Group #18083503 — subgroups

Subgroups — #18083503

Order 4864.

636 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 105 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	#14573631	C₂	1	2	yes	maximal, complemented
2	#14564433	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562034	C₂	1	2	yes	maximal, complemented
4	#14561466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
7	#11926855	—	2	2	no	—
8	#11926821	—	2	2	no	—
9	#11926736	—	2	2	no	—
10	#11926677	—	2	2	no	—
11	C₄×#64525	—	2	4	no	—
12	#11926597	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
15	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
16	C₂×C₁₉×#135	—	2	2	no	—
17	C₁₉×#532	C₂²	1	2	yes	—
18	C₁₉×#497	—	2	2	no	—
19	C₁₉×#496	—	2	2	no	—
20	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
21	C₂×#41×C₁₉	—	2	2	no	—
22	C₂²×D₇₆	D₄	1	1	yes	characteristic
23	C₂²×C₄×D₁₉	—	2	1	no	—
24	C₁₉×#135	—	4	4	no	—
25	C₁₉×#135	—	4	4	no	—
26	C₂×Q₁₆×C₁₉	—	2	2	no	—
27	C₂×SD₁₆×C₁₉	—	2	4	no	—
28	C₂×D₈×C₁₉	—	2	2	no	—
29	C₂²×C₈×C₁₉	D₄	1	2	yes	—
30	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
31	C₁₉×#127	D₄	1	2	yes	—
32	C₁₉×#124	—	2	2	no	—
33	C₁₉×#121	—	2	2	no	—
34	C₁₉×#121	—	2	2	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₄×D₄×C₁₉	—	2	2	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×#64525	—	2	4	no	—
39	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
40	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
41	C₂²×C₁₉⋊C₈	—	2	1	no	—
42	C₄×D₇₆	—	2	2	no	—
43	C₄×D₇₆	—	2	2	no	—
44	C₁₉×#97	—	2	2	no	—
45	#10597289	—	2	4	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
47	(C₂×D₁₉)⋊C₈	—	4	4	no	—
48	#10597266	—	2	4	no	—
49	#10597264	—	2	4	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
52	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
53	C₂³×D₁₉	—	2	1	no	—
54	#41×C₁₉	—	4	4	no	—
55	#41×C₁₉	—	4	4	no	—
56	C₂×Q₈×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	—	2	2	no	—
58	C₂×D₄×C₁₉	—	2	2	no	—
59	C₂×D₄×C₁₉	—	2	2	no	—
60	C₂×D₄×C₁₉	—	4	2	no	—
61	C₂²×C₄×C₁₉	—	4	2	no	—
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
65	C₂²×Dic₁₉	—	2	1	no	—
66	C₂×D₇₆	—	2	2	no	—
67	C₂×D₇₆	—	4	2	no	—
68	C₂×C₄×D₁₉	—	4	1	no	—
69	C₂×C₄×D₁₉	—	4	1	no	—
70	C₂×C₄×D₁₉	—	4	2	no	—
71	C₂×C₄×D₁₉	—	4	2	no	—
72	Q₁₆×C₁₉	—	4	4	no	—
73	SD₁₆×C₁₉	—	4	8	no	—
74	D₈×C₁₉	—	4	4	no	—
75	C₂×C₈×C₁₉	—	2	2	no	—
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	D₈	1	4	yes	complemented
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂²⋊C₄×C₁₉	—	4	2	no	—
81	C₂²⋊C₄×C₁₉	—	4	2	no	—
82	C₄²×C₁₉	C₂×D₄	1	2	yes	—
83	C₄²×C₁₉	C₂×D₄	1	2	yes	—
84	#64525	—	4	8	no	—
85	(C₂×D₁₉)⋊C₄	—	4	2	no	—
86	C₄⋊Dic₁₉	—	2	2	no	—
87	C₂×C₁₉⋊C₈	—	2	4	no	—
88	C₂×C₁₉⋊C₈	—	4	1	no	—
