Group #18071562 — subgroups

Subgroups — #18071562

Order 4864.

682 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14565163	C₂	1	1	yes	maximal, characteristic, complemented
2	#14565038	C₂	1	2	yes	maximal, complemented
3	#14561456	C₂	1	2	yes	maximal, complemented
4	#14561456	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2679	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597264	—	2	1	no	—
7	C₂×#10597289	—	2	1	no	—
8	C₂×#10597289	—	2	2	no	—
9	#11926414	C₂²	1	1	yes	characteristic, complemented
10	#11926306	—	2	2	no	—
11	#11926299	C₂²	1	1	yes	characteristic, complemented
12	#11926299	C₂²	1	2	yes	complemented
13	C₂×C₁₉×#120	—	2	2	no	—
14	C₂×C₁₉×#120	—	2	1	no	—
15	C₁₉×#394	—	2	2	no	—
16	C₁₉×#394	—	2	1	no	—
17	C₁₉×#390	C₂²	1	1	yes	characteristic
18	C₁₉×#390	C₂²	1	2	yes	—
19	C₂⁵×C₁₉	—	2	1	no	—
20	C₂²×D₄×C₁₉	—	2	1	no	—
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×D₄×C₁₉	D₄	1	2	yes	—
23	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
24	C₁₉×#120	—	4	4	no	—
25	C₁₉×#120	—	4	2	no	—
26	C₁₉×#120	—	4	4	no	—
27	C₁₉×#120	—	4	2	no	—
28	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
29	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₂²⋊C₄×C₁₉	—	2	2	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	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	C₂²×C₁₉⋊C₈	—	2	1	no	—
39	C₂²×C₁₉⋊C₈	—	2	2	no	—
40	C₁₉×#95	—	2	1	no	—
41	#10597289	—	4	2	no	—
42	#10597289	—	4	4	no	—
43	#10597264	—	4	2	no	—
44	C₂⁴×C₁₉	—	2	2	no	—
45	C₂⁴×C₁₉	—	2	1	no	—
46	C₂⁴×C₁₉	—	4	4	no	—
47	C₂⁴×C₁₉	—	4	2	no	—
48	C₂⁴×C₁₉	—	8	1	no	—
49	C₂⁴×C₁₉	—	8	2	no	—
50	C₂⁴×C₁₉	—	8	1	no	—
51	C₂×D₄×C₁₉	—	2	2	no	—
52	C₂×D₄×C₁₉	—	2	1	no	—
53	C₂×D₄×C₁₉	—	4	2	no	—
54	C₂×D₄×C₁₉	—	4	2	no	—
55	C₂×D₄×C₁₉	—	4	1	no	—
56	C₂×D₄×C₁₉	—	4	1	no	—
57	C₂×D₄×C₁₉	—	4	4	no	—
58	C₂×D₄×C₁₉	—	4	4	no	—
59	C₂×D₄×C₁₉	—	4	4	no	—
60	C₂×D₄×C₁₉	—	8	1	no	—
61	C₂×D₄×C₁₉	—	8	2	no	—
62	C₂×D₄×C₁₉	D₈	1	4	yes	—
63	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×Dic₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	4	1	no	—
71	C₂²⋊C₄×C₁₉	—	4	4	no	—
72	C₂²⋊C₄×C₁₉	—	4	2	no	—
73	C₂²⋊C₄×C₁₉	—	4	2	no	—
