Group #18079918 — subgroups

Subgroups — #18079918

Order 4864.

470 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 117 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	#14572715	C₂	1	1	yes	maximal, characteristic
2	#14568850	C₂	1	1	yes	maximal, characteristic
3	#14563628	C₂	1	1	yes	maximal, characteristic
4	#14562321	C₂	1	1	yes	maximal, characteristic
5	#14562319	C₂	1	1	yes	maximal, characteristic
6	#14561538	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₈×Dic₃₈	—	2	2	no	—
11	#11926668	—	2	2	no	—
12	#11926597	C₂²	1	1	yes	characteristic
13	#11926594	—	2	2	no	—
14	#11926568	C₂²	1	1	yes	characteristic
15	C₂×#10597281	—	2	1	no	—
16	#11926484	C₄	1	4	yes	—
17	#11926450	—	2	1	no	—
18	#11926449	—	2	2	no	—
19	#11926410	—	2	1	no	—
20	#11926312	—	2	1	no	—
21	#11926291	—	2	2	no	—
22	#11926289	—	2	2	no	—
23	C₁₉×#431	C₂²	1	1	yes	characteristic
24	C₁₉×#423	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×Dic₃₈	—	2	1	no	—
27	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄²×C₁₉	—	2	1	no	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
35	C₂×Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
36	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
37	C₂×#64520	—	2	1	no	—
38	#10597315	—	2	1	no	—
39	#10597315	—	2	1	no	—
40	#10597315	—	2	1	no	—
41	#10597315	—	2	1	no	—
42	C₄×Dic₃₈	—	2	1	no	—
43	C₄×Dic₃₈	—	2	1	no	—
44	C₄×Dic₃₈	—	2	1	no	—
45	C₄×Dic₃₈	—	2	1	no	—
46	C₁₉×C₄⋊C₈	—	2	1	no	—
47	C₁₉×C₄⋊C₈	—	2	1	no	—
48	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
49	C₁₉×C₂²⋊C₈	—	2	1	no	—
50	C₄×C₈×C₁₉	—	2	1	no	—
51	C₁₉×#95	C₂×C₄	1	2	yes	—
52	C₁₉⋊#95	—	2	4	no	—
53	C₁₉⋊#95	—	2	4	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
55	#10597281	—	4	2	no	—
56	Dic₁₉⋊C₈	—	2	4	no	—
57	C₈×Dic₁₉	—	2	4	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
61	C₄×C₁₉⋊C₈	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×Dic₁₉	—	2	2	no	—
67	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
68	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
69	C₂×Dic₃₈	—	2	1	no	—
70	C₂×Dic₃₈	—	2	1	no	—
71	C₂×Dic₃₈	—	2	1	no	—
72	C₂×Dic₃₈	—	2	1	no	—
73	C₂×Dic₃₈	—	4	4	no	—
74	C₂×Dic₃₈	—	4	1	no	—
