Group #18084881 — subgroups

Subgroups — #18084881

Order 4864.

712 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11926834	C₂	1	2	yes	maximal, complemented
2	#14564436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal, complemented
4	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2537	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	#11926834	—	2	4	no	—
8	#11926834	—	2	4	no	—
9	C₂×#10597265	—	2	2	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
11	C₂×#10597267	—	2	2	no	—
12	C₂×#10597289	—	2	2	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
15	C₂×C₁₉×#121	—	2	2	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
17	C₁₉×#394	—	2	2	no	—
18	C₁₉×#384	C₂²	1	1	yes	characteristic
19	C₁₉×#380	—	2	2	no	—
20	C₂²×D₄×C₁₉	—	2	2	no	—
21	C₂²×D₄×C₁₉	D₄	1	2	yes	—
22	C₂³×C₄×C₁₉	—	2	2	no	—
23	C₂²×Dic₃₈	—	2	1	no	—
24	C₁₉×#121	—	4	4	no	—
25	C₁₉×#121	—	4	4	no	—
26	C₄×D₄×C₁₉	—	2	2	no	—
27	C₄×D₄×C₁₉	—	2	2	no	—
28	C₄×D₄×C₁₉	—	2	2	no	—
29	C₄×D₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
33	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊Dic₁₉	—	2	2	no	—
37	C₂²×C₁₉⋊C₈	—	2	2	no	—
38	C₂²×C₁₉⋊C₈	—	2	1	no	—
39	#10597315	—	2	2	no	—
40	#10597315	—	2	1	no	—
41	#10597315	D₄	1	2	yes	complemented
42	C₁₉×#95	—	2	2	no	—
43	#10597289	—	2	8	no	—
44	#10597267	—	4	4	no	—
45	#10597265	—	2	8	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	complemented
48	C₄×C₁₉⋊C₈	—	2	2	no	—
49	C₂⁴×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	—	2	2	no	—
51	C₂×D₄×C₁₉	—	2	2	no	—
52	C₂×D₄×C₁₉	—	2	2	no	—
53	C₂×D₄×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	4	8	no	—
56	C₂×D₄×C₁₉	—	8	2	no	—
57	C₂×D₄×C₁₉	SD₁₆	1	4	yes	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	4	2	no	—
61	C₂²×C₄×C₁₉	—	4	2	no	—
62	C₂²×C₄×C₁₉	—	4	2	no	—
63	C₂²×C₄×C₁₉	—	4	2	no	—
64	C₂²×C₄×C₁₉	—	4	2	no	—
65	C₂²×C₄×C₁₉	—	4	2	no	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
68	C₂²×Dic₁₉	—	4	1	no	—
69	C₂×Dic₃₈	—	2	2	no	—
70	C₂×Dic₃₈	—	4	2	no	—
71	C₂×Dic₃₈	—	4	2	no	—
72	C₂×Dic₃₈	—	4	1	no	—
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	4	2	no	—
