Group #18082262 — subgroups

Subgroups — #18082262

Order 4864.

484 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 107 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	C₂×#11926785	C₂	1	1	yes	maximal, characteristic
2	#14563411	C₂	1	1	yes	maximal, characteristic
3	#14562156	C₂	1	2	yes	maximal
4	#14562000	C₂	1	2	yes	maximal
5	C₁₉×#1810	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₇₆	C₄	1	1	yes	characteristic, complemented
7	C₂×#10597370	C₂²	1	2	yes	—
8	#11926785	—	2	1	no	—
9	#11926785	—	2	1	no	—
10	#11926785	—	2	1	no	—
11	#11926785	—	2	1	no	—
12	C₂×#10597275	C₄	1	1	yes	characteristic, complemented
13	C₂×#10597273	C₄	1	2	yes	complemented
14	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#10597272	—	2	1	no	—
16	C₄×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
17	#11926298	—	2	1	no	—
18	#11926282	—	2	4	no	—
19	#11926269	—	2	4	no	—
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#108	—	2	1	no	—
22	C₁₉×#407	C₂²	1	2	yes	—
23	C₁₉×#341	—	2	1	no	—
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
26	C₂×M₁₆×C₁₉	—	2	2	no	—
27	C₂²×C₈×C₁₉	—	4	2	no	—
28	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
35	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
36	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
37	#10597370	—	2	2	no	—
38	#10597370	—	2	2	no	—
39	#10597370	—	2	2	no	—
40	#10597370	—	2	2	no	—
41	C₂×Dic₁₉⋊C₄	—	2	2	no	—
42	C₂×C₄×Dic₁₉	—	2	1	no	—
43	C₂²×C₁₉⋊C₈	—	2	1	no	—
44	C₂×Dic₇₆	—	2	1	no	—
45	C₂×Dic₇₆	—	2	1	no	—
46	C₂×Dic₇₆	—	4	2	no	—
47	C₁₉×#108	—	4	2	no	—
48	C₁₉×C₂²⋊C₈	—	2	2	no	—
49	C₁₉×C₂²⋊C₈	—	2	2	no	—
50	C₁₉⋊#95	D₄	1	2	yes	—
51	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
52	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
53	#10597275	—	2	1	no	—
54	#10597275	—	2	1	no	—
55	#10597273	—	2	2	no	—
56	#10597273	—	2	2	no	—
57	#10597272	—	4	2	no	—
58	C₂⁴×C₁₉	#41	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	—	4	1	no	—
60	C₂²×C₄×C₁₉	—	4	1	no	—
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂×D₄	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×C₄×C₁₉	#41	1	1	yes	characteristic
67	C₂²×Dic₁₉	—	2	2	no	—
68	C₂²×Dic₁₉	—	2	2	no	—
69	C₂²×Dic₁₉	—	2	2	no	—
70	C₂×Dic₃₈	—	2	2	no	—
71	C₂×Dic₃₈	—	2	2	no	—
72	C₂×Dic₃₈	—	4	2	no	—
73	C₂×Dic₃₈	—	4	2	no	—
74	M₁₆×C₁₉	—	4	2	no	—
75	M₁₆×C₁₉	—	4	2	no	—
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₂×C₈×C₁₉	—	2	2	no	—
79	C₂×C₈×C₁₉	—	4	1	no	—
80	C₂×C₈×C₁₉	—	4	1	no	—
81	C₂×C₈×C₁₉	—	4	1	no	—
82	C₂×C₈×C₁₉	—	4	2	no	—
83	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²⋊Dic₁₉	—	4	2	no	—
88	C₂²⋊Dic₁₉	—	4	2	no	—
89	C₂²⋊Dic₁₉	—	4	2	no	—
90	C₄⋊Dic₁₉	—	2	2	no	—
91	C₄⋊Dic₁₉	—	2	2	no	—
92	Dic₁₉⋊C₄	—	4	2	no	—
93	Dic₁₉⋊C₄	—	4	2	no	—
94	C₄×Dic₁₉	—	4	1	no	—
95	C₄×Dic₁₉	—	4	1	no	—
96	C₂×C₁₉⋊C₈	—	2	2	no	—
97	C₂×C₁₉⋊C₈	—	4	1	no	—
98	C₂×C₁₉⋊C₈	—	4	1	no	—
99	Dic₇₆	—	4	2	no	—
100	Dic₇₆	—	4	2	no	—
101	#9817	—	19	1	no	maximal, Sylow
102	C₂³×C₁₉	—	2	2	no	—
103	C₂³×C₁₉	—	2	2	no	—
