Group #18082063 — subgroups

Subgroups — #18082063

Order 4864.

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

normal subgroups only

This group has 510 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	C₂×#11926785	C₂	1	1	yes	maximal, characteristic
2	#14564619	C₂	1	2	yes	maximal
3	#14563411	C₂	1	1	yes	maximal, characteristic
4	#14562206	C₂	1	2	yes	maximal
5	C₁₉×#1807	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	#11926310	—	2	4	no	—
18	#11926298	—	2	1	no	—
19	#11926280	—	2	4	no	—
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#106	—	2	1	no	—
22	C₁₉×#380	C₂²	1	2	yes	—
23	C₁₉×#340	—	2	1	no	—
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₁₉	—	4	2	no	—
27	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	D₄	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	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
36	C₂×C₂²⋊Dic₁₉	D₄	1	2	yes	—
37	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
38	#10597370	—	2	2	no	—
39	#10597370	—	2	2	no	—
40	#10597370	—	2	2	no	—
41	#10597370	—	2	2	no	—
42	C₂×Dic₁₉⋊C₄	—	2	2	no	—
43	C₂×C₄×Dic₁₉	—	2	1	no	—
44	C₂²×C₁₉⋊C₈	—	2	1	no	—
45	C₂×Dic₇₆	—	2	1	no	—
46	C₂×Dic₇₆	—	2	1	no	—
47	C₂×Dic₇₆	—	4	2	no	—
48	C₁₉×#106	—	4	2	no	—
49	C₁₉×#95	—	2	2	no	—
50	C₁₉⋊#95	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	—	4	1	no	—
60	C₂²×C₄×C₁₉	—	4	1	no	—
61	C₂²×C₄×C₁₉	—	4	2	no	—
62	C₂²×C₄×C₁₉	C₂²×C₄	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×C₄×C₁₉	#41	1	1	yes	characteristic
68	C₂²×Dic₁₉	—	2	2	no	—
69	C₂²×Dic₁₉	—	2	2	no	—
70	C₂²×Dic₁₉	—	2	2	no	—
71	C₂×Dic₃₈	—	2	2	no	—
72	C₂×Dic₃₈	—	2	2	no	—
73	C₂×Dic₃₈	—	4	2	no	—
74	C₂×Dic₃₈	—	4	2	no	—
75	C₂×C₈×C₁₉	—	2	2	no	—
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₂×C₈×C₁₉	—	4	1	no	—
79	C₂×C₈×C₁₉	—	4	1	no	—
80	C₂×C₈×C₁₉	—	4	1	no	—
81	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₄⋊C₄×C₁₉	—	4	2	no	—
86	C₄⋊C₄×C₁₉	—	4	2	no	—
87	C₂²⋊C₄×C₁₉	—	4	4	no	—
88	C₂²⋊Dic₁₉	—	2	4	no	—
89	C₂²⋊Dic₁₉	—	4	2	no	—
90	C₂²⋊Dic₁₉	—	4	2	no	—
91	C₄⋊Dic₁₉	—	2	2	no	—
92	C₄⋊Dic₁₉	—	2	2	no	—
93	Dic₁₉⋊C₄	—	4	2	no	—
94	Dic₁₉⋊C₄	—	4	2	no	—
95	C₄×Dic₁₉	—	4	1	no	—
96	C₄×Dic₁₉	—	4	1	no	—
97	C₂×C₁₉⋊C₈	—	2	2	no	—
98	C₂×C₁₉⋊C₈	—	4	1	no	—
99	C₂×C₁₉⋊C₈	—	4	1	no	—
100	Dic₇₆	—	4	2	no	—
101	Dic₇₆	—	4	2	no	—
102	#9784	—	19	1	no	maximal, Sylow
103	C₂³×C₁₉	—	4	1	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	#127	1	1	yes	characteristic
108	C₂³×C₁₉	#137	1	4	yes	—
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	—	2	1	no	—
115	C₂×C₄×C₁₉	—	4	1	no	—
116	C₂×C₄×C₁₉	—	4	1	no	—
117	C₂×C₄×C₁₉	—	4	1	no	—
118	C₂×C₄×C₁₉	—	8	2	no	—
119	C₂×C₄×C₁₉	—	8	2	no	—
120	C₂×C₄×C₁₉	—	8	2	no	—
121	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
123	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
124	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