89	C₂×C₁₉⋊C₈	—	4	2	no	—
90	#10032	—	19	1	no	maximal, Sylow
91	C₂³×C₁₉	—	4	2	no	—
92	C₂³×C₁₉	#121	1	1	yes	characteristic
93	C₂²×D₁₉	—	2	2	no	—
94	C₂²×D₁₉	—	4	1	no	—
95	C₂²×D₁₉	—	4	2	no	—
96	C₂²×D₁₉	—	4	1	no	—
97	C₂²×D₁₉	—	4	2	no	—
98	Q₈×C₁₉	—	4	4	no	—
99	D₄×C₁₉	—	4	4	no	—
100	D₄×C₁₉	—	4	4	no	—
101	D₄×C₁₉	—	4	4	no	—
102	D₄×C₁₉	—	8	4	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	8	2	no	—
107	C₂×C₄×C₁₉	—	8	2	no	—
108	C₂×C₄×C₁₉	#120	1	2	yes	—
109	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
110	C₂×C₄×C₁₉	#121	1	2	yes	—
111	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
113	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
114	C₂×Dic₁₉	—	4	1	no	—
115	C₂×Dic₁₉	—	4	2	no	—
116	D₇₆	—	2	4	no	—
117	D₇₆	—	4	2	no	—
118	C₄×D₁₉	—	8	2	no	—
119	C₄×D₁₉	—	8	1	no	—
120	C₄×D₁₉	—	8	1	no	—
121	C₈×C₁₉	—	2	4	no	—
122	C₁₉⋊C₈	—	4	4	no	—
123	C₁₉⋊C₈	—	8	1	no	—
124	#3150	D₁₉	1	1	yes	characteristic, complemented
125	#3100	—	19	2	no	—
126	#1955	—	19	1	no	—
127	#1480	—	19	2	no	—
128	#1275	—	19	1	no	—
129	C₂²×C₁₉	—	2	1	no	—
130	C₂²×C₁₉	—	2	1	no	—
131	C₂²×C₁₉	—	8	2	no	—
132	C₂²×C₁₉	—	8	2	no	—
133	C₂²×C₁₉	—	8	2	no	—
134	C₂²×C₁₉	#392	1	1	yes	characteristic
135	C₂²×C₁₉	#459	1	2	yes	—
136	C₂×D₁₉	—	4	4	no	—
137	C₂×D₁₉	—	4	2	no	—
138	C₂×D₁₉	—	8	2	no	—
139	C₂×D₁₉	—	8	1	no	—
140	C₂×D₁₉	—	8	1	no	—
141	C₄×C₁₉	—	2	2	no	—
142	C₄×C₁₉	—	2	2	no	—
143	C₄×C₁₉	—	8	2	no	—
144	C₄×C₁₉	#447	1	2	yes	—
145	C₄×C₁₉	#493	1	1	yes	characteristic
146	C₄×C₁₉	#496	1	1	yes	characteristic
147	Dic₁₉	—	8	1	no	—
148	C₂×#135	—	2	2	no	—
149	#532	C₂×D₁₉	1	2	yes	—
150	C₂×C₄×D₄	—	19	1	no	—
151	#497	—	2	2	no	—
152	#496	—	2	2	no	—
153	#480	—	38	2	no	—
154	#474	—	38	2	no	—
155	#459	—	38	2	no	—
156	#447	—	38	2	no	—
157	C₄×D₈	—	38	4	no	—
158	#431	—	19	2	no	—
159	C₂×C₄⋊C₈	—	19	1	no	—
160	C₂×C₂²⋊C₈	—	38	2	no	—
161	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
162	D₄⋊C₈	—	38	4	no	—
163	C₂×C₁₉	—	2	2	no	—
164	C₂×C₁₉	—	16	2	no	—
165	C₂×C₁₉	#2010	1	1	yes	characteristic
166	C₂×C₁₉	#2011	1	1	yes	characteristic
167	C₂×C₁₉	#2017	1	1	yes	characteristic
168	D₁₉	—	8	2	no	—
169	C₂×#41	—	2	2	no	—
170	C₂²×D₄	—	19	1	no	—
171	C₂³×C₄	—	38	1	no	—
172	#135	—	4	4	no	—
173	#135	—	4	4	no	—
174	C₂×Q₁₆	—	2	2	no	—
175	C₂×SD₁₆	—	2	4	no	—
176	C₂×D₈	—	2	2	no	—
177	C₂×D₈	—	38	4	no	—
178	C₂²×C₈	—	38	1	no	—
179	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
180	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
181	#127	C₂²⋊D₁₉	1	2	yes	—
182	#124	—	2	2	no	—
183	#121	—	2	2	no	—
184	#121	—	2	2	no	—
185	C₄×D₄	—	2	2	no	—
186	C₄×D₄	—	2	2	no	—
187	C₄×D₄	—	38	2	no	—
188	C₄×D₄	—	38	2	no	—
189	C₂×C₄⋊C₄	—	19	1	no	—
190	C₂×C₂²⋊C₄	—	38	1	no	—
191	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