74	C₂²⋊C₄×C₁₉	—	4	2	no	—
75	C₂²⋊C₄×C₁₉	—	4	2	no	—
76	C₂²⋊C₄×C₁₉	—	4	2	no	—
77	C₂²⋊C₄×C₁₉	—	4	2	no	—
78	C₂²⋊C₄×C₁₉	—	4	2	no	—
79	C₄²×C₁₉	—	4	1	no	—
80	C₄⋊Dic₁₉	—	4	1	no	—
81	C₄⋊Dic₁₉	—	4	1	no	—
82	C₄⋊Dic₁₉	—	4	2	no	—
83	C₄⋊Dic₁₉	—	4	2	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	4	1	no	—
86	C₂×C₁₉⋊C₈	—	4	1	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	C₂×C₁₉⋊C₈	—	4	2	no	—
90	#7786	—	19	1	no	maximal, Sylow
91	C₂³×C₁₉	—	2	4	no	—
92	C₂³×C₁₉	—	2	2	no	—
93	C₂³×C₁₉	—	4	2	no	—
94	C₂³×C₁₉	—	4	2	no	—
95	C₂³×C₁₉	—	4	2	no	—
96	C₂³×C₁₉	—	4	1	no	—
97	C₂³×C₁₉	—	4	2	no	—
98	C₂³×C₁₉	—	4	2	no	—
99	C₂³×C₁₉	—	4	2	no	—
100	C₂³×C₁₉	—	4	2	no	—
101	C₂³×C₁₉	—	4	2	no	—
102	C₂³×C₁₉	—	4	1	no	—
103	C₂³×C₁₉	—	8	4	no	—
104	C₂³×C₁₉	—	8	8	no	—
105	C₂³×C₁₉	—	8	8	no	—
106	C₂³×C₁₉	—	8	4	no	—
107	C₂³×C₁₉	—	8	4	no	—
108	C₂³×C₁₉	#120	1	1	yes	characteristic
109	D₄×C₁₉	—	4	4	no	—
110	D₄×C₁₉	—	4	2	no	—
111	D₄×C₁₉	—	8	2	no	—
112	D₄×C₁₉	—	8	1	no	—
113	D₄×C₁₉	—	8	4	no	—
114	D₄×C₁₉	—	8	8	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	2	no	—
117	C₂×C₄×C₁₉	—	2	2	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	4	2	no	—
120	C₂×C₄×C₁₉	—	4	2	no	—
121	C₂×C₄×C₁₉	—	4	2	no	—
122	C₂×C₄×C₁₉	—	4	1	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
125	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
126	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
127	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
128	C₂×Dic₁₉	—	8	2	no	—
129	C₂×Dic₁₉	—	8	1	no	—
130	C₁₉⋊C₈	—	4	2	no	—
131	C₁₉⋊C₈	—	8	2	no	—
132	#2679	D₁₉	1	1	yes	characteristic
133	#2093	—	19	1	no	—
134	#2071	—	19	2	no	—
135	#1270	—	19	1	no	—
136	#1270	—	19	2	no	—
137	C₂²×C₁₉	—	4	4	no	—
138	C₂²×C₁₉	—	4	2	no	—
139	C₂²×C₁₉	—	4	4	no	—
140	C₂²×C₁₉	—	4	4	no	—
141	C₂²×C₁₉	—	4	4	no	—
142	C₂²×C₁₉	—	8	16	no	—
143	C₂²×C₁₉	—	8	2	no	—
144	C₂²×C₁₉	—	8	2	no	—
145	C₂²×C₁₉	—	8	2	no	—
146	C₂²×C₁₉	—	8	1	no	—
147	C₂²×C₁₉	—	8	2	no	—
148	C₂²×C₁₉	—	8	1	no	—
149	C₂²×C₁₉	—	8	2	no	—
150	C₂²×C₁₉	#447	1	2	yes	—
151	C₂²×C₁₉	#450	1	1	yes	characteristic
152	C₂²×C₁₉	#453	1	1	yes	characteristic
153	C₂²×C₁₉	#455	1	2	yes	—
