Group #18074257 — subgroups

Subgroups — #18074257

Order 4864.

802 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 151 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	#14562303	C₂	1	2	yes	maximal
3	#14562064	C₂	1	2	yes	maximal, complemented
4	#14561959	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#559	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	#11926288	—	2	4	no	—
11	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
12	#11926270	—	2	2	no	—
13	C₁₉×#559	—	2	4	no	—
14	C₁₉×#559	—	2	4	no	—
15	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#124	—	2	1	no	—
17	C₂×C₁₉×#124	C₄	1	2	yes	—
18	C₂×C₁₉×#123	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
23	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	—	2	1	no	—
27	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₉	—	2	2	no	—
29	C₁₉×#127	—	2	2	no	—
30	C₁₉×#127	D₄	1	4	yes	—
31	C₁₉×#124	—	2	8	no	—
32	C₁₉×#124	—	2	4	no	—
33	C₁₉×#124	—	2	4	no	—
34	C₁₉×#123	—	2	16	no	—
35	C₄×Q₈×C₁₉	—	2	2	no	—
36	C₄×Q₈×C₁₉	—	2	2	no	—
37	C₄×Q₈×C₁₉	—	2	2	no	—
38	C₄×Q₈×C₁₉	D₄	1	4	yes	—
39	C₄×D₄×C₁₉	—	2	8	no	—
40	C₄×D₄×C₁₉	—	2	4	no	—
41	C₄×D₄×C₁₉	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄²×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	2	no	—
60	C₂×Q₈×C₁₉	—	2	1	no	—
61	C₂×Q₈×C₁₉	—	2	2	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	—	4	2	no	—
66	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
67	C₂×D₄×C₁₉	—	2	2	no	—
68	C₂×D₄×C₁₉	—	2	4	no	—
69	C₂×D₄×C₁₉	—	2	4	no	—
70	C₂×D₄×C₁₉	—	4	4	no	—
71	C₂×D₄×C₁₉	—	4	2	no	—
72	C₂×D₄×C₁₉	—	4	1	no	—
73	C₂×D₄×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	—	8	2	no	—
75	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	8	no	—
79	C₂²×C₄×C₁₉	—	8	4	no	—
80	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₄⋊C₄×C₁₉	—	2	4	no	—
87	C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₄⋊C₄×C₁₉	—	2	4	no	—
89	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
90	C₂²⋊C₄×C₁₉	—	2	8	no	—
91	C₂²⋊C₄×C₁₉	—	2	8	no	—
92	C₂²⋊C₄×C₁₉	—	2	8	no	—
93	C₄²×C₁₉	—	2	2	no	—
94	C₄²×C₁₉	—	2	2	no	—
95	C₄²×C₁₉	—	2	4	no	—
96	C₄²×C₁₉	C₂×D₄	1	2	yes	—
97	C₄²×C₁₉	C₂×D₄	1	2	yes	—
98	#64520	—	4	2	no	—
99	#64520	—	4	2	no	—
100	C₂×C₁₉⋊C₈	—	4	2	no	—
101	C₂×C₁₉⋊C₈	—	4	2	no	—
102	#8386	—	19	1	no	maximal, Sylow
103	C₂³×C₁₉	—	2	4	no	—
104	C₂³×C₁₉	—	4	4	no	—
105	C₂³×C₁₉	—	4	4	no	—
106	C₂³×C₁₉	—	4	2	no	—
107	C₂³×C₁₉	—	4	2	no	—
108	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	Q₈×C₁₉	—	2	4	no	—
110	Q₈×C₁₉	—	4	2	no	—
111	Q₈×C₁₉	—	4	2	no	—
112	Q₈×C₁₉	—	4	2	no	—
113	D₄×C₁₉	—	4	4	no	—
114	D₄×C₁₉	—	4	4	no	—
115	D₄×C₁₉	—	4	4	no	—
116	D₄×C₁₉	—	4	4	no	—
117	D₄×C₁₉	—	8	4	no	—
118	C₂×C₄×C₁₉	—	2	2	no	—
