Group #18074317 — subgroups

Subgroups — #18074317

Order 4864.

782 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 159 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	#14563631	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562320	C₂	1	2	yes	maximal, complemented
3	#14562060	C₂	1	2	yes	maximal
4	#14561959	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#554	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	#11926568	C₂²	1	2	yes	—
8	C₂×#10597293	—	2	1	no	—
9	#11926313	—	2	1	no	—
10	#11926290	—	2	4	no	—
11	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
12	#11926270	—	2	2	no	—
13	C₁₉×#554	—	2	4	no	—
14	C₁₉×#554	—	2	4	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#125	C₄	1	2	yes	—
17	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₂²×Q₈×C₁₉	—	2	1	no	—
24	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	—	2	2	no	—
28	C₁₉×C₄⋊Q₈	—	2	2	no	—
29	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
30	C₁₉×#125	—	2	4	no	—
31	C₁₉×#125	—	2	4	no	—
32	C₁₉×C₂²⋊Q₈	—	2	8	no	—
33	C₁₉×C₂²⋊Q₈	—	2	16	no	—
34	C₄×Q₈×C₁₉	—	2	2	no	—
35	C₄×Q₈×C₁₉	—	2	2	no	—
36	C₄×D₄×C₁₉	—	2	4	no	—
37	C₄×D₄×C₁₉	—	2	4	no	—
38	C₄×D₄×C₁₉	—	2	2	no	—
39	C₄×D₄×C₁₉	D₄	1	4	yes	—
40	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×#64520	—	2	2	no	—
53	#10597293	—	4	2	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
55	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
56	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄×C₁₉⋊C₈	—	2	2	no	—
59	C₂⁴×C₁₉	—	2	1	no	—
60	C₂×Q₈×C₁₉	—	2	2	no	—
61	C₂×Q₈×C₁₉	—	2	4	no	—
62	C₂×Q₈×C₁₉	—	2	2	no	—
63	C₂×Q₈×C₁₉	—	2	1	no	—
64	C₂×Q₈×C₁₉	—	2	1	no	—
65	C₂×Q₈×C₁₉	—	8	2	no	—
66	C₂×D₄×C₁₉	—	2	4	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	8	no	—
72	C₂²×C₄×C₁₉	—	2	4	no	—
73	C₂²×C₄×C₁₉	—	4	2	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	8	4	no	—
77	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₄⋊C₄×C₁₉	—	2	8	no	—
83	C₄⋊C₄×C₁₉	—	2	8	no	—
84	C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₄⋊C₄×C₁₉	—	2	4	no	—
88	C₄⋊C₄×C₁₉	—	2	4	no	—
89	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
90	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
91	C₂²⋊C₄×C₁₉	—	2	8	no	—
92	C₂²⋊C₄×C₁₉	—	2	4	no	—
93	C₄²×C₁₉	—	2	2	no	—
94	C₄²×C₁₉	—	2	2	no	—
95	C₄²×C₁₉	C₂×D₄	1	2	yes	—
96	C₄²×C₁₉	C₂×D₄	1	2	yes	—
97	#64520	—	4	2	no	—
98	#64520	—	4	2	no	—
99	C₂×C₁₉⋊C₈	—	4	2	no	—
100	C₂×C₁₉⋊C₈	—	4	2	no	—
101	#8398	—	19	1	no	maximal, Sylow
102	C₂³×C₁₉	—	2	4	no	—
103	C₂³×C₁₉	—	2	2	no	—
104	C₂³×C₁₉	—	4	2	no	—
105	C₂³×C₁₉	—	4	1	no	—
106	C₂³×C₁₉	—	4	1	no	—
107	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	Q₈×C₁₉	—	4	2	no	—
109	Q₈×C₁₉	—	4	2	no	—
110	Q₈×C₁₉	—	8	4	no	—
111	D₄×C₁₉	—	2	4	no	—
112	D₄×C₁₉	—	2	2	no	—
113	D₄×C₁₉	#101	1	4	yes	complemented
114	C₂×C₄×C₁₉	—	2	2	no	—
115	C₂×C₄×C₁₉	—	2	2	no	—
116	C₂×C₄×C₁₉	—	2	2	no	—