75	C₂×Dic₃₈	—	4	1	no	—
76	C₂×Dic₃₈	SD₁₆	1	2	yes	—
77	C₂×Dic₃₈	Q₁₆	1	2	yes	—
78	M₁₆×C₁₉	—	4	1	no	—
79	M₁₆×C₁₉	—	4	1	no	—
80	C₂×C₈×C₁₉	—	2	2	no	—
81	C₂×C₈×C₁₉	—	4	1	no	—
82	C₄⋊C₄×C₁₉	—	4	2	no	—
83	C₄²×C₁₉	—	4	1	no	—
84	C₄²×C₁₉	—	4	1	no	—
85	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₄²×C₁₉	#41	1	1	yes	characteristic
88	C₄²×C₁₉	#41	1	1	yes	characteristic
89	C₄⋊Dic₁₉	—	2	1	no	—
90	C₄⋊Dic₁₉	—	2	1	no	—
91	C₄⋊Dic₁₉	—	2	2	no	—
92	C₄⋊Dic₁₉	—	2	2	no	—
93	C₄⋊Dic₁₉	—	4	1	no	—
94	C₄⋊Dic₁₉	—	4	1	no	—
95	Dic₁₉⋊C₄	—	2	2	no	—
96	Dic₁₉⋊C₄	—	2	2	no	—
97	C₄×Dic₁₉	—	2	2	no	—
98	C₄×Dic₁₉	—	2	2	no	—
99	#64520	—	4	1	no	—
100	#64520	—	4	1	no	—
101	C₂×C₁₉⋊C₈	—	2	2	no	—
102	C₂×C₁₉⋊C₈	—	4	1	no	—
103	#9396	—	19	1	no	maximal, Sylow
104	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₉	—	2	2	no	—
106	C₂×C₄×C₁₉	—	4	1	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
115	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
118	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
120	C₂×Dic₁₉	—	2	2	no	—
121	C₂×Dic₁₉	—	2	2	no	—
122	C₂×Dic₁₉	—	2	2	no	—
123	C₂×Dic₁₉	—	4	2	no	—
124	C₂×Dic₁₉	—	4	4	no	—
125	C₂×Dic₁₉	—	4	2	no	—
126	C₂×Dic₁₉	#103	1	4	yes	—
127	Dic₃₈	—	2	2	no	—
128	Dic₃₈	—	2	2	no	—
129	Dic₃₈	—	2	2	no	—
130	Dic₃₈	—	2	2	no	—
131	Dic₃₈	—	8	2	no	—
132	Dic₃₈	—	8	2	no	—
133	C₈×C₁₉	—	4	2	no	—
134	C₈×C₁₉	—	8	1	no	—
135	C₁₉⋊C₈	—	4	2	no	—
136	C₁₉⋊C₈	—	8	1	no	—
137	#2982	—	19	1	no	—
138	#2568	—	19	1	no	—
139	#1801	—	19	1	no	—
140	#1549	—	19	1	no	—
141	#1549	—	19	1	no	—
142	#1303	—	19	1	no	—
143	#1303	D₁₉	1	1	yes	characteristic
144	C₂²×C₁₉	—	2	1	no	—
145	C₂²×C₁₉	—	2	1	no	—
146	C₂²×C₁₉	#386	1	1	yes	characteristic
147	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
148	C₂²×C₁₉	#416	1	1	yes	characteristic
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	—	2	1	no	—
151	C₄×C₁₉	—	2	1	no	—
152	C₄×C₁₉	—	8	2	no	—
153	C₄×C₁₉	#454	1	2	yes	—
154	C₄×C₁₉	#465	1	1	yes	characteristic
155	C₄×C₁₉	#465	1	1	yes	characteristic
156	C₄×C₁₉	#467	1	1	yes	characteristic
157	C₄×C₁₉	#467	1	1	yes	characteristic
158	Dic₁₉	—	2	4	no	—
159	Dic₁₉	—	4	2	no	—
160	Dic₁₉	—	8	2	no	—
161	C₂×C₄⋊Q₈	—	19	1	no	—
162	C₂×C₄×Q₈	—	19	1	no	—