192	#107	—	38	4	no	—
193	C₄⋊C₈	—	38	2	no	—
194	C₄⋊C₈	—	38	2	no	—
195	#102	—	38	4	no	—
196	#102	—	38	4	no	—
197	C₂²⋊C₈	—	38	2	no	—
198	C₂²⋊C₈	—	76	4	no	—
199	#97	—	2	2	no	—
200	C₄×C₈	—	19	4	no	—
201	C₁₉	#10032	1	1	yes	characteristic, complemented, Sylow
202	C₂⁴	—	38	1	no	—
203	#41	—	4	4	no	—
204	#41	—	4	4	no	—
205	C₂×Q₈	—	2	2	no	—
206	C₂×D₄	—	2	2	no	—
207	C₂×D₄	—	2	2	no	—
208	C₂×D₄	—	2	2	no	—
209	C₂×D₄	—	4	2	no	—
210	C₂×D₄	—	38	2	no	—
211	C₂×D₄	—	76	2	no	—
212	C₂²×C₄	—	4	2	no	—
213	C₂²×C₄	—	38	1	no	—
214	C₂²×C₄	—	76	2	no	—
215	C₂²×C₄	—	76	2	no	—
216	C₂²×C₄	—	76	1	no	—
217	C₂²×C₄	—	76	1	no	—
218	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
219	C₂²×C₄	#64543	1	1	yes	characteristic
220	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
221	Q₁₆	—	4	4	no	—
222	SD₁₆	—	4	8	no	—
223	D₈	—	4	4	no	—
224	D₈	—	76	8	no	—
225	C₂×C₈	—	2	2	no	—
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	38	4	no	—
228	C₂×C₈	—	76	2	no	—
229	C₂×C₈	—	76	1	no	—
230	C₂×C₈	#64525	1	4	yes	complemented
231	C₄⋊C₄	—	2	2	no	—
232	C₄⋊C₄	—	2	2	no	—
233	C₄⋊C₄	—	38	2	no	—
234	C₂²⋊C₄	—	4	2	no	—
235	C₂²⋊C₄	—	4	2	no	—
236	C₂²⋊C₄	—	76	2	no	—
237	C₄²	D₄×D₁₉	1	2	yes	—
238	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
239	C₂³	—	4	2	no	—
240	C₂³	—	38	2	no	—
241	C₂³	—	76	1	no	—
242	C₂³	—	76	2	no	—
243	C₂³	—	76	1	no	—
244	C₂³	—	76	2	no	—
245	C₂³	#10597384	1	1	yes	characteristic
246	Q₈	—	4	4	no	—
247	D₄	—	4	4	no	—
248	D₄	—	4	4	no	—
249	D₄	—	4	4	no	—
250	D₄	—	8	4	no	—
251	D₄	—	38	4	no	—
252	D₄	—	76	2	no	—
253	C₂×C₄	—	4	1	no	—
254	C₂×C₄	—	4	1	no	—
255	C₂×C₄	—	4	2	no	—
256	C₂×C₄	—	8	2	no	—
257	C₂×C₄	—	8	2	no	—
258	C₂×C₄	—	76	1	no	—
259	C₂×C₄	—	76	2	no	—
260	C₂×C₄	—	152	1	no	—
261	C₂×C₄	—	152	1	no	—
262	C₂×C₄	—	152	2	no	—
263	C₂×C₄	C₂×#64525	1	2	yes	—
264	C₂×C₄	#10597378	1	2	yes	—
265	C₂×C₄	#10597383	1	2	yes	—
266	C₂×C₄	#10597385	1	2	yes	—
267	C₂×C₄	#10597386	1	1	yes	characteristic
268	C₂×C₄	#10597399	1	1	yes	characteristic
269	C₈	—	2	4	no	—
270	C₈	—	76	4	no	—
271	C₈	—	152	1	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	8	2	no	—
275	C₂²	—	8	2	no	—
276	C₂²	—	8	2	no	—
277	C₂²	—	76	4	no	—
278	C₂²	—	76	2	no	—
279	C₂²	—	152	2	no	—
280	C₂²	—	152	1	no	—
281	C₂²	—	152	1	no	—
282	C₂²	#11926452	1	1	yes	characteristic
283	C₂²	#11926736	1	2	yes	—
284	C₄	—	2	2	no	—
285	C₄	—	2	2	no	—
286	C₄	—	8	2	no	—
287	C₄	—	152	1	no	—
288	C₄	#11926678	1	2	yes	—
289	C₄	#11926920	1	1	yes	characteristic
290	C₄	#11926931	1	1	yes	characteristic
291	C₂	—	2	2	no	—
292	C₂	—	16	2	no	—
293	C₂	—	152	2	no	—
294	C₂	#14564699	1	1	yes	characteristic
295	C₂	#14564706	1	1	yes	characteristic
296	C₂	#14564738	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14573631