104	C₂³×C₁₉	—	4	1	no	—
105	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
106	C₂³×C₁₉	#121	1	1	yes	characteristic
107	C₂³×C₁₉	#124	1	1	yes	characteristic
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	4	1	no	—
115	C₂×C₄×C₁₉	—	4	1	no	—
116	C₂×C₄×C₁₉	—	4	1	no	—
117	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
120	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
121	C₂×Dic₁₉	—	4	2	no	—
122	C₂×Dic₁₉	—	4	2	no	—
123	C₂×Dic₁₉	—	4	2	no	—
124	C₂×Dic₁₉	—	4	2	no	—
125	C₂×Dic₁₉	—	4	4	no	—
126	C₂×Dic₁₉	—	4	2	no	—
127	C₂×Dic₁₉	—	8	2	no	—
128	Dic₃₈	—	4	2	no	—
129	Dic₃₈	—	4	2	no	—
130	Dic₃₈	—	8	2	no	—
131	C₈×C₁₉	—	2	1	no	—
132	C₈×C₁₉	—	2	1	no	—
133	C₈×C₁₉	—	2	1	no	—
134	C₈×C₁₉	—	8	2	no	—
135	C₈×C₁₉	#99	1	2	yes	—
136	C₁₉⋊C₈	—	4	2	no	—
137	C₂×#467	—	19	1	no	—
138	#1810	D₁₉	1	1	yes	characteristic
139	#1752	—	19	1	no	—
140	#1508	—	19	2	no	—
141	#1472	—	19	2	no	—
142	C₂²×C₁₉	—	2	1	no	—
143	C₂²×C₁₉	—	2	1	no	—
144	C₂²×C₁₉	—	2	1	no	—
145	C₂²×C₁₉	—	2	1	no	—
146	C₂²×C₁₉	—	2	1	no	—
147	C₂²×C₁₉	—	2	1	no	—
148	C₂²×C₁₉	—	2	1	no	—
149	C₂²×C₁₉	—	4	4	no	—
150	C₂²×C₁₉	#390	1	1	yes	characteristic
151	C₂²×C₁₉	#444	1	2	yes	—
152	C₂²×C₁₉	#473	1	2	yes	—
153	C₄×C₁₉	—	2	1	no	—
154	C₄×C₁₉	—	2	1	no	—
155	C₄×C₁₉	—	2	1	no	—
156	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
157	C₄×C₁₉	#410	1	1	yes	characteristic
158	Dic₁₉	—	8	2	no	—
159	Dic₁₉	—	8	2	no	—
160	Dic₁₉	—	8	2	no	—
161	C₂²×Q₁₆	—	19	1	no	—
162	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
163	C₂×C₂²⋊Q₈	—	19	2	no	—
164	#467	—	38	1	no	—
165	#467	—	38	1	no	—
166	#467	—	38	1	no	—
167	#467	—	38	1	no	—
168	C₂×#108	—	2	1	no	—
169	C₂×#107	—	19	1	no	—
170	C₂×#103	—	19	2	no	—
171	#407	C₂×D₁₉	1	2	yes	—
172	C₂×C₂²⋊C₈	—	19	1	no	—
173	C₂×#97	—	38	1	no	—
174	C₄×C₂²⋊C₄	—	19	1	no	—
175	#341	—	2	1	no	—
176	#336	—	38	1	no	—
177	#328	—	38	4	no	—
178	#324	—	38	4	no	—
179	C₂×C₁₉	—	2	2	no	—
180	C₂×C₁₉	—	2	2	no	—
181	C₂×C₁₉	—	4	1	no	—
182	C₂×C₁₉	#1964	1	1	yes	characteristic
183	C₂×C₁₉	#1975	1	1	yes	characteristic
184	C₂×C₁₉	#1979	1	1	yes	characteristic
185	C₂²×Q₈	—	19	2	no	—
186	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
187	C₂×Q₁₆	—	38	1	no	—
188	C₂×Q₁₆	—	38	1	no	—
189	C₂×Q₁₆	—	76	2	no	—
190	C₂×M₁₆	—	2	2	no	—
191	C₂²×C₈	—	4	2	no	—
192	C₂²×C₈	—	38	1	no	—
193	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
194	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
195	C₂²×C₈	D₇₆	1	1	yes	characteristic
196	C₂²×C₈	D₇₆	1	1	yes	characteristic
197	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
198	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
199	C₂²⋊Q₈	—	38	2	no	—
200	C₂²⋊Q₈	—	38	2	no	—
201	C₂²⋊Q₈	—	38	2	no	—
202	C₂²⋊Q₈	—	38	2	no	—
203	C₂×C₄⋊C₄	—	19	2	no	—
204	C₂×C₄⋊C₄	—	38	2	no	—
205	C₂×C₂²⋊C₄	—	38	2	no	—
206	C₂×C₂²⋊C₄	—	38	1	no	—
207	C₂×C₄²	—	38	1	no	—
208	#108	—	4	2	no	—
209	#107	—	38	1	no	—
210	#107	—	38	1	no	—
211	#103	—	38	2	no	—
212	#103	—	38	2	no	—
213	C₂²⋊C₈	—	2	2	no	—
214	C₂²⋊C₈	—	2	2	no	—