117	C₂×C₄×C₁₉	—	2	2	no	—
118	C₂×C₄×C₁₉	—	2	4	no	—
119	C₂×C₄×C₁₉	—	2	2	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	4	1	no	—
122	C₂×C₄×C₁₉	—	4	4	no	—
123	C₂×C₄×C₁₉	—	4	1	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	4	no	—
126	C₂×C₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	8	8	no	—
129	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#120	1	2	yes	—
132	C₂×C₄×C₁₉	#120	1	2	yes	—
133	C₂×C₄×C₁₉	#135	1	2	yes	—
134	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
136	C₁₉⋊C₈	—	8	2	no	—
137	C₁₉⋊C₈	—	8	2	no	—
138	C₂×#554	D₁₉	1	1	yes	characteristic
139	#1801	—	19	1	no	—
140	#1549	—	19	2	no	—
141	#1486	—	19	2	no	—
142	#1461	—	19	1	no	—
143	C₂²×C₁₉	—	2	1	no	—
144	C₂²×C₁₉	—	2	1	no	—
145	C₂²×C₁₉	—	2	4	no	—
146	C₂²×C₁₉	—	4	4	no	—
147	C₂²×C₁₉	—	4	4	no	—
148	C₂²×C₁₉	—	4	2	no	—
149	C₂²×C₁₉	—	4	2	no	—
150	C₂²×C₁₉	#379	1	1	yes	characteristic
151	C₂²×C₁₉	#416	1	1	yes	characteristic
152	C₂²×C₁₉	#417	1	1	yes	characteristic
153	C₄×C₁₉	—	2	2	no	—
154	C₄×C₁₉	—	2	1	no	—
155	C₄×C₁₉	—	4	4	no	—
156	C₄×C₁₉	—	4	2	no	—
157	C₄×C₁₉	—	4	2	no	—
158	C₄×C₁₉	—	4	2	no	—
159	C₄×C₁₉	C₂×#101	1	2	yes	—
160	C₄×C₁₉	#449	1	2	yes	—
161	C₄×C₁₉	#452	1	2	yes	—
162	#554	—	2	4	no	—
163	#554	—	2	4	no	—
164	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
165	C₂×#125	Dic₁₉	1	2	yes	—
166	C₂×C₂²⋊Q₈	—	2	1	no	—
167	C₂×C₂²⋊Q₈	—	2	2	no	—
168	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
169	C₂×C₄×D₄	Dic₁₉	1	2	yes	—
170	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
171	C₂²×C₄⋊C₄	—	2	1	no	—
172	#431	—	19	2	no	—
173	#423	—	19	2	no	—
174	C₂×#101	—	38	1	no	—
175	#343	—	38	1	no	—
176	#332	—	38	4	no	—
177	D₄⋊C₈	—	38	4	no	—
178	#324	—	38	2	no	—
179	C₂×C₁₉	—	2	1	no	—
180	C₂×C₁₉	—	2	1	no	—
181	C₂×C₁₉	—	4	4	no	—
182	C₂×C₁₉	#1784	1	1	yes	characteristic
183	C₂×C₁₉	#1788	1	1	yes	characteristic
184	C₂×C₁₉	#1795	1	1	yes	characteristic
185	C₂²×Q₈	—	2	1	no	—
186	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
187	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
188	C₂³×C₄	—	2	1	no	—
189	C₂³×C₄	—	2	2	no	—
190	C₂×M₁₆	—	38	2	no	—
191	C₄⋊Q₈	—	2	2	no	—
192	C₄⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
193	#125	—	2	4	no	—
194	#125	—	2	4	no	—
195	C₂²⋊Q₈	—	2	8	no	—
196	C₂²⋊Q₈	—	2	16	no	—
197	C₄×Q₈	—	2	2	no	—
198	C₄×Q₈	—	2	2	no	—
199	C₄×D₄	—	2	4	no	—
200	C₄×D₄	—	2	4	no	—
201	C₄×D₄	—	2	2	no	—
202	C₄×D₄	C₂²⋊D₁₉	1	4	yes	—
203	C₂×C₄⋊C₄	—	2	8	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	—	2	1	no	—
207	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
208	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
211	C₂×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₂²⋊C₄	—	2	1	no	—
213	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
214	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
215	C₄⋊C₈	—	38	2	no	—
216	C₄⋊C₈	—	38	2	no	—
217	C₄⋊C₈	—	38	2	no	—
218	#101	—	76	2	no	—
