉	#8355
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3501

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3501

C₂

socle

C₂²×C₁₉

#379

prime radical

C₂²×D₄×C₁₉

D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3501

N	H ≅ G/N	type
3. #14562325	C₂	semidirect
4. #14562090	C₂	semidirect
224. C₁₉	#8355	semidirect

H ≅ G/N

type

3. #14562325

C₂

semidirect

4. #14562090

C₂

semidirect

224. C₁₉

#8355

semidirect

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

subgroup	index
#14564430	2
#14563627	2
#14562325	2
#14562090	2
C₁₉×#3501	2
#8355	19

subgroup

index

C₁₉×#3501

Subgroups — #18074097

Conjugacy classes of subgroups

Complements

Maximal subgroups