215	C₂²⋊C₈	—	19	2	no	—
216	C₂²⋊C₈	—	38	1	no	—
217	#97	—	76	2	no	—
218	#95	—	19	2	no	—
219	C₁₉	#9817	1	1	yes	characteristic, complemented, Sylow
220	C₂⁴	#64545	1	1	yes	characteristic
221	C₂×Q₈	—	38	2	no	—
222	C₂×Q₈	—	38	2	no	—
223	C₂×Q₈	—	76	2	no	—
224	C₂×Q₈	—	76	2	no	—
225	C₂²×C₄	—	4	1	no	—
226	C₂²×C₄	—	4	1	no	—
227	C₂²×C₄	—	38	2	no	—
228	C₂²×C₄	—	38	2	no	—
229	C₂²×C₄	—	38	2	no	—
230	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
231	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
232	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
233	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
234	C₂²×C₄	#64545	1	1	yes	characteristic
235	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
236	Q₁₆	—	76	2	no	—
237	Q₁₆	—	76	2	no	—
238	M₁₆	—	4	2	no	—
239	M₁₆	—	4	2	no	—
240	C₂×C₈	—	2	2	no	—
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	—	4	1	no	—
244	C₂×C₈	—	4	1	no	—
245	C₂×C₈	—	4	1	no	—
246	C₂×C₈	—	4	2	no	—
247	C₂×C₈	—	38	2	no	—
248	C₂×C₈	—	76	1	no	—
249	C₂×C₈	—	76	1	no	—
250	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
251	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
252	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
253	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
254	C₄⋊C₄	—	38	2	no	—
255	C₄⋊C₄	—	38	2	no	—
256	C₄⋊C₄	—	76	2	no	—
257	C₄⋊C₄	—	76	2	no	—
258	C₂²⋊C₄	—	76	2	no	—
259	C₂²⋊C₄	—	76	2	no	—
260	C₂²⋊C₄	—	76	2	no	—
261	C₄²	—	76	1	no	—
262	C₄²	—	76	1	no	—
263	C₂³	—	2	2	no	—
264	C₂³	—	2	2	no	—
265	C₂³	—	4	1	no	—
266	C₂³	#10597339	1	1	yes	characteristic
267	C₂³	#10597341	1	1	yes	characteristic
268	C₂³	#10597393	1	1	yes	characteristic
269	Q₈	—	76	2	no	—
270	Q₈	—	76	2	no	—
271	Q₈	—	152	2	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	4	1	no	—
279	C₂×C₄	—	4	1	no	—
280	C₂×C₄	—	4	1	no	—
281	C₂×C₄	—	76	2	no	—
282	C₂×C₄	—	76	2	no	—
283	C₂×C₄	—	76	2	no	—
284	C₂×C₄	—	76	4	no	—
285	C₂×C₄	—	76	2	no	—
286	C₂×C₄	—	76	2	no	—
287	C₂×C₄	—	152	2	no	—
288	C₂×C₄	#10597339	1	1	yes	characteristic
289	C₂×C₄	#10597341	1	1	yes	characteristic
290	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
291	C₂×C₄	#10597386	1	1	yes	characteristic
292	C₈	—	2	1	no	—
293	C₈	—	2	1	no	—
294	C₈	—	2	1	no	—
295	C₈	—	8	2	no	—
296	C₈	—	76	2	no	—
297	C₈	#10597263	1	2	yes	—
298	C₂²	—	2	1	no	—
299	C₂²	—	2	1	no	—
300	C₂²	—	2	1	no	—
301	C₂²	—	2	1	no	—
302	C₂²	—	2	1	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	2	1	no	—
305	C₂²	—	4	4	no	—
306	C₂²	#11926445	1	1	yes	characteristic
307	C₂²	#11926665	1	2	yes	—
308	C₂²	#11926820	1	2	yes	—
309	C₄	—	2	1	no	—
310	C₄	—	2	1	no	—
311	C₄	—	2	1	no	—
312	C₄	—	152	2	no	—
313	C₄	—	152	2	no	—
314	C₄	—	152	2	no	—
315	C₄	C₂×#10597263	1	1	yes	characteristic
316	C₄	#11926517	1	1	yes	characteristic
317	C₂	—	2	2	no	—
318	C₂	—	2	2	no	—
319	C₂	—	4	1	no	—
320	C₂	#14564470	1	1	yes	characteristic
321	C₂	#14564526	1	1	yes	characteristic
322	C₂	#14564548	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926785