219	C₂²⋊C₈	—	38	2	no	—
220	C₄×C₈	—	38	2	no	—
221	C₁₉	#8398	1	1	yes	characteristic, complemented, Sylow
222	C₂⁴	—	2	1	no	—
223	C₂×Q₈	—	2	1	no	—
224	C₂×Q₈	—	2	2	no	—
225	C₂×Q₈	—	2	1	no	—
226	C₂×Q₈	—	2	2	no	—
227	C₂×Q₈	—	2	4	no	—
228	C₂×Q₈	—	8	2	no	—
229	C₂×D₄	—	2	4	no	—
230	C₂×D₄	—	2	1	no	—
231	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
232	C₂²×C₄	—	2	1	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	8	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	4	1	no	—
237	C₂²×C₄	—	4	2	no	—
238	C₂²×C₄	—	4	1	no	—
239	C₂²×C₄	—	8	4	no	—
240	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
241	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
242	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
243	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
244	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
245	M₁₆	—	76	2	no	—
246	M₁₆	—	76	2	no	—
247	C₂×C₈	—	76	2	no	—
248	C₂×C₈	—	76	2	no	—
249	C₄⋊C₄	—	2	8	no	—
250	C₄⋊C₄	—	2	8	no	—
251	C₄⋊C₄	—	2	1	no	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	2	4	no	—
255	C₄⋊C₄	—	2	4	no	—
256	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
257	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
258	C₂²⋊C₄	—	2	8	no	—
259	C₂²⋊C₄	—	2	4	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
263	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
264	C₂³	—	2	4	no	—
265	C₂³	—	2	2	no	—
266	C₂³	—	4	2	no	—
267	C₂³	—	4	1	no	—
268	C₂³	—	4	1	no	—
269	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
270	Q₈	—	4	2	no	—
271	Q₈	—	4	2	no	—
272	Q₈	—	8	4	no	—
273	D₄	—	2	4	no	—
274	D₄	—	2	2	no	—
275	D₄	#10597293	1	4	yes	complemented
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	4	1	no	—
284	C₂×C₄	—	4	4	no	—
285	C₂×C₄	—	4	1	no	—
286	C₂×C₄	—	4	1	no	—
287	C₂×C₄	—	4	4	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	8	8	no	—
291	C₂×C₄	#10597395	1	1	yes	characteristic
292	C₂×C₄	#10597396	1	2	yes	—
293	C₂×C₄	#10597397	1	1	yes	characteristic
294	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
295	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
296	C₂×C₄	#10597399	1	2	yes	—
297	C₂×C₄	#10597399	1	2	yes	—
298	C₈	—	152	2	no	—
299	C₈	—	152	2	no	—
300	C₂²	—	2	1	no	—
301	C₂²	—	2	1	no	—
302	C₂²	—	2	4	no	—
303	C₂²	—	4	4	no	—
304	C₂²	—	4	4	no	—
305	C₂²	—	4	2	no	—
306	C₂²	—	4	2	no	—
307	C₂²	#11926400	1	1	yes	characteristic
308	C₂²	#11926540	1	1	yes	characteristic
309	C₂²	#11926545	1	1	yes	characteristic
310	C₄	—	2	2	no	—
311	C₄	—	2	1	no	—
312	C₄	—	4	4	no	—
313	C₄	—	4	2	no	—
314	C₄	—	4	2	no	—
315	C₄	—	4	2	no	—
316	C₄	C₂×#10597293	1	2	yes	—
317	C₄	#11926689	1	2	yes	—
318	C₄	#11926706	1	2	yes	—
319	C₂	—	2	1	no	—
320	C₂	—	2	1	no	—
321	C₂	—	4	4	no	—
322	C₂	#14563559	1	1	yes	characteristic
323	C₂	#14563575	1	1	yes	characteristic
324	C₂	#14563605	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563631

