Group #18074277 — subgroups

Subgroups — #18074277

Order 4864.

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

normal subgroups only

This group has 706 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
2	#14562307	C₂	1	2	yes	maximal
3	#14562064	C₂	1	2	yes	maximal
4	#14561959	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#557	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	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
12	#11926270	—	2	2	no	—
13	C₁₉×#557	—	2	4	no	—
14	C₁₉×#557	—	2	4	no	—
15	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	—	2	2	no	—
18	C₂×C₁₉×#125	C₄	1	2	yes	—
19	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×Q₈×C₁₉	—	2	1	no	—
24	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
26	C₁₉×C₄⋊Q₈	—	2	8	no	—
27	C₁₉×C₄⋊Q₈	—	2	2	no	—
28	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
29	C₁₉×#125	—	2	16	no	—
30	C₁₉×#125	—	2	4	no	—
31	C₁₉×#125	—	2	4	no	—
32	C₄×Q₈×C₁₉	—	2	8	no	—
33	C₄×Q₈×C₁₉	—	2	4	no	—
34	C₄×Q₈×C₁₉	—	2	4	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	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	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×C₄²×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	C₂×Q₈×C₁₉	—	2	4	no	—
60	C₂×Q₈×C₁₉	—	2	1	no	—
61	C₂×Q₈×C₁₉	—	2	2	no	—
62	C₂×Q₈×C₁₉	—	2	4	no	—
63	C₂×Q₈×C₁₉	—	2	2	no	—
64	C₂×Q₈×C₁₉	—	2	1	no	—
65	C₂×Q₈×C₁₉	—	2	1	no	—
66	C₂×Q₈×C₁₉	—	4	2	no	—
67	C₂×Q₈×C₁₉	—	4	1	no	—
68	C₂×Q₈×C₁₉	—	4	1	no	—
69	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄⋊C₄×C₁₉	—	2	8	no	—
79	C₄⋊C₄×C₁₉	—	2	8	no	—
80	C₄⋊C₄×C₁₉	—	2	8	no	—
81	C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₄⋊C₄×C₁₉	—	2	4	no	—
84	C₄⋊C₄×C₁₉	—	2	4	no	—
85	C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₄⋊C₄×C₁₉	—	2	4	no	—
87	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
88	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
89	C₄²×C₁₉	—	2	8	no	—
90	C₄²×C₁₉	—	2	2	no	—
91	C₄²×C₁₉	—	2	2	no	—
92	C₄²×C₁₉	—	2	4	no	—
93	C₄²×C₁₉	C₂×D₄	1	2	yes	—
94	C₄²×C₁₉	C₂×D₄	1	2	yes	—
95	#64520	—	4	2	no	—
96	#64520	—	4	2	no	—
97	C₂×C₁₉⋊C₈	—	4	2	no	—
98	C₂×C₁₉⋊C₈	—	4	2	no	—
99	#8390	—	19	1	no	maximal, Sylow
100	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	Q₈×C₁₉	—	2	4	no	—
102	Q₈×C₁₉	—	2	2	no	—
103	Q₈×C₁₉	—	4	2	no	—
104	Q₈×C₁₉	—	4	4	no	—
105	Q₈×C₁₉	—	4	2	no	—
106	Q₈×C₁₉	—	4	4	no	—
107	Q₈×C₁₉	#101	1	4	yes	complemented
108	C₂×C₄×C₁₉	—	2	4	no	—
109	C₂×C₄×C₁₉	—	2	2	no	—
110	C₂×C₄×C₁₉	—	2	2	no	—
111	C₂×C₄×C₁₉	—	2	2	no	—
112	C₂×C₄×C₁₉	—	2	2	no	—
113	C₂×C₄×C₁₉	—	2	2	no	—
114	C₂×C₄×C₁₉	—	2	4	no	—
115	C₂×C₄×C₁₉	—	2	2	no	—
116	C₂×C₄×C₁₉	—	2	2	no	—
117	C₂×C₄×C₁₉	—	4	1	no	—
118	C₂×C₄×C₁₉	—	4	2	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₉	#120	1	2	yes	—
125	C₂×C₄×C₁₉	#120	1	2	yes	—
126	C₂×C₄×C₁₉	#135	1	2	yes	—
127	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
128	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
129	C₁₉⋊C₈	—	8	2	no	—
130	C₁₉⋊C₈	—	8	2	no	—
131	C₂×#557	D₁₉	1	1	yes	characteristic
132	#1801	—	19	1	no	—
133	#1546	—	19	2	no	—
134	#1487	—	19	2	no	—
135	#1461	—	19	1	no	—
136	C₂²×C₁₉	—	2	1	no	—
137	C₂²×C₁₉	—	2	1	no	—
138	C₂²×C₁₉	#379	1	1	yes	characteristic
139	C₂²×C₁₉	#416	1	1	yes	characteristic
140	C₂²×C₁₉	#417	1	1	yes	characteristic
141	C₄×C₁₉	—	2	2	no	—
142	C₄×C₁₉	—	2	4	no	—
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	4	2	no	—
145	C₄×C₁₉	—	4	2	no	—
146	C₄×C₁₉	—	4	2	no	—
147	C₄×C₁₉	—	4	4	no	—
148	C₄×C₁₉	C₂×#101	1	2	yes	—
149	C₄×C₁₉	#449	1	2	yes	—
150	C₄×C₁₉	#452	1	2	yes	—
151	#557	—	2	4	no	—
152	#557	—	2	4	no	—
153	C₂×C₄⋊Q₈	—	2	1	no	—
154	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
155	C₂×#125	—	2	2	no	—
156	C₂×#125	Dic₁₉	1	2	yes	—
157	C₂×C₄×Q₈	—	2	1	no	—
158	C₂×C₄×Q₈	Dic₁₉	1	2	yes	—
159	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
160	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
161	#431	—	19	2	no	—
162	#423	—	19	2	no	—
163	C₂×#101	—	38	1	no	—
164	#343	—	38	1	no	—
165	#332	—	38	4	no	—
166	Q₈⋊C₈	—	38	4	no	—
167	#324	—	38	2	no	—