C₂

yes

maximal, complemented

#14564433

C₂

yes

maximal, characteristic, complemented

#14562034

C₂

yes

maximal, complemented

#14561466

C₂

yes

maximal, characteristic, complemented

C₁₉×#3150

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₇₆

C₂²

yes

—

—

—

—

—

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₈

—

D₄⋊(C₁₉⋊C₈)

—

C₂×C₁₉×#135

—

C₁₉×#532

C₂²

yes

—

C₁₉×#497

—

C₁₉×#496

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂²×D₇₆

D₄

yes

characteristic

C₂²×C₄×D₁₉

—

C₁₉×#135

—

C₁₉×#135

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#127

D₄

yes

—

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64525

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₄×D₇₆

—

C₄×D₇₆

—

C₁₉×#97

—

#10597289

—

C₂²⋊(C₁₉⋊C₈)

—

(C₂×D₁₉)⋊C₈

—

#10597266

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂³×D₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

complemented

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64525

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10032

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#121

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

100

D₄×C₁₉

—

101

D₄×C₁₉

—

102

D₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

#120

yes

—

109

C₂×C₄×C₁₉

#120

yes

characteristic

110

C₂×C₄×C₁₉

#121

yes

—

111

C₂×C₄×C₁₉

#127

yes

characteristic

112

C₂×C₄×C₁₉

C₂×D₈

yes

—

113

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

114

C₂×Dic₁₉

—

115

C₂×Dic₁₉

—

116

D₇₆

—

117

D₇₆

—

118

C₄×D₁₉

—

119

C₄×D₁₉

—

120

C₄×D₁₉

—

121

C₈×C₁₉

—

122

C₁₉⋊C₈

—

123

C₁₉⋊C₈

—

124

#3150

D₁₉

yes

characteristic, complemented

125

#3100

—

126

#1955

—

127

#1480

—

128

#1275

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

#392

yes

characteristic

135

C₂²×C₁₉

#459

yes

—

136

C₂×D₁₉

—

137

C₂×D₁₉

—

138

C₂×D₁₉

—

139

C₂×D₁₉

—

140

C₂×D₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

#447

yes

—

145

C₄×C₁₉

#493

yes

characteristic

146

C₄×C₁₉

#496

yes

characteristic

147

Dic₁₉

—

148

C₂×#135

—

149

#532

C₂×D₁₉

yes

—

150

C₂×C₄×D₄

—

151

#497

—

152

#496

—

153

#480

—

154

#474

—

155

#459

—

156

#447

—

157

C₄×D₈

—

158

#431

—

159

C₂×C₄⋊C₈

—

160

C₂×C₂²⋊C₈

—

161

C₂×#97

C₂×D₁₉

yes

characteristic

162

D₄⋊C₈

—

163

C₂×C₁₉

—

164

C₂×C₁₉

—

165

C₂×C₁₉

#2010

yes

characteristic

166

C₂×C₁₉

#2011

yes

characteristic

167

C₂×C₁₉

#2017

yes

characteristic

168

D₁₉

—

169

C₂×#41

—

170

C₂²×D₄

—

171

C₂³×C₄

—

172

#135

—

173

#135

—

174

C₂×Q₁₆

—

175

C₂×SD₁₆

—

176

C₂×D₈

—

177

C₂×D₈

—

178

C₂²×C₈

—

179

C₂²×C₈

C₂²⋊D₁₉

yes

—

180

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

181

#127

C₂²⋊D₁₉

yes

—

182

#124

—

183

#121

—

184

#121

—

185

C₄×D₄

—

186

C₄×D₄

—

187

C₄×D₄

—

188

C₄×D₄

—

189

C₂×C₄⋊C₄

—

190

C₂×C₂²⋊C₄

—

191

C₂×C₄²

C₂²×D₁₉