C₂

yes

maximal, characteristic, complemented

#14562320

C₂

yes

maximal, complemented

#14562060

C₂

yes

maximal

#14561959

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#554

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597293

—

#11926313

—

#11926290

—

D₄⋊(C₁₉⋊C₈)

—

#11926270

—

C₁₉×#554

—

C₁₉×#554

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#125

C₄

yes

—

C₂×C₁₉×C₂²⋊Q₈

—

C₂×C₁₉×C₂²⋊Q₈

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

C₄

yes

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂²×C₄⋊C₄×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

#10597293

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

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

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

100

C₂×C₁₉⋊C₈

—

101

#8398

—

maximal, Sylow

102

C₂³×C₁₉

—

103

C₂³×C₁₉

—

104

C₂³×C₁₉

—

105

C₂³×C₁₉

—

106

C₂³×C₁₉

—

107

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

108

Q₈×C₁₉

—

109

Q₈×C₁₉

—

110

Q₈×C₁₉

—

111

D₄×C₁₉

—

112

D₄×C₁₉

—

113

D₄×C₁₉

#101

yes

complemented

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

—

122

C₂×C₄×C₁₉

—

123

C₂×C₄×C₁₉

—

124

C₂×C₄×C₁₉

—

125

C₂×C₄×C₁₉

—

126

C₂×C₄×C₁₉

—

127

C₂×C₄×C₁₉

—

128

C₂×C₄×C₁₉

—

129

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

130

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

131

C₂×C₄×C₁₉

#120

yes

—

132

C₂×C₄×C₁₉

#120

yes

—

133

C₂×C₄×C₁₉

#135

yes

—

134

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

135

C₂×C₄×C₁₉

#137

yes

characteristic

136

C₁₉⋊C₈

—

137

C₁₉⋊C₈

—

138

C₂×#554

D₁₉

yes

characteristic

139

#1801

—

140

#1549

—

141

#1486

—

142

#1461

—

143

C₂²×C₁₉

—

144

C₂²×C₁₉

—

145

C₂²×C₁₉

—

146

C₂²×C₁₉

—

147

C₂²×C₁₉

—

148

C₂²×C₁₉

—

149

C₂²×C₁₉

—

150

C₂²×C₁₉

#379

yes

characteristic

151

C₂²×C₁₉

#416

yes

characteristic

152

C₂²×C₁₉

#417

yes

characteristic

153

C₄×C₁₉

—

154

C₄×C₁₉

—

155

C₄×C₁₉

—

156

C₄×C₁₉

—

157

C₄×C₁₉

—

158

C₄×C₁₉

—

159

C₄×C₁₉

C₂×#101

yes

—

160

C₄×C₁₉

#449

yes

—

161

C₄×C₁₉

#452

yes

—

162

#554

—

163

#554

—

164

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

165

C₂×#125

Dic₁₉

yes

—

166

C₂×C₂²⋊Q₈

—

167

C₂×C₂²⋊Q₈

—

168

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

169

C₂×C₄×D₄

Dic₁₉

yes

—

170

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

171

C₂²×C₄⋊C₄

—

172

#431

—

173

#423

—

174

C₂×#101

—

175

#343

—

176

#332

—

177

D₄⋊C₈

—

178

#324

—

179

C₂×C₁₉

—

180

C₂×C₁₉

—

181

C₂×C₁₉

—

182

C₂×C₁₉

#1784

yes

characteristic

183

C₂×C₁₉

#1788

yes

characteristic

184

C₂×C₁₉

#1795

yes

characteristic

185

C₂²×Q₈

—

186

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

187

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

188

C₂³×C₄

—

189

C₂³×C₄

—

190

C₂×M₁₆

—

191

C₄⋊Q₈

—

192

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

193

#125

—

194

#125

—

195

C₂²⋊Q₈

—

196

C₂²⋊Q₈

—

197

C₄×Q₈

—

198

C₄×Q₈

—

199

C₄×D₄

—

200

C₄×D₄

—

201

C₄×D₄

—

202

C₄×D₄

C₂²⋊D₁₉

yes

—

203

C₂×C₄⋊C₄

—

204

C₂×C₄⋊C₄

—

205

C₂×C₄⋊C₄

—

206

C₂×C₄⋊C₄

—

207

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

208

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

209

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

210