125	C₂×Dic₁₉	—	4	2	no	—
126	C₂×Dic₁₉	—	4	2	no	—
127	C₂×Dic₁₉	—	4	2	no	—
128	C₂×Dic₁₉	—	4	2	no	—
129	C₂×Dic₁₉	—	4	2	no	—
130	C₂×Dic₁₉	—	8	2	no	—
131	C₂×Dic₁₉	—	8	2	no	—
132	Dic₃₈	—	4	2	no	—
133	Dic₃₈	—	4	2	no	—
134	Dic₃₈	—	8	2	no	—
135	C₈×C₁₉	—	2	1	no	—
136	C₈×C₁₉	—	2	1	no	—
137	C₈×C₁₉	—	2	1	no	—
138	C₈×C₁₉	#99	1	2	yes	—
139	C₁₉⋊C₈	—	4	2	no	—
140	C₂×#467	—	19	1	no	—
141	#1996	—	19	2	no	—
142	#1807	D₁₉	1	1	yes	characteristic
143	#1752	—	19	1	no	—
144	#1520	—	19	2	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	—	2	1	no	—
150	C₂²×C₁₉	—	2	1	no	—
151	C₂²×C₁₉	—	4	4	no	—
152	C₂²×C₁₉	#390	1	1	yes	characteristic
153	C₂²×C₁₉	#441	1	2	yes	—
154	C₂²×C₁₉	#470	1	2	yes	—
155	C₂²×C₁₉	#497	1	2	yes	—
156	C₄×C₁₉	—	2	1	no	—
157	C₄×C₁₉	—	2	1	no	—
158	C₄×C₁₉	—	2	1	no	—
159	C₄×C₁₉	—	16	2	no	—
160	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
161	C₄×C₁₉	#410	1	1	yes	characteristic
162	Dic₁₉	—	8	2	no	—
163	Dic₁₉	—	8	2	no	—
164	Dic₁₉	—	8	2	no	—
165	C₂²×Q₁₆	—	19	1	no	—
166	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
167	C₂×C₂²⋊Q₈	—	19	2	no	—
168	#467	—	38	1	no	—
169	#467	—	38	1	no	—
170	#467	—	38	1	no	—
171	#467	—	38	1	no	—
172	C₂×#107	—	19	1	no	—
173	C₂×#106	—	2	1	no	—
174	C₂×#103	—	19	2	no	—
175	C₂×C₂²⋊C₈	—	19	1	no	—
176	C₂×#97	—	38	1	no	—
177	#380	C₂×D₁₉	1	2	yes	—
178	C₄×C₂²⋊C₄	—	19	1	no	—
179	#342	—	38	4	no	—
180	#340	—	2	1	no	—
181	#336	—	38	1	no	—
182	#328	—	38	4	no	—
183	C₂×C₁₉	—	2	2	no	—
184	C₂×C₁₉	—	2	2	no	—
185	C₂×C₁₉	—	2	2	no	—
186	C₂×C₁₉	#1964	1	1	yes	characteristic
187	C₂×C₁₉	#1971	1	1	yes	characteristic
188	C₂×C₁₉	#1976	1	1	yes	characteristic
189	C₂²×Q₈	—	19	2	no	—
190	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
191	C₂×Q₁₆	—	38	1	no	—
192	C₂×Q₁₆	—	38	1	no	—
193	C₂×Q₁₆	—	76	2	no	—
194	C₂²×C₈	—	4	2	no	—
195	C₂²×C₈	—	38	1	no	—
196	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
197	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
198	C₂²×C₈	D₇₆	1	1	yes	characteristic
199	C₂²×C₈	D₇₆	1	1	yes	characteristic
200	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
201	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
202	C₂²⋊Q₈	—	38	2	no	—
203	C₂²⋊Q₈	—	38	2	no	—
204	C₂²⋊Q₈	—	38	2	no	—
205	C₂²⋊Q₈	—	38	2	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	—	19	2	no	—
208	C₂×C₄⋊C₄	—	38	2	no	—
209	C₂×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₂²⋊C₄	—	19	2	no	—
211	C₂×C₂²⋊C₄	—	38	2	no	—
212	C₂×C₄²	—	38	1	no	—
213	#107	—	38	1	no	—
214	#107	—	38	1	no	—
215	#106	—	4	2	no	—
216	#103	—	38	2	no	—
217	#103	—	38	2	no	—
218	C₂²⋊C₈	—	19	2	no	—
219	C₂²⋊C₈	—	38	1	no	—
220	#97	—	76	2	no	—
221	#95	—	2	2	no	—
222	#95	—	38	1	no	—
223	C₁₉	#9784	1	1	yes	characteristic, complemented, Sylow
224	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
225	C₂×Q₈	—	38	2	no	—
226	C₂×Q₈	—	38	2	no	—
227	C₂×Q₈	—	76	2	no	—