154	C₂²×C₁₉	#458	1	1	yes	characteristic
155	C₄×C₁₉	—	2	2	no	—
156	C₄×C₁₉	—	2	2	no	—
157	C₄×C₁₉	—	2	1	no	—
158	C₄×C₁₉	—	2	1	no	—
159	C₄×C₁₉	—	8	1	no	—
160	C₄×C₁₉	—	8	2	no	—
161	Dic₁₉	—	16	1	no	—
162	C₂×#120	—	2	2	no	—
163	C₂×#120	—	2	1	no	—
164	C₂×#107	—	38	1	no	—
165	C₂×#102	—	38	2	no	—
166	C₂×#102	—	38	1	no	—
167	#394	—	2	2	no	—
168	#394	—	2	1	no	—
169	#390	C₂×D₁₉	1	2	yes	—
170	#390	C₂×D₁₉	1	1	yes	characteristic
171	#384	—	19	1	no	—
172	#340	—	38	2	no	—
173	#336	—	19	2	no	—
174	#336	—	19	1	no	—
175	C₂×C₁₉	—	8	4	no	—
176	C₂×C₁₉	—	8	2	no	—
177	C₂×C₁₉	#1607	1	2	yes	—
178	C₂×C₁₉	#1613	1	1	yes	characteristic
179	C₂×C₁₉	#1619	1	1	yes	characteristic
180	C₂×C₁₉	#1639	1	2	yes	—
181	C₂×C₁₉	#1659	1	1	yes	characteristic
182	C₂⁵	—	2	1	no	—
183	C₂²×D₄	—	2	1	no	—
184	C₂²×D₄	—	2	2	no	—
185	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
186	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
187	C₂²×C₈	—	38	1	no	—
188	C₂²×C₈	—	38	2	no	—
189	#120	—	4	4	no	—
190	#120	—	4	2	no	—
191	#120	—	4	4	no	—
192	#120	—	4	2	no	—
193	C₂×C₄⋊C₄	—	38	2	no	—
194	C₂×C₄⋊C₄	—	38	1	no	—
195	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
196	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
197	C₂×C₂²⋊C₄	—	2	2	no	—
198	C₂×C₂²⋊C₄	—	2	1	no	—
199	C₂×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
203	#107	—	76	2	no	—
204	#102	—	76	2	no	—
205	#102	—	76	4	no	—
206	#95	—	2	1	no	—
207	C₁₉	#7786	1	1	yes	characteristic, complemented, Sylow
208	C₂⁴	—	2	2	no	—
209	C₂⁴	—	2	1	no	—
210	C₂⁴	—	4	4	no	—
211	C₂⁴	—	4	2	no	—
212	C₂⁴	—	8	1	no	—
213	C₂⁴	—	8	2	no	—
214	C₂⁴	—	8	1	no	—
215	C₂×D₄	—	2	2	no	—
216	C₂×D₄	—	2	1	no	—
217	C₂×D₄	—	4	1	no	—
218	C₂×D₄	—	4	2	no	—
219	C₂×D₄	—	4	2	no	—
220	C₂×D₄	—	4	1	no	—
221	C₂×D₄	—	4	4	no	—
222	C₂×D₄	—	4	4	no	—
223	C₂×D₄	—	4	4	no	—
224	C₂×D₄	—	8	1	no	—
225	C₂×D₄	—	8	2	no	—
226	C₂×D₄	#64525	1	4	yes	—
227	C₂×D₄	#64526	1	2	yes	—
228	C₂²×C₄	—	2	1	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	76	1	no	—
231	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
232	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
233	C₂×C₈	—	38	2	no	—
234	C₂×C₈	—	76	1	no	—