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

211

C₂×C₂²⋊C₄

—

212

C₂×C₂²⋊C₄

—

213

C₂×C₄²

C₂×Dic₁₉

yes

—

214

C₂×C₄²

C₂²×D₁₉

yes

characteristic

215

C₄⋊C₈

—

216

C₄⋊C₈

—

217

C₄⋊C₈

—

218

#101

—

219

C₂²⋊C₈

—

220

C₄×C₈

—

221

C₁₉

#8398

yes

characteristic, complemented, Sylow

222

C₂⁴

—

223

C₂×Q₈

—

224

C₂×Q₈

—

225

C₂×Q₈

—

226

C₂×Q₈

—

227

C₂×Q₈

—

228

C₂×Q₈

—

229

C₂×D₄

—

230

C₂×D₄

—

231

C₂×D₄

C₂²⋊Dic₁₉

yes

—

232

C₂²×C₄

—

233

C₂²×C₄

—

234

C₂²×C₄

—

235

C₂²×C₄

—

236

C₂²×C₄

—

237

C₂²×C₄

—

238

C₂²×C₄

—

239

C₂²×C₄

—

240

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

241

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

242

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

243

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

244

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

245

M₁₆

—

246

M₁₆

—

247

C₂×C₈

—

248

C₂×C₈

—

249

C₄⋊C₄

—

250

C₄⋊C₄

—

251

C₄⋊C₄

—

252

C₄⋊C₄

—

253

C₄⋊C₄

—

254

C₄⋊C₄

—

255

C₄⋊C₄

—

256

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

257

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

258

C₂²⋊C₄

—

259

C₂²⋊C₄

—

260

C₄²

—

261

C₄²

—

262

C₄²

C₂×C₂²⋊D₁₉

yes

—

263

C₄²

C₂×C₂²⋊D₁₉

yes

—

264

C₂³

—

265

C₂³

—

266

C₂³

—

267

C₂³

—

268

C₂³

—

269

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

270

Q₈

—

271

Q₈

—

272

Q₈

—

273

D₄

—

274

D₄

—

275

D₄

#10597293

yes

complemented

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

—

288

C₂×C₄

—

289

C₂×C₄

—

290

C₂×C₄

—

291

C₂×C₄

#10597395

yes

characteristic

292

C₂×C₄

#10597396

yes

—

293

C₂×C₄

#10597397

yes

characteristic

294

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

295

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

296

C₂×C₄

#10597399

yes

—

297

C₂×C₄

#10597399

yes

—

298

C₈

—

152

—

299

C₈

—

152

—

300

C₂²

—

301

C₂²

—

302

C₂²

—

303

C₂²

—

304

C₂²

—

305

C₂²

—

306

C₂²

—

307

C₂²

#11926400

yes

characteristic

308

C₂²

#11926540

yes

characteristic

309

C₂²

#11926545

yes

characteristic

310

C₄

—

311

C₄

—

312

C₄

—

313

C₄

—

314

C₄

—

315

C₄

—

316

C₄

C₂×#10597293

yes

—

317

C₄

#11926689

yes

—

318

C₄

#11926706

yes

—

319

C₂

—

320

C₂

—

321

C₂

—

322

C₂

#14563559

yes

characteristic

323

C₂

#14563575

yes

characteristic

324

C₂

#14563605

yes

characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#554	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#554	D₁₉
hypocenter	C₁₉	#8398
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#554

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#554

C₂

socle

C₂²×C₁₉

#379

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#554

N	H ≅ G/N	type
1. #14563631	C₂	semidirect
2. #14562320	C₂	semidirect
4. #14561959	C₂	semidirect
113. D₄×C₁₉	#101	semidirect
221. C₁₉	#8398	semidirect
275. D₄	#10597293	semidirect

H ≅ G/N

type

1. #14563631

C₂

semidirect

2. #14562320

C₂

semidirect

4. #14561959

C₂

semidirect

113. D₄×C₁₉

#101

semidirect

221. C₁₉

#8398

semidirect

275. D₄

#10597293

semidirect

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

subgroup	index
#14563631	2
#14562320	2
#14562060	2
#14561959	2
C₂×C₁₉×#554	2
#8398	19

subgroup

index

C₂×C₁₉×#554

Subgroups — #18074317

Conjugacy classes of subgroups

Complements

Maximal subgroups