228	C₂×Q₈	—	76	2	no	—
229	C₂²×C₄	—	4	1	no	—
230	C₂²×C₄	—	4	1	no	—
231	C₂²×C₄	—	4	2	no	—
232	C₂²×C₄	—	38	2	no	—
233	C₂²×C₄	—	38	2	no	—
234	C₂²×C₄	—	38	2	no	—
235	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
236	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
237	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
238	C₂²×C₄	#64545	1	1	yes	characteristic
239	C₂²×C₄	#64545	1	1	yes	characteristic
240	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
241	Q₁₆	—	76	2	no	—
242	Q₁₆	—	76	2	no	—
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	4	1	no	—
247	C₂×C₈	—	4	1	no	—
248	C₂×C₈	—	4	1	no	—
249	C₂×C₈	—	38	2	no	—
250	C₂×C₈	—	76	1	no	—
251	C₂×C₈	—	76	1	no	—
252	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
253	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
254	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
255	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
256	C₄⋊C₄	—	4	2	no	—
257	C₄⋊C₄	—	4	2	no	—
258	C₄⋊C₄	—	38	2	no	—
259	C₄⋊C₄	—	38	2	no	—
260	C₄⋊C₄	—	76	2	no	—
261	C₄⋊C₄	—	76	2	no	—
262	C₂²⋊C₄	—	4	4	no	—
263	C₂²⋊C₄	—	38	4	no	—
264	C₂²⋊C₄	—	76	2	no	—
265	C₂²⋊C₄	—	76	2	no	—
266	C₄²	—	76	1	no	—
267	C₄²	—	76	1	no	—
268	C₂³	—	4	1	no	—
269	C₂³	—	4	1	no	—
270	C₂³	#10597339	1	1	yes	characteristic
271	C₂³	#10597341	1	1	yes	characteristic
272	C₂³	#10597361	1	4	yes	—
273	C₂³	#10597386	1	1	yes	characteristic
274	Q₈	—	76	2	no	—
275	Q₈	—	76	2	no	—
276	Q₈	—	152	2	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	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	—	4	1	no	—
284	C₂×C₄	—	4	1	no	—
285	C₂×C₄	—	4	1	no	—
286	C₂×C₄	—	8	2	no	—
287	C₂×C₄	—	8	2	no	—
288	C₂×C₄	—	8	2	no	—
289	C₂×C₄	—	76	2	no	—
290	C₂×C₄	—	76	2	no	—
291	C₂×C₄	—	76	2	no	—
292	C₂×C₄	—	76	2	no	—
293	C₂×C₄	—	76	2	no	—
294	C₂×C₄	—	152	2	no	—
295	C₂×C₄	—	152	2	no	—
296	C₂×C₄	#10597339	1	1	yes	characteristic
297	C₂×C₄	#10597341	1	1	yes	characteristic
298	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
299	C₂×C₄	#10597393	1	1	yes	characteristic
300	C₈	—	2	1	no	—
301	C₈	—	2	1	no	—
302	C₈	—	2	1	no	—
303	C₈	—	76	2	no	—
304	C₈	#10597263	1	2	yes	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	1	no	—
307	C₂²	—	2	1	no	—
308	C₂²	—	2	1	no	—
309	C₂²	—	2	1	no	—
310	C₂²	—	2	1	no	—
311	C₂²	—	4	4	no	—
312	C₂²	#11926445	1	1	yes	characteristic
313	C₂²	#11926650	1	2	yes	—
314	C₂²	#11926803	1	2	yes	—
315	C₂²	#11926935	1	2	yes	—
316	C₄	—	2	1	no	—
317	C₄	—	2	1	no	—
318	C₄	—	2	1	no	—
319	C₄	—	16	2	no	—
320	C₄	—	152	2	no	—
321	C₄	—	152	2	no	—
322	C₄	—	152	2	no	—
323	C₄	C₂×#10597263	1	1	yes	characteristic
324	C₄	#11926517	1	1	yes	characteristic
325	C₂	—	2	2	no	—
326	C₂	—	2	2	no	—
327	C₂	—	2	2	no	—
328	C₂	#14564470	1	1	yes	characteristic
329	C₂	#14564504	1	1	yes	characteristic
330	C₂	#14564531	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926785