168	C₂×C₁₉	—	2	1	no	—
169	C₂×C₁₉	—	2	1	no	—
170	C₂×C₁₉	#1784	1	1	yes	characteristic
171	C₂×C₁₉	#1788	1	1	yes	characteristic
172	C₂×C₁₉	#1796	1	1	yes	characteristic
173	C₂²×Q₈	—	2	1	no	—
174	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
175	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
176	C₂×M₁₆	—	38	2	no	—
177	C₄⋊Q₈	—	2	8	no	—
178	C₄⋊Q₈	—	2	2	no	—
179	C₄⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
180	#125	—	2	16	no	—
181	#125	—	2	4	no	—
182	#125	—	2	4	no	—
183	C₄×Q₈	—	2	8	no	—
184	C₄×Q₈	—	2	4	no	—
185	C₄×Q₈	—	2	4	no	—
186	C₄×Q₈	—	2	2	no	—
187	C₄×Q₈	—	2	2	no	—
188	C₄×Q₈	—	2	2	no	—
189	C₄×Q₈	C₂²⋊D₁₉	1	4	yes	—
190	C₂×C₄⋊C₄	—	2	2	no	—
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₄⋊C₄	—	2	2	no	—
193	C₂×C₄⋊C₄	—	2	1	no	—
194	C₂×C₄⋊C₄	—	2	1	no	—
195	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
196	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
197	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
198	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
199	C₂×C₄²	—	2	2	no	—
200	C₂×C₄²	—	2	1	no	—
201	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
202	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
203	C₄⋊C₈	—	38	2	no	—
204	C₄⋊C₈	—	38	2	no	—
205	C₄⋊C₈	—	38	2	no	—
206	#101	—	76	2	no	—
207	C₂²⋊C₈	—	38	2	no	—
208	C₄×C₈	—	38	2	no	—
209	C₁₉	#8390	1	1	yes	characteristic, complemented, Sylow
210	C₂×Q₈	—	2	4	no	—
211	C₂×Q₈	—	2	1	no	—
212	C₂×Q₈	—	2	2	no	—
213	C₂×Q₈	—	2	1	no	—
214	C₂×Q₈	—	2	1	no	—
215	C₂×Q₈	—	2	2	no	—
216	C₂×Q₈	—	2	4	no	—
217	C₂×Q₈	—	4	1	no	—
218	C₂×Q₈	—	4	2	no	—
219	C₂×Q₈	—	4	1	no	—
220	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
221	C₂²×C₄	—	2	1	no	—
222	C₂²×C₄	—	2	1	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
225	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
226	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
227	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
228	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
229	M₁₆	—	76	2	no	—
230	M₁₆	—	76	2	no	—
231	C₂×C₈	—	76	2	no	—
232	C₂×C₈	—	76	2	no	—
233	C₄⋊C₄	—	2	8	no	—
234	C₄⋊C₄	—	2	8	no	—
235	C₄⋊C₄	—	2	8	no	—
236	C₄⋊C₄	—	2	1	no	—
237	C₄⋊C₄	—	2	2	no	—
238	C₄⋊C₄	—	2	4	no	—
239	C₄⋊C₄	—	2	4	no	—
240	C₄⋊C₄	—	2	2	no	—
241	C₄⋊C₄	—	2	4	no	—
242	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
243	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
244	C₄²	—	2	8	no	—
245	C₄²	—	2	2	no	—
246	C₄²	—	2	2	no	—
247	C₄²	—	2	4	no	—
248	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
249	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
250	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
251	Q₈	—	2	4	no	—
252	Q₈	—	2	2	no	—
253	Q₈	—	4	2	no	—
254	Q₈	—	4	4	no	—
255	Q₈	—	4	2	no	—
256	Q₈	—	4	4	no	—
257	Q₈	#10597293	1	4	yes	complemented
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	2	no	—
262	C₂×C₄	—	2	2	no	—
263	C₂×C₄	—	2	2	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	2	2	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	4	1	no	—
268	C₂×C₄	—	4	2	no	—
269	C₂×C₄	—	4	2	no	—
270	C₂×C₄	—	4	2	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	#10597395	1	1	yes	characteristic
273	C₂×C₄	#10597396	1	2	yes	—
274	C₂×C₄	#10597397	1	1	yes	characteristic
275	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
276	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
277	C₂×C₄	#10597399	1	2	yes	—
278	C₂×C₄	#10597399	1	2	yes	—
279	C₈	—	152	2	no	—
280	C₈	—	152	2	no	—
281	C₂²	—	2	1	no	—
282	C₂²	—	2	1	no	—
283	C₂²	#11926400	1	1	yes	characteristic
284	C₂²	#11926540	1	1	yes	characteristic
285	C₂²	#11926545	1	1	yes	characteristic
286	C₄	—	2	2	no	—
287	C₄	—	2	4	no	—
288	C₄	—	2	1	no	—
289	C₄	—	4	2	no	—
290	C₄	—	4	2	no	—
291	C₄	—	4	2	no	—
292	C₄	—	4	4	no	—
293	C₄	C₂×#10597293	1	2	yes	—
294	C₄	#11926689	1	2	yes	—
295	C₄	#11926706	1	2	yes	—
296	C₂	—	2	1	no	—
297	C₂	—	2	1	no	—
298	C₂	#14563559	1	1	yes	characteristic
299	C₂	#14563575	1	1	yes	characteristic
300	C₂	#14563610	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563631