76	C₄⋊C₄×C₁₉	—	4	2	no	—
77	C₄⋊C₄×C₁₉	—	4	2	no	—
78	C₂²⋊C₄×C₁₉	—	4	8	no	—
79	C₂²⋊C₄×C₁₉	—	4	2	no	—
80	C₂²⋊C₄×C₁₉	—	4	2	no	—
81	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₁₉	C₂×D₄	1	2	yes	—
83	C₄²×C₁₉	#41	1	1	yes	characteristic
84	C₄⋊Dic₁₉	—	2	4	no	—
85	C₄⋊Dic₁₉	—	4	2	no	—
86	C₂×C₁₉⋊C₈	—	2	2	no	—
87	C₂×C₁₉⋊C₈	—	2	4	no	—
88	C₂×C₁₉⋊C₈	—	4	1	no	—
89	C₂×C₁₉⋊C₈	—	4	1	no	—
90	C₂×C₁₉⋊C₈	—	4	2	no	—
91	C₂×C₁₉⋊C₈	—	4	2	no	—
92	#10235	—	19	1	no	maximal, Sylow
93	C₂³×C₁₉	—	2	4	no	—
94	C₂³×C₁₉	—	4	2	no	—
95	C₂³×C₁₉	—	4	2	no	—
96	C₂³×C₁₉	—	4	2	no	—
97	C₂³×C₁₉	—	4	2	no	—
98	C₂³×C₁₉	—	4	2	no	—
99	C₂³×C₁₉	—	4	2	no	—
100	C₂³×C₁₉	#120	1	1	yes	characteristic
101	D₄×C₁₉	—	2	4	no	—
102	D₄×C₁₉	—	2	4	no	—
103	D₄×C₁₉	—	4	2	no	—
104	D₄×C₁₉	—	4	2	no	—
105	D₄×C₁₉	—	8	8	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	—	4	4	no	—
111	C₂×C₄×C₁₉	—	4	2	no	—
112	C₂×C₄×C₁₉	—	4	2	no	—
113	C₂×C₄×C₁₉	—	8	2	no	—
114	C₂×C₄×C₁₉	—	8	2	no	—
115	C₂×C₄×C₁₉	—	8	2	no	—
116	C₂×C₄×C₁₉	—	8	2	no	—
117	C₂×C₄×C₁₉	#120	1	2	yes	—
118	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#121	1	2	yes	—
120	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
122	C₂×C₄×C₁₉	#135	1	2	yes	—
123	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
124	C₂×C₄×C₁₉	#137	1	2	yes	—
125	C₂×Dic₁₉	—	4	2	no	—
126	C₂×Dic₁₉	—	8	1	no	—
127	C₂×Dic₁₉	—	8	1	no	—
128	Dic₃₈	—	4	4	no	—
129	Dic₃₈	—	8	2	no	—
130	C₁₉⋊C₈	—	4	2	no	—
131	C₁₉⋊C₈	—	4	4	no	—
132	C₂×#476	—	19	2	no	—
133	#2537	D₁₉	1	1	yes	characteristic
134	#1956	—	19	1	no	—
135	C₂×D₄⋊C₈	—	19	2	no	—
136	#1296	—	19	1	no	—
137	C₂²×C₁₉	—	4	4	no	—
138	C₂²×C₁₉	—	4	4	no	—
139	C₂²×C₁₉	—	4	4	no	—
140	C₂²×C₁₉	—	8	2	no	—
141	C₂²×C₁₉	—	8	2	no	—
142	C₂²×C₁₉	—	8	2	no	—
143	C₂²×C₁₉	—	8	2	no	—
144	C₂²×C₁₉	#392	1	1	yes	characteristic
145	C₂²×C₁₉	#450	1	2	yes	—
146	C₂²×C₁₉	#452	1	2	yes	—
147	C₂²×C₁₉	#453	1	1	yes	characteristic
148	C₂²×C₁₉	#454	1	1	yes	characteristic
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	—	2	1	no	—
151	C₄×C₁₉	—	8	2	no	—
152	C₄×C₁₉	—	8	2	no	—
153	C₄×C₁₉	#448	1	2	yes	—
154	C₄×C₁₉	#449	1	2	yes	—
155	C₄×C₁₉	#465	1	2	yes	—