119	C₂×C₄×C₁₉	—	2	2	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	4	1	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	—	8	8	no	—
130	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#120	1	2	yes	—
133	C₂×C₄×C₁₉	#120	1	2	yes	—
134	C₂×C₄×C₁₉	#135	1	2	yes	—
135	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
137	C₁₉⋊C₈	—	8	2	no	—
138	C₁₉⋊C₈	—	8	2	no	—
139	C₂×#559	D₁₉	1	1	yes	characteristic
140	#1801	—	19	1	no	—
141	#1545	—	19	2	no	—
142	#1487	—	19	2	no	—
143	#1461	—	19	1	no	—
144	C₂²×C₁₉	—	2	1	no	—
145	C₂²×C₁₉	—	2	1	no	—
146	C₂²×C₁₉	—	4	4	no	—
147	C₂²×C₁₉	—	4	4	no	—
148	C₂²×C₁₉	—	4	4	no	—
149	C₂²×C₁₉	—	8	4	no	—
150	C₂²×C₁₉	—	8	4	no	—
151	C₂²×C₁₉	#379	1	1	yes	characteristic
152	C₂²×C₁₉	#416	1	1	yes	characteristic
153	C₂²×C₁₉	#417	1	1	yes	characteristic
154	C₄×C₁₉	—	2	2	no	—
155	C₄×C₁₉	—	2	1	no	—
156	C₄×C₁₉	—	4	2	no	—
157	C₄×C₁₉	—	4	2	no	—
158	C₄×C₁₉	—	4	2	no	—
159	C₄×C₁₉	—	4	2	no	—
160	C₄×C₁₉	#413	1	2	yes	—
161	C₄×C₁₉	#449	1	2	yes	—
162	C₄×C₁₉	#452	1	2	yes	—
163	#559	—	2	4	no	—
164	#559	—	2	4	no	—
165	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
166	C₂×#124	—	2	1	no	—
167	C₂×#124	Dic₁₉	1	2	yes	—
168	C₂×#123	—	2	2	no	—
169	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
170	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
171	C₂×C₄×D₄	—	2	1	no	—
172	C₂×C₄×D₄	Dic₁₉	1	2	yes	—
173	#431	—	19	2	no	—
174	#423	—	19	2	no	—
175	C₂×#101	—	38	1	no	—
176	#343	—	38	1	no	—
177	#331	—	38	4	no	—
178	Q₈⋊C₈	—	38	4	no	—
179	#324	—	38	2	no	—
180	C₂×C₁₉	—	2	1	no	—
181	C₂×C₁₉	—	2	1	no	—
182	C₂×C₁₉	—	8	4	no	—
183	C₂×C₁₉	#1785	1	1	yes	characteristic
184	C₂×C₁₉	#1788	1	1	yes	characteristic
185	C₂×C₁₉	#1795	1	1	yes	characteristic
186	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
187	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
188	C₂²×D₄	—	2	1	no	—
189	C₂²×D₄	—	2	1	no	—
190	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
191	C₂³×C₄	—	2	2	no	—
192	C₂×M₁₆	—	38	2	no	—
193	#127	—	2	2	no	—
194	#127	C₂²⋊D₁₉	1	4	yes	—
195	#124	—	2	8	no	—
196	#124	—	2	4	no	—
197	#124	—	2	4	no	—
198	#123	—	2	16	no	—
199	C₄×Q₈	—	2	2	no	—
200	C₄×Q₈	—	2	2	no	—
201	C₄×Q₈	—	2	2	no	—
202	C₄×Q₈	C₂²⋊D₁₉	1	4	yes	—
203	C₄×D₄	—	2	8	no	—
204	C₄×D₄	—	2	4	no	—
205	C₄×D₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	2	1	no	—
207	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
210	C₂×C₂²⋊C₄	—	2	2	no	—
211	C₂×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₂²⋊C₄	—	2	2	no	—
213	C₂×C₄²	—	2	1	no	—
214	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
215	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
216	C₄⋊C₈	—	38	2	no	—
217	C₄⋊C₈	—	38	2	no	—
218	C₄⋊C₈	—	38	2	no	—
219	#101	—	76	2	no	—
220	C₂²⋊C₈	—	38	2	no	—
221	C₄×C₈	—	38	2	no	—
222	C₁₉	#8386	1	1	yes	characteristic, complemented, Sylow