163	C₈×Q₈	—	38	2	no	—
164	C₈×Q₈	—	38	2	no	—
165	#431	—	19	1	no	—
166	#431	—	38	2	no	—
167	#431	C₂×D₁₉	1	1	yes	characteristic
168	#423	—	19	1	no	—
169	#423	C₂×D₁₉	1	1	yes	characteristic
170	C₂×#101	—	38	1	no	—
171	#400	—	19	4	no	—
172	#391	—	38	1	no	—
173	#391	—	38	2	no	—
174	#382	—	38	1	no	—
175	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
176	#343	—	38	1	no	—
177	#332	—	38	2	no	—
178	#332	—	38	2	no	—
179	C₂×C₁₉	—	2	1	no	—
180	C₂×C₁₉	—	2	1	no	—
181	C₂×C₁₉	#1888	1	1	yes	characteristic
182	C₂×C₁₉	#1892	1	1	yes	characteristic
183	C₂×C₁₉	#1915	1	1	yes	characteristic
184	C₂²×Q₈	—	19	1	no	—
185	C₂²×Q₈	—	38	1	no	—
186	C₂×M₁₆	—	2	1	no	—
187	C₂×M₁₆	—	38	1	no	—
188	C₄⋊Q₈	—	38	1	no	—
189	C₄⋊Q₈	—	38	1	no	—
190	C₄⋊Q₈	—	38	1	no	—
191	C₄⋊Q₈	—	38	1	no	—
192	C₄×Q₈	—	38	1	no	—
193	C₄×Q₈	—	38	1	no	—
194	C₄×Q₈	—	38	1	no	—
195	C₄×Q₈	—	38	1	no	—
196	C₂×C₄⋊C₄	—	2	1	no	—
197	C₂×C₄⋊C₄	—	19	2	no	—
198	C₂×C₄⋊C₄	—	19	1	no	—
199	C₂×C₄⋊C₄	—	19	2	no	—
200	C₂×C₄⋊C₄	—	38	1	no	—
201	C₂×C₄²	—	2	1	no	—
202	C₂×C₄²	—	19	2	no	—
203	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
204	C₄⋊C₈	—	2	1	no	—
205	C₄⋊C₈	—	2	1	no	—
206	C₄⋊C₈	—	19	2	no	—
207	C₄⋊C₈	—	38	4	no	—
208	C₄⋊C₈	—	38	1	no	—
209	C₄⋊C₈	—	38	1	no	—
210	C₄⋊C₈	D₇₆	1	2	yes	—
211	#101	—	76	2	no	—
212	C₂²⋊C₈	—	2	1	no	—
213	C₂²⋊C₈	—	38	1	no	—
214	C₄×C₈	—	2	1	no	—
215	C₄×C₈	—	38	4	no	—
216	C₄×C₈	—	38	1	no	—
217	#95	—	38	4	no	—
218	#95	—	38	4	no	—
219	#95	C₄×D₁₉	1	2	yes	—
220	C₁₉	#9396	1	1	yes	characteristic, complemented, Sylow
221	C₂×Q₈	—	19	2	no	—
222	C₂×Q₈	—	19	2	no	—
223	C₂×Q₈	—	38	1	no	—
224	C₂×Q₈	—	38	1	no	—
225	C₂×Q₈	—	38	1	no	—
226	C₂×Q₈	—	38	1	no	—
227	C₂×Q₈	—	76	4	no	—
228	C₂×Q₈	—	76	1	no	—
229	C₂×Q₈	—	76	1	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	19	2	no	—
232	C₂²×C₄	—	19	2	no	—
233	C₂²×C₄	—	38	2	no	—
234	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
235	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
236	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
237	M₁₆	—	4	1	no	—
238	M₁₆	—	4	1	no	—
239	M₁₆	—	76	1	no	—
240	M₁₆	—	76	1	no	—
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	4	1	no	—
243	C₂×C₈	—	38	2	no	—