C₂

yes

maximal, characteristic

#14563411

C₂

yes

maximal, characteristic

#14562156

C₂

yes

maximal

#14562000

C₂

yes

maximal

C₁₉×#1810

C₂

yes

maximal, characteristic

C₂²×Dic₇₆

C₄

yes

characteristic, complemented

C₂×#10597370

C₂²

yes

—

—

—

—

—

C₄

yes

characteristic, complemented

C₂×#10597273

C₄

yes

complemented

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597272

—

C₄×C₂²⋊Dic₁₉

C₂²

yes

—

—

—

C₂³×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#108

—

C₁₉×#407

C₂²

yes

—

C₁₉×#341

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₃₈

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

—

—

—

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₁₉×#108

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉⋊#95

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

D₄

yes

—

—

—

—

—

—

C₂⁴×C₁₉

#41

yes

characteristic

C₂²×C₄×C₁₉

—

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×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

100

Dic₇₆

—

101

#9817

—

maximal, Sylow

102

C₂³×C₁₉

—

103

C₂³×C₁₉

—

104

C₂³×C₁₉

—

105

C₂³×C₁₉

C₄×D₄

yes

characteristic

106

C₂³×C₁₉

#121

yes

characteristic

107

C₂³×C₁₉

#124

yes

characteristic

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×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