C₂

yes

maximal, characteristic

#14564619

C₂

yes

maximal

#14563411

C₂

yes

maximal, characteristic

#14562206

C₂

yes

maximal

C₁₉×#1807

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×#106

—

C₁₉×#380

C₂²

yes

—

C₁₉×#340

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₃₈

C₂×C₄

yes

—

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×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

—

—

—

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₁₉×#106

—

C₁₉×#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

D₄

yes

—

—

—

—

—

—

C₂⁴×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

—

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

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

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

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

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

—

100

Dic₇₆

—

101

Dic₇₆

—

102

#9784

—

maximal, Sylow

103

C₂³×C₁₉

—

104

C₂³×C₁₉

—

105

C₂³×C₁₉

C₄×D₄

yes

characteristic

106

C₂³×C₁₉

#121

yes

characteristic

107

C₂³×C₁₉

#127

yes

characteristic

108

C₂³×C₁₉

#137

yes

—

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

—

118

C₂×C₄×C₁₉

—

119

C₂×C₄×C₁₉

—

120

C₂×C₄×C₁₉

—

121

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

122

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

123

C₂×C₄×C₁₉

#121

yes

characteristic

124

C₂×C₄×C₁₉

#124

yes

characteristic

125

C₂×Dic₁₉

—

126

C₂×Dic₁₉

—

127

C₂×Dic₁₉

—

128

C₂×Dic₁₉

—

129

C₂×Dic₁₉

—

130

C₂×Dic₁₉

—

131

C₂×Dic₁₉

—

132

Dic₃₈

—

133

Dic₃₈

—

134

Dic₃₈

—

135

C₈×C₁₉

—

136

C₈×C₁₉

—

137

C₈×C₁₉

—

138

C₈×C₁₉

#99

yes

—

139

C₁₉⋊C₈

—

140

C₂×#467

—

141

#1996

—

142

#1807

D₁₉

yes

characteristic

143

#1752

—

144

#1520

—

145

C₂²×C₁₉

—

146

C₂²×C₁₉

—

147

C₂²×C₁₉

—

148

C₂²×C₁₉

—

149

C₂²×C₁₉

—

150

C₂²×C₁₉

—

151

C₂²×C₁₉

—

152

C₂²×C₁₉

#390

yes

characteristic

153

C₂²×C₁₉

#441

yes

—

154

C₂²×C₁₉

#470

yes

—

155

C₂²×C₁₉

#497

yes

—

156

C₄×C₁₉

—

157

C₄×C₁₉

—

158

C₄×C₁₉

—

159

C₄×C₁₉

—

160

C₄×C₁₉

C₂×#99

yes

characteristic

161

C₄×C₁₉

#410

yes

characteristic

162

Dic₁₉

—

163

Dic₁₉

—

164

Dic₁₉

—

165

C₂²×Q₁₆

—

166

C₂³×C₈

C₂×D₁₉

yes

characteristic

167

C₂×C₂²⋊Q₈

—

168

#467

—

169

#467

—

170

#467

—

171

#467

—

172

C₂×#107

—

173

C₂×#106

—

174

C₂×#103

—

175

C₂×C₂²⋊C₈

—

176

C₂×#97

—

177

#380

C₂×D₁₉

yes

—

178

C₄×C₂²⋊C₄

—

179

#342

—

180

#340

—

181

#336

—

182

#328

—

183

C₂×C₁₉

—

184

C₂×C₁₉

—

185

C₂×C₁₉

—

186

C₂×C₁₉

#1964

yes

characteristic

187

C₂×C₁₉

#1971

yes

characteristic

188

C₂×C₁₉

#1976

yes

characteristic

189

C₂²×Q₈

—

190

C₂³×C₄

C₂²×D₁₉

yes

characteristic

191

C₂×Q₁₆

—

192

C₂×Q₁₆

—

193

C₂×Q₁₆

—

194

C₂²×C₈

—

195

C₂²×C₈

—

196

C₂²×C₈

C₄×D₁₉

yes

characteristic

197

C₂²×C₈

C₄×D₁₉

yes

characteristic

198

C₂²×C₈

D₇₆

yes

characteristic

199

C₂²×C₈

D₇₆

yes

characteristic

200

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

201

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

202

C₂²⋊Q₈

—

203

C₂²⋊Q₈

—

204

C₂²⋊Q₈

—

205

C₂²⋊Q₈

—

206

C₂×C₄⋊C₄

—

207

C₂×C₄⋊C₄

—

208

C₂×C₄⋊C₄

—

209

C₂×C₂²⋊C₄

—

210

C₂×C₂²⋊C₄

—

211

C₂×C₂²⋊C₄

—

212

C₂×C₄²

—

213

#107

—

214

#107

—

215