244	C₂×C₈	—	76	1	no	—
245	C₄⋊C₄	—	4	2	no	—
246	C₄⋊C₄	—	38	2	no	—
247	C₄⋊C₄	—	38	1	no	—
248	C₄⋊C₄	—	38	2	no	—
249	C₄⋊C₄	—	38	1	no	—
250	C₄⋊C₄	—	38	2	no	—
251	C₄⋊C₄	—	38	2	no	—
252	C₄⋊C₄	—	76	1	no	—
253	C₄⋊C₄	—	76	1	no	—
254	C₄²	—	4	1	no	—
255	C₄²	—	4	1	no	—
256	C₄²	—	38	2	no	—
257	C₄²	—	38	2	no	—
258	C₄²	C₂×D₇₆	1	1	yes	characteristic
259	C₄²	#64541	1	1	yes	characteristic
260	C₄²	D₄×D₁₉	1	1	yes	characteristic
261	C₄²	#64545	1	1	yes	characteristic
262	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
263	Q₈	—	38	2	no	—
264	Q₈	—	38	2	no	—
265	Q₈	—	38	2	no	—
266	Q₈	—	38	2	no	—
267	Q₈	—	152	2	no	—
268	Q₈	—	152	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	4	1	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	4	2	no	—
274	C₂×C₄	—	19	4	no	—
275	C₂×C₄	—	38	2	no	—
276	C₂×C₄	—	38	2	no	—
277	C₂×C₄	—	38	2	no	—
278	C₂×C₄	—	76	2	no	—
279	C₂×C₄	—	76	4	no	—
280	C₂×C₄	—	76	2	no	—
281	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
282	C₂×C₄	#10597328	1	1	yes	characteristic
283	C₂×C₄	#10597330	1	1	yes	characteristic
284	C₂×C₄	#10597339	1	1	yes	characteristic
285	C₂×C₄	#10597340	1	1	yes	characteristic
286	C₂×C₄	#10597341	1	1	yes	characteristic
287	C₂×C₄	#10597358	1	1	yes	characteristic
288	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
289	C₂×C₄	#10597362	1	1	yes	characteristic
290	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
291	C₈	—	4	2	no	—
292	C₈	—	8	1	no	—
293	C₈	—	76	2	no	—
294	C₈	—	152	1	no	—
295	C₂²	—	2	1	no	—
296	C₂²	—	2	1	no	—
297	C₂²	#11926422	1	1	yes	characteristic
298	C₂²	#103×D₁₉	1	1	yes	characteristic
299	C₂²	#11926537	1	1	yes	characteristic
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	2	1	no	—
303	C₄	—	8	2	no	—
304	C₄	—	38	4	no	—
305	C₄	—	76	2	no	—
306	C₄	—	152	2	no	—
307	C₄	#11926718	1	2	yes	—
308	C₄	#11926772	1	1	yes	characteristic
309	C₄	#11926774	1	1	yes	characteristic
310	C₄	#11926784	1	1	yes	characteristic
311	C₄	#11926786	1	1	yes	characteristic
312	C₂	—	2	1	no	—
313	C₂	—	2	1	no	—
314	C₂	#14564037	1	1	yes	characteristic
315	C₂	#14564057	1	1	yes	characteristic
316	C₂	#14564186	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572715