156	C₄×C₁₉	#468	1	2	yes	—
157	Dic₁₉	—	8	2	no	—
158	C₂×C₄⋊Q₈	—	19	1	no	—
159	C₂×#121	—	2	2	no	—
160	C₂×C₄×D₄	C₂×D₁₉	1	2	yes	—
161	#476	—	38	4	no	—
162	#476	—	38	4	no	—
163	C₂×#106	—	38	2	no	—
164	C₂×C₄⋊C₈	—	19	2	no	—
165	C₂×#103	—	38	2	no	—
166	C₂×#102	—	38	2	no	—
167	C₂×C₄×C₈	—	19	1	no	—
168	#394	—	2	2	no	—
169	#384	C₂×D₁₉	1	1	yes	characteristic
170	#380	—	2	2	no	—
171	D₄⋊C₈	—	38	4	no	—
172	C₂×C₁₉	—	8	4	no	—
173	C₂×C₁₉	#1629	1	1	yes	characteristic
174	C₂×C₁₉	#1634	1	1	yes	characteristic
175	C₂×C₁₉	#1635	1	2	yes	—
176	C₂×C₁₉	#2000	1	2	yes	—
177	C₂×C₁₉	#2006	1	1	yes	characteristic
178	C₂²×Q₈	—	38	1	no	—
179	C₂²×D₄	—	2	2	no	—
180	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
181	C₂³×C₄	—	2	2	no	—
182	C₂²×C₈	—	38	1	no	—
183	C₂²×C₈	—	38	2	no	—
184	C₄⋊Q₈	—	19	2	no	—
185	C₄⋊Q₈	—	38	2	no	—
186	C₄⋊Q₈	—	38	1	no	—
187	#121	—	4	4	no	—
188	#121	—	4	4	no	—
189	C₄×D₄	—	2	2	no	—
190	C₄×D₄	—	2	2	no	—
191	C₄×D₄	—	2	2	no	—
192	C₄×D₄	—	2	2	no	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	—	38	2	no	—
195	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
196	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
197	C₂×C₂²⋊C₄	—	2	4	no	—
198	C₂×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
200	#106	—	38	8	no	—
201	C₄⋊C₈	—	19	4	no	—
202	C₄⋊C₈	—	38	2	no	—
203	#103	—	76	4	no	—
204	#102	—	38	8	no	—
205	C₄×C₈	—	38	2	no	—
206	#95	—	2	2	no	—
207	C₁₉	#10235	1	1	yes	characteristic, complemented, Sylow
208	C₂⁴	—	2	2	no	—
209	C₂×Q₈	—	38	2	no	—
210	C₂×Q₈	—	76	2	no	—
211	C₂×Q₈	—	76	2	no	—
212	C₂×Q₈	—	76	1	no	—
213	C₂×D₄	—	2	2	no	—
214	C₂×D₄	—	2	2	no	—
215	C₂×D₄	—	2	2	no	—
216	C₂×D₄	—	2	2	no	—
217	C₂×D₄	—	2	2	no	—
218	C₂×D₄	—	4	8	no	—
219	C₂×D₄	—	8	2	no	—
220	C₂×D₄	#64526	1	4	yes	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	4	2	no	—
224	C₂²×C₄	—	4	2	no	—
225	C₂²×C₄	—	4	2	no	—
226	C₂²×C₄	—	4	2	no	—
227	C₂²×C₄	—	4	2	no	—
228	C₂²×C₄	—	4	2	no	—
229	C₂²×C₄	—	76	1	no	—
230	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
231	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
232	C₂×C₈	—	38	2	no	—
233	C₂×C₈	—	38	4	no	—