235	C₂×C₈	—	76	1	no	—
236	C₂×C₈	—	76	2	no	—
237	C₂×C₈	—	76	2	no	—
238	C₂×C₈	—	76	2	no	—
239	C₄⋊C₄	—	4	1	no	—
240	C₄⋊C₄	—	4	2	no	—
241	C₄⋊C₄	—	76	1	no	—
242	C₄⋊C₄	—	76	1	no	—
243	C₄⋊C₄	—	76	2	no	—
244	C₄⋊C₄	—	76	2	no	—
245	C₂²⋊C₄	—	4	4	no	—
246	C₂²⋊C₄	—	4	2	no	—
247	C₂²⋊C₄	—	4	2	no	—
248	C₂²⋊C₄	—	4	2	no	—
249	C₂²⋊C₄	—	4	2	no	—
250	C₂²⋊C₄	—	4	2	no	—
251	C₂²⋊C₄	—	4	2	no	—
252	C₂²⋊C₄	—	4	2	no	—
253	C₄²	—	4	1	no	—
254	C₂³	—	2	4	no	—
255	C₂³	—	2	2	no	—
256	C₂³	—	4	2	no	—
257	C₂³	—	4	2	no	—
258	C₂³	—	4	2	no	—
259	C₂³	—	4	1	no	—
260	C₂³	—	4	2	no	—
261	C₂³	—	4	2	no	—
262	C₂³	—	4	2	no	—
263	C₂³	—	4	2	no	—
264	C₂³	—	4	2	no	—
265	C₂³	—	4	1	no	—
266	C₂³	—	8	4	no	—
267	C₂³	—	8	8	no	—
268	C₂³	—	8	8	no	—
269	C₂³	—	8	4	no	—
270	C₂³	—	8	4	no	—
271	C₂³	#10597399	1	1	yes	characteristic
272	D₄	—	4	4	no	—
273	D₄	—	4	2	no	—
274	D₄	—	8	2	no	—
275	D₄	—	8	1	no	—
276	D₄	—	8	4	no	—
277	D₄	—	8	8	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	4	2	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	1	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	152	2	no	—
288	C₂×C₄	—	152	1	no	—
289	C₂×C₄	C₂×#64525	1	2	yes	—
290	C₂×C₄	#10597378	1	2	yes	—
291	C₂×C₄	#10597378	1	1	yes	characteristic
292	C₂×C₄	C₂×#64526	1	1	yes	characteristic
293	C₈	—	76	2	no	—
294	C₈	—	152	2	no	—
295	C₂²	—	4	4	no	—
296	C₂²	—	4	2	no	—
297	C₂²	—	4	4	no	—
298	C₂²	—	4	4	no	—
299	C₂²	—	4	4	no	—
300	C₂²	—	8	16	no	—
301	C₂²	—	8	2	no	—
302	C₂²	—	8	2	no	—
303	C₂²	—	8	2	no	—
304	C₂²	—	8	1	no	—
305	C₂²	—	8	2	no	—
306	C₂²	—	8	1	no	—
307	C₂²	—	8	2	no	—
308	C₂²	#11926678	1	2	yes	—
309	C₂²	#11926695	1	1	yes	characteristic
310	C₂²	#11926712	1	1	yes	characteristic
311	C₂²	#11926722	1	2	yes	—
312	C₂²	#11926734	1	1	yes	characteristic
313	C₄	—	2	2	no	—
314	C₄	—	2	2	no	—
315	C₄	—	2	1	no	—
316	C₄	—	2	1	no	—
317	C₄	—	8	1	no	—
318	C₄	—	8	2	no	—
319	C₄	—	304	1	no	—
320	C₂	—	8	4	no	—
321	C₂	—	8	2	no	—
322	C₂	#14562621	1	2	yes	—
323	C₂	#14562655	1	1	yes	characteristic
324	C₂	#14562689	1	1	yes	characteristic
325	C₂	#14562814	1	2	yes	—
326	C₂	#14562941	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565163