C₂

yes

maximal, characteristic

#14568850

C₂

yes

maximal, characteristic

#14563628

C₂

yes

maximal, characteristic

#14562321

C₂

yes

maximal, characteristic

#14562319

C₂

yes

maximal, characteristic

#14561538

C₂

yes

maximal, characteristic

C₁₉×#1303

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×C₄×Dic₃₈

C₂²

yes

characteristic

C₈×Dic₃₈

—

#11926668

—

#11926597

C₂²

yes

characteristic

#11926594

—

#11926568

C₂²

yes

characteristic

C₂×#10597281

—

#11926484

C₄

yes

—

—

—

—

—

—

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂²×Dic₃₈

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×Dic₁₉⋊C₄

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

D₄

yes

—

—

—

—

—

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉×#95

C₂×C₄

yes

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597281

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂²⋊C₄

yes

—

C₂²×Dic₁₉

C₂²⋊C₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

SD₁₆

yes

—

C₂×Dic₃₈

Q₁₆

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

100

#64520

—

101

C₂×C₁₉⋊C₈

—

102

C₂×C₁₉⋊C₈

—

103

#9396

—

maximal, Sylow

104

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

111

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

112

C₂×C₄×C₁₉

#120

yes

characteristic

113

C₂×C₄×C₁₉

#121

yes

characteristic

114

C₂×C₄×C₁₉

#121

yes

characteristic

115

C₂×C₄×C₁₉

#123

yes

characteristic

116

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

117

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

118

C₂×C₄×C₁₉

#135

yes

characteristic

119

C₂×C₄×C₁₉

#135

yes

characteristic

120

C₂×Dic₁₉

—

121

C₂×Dic₁₉

—

122

C₂×Dic₁₉

—

123

C₂×Dic₁₉

—

124

C₂×Dic₁₉

—

125

C₂×Dic₁₉

—

126

C₂×Dic₁₉

#103

yes

—

127

Dic₃₈

—

128

Dic₃₈

—

129

Dic₃₈

—

130

Dic₃₈

—

131

Dic₃₈

—

132

Dic₃₈

—

133

C₈×C₁₉

—

134

C₈×C₁₉

—

135

C₁₉⋊C₈

—

136

C₁₉⋊C₈

—

137

#2982

—

138

#2568

—

139

#1801

—

140

#1549

—

141

#1549

—

142

#1303

—

143

#1303

D₁₉

yes

characteristic

144

C₂²×C₁₉

—

145

C₂²×C₁₉

—

146

C₂²×C₁₉

#386

yes

characteristic

147

C₂²×C₁₉

C₂×#103

yes

characteristic

148

C₂²×C₁₉

#416

yes

characteristic

149

C₄×C₁₉

—

150

C₄×C₁₉

—

151

C₄×C₁₉

—

152

C₄×C₁₉

—

153

C₄×C₁₉

#454

yes

—

154

C₄×C₁₉

#465

yes

characteristic

155

C₄×C₁₉

#465

yes

characteristic

156

C₄×C₁₉

#467

yes

characteristic

157

C₄×C₁₉

#467

yes

characteristic

158

Dic₁₉

—

159

Dic₁₉

—

160

Dic₁₉

—

161

C₂×C₄⋊Q₈

—

162

C₂×C₄×Q₈

—

163

C₈×Q₈

—

164

C₈×Q₈

—

165

#431

—

166

#431

—

167

#431

C₂×D₁₉

yes

characteristic

168

#423

—

169

#423

C₂×D₁₉

yes

characteristic

170

C₂×#101

—

171

#400

—

172

#391

—

173

#391

—

174

#382

—

175

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

176

#343

—

177

#332

—

178

#332

—

179

C₂×C₁₉

—

180

C₂×C₁₉

—

181

C₂×C₁₉

#1888

yes

characteristic

182

C₂×C₁₉

#1892

yes

characteristic

183

C₂×C₁₉

#1915

yes

characteristic

184

C₂²×Q₈

—

185

C₂²×Q₈

—

186

C₂×M₁₆

—

187

C₂×M₁₆

—

188

C₄⋊Q₈

—

189

C₄⋊Q₈

—

190

C₄⋊Q₈

—

191

C₄⋊Q₈

—

192

C₄×Q₈

—

193

C₄×Q₈

—

194

C₄×Q₈

—

195

C₄×Q₈

—

196

C₂×C₄⋊C₄

—

197

C₂×C₄⋊C₄

—

198

C₂×C₄⋊C₄

—

199

C₂×C₄⋊C₄

—

200

C₂×C₄⋊C₄

—