223	C₂⁴	—	2	2	no	—
224	C₂×Q₈	—	2	1	no	—
225	C₂×Q₈	—	2	2	no	—
226	C₂×Q₈	—	2	1	no	—
227	C₂×Q₈	—	2	1	no	—
228	C₂×Q₈	—	2	2	no	—
229	C₂×Q₈	—	4	2	no	—
230	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
231	C₂×D₄	—	2	2	no	—
232	C₂×D₄	—	2	4	no	—
233	C₂×D₄	—	2	4	no	—
234	C₂×D₄	—	4	4	no	—
235	C₂×D₄	—	4	1	no	—
236	C₂×D₄	—	4	2	no	—
237	C₂×D₄	—	4	1	no	—
238	C₂×D₄	—	8	2	no	—
239	C₂×D₄	C₂²⋊Dic₁₉	1	4	yes	—
240	C₂²×C₄	—	2	1	no	—
241	C₂²×C₄	—	2	1	no	—
242	C₂²×C₄	—	2	8	no	—
243	C₂²×C₄	—	8	4	no	—
244	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
245	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
246	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
247	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
248	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
249	M₁₆	—	76	2	no	—
250	M₁₆	—	76	2	no	—
251	C₂×C₈	—	76	2	no	—
252	C₂×C₈	—	76	2	no	—
253	C₄⋊C₄	—	2	1	no	—
254	C₄⋊C₄	—	2	4	no	—
255	C₄⋊C₄	—	2	2	no	—
256	C₄⋊C₄	—	2	4	no	—
257	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
258	C₂²⋊C₄	—	2	8	no	—
259	C₂²⋊C₄	—	2	8	no	—
260	C₂²⋊C₄	—	2	8	no	—
261	C₄²	—	2	2	no	—
262	C₄²	—	2	2	no	—
263	C₄²	—	2	4	no	—
264	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
265	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
266	C₂³	—	2	4	no	—
267	C₂³	—	4	4	no	—
268	C₂³	—	4	4	no	—
269	C₂³	—	4	2	no	—
270	C₂³	—	4	2	no	—
271	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
272	Q₈	—	2	4	no	—
273	Q₈	—	4	2	no	—
274	Q₈	—	4	2	no	—
275	Q₈	—	4	2	no	—
276	D₄	—	4	4	no	—
277	D₄	—	4	4	no	—
278	D₄	—	4	4	no	—
279	D₄	—	4	4	no	—
280	D₄	—	8	4	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	4	1	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	8	8	no	—
293	C₂×C₄	#10597395	1	1	yes	characteristic
294	C₂×C₄	#10597396	1	2	yes	—
295	C₂×C₄	#10597397	1	1	yes	characteristic
296	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
297	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
298	C₂×C₄	#10597399	1	2	yes	—
299	C₂×C₄	#10597399	1	2	yes	—
300	C₈	—	152	2	no	—
301	C₈	—	152	2	no	—
302	C₂²	—	2	1	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	4	4	no	—
305	C₂²	—	4	4	no	—
306	C₂²	—	4	4	no	—
307	C₂²	—	8	4	no	—
308	C₂²	—	8	4	no	—
309	C₂²	#11926400	1	1	yes	characteristic
310	C₂²	#11926540	1	1	yes	characteristic
311	C₂²	#11926545	1	1	yes	characteristic
312	C₄	—	2	2	no	—
313	C₄	—	2	1	no	—
314	C₄	—	4	2	no	—
315	C₄	—	4	2	no	—
316	C₄	—	4	2	no	—
317	C₄	—	4	2	no	—
318	C₄	#11926528	1	2	yes	—
319	C₄	#11926689	1	2	yes	—
320	C₄	#11926706	1	2	yes	—
321	C₂	—	2	1	no	—
322	C₂	—	2	1	no	—
323	C₂	—	8	4	no	—
324	C₂	#14563563	1	1	yes	characteristic
325	C₂	#14563575	1	1	yes	characteristic
326	C₂	#14563605	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563631