C₂

yes

maximal, characteristic, complemented

#14565038

C₂

yes

maximal, complemented

#14561456

C₂

yes

maximal, complemented

#14561456

C₂

yes

maximal, characteristic, complemented

C₁₉×#2679

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

characteristic, complemented

#11926306

—

#11926299

C₂²

yes

characteristic, complemented

#11926299

C₂²

yes

complemented

C₂×C₁₉×#120

—

C₂×C₁₉×#120

—

C₁₉×#394

—

C₁₉×#394

—

C₁₉×#390

C₂²

yes

characteristic

C₁₉×#390

C₂²

yes

—

C₂⁵×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₁₉×#120

—

C₁₉×#120

—

C₁₉×#120

—

C₁₉×#120

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

#10597289

—

#10597289

—

#10597264

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

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

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₈

yes

—

C₂×D₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊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

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7786

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

100

C₂³×C₁₉

—

101

C₂³×C₁₉

—

102

C₂³×C₁₉

—

103

C₂³×C₁₉

—

104

C₂³×C₁₉

—

105

C₂³×C₁₉

—

106

C₂³×C₁₉

—

107

C₂³×C₁₉

—

108

C₂³×C₁₉

#120

yes

characteristic

109

D₄×C₁₉

—

110

D₄×C₁₉

—

111

D₄×C₁₉

—

112

D₄×C₁₉

—

113

D₄×C₁₉

—

114

D₄×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

—

122

C₂×C₄×C₁₉

—

123

C₂×C₄×C₁₉

—

124

C₂×C₄×C₁₉

C₂×D₈

yes

—

125

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

126

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

127

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

128

C₂×Dic₁₉

—

129

C₂×Dic₁₉

—

130

C₁₉⋊C₈

—

131

C₁₉⋊C₈

—

132

#2679

D₁₉

yes

characteristic

133

#2093

—

134

#2071

—

135

#1270

—

136

#1270

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

—

139

C₂²×C₁₉

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

—

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

#447

yes

—

151

C₂²×C₁₉

#450

yes

characteristic

152

C₂²×C₁₉

#453

yes

characteristic

153

C₂²×C₁₉

#455

yes

—

154

C₂²×C₁₉

#458

yes

characteristic

155

C₄×C₁₉

—

156

C₄×C₁₉

—

157

C₄×C₁₉

—

158

C₄×C₁₉

—

159

C₄×C₁₉

—

160

C₄×C₁₉

—

161

Dic₁₉

—

162

C₂×#120

—

163

C₂×#120

—

164

C₂×#107

—

165

C₂×#102

—

166

C₂×#102

—

167

#394

—

168

#394

—

169

#390

C₂×D₁₉

yes

—

170

#390

C₂×D₁₉

yes

characteristic

171

#384

—

172

#340

—

173

#336

—

174

#336

—

175

C₂×C₁₉

—

176

C₂×C₁₉

—

177

C₂×C₁₉

#1607

yes

—

178

C₂×C₁₉

#1613

yes

characteristic

179

C₂×C₁₉

#1619

yes

characteristic

180

C₂×C₁₉

#1639

yes

—

181

C₂×C₁₉

#1659

yes

characteristic

182

C₂⁵

—

183

C₂²×D₄

—

184

C₂²×D₄

—

185

C₂²×D₄

C₂²⋊D₁₉

yes

—

186

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

187

C₂²×C₈

—

188

C₂²×C₈

—

189

#120

—

190

#120

—

191

#120

—

192

#120

—

193

C₂×C₄⋊C₄

—

194

C₂×C₄⋊C₄

—

195

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

196

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

197

C₂×C₂²⋊C₄

—

198

C₂×C₂²⋊C₄

—

199

C₂×C₂²⋊C₄

—

200