#106

—

216

#103

—

217

#103

—

218

C₂²⋊C₈

—

219

C₂²⋊C₈

—

220

#97

—

221

#95

—

222

#95

—

223

C₁₉

#9784

yes

characteristic, complemented, Sylow

224

C₂⁴

D₄×D₁₉

yes

characteristic

225

C₂×Q₈

—

226

C₂×Q₈

—

227

C₂×Q₈

—

228

C₂×Q₈

—

229

C₂²×C₄

—

230

C₂²×C₄

—

231

C₂²×C₄

—

232

C₂²×C₄

—

233

C₂²×C₄

—

234

C₂²×C₄

—

235

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

236

C₂²×C₄

C₂×D₇₆

yes

characteristic

237

C₂²×C₄

D₄×D₁₉

yes

characteristic

238

C₂²×C₄

#64545

yes

characteristic

239

C₂²×C₄

#64545

yes

characteristic

240

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

241

Q₁₆

—

242

Q₁₆

—

243

C₂×C₈

—

244

C₂×C₈

—

245

C₂×C₈

—

246

C₂×C₈

—

247

C₂×C₈

—

248

C₂×C₈

—

249

C₂×C₈

—

250

C₂×C₈

—

251

C₂×C₈

—

252

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

253

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

254

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

255

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

256

C₄⋊C₄

—

257

C₄⋊C₄

—

258

C₄⋊C₄

—

259

C₄⋊C₄

—

260

C₄⋊C₄

—

261

C₄⋊C₄

—

262

C₂²⋊C₄

—

263

C₂²⋊C₄

—

264

C₂²⋊C₄

—

265

C₂²⋊C₄

—

266

C₄²

—

267

C₄²

—

268

C₂³

—

269

C₂³

—

270

C₂³

#10597339

yes

characteristic

271

C₂³

#10597341

yes

characteristic

272

C₂³

#10597361

yes

—

273

C₂³

#10597386

yes

characteristic

274

Q₈

—

275

Q₈

—

276

Q₈

—

152

—

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

—

291

C₂×C₄

—

292

C₂×C₄

—

293

C₂×C₄

—

294

C₂×C₄

—

152

—

295

C₂×C₄

—

152

—

296

C₂×C₄

#10597339

yes

characteristic

297

C₂×C₄

#10597341

yes

characteristic

298

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

299

C₂×C₄

#10597393

yes

characteristic

300

C₈

—

301

C₈

—

302

C₈

—

303

C₈

—

304

C₈

#10597263

yes

—

305

C₂²

—

306

C₂²

—

307

C₂²

—

308

C₂²

—

309

C₂²

—

310

C₂²

—

311

C₂²

—

312

C₂²

#11926445

yes

characteristic

313

C₂²

#11926650

yes

—

314

C₂²

#11926803

yes

—

315

C₂²

#11926935

yes

—

316

C₄

—

317

C₄

—

318

C₄

—

319

C₄

—

320

C₄

—

152

—

321

C₄

—

152

—

322

C₄

—

152

—

323

C₄

C₂×#10597263

yes

characteristic

324

C₄

#11926517

yes

characteristic

325

C₂

—

326

C₂

—

327

C₂

—

328

C₂

#14564470

yes

characteristic

329

C₂

#14564504

yes

characteristic

330

C₂

#14564531

yes

characteristic

	subgroup	G/H
center	C₂²	#11926445
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1807	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1807	D₁₉
hypocenter	C₁₉	#9784
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1807

subgroup

G/H

center

C₂²

#11926445

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₁₉×#1807

C₂

socle

C₂²×C₁₉

#390

prime radical

C₂⁴×C₁₉

C₂×D₄

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1807

N	H ≅ G/N	type
6. C₂²×Dic₇₆	C₄	semidirect
12. C₂×#10597275	C₄	semidirect
13. C₂×#10597273	C₄	semidirect
223. C₁₉	#9784	semidirect

H ≅ G/N

type

6. C₂²×Dic₇₆

C₄

semidirect

12. C₂×#10597275

C₄

semidirect

13. C₂×#10597273

C₄

semidirect

223. C₁₉

#9784

semidirect

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

subgroup	index
C₂×#11926785	2
#14564619	2
#14563411	2
#14562206	2
C₁₉×#1807	2
#9784	19

subgroup

index

C₁₉×#1807

Subgroups — #18082063

Conjugacy classes of subgroups

Complements

Maximal subgroups