C₂

yes

maximal, characteristic

#14562307

C₂

yes

maximal

#14562064

C₂

yes

maximal

#14561959

C₂

yes

maximal, characteristic

C₂×C₁₉×#557

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597293

—

#11926313

—

#11926290

—

Q₈⋊(C₁₉⋊C₈)

—

#11926270

—

C₁₉×#557

—

C₁₉×#557

—

C₂×C₁₉×C₄⋊Q₈

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#125

—

C₂×C₁₉×#125

C₄

yes

—

C₂×C₄×Q₈×C₁₉

—

C₂×C₄×Q₈×C₁₉

C₄

yes

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×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⋊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×C₄²×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

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×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

—

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

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8390

—

maximal, Sylow

100

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

101

Q₈×C₁₉

—

102

Q₈×C₁₉

—

103

Q₈×C₁₉

—

104

Q₈×C₁₉

—

105

Q₈×C₁₉

—

106

Q₈×C₁₉

—

107

Q₈×C₁₉

#101

yes

complemented

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

—

118

C₂×C₄×C₁₉

—

119

C₂×C₄×C₁₉

—

120

C₂×C₄×C₁₉

—

121

C₂×C₄×C₁₉

—

122

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

123

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

124

C₂×C₄×C₁₉

#120

yes

—

125

C₂×C₄×C₁₉

#120

yes

—

126

C₂×C₄×C₁₉

#135

yes

—

127

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

128

C₂×C₄×C₁₉

#137

yes

characteristic

129

C₁₉⋊C₈

—

130

C₁₉⋊C₈

—

131

C₂×#557

D₁₉

yes

characteristic

132

#1801

—

133

#1546

—

134

#1487

—

135

#1461

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

#379

yes

characteristic

139

C₂²×C₁₉

#416

yes

characteristic

140

C₂²×C₁₉

#417

yes

characteristic

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₄×C₁₉

C₂×#101

yes

—

149

C₄×C₁₉

#449

yes

—

150

C₄×C₁₉

#452

yes

—

151

#557

—

152

#557

—

153

C₂×C₄⋊Q₈

—

154

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

155

C₂×#125

—

156

C₂×#125

Dic₁₉

yes

—

157

C₂×C₄×Q₈

—

158

C₂×C₄×Q₈

Dic₁₉

yes

—

159

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

160

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

161

#431

—

162

#423

—

163

C₂×#101

—

164

#343

—

165

#332

—

166

Q₈⋊C₈

—

167

#324

—

168

C₂×C₁₉

—

169

C₂×C₁₉

—

170

C₂×C₁₉

#1784

yes

characteristic

171

C₂×C₁₉

#1788

yes

characteristic

172

C₂×C₁₉

#1796

yes

characteristic

173

C₂²×Q₈

—

174

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

175

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

176

C₂×M₁₆

—

177

C₄⋊Q₈

—

178

C₄⋊Q₈

—

179

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

180

#125

—

181

#125

—

182

#125

—

183

C₄×Q₈

—

184

C₄×Q₈

—

185

C₄×Q₈

—

186

C₄×Q₈

—

187

C₄×Q₈

—

188

C₄×Q₈

—

189

C₄×Q₈

C₂²⋊D₁₉

yes

—

190

C₂×C₄⋊C₄

—

191

C₂×C₄⋊C₄

—

192

C₂×C₄⋊C₄

—

193

C₂×C₄⋊C₄

—

194

C₂×C₄⋊C₄

—

195

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

196

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

197

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