C₂×C₂²⋊C₄

yes

characteristic

118

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

119

C₂×C₄×C₁₉

#121

yes

characteristic

120

C₂×C₄×C₁₉

#127

yes

characteristic

121

C₂×Dic₁₉

—

122

C₂×Dic₁₉

—

123

C₂×Dic₁₉

—

124

C₂×Dic₁₉

—

125

C₂×Dic₁₉

—

126

C₂×Dic₁₉

—

127

C₂×Dic₁₉

—

128

Dic₃₈

—

129

Dic₃₈

—

130

Dic₃₈

—

131

C₈×C₁₉

—

132

C₈×C₁₉

—

133

C₈×C₁₉

—

134

C₈×C₁₉

—

135

C₈×C₁₉

#99

yes

—

136

C₁₉⋊C₈

—

137

C₂×#467

—

138

#1810

D₁₉

yes

characteristic

139

#1752

—

140

#1508

—

141

#1472

—

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

#390

yes

characteristic

151

C₂²×C₁₉

#444

yes

—

152

C₂²×C₁₉

#473

yes

—

153

C₄×C₁₉

—

154

C₄×C₁₉

—

155

C₄×C₁₉

—

156

C₄×C₁₉

C₂×#99

yes

characteristic

157

C₄×C₁₉

#410

yes

characteristic

158

Dic₁₉

—

159

Dic₁₉

—

160

Dic₁₉

—

161

C₂²×Q₁₆

—

162

C₂³×C₈

C₂×D₁₉

yes

characteristic

163

C₂×C₂²⋊Q₈

—

164

#467

—

165

#467

—

166

#467

—

167

#467

—

168

C₂×#108

—

169

C₂×#107

—

170

C₂×#103

—

171

#407

C₂×D₁₉

yes

—

172

C₂×C₂²⋊C₈

—

173

C₂×#97

—

174

C₄×C₂²⋊C₄

—

175

#341

—

176

#336

—

177

#328

—

178

#324

—

179

C₂×C₁₉

—

180

C₂×C₁₉

—

181

C₂×C₁₉

—

182

C₂×C₁₉

#1964

yes

characteristic

183

C₂×C₁₉

#1975

yes

characteristic

184

C₂×C₁₉

#1979

yes

characteristic

185

C₂²×Q₈

—

186

C₂³×C₄

C₂²×D₁₉

yes

characteristic

187

C₂×Q₁₆

—

188

C₂×Q₁₆

—

189

C₂×Q₁₆

—

190

C₂×M₁₆

—

191

C₂²×C₈

—

192

C₂²×C₈

—

193

C₂²×C₈

C₄×D₁₉

yes

characteristic

194

C₂²×C₈

C₄×D₁₉

yes

characteristic

195

C₂²×C₈

D₇₆

yes

characteristic

196

C₂²×C₈

D₇₆

yes

characteristic

197

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

198

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

199

C₂²⋊Q₈

—

200

C₂²⋊Q₈

—

201

C₂²⋊Q₈

—

202

C₂²⋊Q₈

—

203

C₂×C₄⋊C₄

—

204

C₂×C₄⋊C₄

—

205

C₂×C₂²⋊C₄

—

206

C₂×C₂²⋊C₄

—

207

C₂×C₄²

—

208

#108

—

209

#107

—

210

#107

—

211

#103

—

212

#103

—

213

C₂²⋊C₈

—

214

C₂²⋊C₈

—

215

C₂²⋊C₈

—

216

C₂²⋊C₈

—

217

#97

—

218

#95

—

219

C₁₉

#9817

yes

characteristic, complemented, Sylow

220

C₂⁴

#64545

yes

characteristic

221

C₂×Q₈

—

222

C₂×Q₈

—

223

C₂×Q₈

—

224

C₂×Q₈

—

225

C₂²×C₄

—

226

C₂²×C₄

—

227

C₂²×C₄

—

228

C₂²×C₄

—

229

C₂²×C₄

—

230

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

231

C₂²×C₄

C₂×D₇₆

yes

characteristic

232

C₂²×C₄

D₄×D₁₉

yes

characteristic

233

C₂²×C₄

D₄×D₁₉

yes

characteristic

234

C₂²×C₄

#64545

yes

characteristic

235

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

236

Q₁₆

—

237

Q₁₆

—

238

M₁₆