234	C₂×C₈	—	76	1	no	—
235	C₂×C₈	—	76	2	no	—
236	C₂×C₈	—	76	1	no	—
237	C₂×C₈	—	76	2	no	—
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	—	2	2	no	—
240	C₄⋊C₄	—	4	2	no	—
241	C₄⋊C₄	—	4	2	no	—
242	C₄⋊C₄	—	4	2	no	—
243	C₄⋊C₄	—	38	4	no	—
244	C₄⋊C₄	—	76	2	no	—
245	C₂²⋊C₄	—	4	8	no	—
246	C₂²⋊C₄	—	4	2	no	—
247	C₂²⋊C₄	—	4	2	no	—
248	C₄²	D₄×D₁₉	1	1	yes	characteristic
249	C₄²	D₄×D₁₉	1	2	yes	—
250	C₄²	#64543	1	1	yes	characteristic
251	C₂³	—	2	4	no	—
252	C₂³	—	4	2	no	—
253	C₂³	—	4	2	no	—
254	C₂³	—	4	2	no	—
255	C₂³	—	4	2	no	—
256	C₂³	—	4	2	no	—
257	C₂³	—	4	2	no	—
258	C₂³	#10597399	1	1	yes	characteristic
259	Q₈	—	76	4	no	—
260	Q₈	—	152	2	no	—
261	D₄	—	2	4	no	—
262	D₄	—	2	4	no	—
263	D₄	—	4	2	no	—
264	D₄	—	4	2	no	—
265	D₄	—	8	8	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	4	2	no	—
269	C₂×C₄	—	4	4	no	—
270	C₂×C₄	—	4	2	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	8	2	no	—
274	C₂×C₄	—	8	2	no	—
275	C₂×C₄	—	8	2	no	—
276	C₂×C₄	—	8	2	no	—
277	C₂×C₄	—	76	2	no	—
278	C₂×C₄	—	152	1	no	—
279	C₂×C₄	—	152	1	no	—
280	C₂×C₄	#10597378	1	2	yes	—
281	C₂×C₄	C₂×#64526	1	2	yes	—
282	C₂×C₄	#10597383	1	2	yes	—
283	C₂×C₄	#10597384	1	1	yes	characteristic
284	C₂×C₄	#10597385	1	2	yes	—
285	C₂×C₄	#10597386	1	1	yes	characteristic
286	C₂×C₄	#10597396	1	2	yes	—
287	C₂×C₄	#10597397	1	2	yes	—
288	C₈	—	76	2	no	—
289	C₈	—	76	4	no	—
290	C₂²	—	4	4	no	—
291	C₂²	—	4	4	no	—
292	C₂²	—	4	4	no	—
293	C₂²	—	8	2	no	—
294	C₂²	—	8	2	no	—
295	C₂²	—	8	2	no	—
296	C₂²	—	8	2	no	—
297	C₂²	#11926452	1	1	yes	characteristic
298	C₂²	#11926695	1	2	yes	—
299	C₂²	#11926706	1	2	yes	—
300	C₂²	#11926712	1	1	yes	characteristic
301	C₂²	#11926717	1	1	yes	characteristic
302	C₄	—	2	1	no	—
303	C₄	—	2	1	no	—
304	C₄	—	8	2	no	—
305	C₄	—	8	2	no	—
306	C₄	—	152	2	no	—
307	C₄	#11926682	1	2	yes	—
308	C₄	#11926687	1	2	yes	—
309	C₄	#11926771	1	2	yes	—
310	C₄	#11926788	1	2	yes	—
311	C₂	—	8	4	no	—
312	C₂	#14562751	1	1	yes	characteristic
313	C₂	#14562780	1	1	yes	characteristic
314	C₂	#14562786	1	2	yes	—
315	C₂	#14564638	1	2	yes	—
316	C₂	#14564677	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926834