C₂

yes

maximal, characteristic, complemented

#14562303

C₂

yes

maximal

#14562064

C₂

yes

maximal, complemented

#14561959

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#559

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597293

—

#11926313

—

#11926288

—

Q₈⋊(C₁₉⋊C₈)

—

#11926270

—

C₁₉×#559

—

C₁₉×#559

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×#124

—

C₂×C₁₉×#124

C₄

yes

—

C₂×C₁₉×#123

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

—

C₂×C₄×D₄×C₁₉

C₄

yes

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₁₉×#127

—

C₁₉×#127

D₄

yes

—

C₁₉×#124

—

C₁₉×#124

—

C₁₉×#124

—

C₁₉×#123

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

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×C₂²⋊C₄×C₁₉

—

C₂×C₄²×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×Q₈×C₁₉

C₂²⋊C₄

yes

—

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

C₂²⋊C₄

yes

—

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

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64520

—

#64520

—

100

C₂×C₁₉⋊C₈

—

101

C₂×C₁₉⋊C₈

—

102

#8386

—

maximal, Sylow

103

C₂³×C₁₉

—

104

C₂³×C₁₉

—

105

C₂³×C₁₉

—

106

C₂³×C₁₉

—

107

C₂³×C₁₉

—

108

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

109

Q₈×C₁₉

—

110

Q₈×C₁₉

—

111

Q₈×C₁₉

—

112

Q₈×C₁₉

—

113

D₄×C₁₉

—

114

D₄×C₁₉

—

115

D₄×C₁₉

—

116

D₄×C₁₉

—

117

D₄×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

—

130

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

131

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

132

C₂×C₄×C₁₉

#120

yes

—

133

C₂×C₄×C₁₉

#120

yes

—

134

C₂×C₄×C₁₉

#135

yes

—

135

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

136

C₂×C₄×C₁₉

#137

yes

characteristic

137

C₁₉⋊C₈

—

138

C₁₉⋊C₈

—

139

C₂×#559

D₁₉

yes

characteristic

140

#1801

—

141

#1545

—

142

#1487

—

143

#1461

—

144

C₂²×C₁₉

—

145

C₂²×C₁₉

—

146

C₂²×C₁₉

—

147

C₂²×C₁₉

—

148

C₂²×C₁₉

—

149

C₂²×C₁₉

—

150

C₂²×C₁₉

—

151

C₂²×C₁₉

#379

yes

characteristic

152

C₂²×C₁₉

#416

yes

characteristic

153

C₂²×C₁₉

#417

yes

characteristic

154

C₄×C₁₉

—

155

C₄×C₁₉

—

156

C₄×C₁₉

—

157

C₄×C₁₉

—

158

C₄×C₁₉

—

159

C₄×C₁₉

—

160

C₄×C₁₉

#413

yes

—

161

C₄×C₁₉

#449

yes

—

162

C₄×C₁₉

#452

yes

—

163

#559

—

164

#559

—

165

C₂×#127

C₂×D₁₉

yes

characteristic

166

C₂×#124

—

167

C₂×#124

Dic₁₉

yes

—

168

C₂×#123

—

169

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

170

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

171

C₂×C₄×D₄

—

172

C₂×C₄×D₄

Dic₁₉

yes

—

173

#431

—

174

#423

—

175

C₂×#101

—

176

#343

—

177

#331

—

178

Q₈⋊C₈

—

179

#324

—

180

C₂×C₁₉

—

181

C₂×C₁₉

—

182

C₂×C₁₉

—

183

C₂×C₁₉

#1785

yes

characteristic

184

C₂×C₁₉

#1788

yes

characteristic

185

C₂×C₁₉

#1795

yes

characteristic

186

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

187

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

188

C₂²×D₄

—

189

C₂²×D₄

—

190

C₂²×D₄

C₂×Dic₁₉

yes

—

191

C₂³×C₄

—

192

C₂×M₁₆

—

193

#127

—

194

#127

C₂²⋊D₁₉

yes

—

195

#124

—

196

#124

—

197

#124

—

198

#123

—

199

C₄×Q₈

—

200

C₄×Q₈

—

201

C₄×Q₈

—

202

C₄×Q₈

C₂²⋊D₁₉

yes

—

203

C₄×D₄

—

204

C₄×D₄

—

205

C₄×D₄

—

206

C₂×C₄⋊C₄

—

207

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

208