yes

characteristic

192

#107

—

193

C₄⋊C₈

—

194

C₄⋊C₈

—

195

#102

—

196

#102

—

197

C₂²⋊C₈

—

198

C₂²⋊C₈

—

199

#97

—

200

C₄×C₈

—

201

C₁₉

#10032

yes

characteristic, complemented, Sylow

202

C₂⁴

—

203

#41

—

204

#41

—

205

C₂×Q₈

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂²×C₄

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

—

218

C₂²×C₄

D₄×D₁₉

yes

characteristic

219

C₂²×C₄

#64543

yes

characteristic

220

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

221

Q₁₆

—

222

SD₁₆

—

223

D₈

—

224

D₈

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

—

230

C₂×C₈

#64525

yes

complemented

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₂²⋊C₄

—

235

C₂²⋊C₄

—

236

C₂²⋊C₄

—

237

C₄²

D₄×D₁₉

yes

—

238

C₄²

C₂×C₂²⋊D₁₉

yes

—

239

C₂³

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

#10597384

yes

characteristic

246

Q₈

—

247

D₄

—

248

D₄

—

249

D₄

—

250

D₄

—

251

D₄

—

252

D₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

152

—

261

C₂×C₄

—

152

—

262

C₂×C₄

—

152

—

263

C₂×C₄

C₂×#64525

yes

—

264

C₂×C₄

#10597378

yes

—

265

C₂×C₄

#10597383

yes

—

266

C₂×C₄

#10597385

yes

—

267

C₂×C₄

#10597386

yes

characteristic

268

C₂×C₄

#10597399

yes

characteristic

269

C₈

—

270

C₈

—

271

C₈

—

152

—

272

C₂²

—

273

C₂²

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

152

—

280

C₂²

—

152

—

281

C₂²

—

152

—

282

C₂²

#11926452

yes

characteristic

283

C₂²

#11926736

yes

—

284

C₄

—

285

C₄

—

286

C₄

—

287

C₄

—

152

—

288

C₄

#11926678

yes

—

289

C₄

#11926920

yes

characteristic

290

C₄

#11926931

yes

characteristic

291

C₂

—

292

C₂

—

293

C₂

—

152

—

294

C₂

#14564699

yes

characteristic

295

C₂

#14564706

yes

characteristic

296

C₂

#14564738

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3150	C₂
socle	C₂²×C₁₉	#392
hypercenter	#3150	D₁₉
hypocenter	C₁₉	#10032
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3150

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3150

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3150

N	H ≅ G/N	type
1. #14573631	C₂	semidirect
2. #14564433	C₂	semidirect
3. #14562034	C₂	semidirect
4. #14561466	C₂	semidirect
5. C₁₉×#3150	C₂	semidirect
77. C₂×C₈×C₁₉	D₈	semidirect
124. #3150	D₁₉	semidirect
201. C₁₉	#10032	semidirect
230. C₂×C₈	#64525	semidirect

H ≅ G/N

type

1. #14573631

C₂

semidirect

2. #14564433

C₂

semidirect

3. #14562034

C₂

semidirect

4. #14561466

C₂

semidirect

5. C₁₉×#3150

C₂

semidirect

77. C₂×C₈×C₁₉

D₈

semidirect

124. #3150

D₁₉

semidirect

201. C₁₉

#10032

semidirect

230. C₂×C₈

#64525

semidirect

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

subgroup	index
#14573631	2
#14564433	2
#14562034	2
#14561466	2
C₁₉×#3150	2
#10032	19

subgroup

index

C₁₉×#3150

Subgroups — #18083503

Conjugacy classes of subgroups

Complements

Maximal subgroups