C₂

yes

maximal, complemented

#14564436

C₂

yes

maximal, characteristic, complemented

C₂×D₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, complemented

#14561518

C₂

yes

maximal, characteristic, complemented

C₁₉×#2537

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

—

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597267

—

C₂×#10597289

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

D₄⋊(C₁₉⋊C₈)

—

C₂×C₁₉×#121

—

C₂×C₄×D₄×C₁₉

C₂²

yes

—

C₁₉×#394

—

C₁₉×#384

C₂²

yes

characteristic

C₁₉×#380

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

—

C₂²×Dic₃₈

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

#10597315

—

#10597315

—

#10597315

D₄

yes

complemented

C₁₉×#95

—

#10597289

—

#10597267

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

complemented

C₄×C₁₉⋊C₈

—

C₂⁴×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

SD₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10235

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

100

C₂³×C₁₉

#120

yes

characteristic

101

D₄×C₁₉

—

102

D₄×C₁₉

—

103

D₄×C₁₉

—

104

D₄×C₁₉

—

105

D₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

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

#120

yes

—

118

C₂×C₄×C₁₉

#121

yes

characteristic

119

C₂×C₄×C₁₉

#121

yes

—

120

C₂×C₄×C₁₉

#127

yes

characteristic

121

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

122

C₂×C₄×C₁₉

#135

yes

—

123

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

124

C₂×C₄×C₁₉

#137

yes

—

125

C₂×Dic₁₉

—

126

C₂×Dic₁₉

—

127

C₂×Dic₁₉

—

128

Dic₃₈

—

129

Dic₃₈

—

130

C₁₉⋊C₈

—

131

C₁₉⋊C₈

—

132

C₂×#476

—

133

#2537

D₁₉

yes

characteristic

134

#1956

—

135

C₂×D₄⋊C₈

—

136

#1296

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

—

139

C₂²×C₁₉

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

—

142

C₂²×C₁₉

—

143

C₂²×C₁₉

—

144

C₂²×C₁₉

#392

yes

characteristic

145

C₂²×C₁₉

#450

yes

—

146

C₂²×C₁₉

#452

yes

—

147

C₂²×C₁₉

#453

yes

characteristic

148

C₂²×C₁₉

#454

yes

characteristic

149

C₄×C₁₉

—

150

C₄×C₁₉

—

151

C₄×C₁₉

—

152

C₄×C₁₉

—

153

C₄×C₁₉

#448

yes

—

154

C₄×C₁₉

#449

yes

—

155

C₄×C₁₉

#465

yes

—

156

C₄×C₁₉

#468

yes

—

157

Dic₁₉

—

158

C₂×C₄⋊Q₈

—

159

C₂×#121

—

160

C₂×C₄×D₄

C₂×D₁₉

yes

—

161

#476

—

162

#476

—

163

C₂×#106

—

164

C₂×C₄⋊C₈

—

165

C₂×#103

—

166

C₂×#102

—

167

C₂×C₄×C₈

—

168

#394

—

169

#384

C₂×D₁₉

yes

characteristic

170

#380

—

171

D₄⋊C₈

—

172

C₂×C₁₉

—

173

C₂×C₁₉

#1629

yes

characteristic

174

C₂×C₁₉

#1634

yes

characteristic

175

C₂×C₁₉

#1635

yes

—

176

C₂×C₁₉

#2000

yes

—

177

C₂×C₁₉

#2006

yes

characteristic

178

C₂²×Q₈

—

179

C₂²×D₄

—

180

C₂²×D₄

C₂²⋊D₁₉

yes

—

181

C₂³×C₄

—

182

C₂²×C₈

—

183

C₂²×C₈

—

184

C₄⋊Q₈

—

185

C₄⋊Q₈

—

186

C₄⋊Q₈

—

187

#121

—

188

#121

—

189

C₄×D₄

—

190

C₄×D₄

—

191

C₄×D₄

—

192

C₄×D₄

—

193

C₂×C₄⋊C₄

—

194

C₂×C₄⋊C₄

—

195

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

196

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

197

C₂×C₂²⋊C₄

—

198

C₂×C₂²⋊C₄

—

199

C₂×C₄²

C₂²×D₁₉

yes

characteristic

200

#106

—

201

C₄⋊C₈

—

202

C₄⋊C₈

—

203

#103

—

204

#102

—

205