C₂×C₂²⋊C₄

—

201

C₂×C₂²⋊C₄

—

202

C₂×C₄²

C₂²×D₁₉

yes

characteristic

203

#107

—

204

#102

—

205

#102

—

206

#95

—

207

C₁₉

#7786

yes

characteristic, complemented, Sylow

208

C₂⁴

—

209

C₂⁴

—

210

C₂⁴

—

211

C₂⁴

—

212

C₂⁴

—

213

C₂⁴

—

214

C₂⁴

—

215

C₂×D₄

—

216

C₂×D₄

—

217

C₂×D₄

—

218

C₂×D₄

—

219

C₂×D₄

—

220

C₂×D₄

—

221

C₂×D₄

—

222

C₂×D₄

—

223

C₂×D₄

—

224

C₂×D₄

—

225

C₂×D₄

—

226

C₂×D₄

#64525

yes

—

227

C₂×D₄

#64526

yes

—

228

C₂²×C₄

—

229

C₂²×C₄

—

230

C₂²×C₄

—

231

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

232

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

233

C₂×C₈

—

234

C₂×C₈

—

235

C₂×C₈

—

236

C₂×C₈

—

237

C₂×C₈

—

238

C₂×C₈

—

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

C₂²⋊C₄

—

249

C₂²⋊C₄

—

250

C₂²⋊C₄

—

251

C₂²⋊C₄

—

252

C₂²⋊C₄

—

253

C₄²

—

254

C₂³

—

255

C₂³

—

256

C₂³

—

257

C₂³

—

258

C₂³

—

259

C₂³

—

260

C₂³

—

261

C₂³

—

262

C₂³

—

263

C₂³

—

264

C₂³

—

265

C₂³

—

266

C₂³

—

267

C₂³

—

268

C₂³

—

269

C₂³

—

270

C₂³

—

271

C₂³

#10597399

yes

characteristic

272

D₄

—

273

D₄

—

274

D₄

—

275

D₄

—

276

D₄

—

277

D₄

—

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

—

152

—

289

C₂×C₄

C₂×#64525

yes

—

290

C₂×C₄

#10597378

yes

—

291

C₂×C₄

#10597378

yes

characteristic

292

C₂×C₄

C₂×#64526

yes

characteristic

293

C₈

—

294

C₈

—

152

—

295

C₂²

—

296

C₂²

—

297

C₂²

—

298

C₂²

—

299

C₂²

—

300

C₂²

—

301

C₂²

—

302

C₂²

—

303

C₂²

—

304

C₂²

—

305

C₂²

—

306

C₂²

—

307

C₂²

—

308

C₂²

#11926678

yes

—

309

C₂²

#11926695

yes

characteristic

310

C₂²

#11926712

yes

characteristic

311

C₂²

#11926722

yes

—

312

C₂²

#11926734

yes

characteristic

313

C₄

—

314

C₄

—

315

C₄

—

316

C₄

—

317

C₄

—

318

C₄

—

319

C₄

—

304

—

320

C₂

—

321

C₂

—

322

C₂

#14562621

yes

—

323

C₂

#14562655

yes

characteristic

324

C₂

#14562689

yes

characteristic

325

C₂

#14562814

yes

—

326

C₂

#14562941

yes

characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#2679	C₂
socle	C₂³×C₁₉	#120
hypercenter	#2679	D₁₉
hypocenter	C₁₉	#7786
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2679

subgroup

G/H

center

C₂³

#10597399

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#2679

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2679

N	H ≅ G/N	type
1. #14565163	C₂	semidirect
2. #14565038	C₂	semidirect
3. #14561456	C₂	semidirect
4. #14561456	C₂	semidirect
9. #11926414	C₂²	semidirect
11. #11926299	C₂²	semidirect
12. #11926299	C₂²	semidirect
207. C₁₉	#7786	semidirect

H ≅ G/N

type

1. #14565163

C₂

semidirect

2. #14565038

C₂

semidirect

3. #14561456

C₂

semidirect

4. #14561456

C₂

semidirect

9. #11926414

C₂²

semidirect

11. #11926299

C₂²

semidirect

12. #11926299

C₂²

semidirect

207. C₁₉

#7786

semidirect

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

subgroup	index
#14565163	2
#14565038	2
#14561456	2
C₁₉×#2679	2
#7786	19

subgroup

index

C₁₉×#2679

Subgroups — #18071562

Conjugacy classes of subgroups

Complements

Maximal subgroups