201

C₂×C₄²

—

202

C₂×C₄²

—

203

C₂×C₄²

C₂²×D₁₉

yes

characteristic

204

C₄⋊C₈

—

205

C₄⋊C₈

—

206

C₄⋊C₈

—

207

C₄⋊C₈

—

208

C₄⋊C₈

—

209

C₄⋊C₈

—

210

C₄⋊C₈

D₇₆

yes

—

211

#101

—

212

C₂²⋊C₈

—

213

C₂²⋊C₈

—

214

C₄×C₈

—

215

C₄×C₈

—

216

C₄×C₈

—

217

#95

—

218

#95

—

219

#95

C₄×D₁₉

yes

—

220

C₁₉

#9396

yes

characteristic, complemented, Sylow

221

C₂×Q₈

—

222

C₂×Q₈

—

223

C₂×Q₈

—

224

C₂×Q₈

—

225

C₂×Q₈

—

226

C₂×Q₈

—

227

C₂×Q₈

—

228

C₂×Q₈

—

229

C₂×Q₈

—

230

C₂²×C₄

—

231

C₂²×C₄

—

232

C₂²×C₄

—

233

C₂²×C₄

—

234

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

235

C₂²×C₄

D₄×D₁₉

yes

characteristic

236

C₂²×C₄

D₄×D₁₉

yes

characteristic

237

M₁₆

—

238

M₁₆

—

239

M₁₆

—

240

M₁₆

—

241

C₂×C₈

—

242

C₂×C₈

—

243

C₂×C₈

—

244

C₂×C₈

—

245

C₄⋊C₄

—

246

C₄⋊C₄

—

247

C₄⋊C₄

—

248

C₄⋊C₄

—

249

C₄⋊C₄

—

250

C₄⋊C₄

—

251

C₄⋊C₄

—

252

C₄⋊C₄

—

253

C₄⋊C₄

—

254

C₄²

—

255

C₄²

—

256

C₄²

—

257

C₄²

—

258

C₄²

C₂×D₇₆

yes

characteristic

259

C₄²

#64541

yes

characteristic

260

C₄²

D₄×D₁₉

yes

characteristic

261

C₄²

#64545

yes

characteristic

262

C₂³

C₂²⋊C₄×D₁₉

yes

characteristic

263

Q₈

—

264

Q₈

—

265

Q₈

—

266

Q₈

—

267

Q₈

—

152

—

268

Q₈

—

152

—

269

C₂×C₄

—

270

C₂×C₄

—

271

C₂×C₄

—

272

C₂×C₄

—

273

C₂×C₄

—

274

C₂×C₄

—

275

C₂×C₄

—

276

C₂×C₄

—

277

C₂×C₄

—

278

C₂×C₄

—

279

C₂×C₄

—

280

C₂×C₄

—

281

C₂×C₄

C₄×D₇₆

yes

characteristic

282

C₂×C₄

#10597328

yes

characteristic

283

C₂×C₄

#10597330

yes

characteristic

284

C₂×C₄

#10597339

yes

characteristic

285

C₂×C₄

#10597340

yes

characteristic

286

C₂×C₄

#10597341

yes

characteristic

287

C₂×C₄

#10597358

yes

characteristic

288

C₂×C₄

SD₁₆×D₁₉

yes

characteristic

289

C₂×C₄

#10597362

yes

characteristic

290

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

291

C₈

—

292

C₈

—

293

C₈

—

294

C₈

—

152

—

295

C₂²

—

296

C₂²

—

297

C₂²

#11926422

yes

characteristic

298

C₂²

#103×D₁₉

yes

characteristic

299

C₂²

#11926537

yes

characteristic

300

C₄

—

301

C₄

—

302

C₄

—

303

C₄

—

304

C₄

—

305

C₄

—

306

C₄

—

152

—

307

C₄

#11926718

yes

—

308

C₄

#11926772

yes

characteristic

309

C₄

#11926774

yes

characteristic

310

C₄

#11926784

yes

characteristic

311

C₄

#11926786

yes

characteristic

312

C₂

—

313

C₂

—

314

C₂

#14564037

yes

characteristic

315

C₂

#14564057

yes

characteristic

316

C₂

#14564186

yes

characteristic

	subgroup	G/H
center	C₂²	#11926422
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1303	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1303	D₁₉
hypocenter	C₁₉	#9396
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1303

subgroup

G/H

center

C₂²

#11926422

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1303

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1303

N	H ≅ G/N	type
220. C₁₉	#9396	semidirect

H ≅ G/N

type

220. C₁₉

#9396

semidirect

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

subgroup	index
#14572715	2
#14568850	2
#14563628	2
#14562321	2
#14562319	2
#14561538	2
C₁₉×#1303	2
#9396	19

subgroup

index

C₁₉×#1303

Subgroups — #18079918

Conjugacy classes of subgroups

Complements

Maximal subgroups