C₄×C₈

—

206

#95

—

207

C₁₉

#10235

yes

characteristic, complemented, Sylow

208

C₂⁴

—

209

C₂×Q₈

—

210

C₂×Q₈

—

211

C₂×Q₈

—

212

C₂×Q₈

—

213

C₂×D₄

—

214

C₂×D₄

—

215

C₂×D₄

—

216

C₂×D₄

—

217

C₂×D₄

—

218

C₂×D₄

—

219

C₂×D₄

—

220

C₂×D₄

#64526

yes

—

221

C₂²×C₄

—

222

C₂²×C₄

—

223

C₂²×C₄

—

224

C₂²×C₄

—

225

C₂²×C₄

—

226

C₂²×C₄

—

227

C₂²×C₄

—

228

C₂²×C₄

—

229

C₂²×C₄

—

230

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

231

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

232

C₂×C₈

—

233

C₂×C₈

—

234

C₂×C₈

—

235

C₂×C₈

—

236

C₂×C₈

—

237

C₂×C₈

—

238

C₄⋊C₄

—

239

C₄⋊C₄

—

240

C₄⋊C₄

—

241

C₄⋊C₄

—

242

C₄⋊C₄

—

243

C₄⋊C₄

—

244

C₄⋊C₄

—

245

C₂²⋊C₄

—

246

C₂²⋊C₄

—

247

C₂²⋊C₄

—

248

C₄²

D₄×D₁₉

yes

characteristic

249

C₄²

D₄×D₁₉

yes

—

250

C₄²

#64543

yes

characteristic

251

C₂³

—

252

C₂³

—

253

C₂³

—

254

C₂³

—

255

C₂³

—

256

C₂³

—

257

C₂³

—

258

C₂³

#10597399

yes

characteristic

259

Q₈

—

260

Q₈

—

152

—

261

D₄

—

262

D₄

—

263

D₄

—

264

D₄

—

265

D₄

—

266

C₂×C₄

—

267

C₂×C₄

—

268

C₂×C₄

—

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

—

152

—

279

C₂×C₄

—

152

—

280

C₂×C₄

#10597378

yes

—

281

C₂×C₄

C₂×#64526

yes

—

282

C₂×C₄

#10597383

yes

—

283

C₂×C₄

#10597384

yes

characteristic

284

C₂×C₄

#10597385

yes

—

285

C₂×C₄

#10597386

yes

characteristic

286

C₂×C₄

#10597396

yes

—

287

C₂×C₄

#10597397

yes

—

288

C₈

—

289

C₈

—

290

C₂²

—

291

C₂²

—

292

C₂²

—

293

C₂²

—

294

C₂²

—

295

C₂²

—

296

C₂²

—

297

C₂²

#11926452

yes

characteristic

298

C₂²

#11926695

yes

—

299

C₂²

#11926706

yes

—

300

C₂²

#11926712

yes

characteristic

301

C₂²

#11926717

yes

characteristic

302

C₄

—

303

C₄

—

304

C₄

—

305

C₄

—

306

C₄

—

152

—

307

C₄

#11926682

yes

—

308

C₄

#11926687

yes

—

309

C₄

#11926771

yes

—

310

C₄

#11926788

yes

—

311

C₂

—

312

C₂

#14562751

yes

characteristic

313

C₂

#14562780

yes

characteristic

314

C₂

#14562786

yes

—

315

C₂

#14564638

yes

—

316

C₂

#14564677

yes

characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#2537	C₂
socle	C₂³×C₁₉	#120
hypercenter	#2537	D₁₉
hypocenter	C₁₉	#10235
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2537

subgroup

G/H

center

C₂³

#10597399

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#2537

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2537

N	H ≅ G/N	type
1. C₂×#11926834	C₂	semidirect
2. #14564436	C₂	semidirect
3. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
4. #14561518	C₂	semidirect
41. #10597315	D₄	semidirect
47. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
207. C₁₉	#10235	semidirect

H ≅ G/N

type

1. C₂×#11926834

C₂

semidirect

2. #14564436

C₂

semidirect

3. C₂×D₄⋊(C₁₉⋊C₈)

C₂

semidirect

4. #14561518

C₂

semidirect

41. #10597315

D₄

semidirect

47. C₄⋊(C₁₉⋊C₈)

D₄

semidirect

207. C₁₉

#10235

semidirect

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

subgroup	index
C₂×#11926834	2
#14564436	2
C₂×D₄⋊(C₁₉⋊C₈)	2
#14561518	2
C₁₉×#2537	2
#10235	19

subgroup

index

C₂×D₄⋊(C₁₉⋊C₈)

C₁₉×#2537

Subgroups — #18084881

Conjugacy classes of subgroups

Complements

Maximal subgroups