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

209

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

210

C₂×C₂²⋊C₄

—

211

C₂×C₂²⋊C₄

—

212

C₂×C₂²⋊C₄

—

213

C₂×C₄²

—

214

C₂×C₄²

C₂×Dic₁₉

yes

—

215

C₂×C₄²

C₂²×D₁₉

yes

characteristic

216

C₄⋊C₈

—

217

C₄⋊C₈

—

218

C₄⋊C₈

—

219

#101

—

220

C₂²⋊C₈

—

221

C₄×C₈

—

222

C₁₉

#8386

yes

characteristic, complemented, Sylow

223

C₂⁴

—

224

C₂×Q₈

—

225

C₂×Q₈

—

226

C₂×Q₈

—

227

C₂×Q₈

—

228

C₂×Q₈

—

229

C₂×Q₈

—

230

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

231

C₂×D₄

—

232

C₂×D₄

—

233

C₂×D₄

—

234

C₂×D₄

—

235

C₂×D₄

—

236

C₂×D₄

—

237

C₂×D₄

—

238

C₂×D₄

—

239

C₂×D₄

C₂²⋊Dic₁₉

yes

—

240

C₂²×C₄

—

241

C₂²×C₄

—

242

C₂²×C₄

—

243

C₂²×C₄

—

244

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

245

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

246

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

247

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

248

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

249

M₁₆

—

250

M₁₆

—

251

C₂×C₈

—

252

C₂×C₈

—

253

C₄⋊C₄

—

254

C₄⋊C₄

—

255

C₄⋊C₄

—

256

C₄⋊C₄

—

257

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

258

C₂²⋊C₄

—

259

C₂²⋊C₄

—

260

C₂²⋊C₄

—

261

C₄²

—

262

C₄²

—

263

C₄²

—

264

C₄²

C₂×C₂²⋊D₁₉

yes

—

265

C₄²

C₂×C₂²⋊D₁₉

yes

—

266

C₂³

—

267

C₂³

—

268

C₂³

—

269

C₂³

—

270

C₂³

—

271

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

272

Q₈

—

273

Q₈

—

274

Q₈

—

275

Q₈

—

276

D₄

—

277

D₄

—

278

D₄

—

279

D₄

—

280

D₄

—

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

#10597395

yes

characteristic

294

C₂×C₄

#10597396

yes

—

295

C₂×C₄

#10597397

yes

characteristic

296

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

297

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

298

C₂×C₄

#10597399

yes

—

299

C₂×C₄

#10597399

yes

—

300

C₈

—

152

—

301

C₈

—

152

—

302

C₂²

—

303

C₂²

—

304

C₂²

—

305

C₂²

—

306

C₂²

—

307

C₂²

—

308

C₂²

—

309

C₂²

#11926400

yes

characteristic

310

C₂²

#11926540

yes

characteristic

311

C₂²

#11926545

yes

characteristic

312

C₄

—

313

C₄

—

314

C₄

—

315

C₄

—

316

C₄

—

317

C₄

—

318

C₄

#11926528

yes

—

319

C₄

#11926689

yes

—

320

C₄

#11926706

yes

—

321

C₂

—

322

C₂

—

323

C₂

—

324

C₂

#14563563

yes

characteristic

325

C₂

#14563575

yes

characteristic

326

C₂

#14563605

yes

characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#559	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#559	D₁₉
hypocenter	C₁₉	#8386
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#559

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#559

C₂

socle

C₂²×C₁₉

#379

prime radical

C₂×C₁₉×#127

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#559

N	H ≅ G/N	type
1. #14563631	C₂	semidirect
3. #14562064	C₂	semidirect
4. #14561959	C₂	semidirect
222. C₁₉	#8386	semidirect

H ≅ G/N

type

1. #14563631

C₂

semidirect

3. #14562064

C₂

semidirect

4. #14561959

C₂

semidirect

222. C₁₉

#8386

semidirect

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

subgroup	index
#14563631	2
#14562303	2
#14562064	2
#14561959	2
C₂×C₁₉×#559	2
#8386	19

subgroup

index

C₂×C₁₉×#559

Subgroups — #18074257

Conjugacy classes of subgroups

Complements

Maximal subgroups