198

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

199

C₂×C₄²

—

200

C₂×C₄²

—

201

C₂×C₄²

C₂×Dic₁₉

yes

—

202

C₂×C₄²

C₂²×D₁₉

yes

characteristic

203

C₄⋊C₈

—

204

C₄⋊C₈

—

205

C₄⋊C₈

—

206

#101

—

207

C₂²⋊C₈

—

208

C₄×C₈

—

209

C₁₉

#8390

yes

characteristic, complemented, Sylow

210

C₂×Q₈

—

211

C₂×Q₈

—

212

C₂×Q₈

—

213

C₂×Q₈

—

214

C₂×Q₈

—

215

C₂×Q₈

—

216

C₂×Q₈

—

217

C₂×Q₈

—

218

C₂×Q₈

—

219

C₂×Q₈

—

220

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

221

C₂²×C₄

—

222

C₂²×C₄

—

223

C₂²×C₄

—

224

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

225

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

226

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

227

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

228

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

229

M₁₆

—

230

M₁₆

—

231

C₂×C₈

—

232

C₂×C₈

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₄⋊C₄

—

239

C₄⋊C₄

—

240

C₄⋊C₄

—

241

C₄⋊C₄

—

242

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

243

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

244

C₄²

—

245

C₄²

—

246

C₄²

—

247

C₄²

—

248

C₄²

C₂×C₂²⋊D₁₉

yes

—

249

C₄²

C₂×C₂²⋊D₁₉

yes

—

250

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

251

Q₈

—

252

Q₈

—

253

Q₈

—

254

Q₈

—

255

Q₈

—

256

Q₈

—

257

Q₈

#10597293

yes

complemented

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

—

267

C₂×C₄

—

268

C₂×C₄

—

269

C₂×C₄

—

270

C₂×C₄

—

271

C₂×C₄

—

272

C₂×C₄

#10597395

yes

characteristic

273

C₂×C₄

#10597396

yes

—

274

C₂×C₄

#10597397

yes

characteristic

275

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

276

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

277

C₂×C₄

#10597399

yes

—

278

C₂×C₄

#10597399

yes

—

279

C₈

—

152

—

280

C₈

—

152

—

281

C₂²

—

282

C₂²

—

283

C₂²

#11926400

yes

characteristic

284

C₂²

#11926540

yes

characteristic

285

C₂²

#11926545

yes

characteristic

286

C₄

—

287

C₄

—

288

C₄

—

289

C₄

—

290

C₄

—

291

C₄

—

292

C₄

—

293

C₄

C₂×#10597293

yes

—

294

C₄

#11926689

yes

—

295

C₄

#11926706

yes

—

296

C₂

—

297

C₂

—

298

C₂

#14563559

yes

characteristic

299

C₂

#14563575

yes

characteristic

300

C₂

#14563610

yes

characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#557	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#557	D₁₉
hypocenter	C₁₉	#8390
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#557

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#557

C₂

socle

C₂²×C₁₉

#379

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#557

N	H ≅ G/N	type
107. Q₈×C₁₉	#101	semidirect
209. C₁₉	#8390	semidirect
257. Q₈	#10597293	semidirect

H ≅ G/N

type

107. Q₈×C₁₉

#101

semidirect

209. C₁₉

#8390

semidirect

257. Q₈

#10597293

semidirect

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

subgroup	index
#14563631	2
#14562307	2
#14562064	2
#14561959	2
C₂×C₁₉×#557	2
#8390	19

subgroup

index

C₂×C₁₉×#557

Subgroups — #18074277

Conjugacy classes of subgroups

Complements

Maximal subgroups