—

239

M₁₆

—

240

C₂×C₈

—

241

C₂×C₈

—

242

C₂×C₈

—

243

C₂×C₈

—

244

C₂×C₈

—

245

C₂×C₈

—

246

C₂×C₈

—

247

C₂×C₈

—

248

C₂×C₈

—

249

C₂×C₈

—

250

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

251

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

252

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

253

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

254

C₄⋊C₄

—

255

C₄⋊C₄

—

256

C₄⋊C₄

—

257

C₄⋊C₄

—

258

C₂²⋊C₄

—

259

C₂²⋊C₄

—

260

C₂²⋊C₄

—

261

C₄²

—

262

C₄²

—

263

C₂³

—

264

C₂³

—

265

C₂³

—

266

C₂³

#10597339

yes

characteristic

267

C₂³

#10597341

yes

characteristic

268

C₂³

#10597393

yes

characteristic

269

Q₈

—

270

Q₈

—

271

Q₈

—

152

—

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

—

282

C₂×C₄

—

283

C₂×C₄

—

284

C₂×C₄

—

285

C₂×C₄

—

286

C₂×C₄

—

287

C₂×C₄

—

152

—

288

C₂×C₄

#10597339

yes

characteristic

289

C₂×C₄

#10597341

yes

characteristic

290

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

291

C₂×C₄

#10597386

yes

characteristic

292

C₈

—

293

C₈

—

294

C₈

—

295

C₈

—

296

C₈

—

297

C₈

#10597263

yes

—

298

C₂²

—

299

C₂²

—

300

C₂²

—

301

C₂²

—

302

C₂²

—

303

C₂²

—

304

C₂²

—

305

C₂²

—

306

C₂²

#11926445

yes

characteristic

307

C₂²

#11926665

yes

—

308

C₂²

#11926820

yes

—

309

C₄

—

310

C₄

—

311

C₄

—

312

C₄

—

152

—

313

C₄

—

152

—

314

C₄

—

152

—

315

C₄

C₂×#10597263

yes

characteristic

316

C₄

#11926517

yes

characteristic

317

C₂

—

318

C₂

—

319

C₂

—

320

C₂

#14564470

yes

characteristic

321

C₂

#14564526

yes

characteristic

322

C₂

#14564548

yes

characteristic

	subgroup	G/H
center	C₂²	#11926445
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1810	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1810	D₁₉
hypocenter	C₁₉	#9817
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1810

subgroup

G/H

center

C₂²

#11926445

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₁₉×#1810

C₂

C₂²×C₁₉

C₂⁴×C₁₉

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1810

N	H ≅ G/N	type
6. C₂²×Dic₇₆	C₄	semidirect
12. C₂×#10597275	C₄	semidirect
13. C₂×#10597273	C₄	semidirect
219. C₁₉	#9817	semidirect

H ≅ G/N

type

6. C₂²×Dic₇₆

C₄

semidirect

12. C₂×#10597275

C₄

semidirect

13. C₂×#10597273

C₄

semidirect

219. C₁₉

#9817

semidirect

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

subgroup	index
C₂×#11926785	2
#14563411	2
#14562156	2
#14562000	2
C₁₉×#1810	2
#9817	19

subgroup

index

C₁₉×#1810

Subgroups — #18082262

Conjugacy classes of subgroups

Complements

Maximal subgroups