Subgroups — #14294914

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₃×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	#11751788	C₂	1	1	yes	maximal, characteristic
3	D₅×#815	C₂	1	1	yes	maximal, characteristic
4	#11746763	C₂	1	1	yes	maximal, characteristic
5	C₃×(C₂×AGL(1,𝔽₅))⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#11746517	C₂	1	1	yes	maximal, characteristic
7	(C₂×AGL(1,𝔽₅))⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
8	#10603878	—	3	1	no	maximal, Hall
9	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
10	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
12	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×Dic₃×AGL(1,𝔽₅)	C₄	1	2	yes	—
14	C₂×Dic₃×AGL(1,𝔽₅)	C₄	1	2	yes	—
15	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
16	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
17	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	#91169	C₄	1	2	yes	complemented
19	#91169	C₄	1	2	yes	complemented
20	#91099	C₄	1	1	yes	characteristic, complemented
21	C₅×#815	C₄	1	1	yes	characteristic, complemented
22	#90954	C₄	1	1	yes	characteristic, complemented
23	#90953	C₄	1	1	yes	characteristic, complemented
24	#68597	—	5	1	no	maximal, Hall
25	C₄²×AGL(1,𝔽₅)	—	3	1	no	—
26	#65676	—	3	1	no	—
27	D₅×#97	—	3	1	no	—
28	(C₂×AGL(1,𝔽₅))⋊C₈	—	3	1	no	—
29	(C₂×AGL(1,𝔽₅))⋊C₈	—	3	1	no	—
30	(C₂×AGL(1,𝔽₅))⋊C₈	—	3	1	no	—
31	(C₂×AGL(1,𝔽₅))⋊C₈	D₃	1	1	yes	characteristic
32	C₂²×ΓL(1,𝔽₁₆)	C₂×C₄	1	2	yes	—
33	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
34	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
35	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
36	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃⋊#170	C₂×C₄	1	2	yes	—
38	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
39	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
40	D₅⋊(C₃⋊C₈)	—	2	1	no	—
41	D₅⋊(C₃⋊C₈)	—	2	1	no	—
42	C₂×C₃×#170	C₂×C₄	1	2	yes	—
43	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
44	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
45	C₃×D₅⋊C₈	—	2	1	no	—
46	C₃×D₅⋊C₈	—	2	1	no	—
47	Dic₃×AGL(1,𝔽₅)	—	2	4	no	—
48	Dic₃×AGL(1,𝔽₅)	—	2	4	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
52	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
55	C₃×C₈×D₅	—	2	1	no	—
56	C₃×C₈×D₅	—	2	1	no	—
57	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
58	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
59	D₅×C₃⋊C₈	—	2	1	no	—
60	D₅×C₃⋊C₈	—	2	1	no	—
61	C₂×#815	—	5	1	no	—
62	C₂×#815	—	5	1	no	—
63	C₄²×Dic₃	—	5	1	no	—
64	C₃×#336	—	5	1	no	—
65	#4550	—	5	1	no	—
66	#4550	—	5	1	no	—
67	#4524	—	5	1	no	—
68	C₂×C₄×AGL(1,𝔽₅)	—	3	2	no	—
69	C₂×C₄×AGL(1,𝔽₅)	—	3	2	no	—
70	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
71	C₂×C₄×AGL(1,𝔽₅)	C₂×D₃	1	1	yes	characteristic
72	C₂×D₅⋊C₈	—	3	1	no	—
73	C₂×D₅⋊C₈	C₂×D₃	1	1	yes	characteristic
74	C₂×C₈×D₅	—	3	1	no	—
75	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
76	C₄²×D₅	—	3	1	no	—
77	#4002	—	3	2	no	—
78	#4002	—	3	2	no	—
79	C₅×#97	—	3	1	no	—
80	#3947	—	3	1	no	—
81	#3947	—	3	1	no	—
82	#3935	—	3	1	no	—
83	#1745	—	15	1	no	Sylow
84	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
85	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
86	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
87	C₂×ΓL(1,𝔽₁₆)	M₁₆	1	4	yes	—
88	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
89	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
90	C₂×C₃×AGL(1,𝔽₅)	M₁₆	1	4	yes	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×Dic₁₅	C₄²	1	1	yes	characteristic
93	C₂×Dic₁₅	C₄²	1	1	yes	characteristic
94	C₂×C₅×Dic₃	C₄²	1	1	yes	characteristic
95	C₂×C₅×Dic₃	C₄²	1	1	yes	characteristic
96	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
97	C₃×C₄×D₅	#41	1	1	yes	characteristic
98	C₃×C₄×D₅	#41	1	1	yes	characteristic
99	C₃×C₄×D₅	#41	1	1	yes	characteristic
100	C₃×C₄×D₅	#41	1	1	yes	characteristic
101	D₅×Dic₃	—	2	2	no	—
102	D₅×Dic₃	—	2	2	no	—
103	C₃⋊#170	—	2	2	no	—
104	C₃×#170	—	2	2	no	—
105	C₃×C₅×C₈	—	2	1	no	—
106	C₃⋊#168	—	2	1	no	—
107	C₃×#168	—	2	1	no	—
108	C₅×C₃⋊C₈	—	2	1	no	—
109	C₂²×C₃×C₈	—	5	1	no	—
110	C₂²×C₃×C₈	—	5	1	no	—
111	C₂×C₃×C₄²	—	5	1	no	—
112	C₂×C₄×Dic₃	—	5	1	no	—
113	C₂×C₄×Dic₃	—	5	2	no	—
114	C₂×C₄×Dic₃	—	5	2	no	—
115	C₂×C₄×Dic₃	—	5	1	no	—
116	C₂²×C₃⋊C₈	—	5	1	no	—
117	C₂²×C₃⋊C₈	—	5	1	no	—
118	#815	—	5	2	no	—
119	#815	—	5	2	no	—
120	#815	—	5	1	no	—
121	#815	—	5	1	no	—
122	#815	—	5	1	no	—
123	#815	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
124	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
125	C₂²×AGL(1,𝔽₅)	C₄×D₃	1	2	yes	—
126	C₂×C₄×D₅	—	3	1	no	—
127	C₂×C₄×D₅	—	3	1	no	—
128	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
129	C₂×#170	—	3	2	no	—
130	C₂×#170	C₄×D₃	1	2	yes	—
131	C₄×AGL(1,𝔽₅)	—	2	1	no	—
132	C₄×AGL(1,𝔽₅)	—	2	1	no	—
133	C₄×AGL(1,𝔽₅)	—	6	4	no	—
134	C₄×AGL(1,𝔽₅)	—	6	4	no	—
135	C₄×AGL(1,𝔽₅)	—	6	1	no	—
136	C₄×AGL(1,𝔽₅)	—	6	1	no	—
137	D₅⋊C₈	—	2	1	no	—
138	D₅⋊C₈	—	2	1	no	—
139	D₅⋊C₈	—	6	1	no	—
140	D₅⋊C₈	—	6	1	no	—
141	C₂×C₅×C₈	—	3	1	no	—
142	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
143	C₄²×C₅	—	3	1	no	—
144	C₄×Dic₅	—	3	1	no	—
145	C₄×Dic₅	—	3	1	no	—
146	C₄×Dic₅	—	3	1	no	—
147	C₂×#168	—	3	1	no	—
148	C₂×#168	C₄×D₃	1	1	yes	characteristic
149	C₈×D₅	—	2	1	no	—
150	C₈×D₅	—	2	1	no	—
151	C₈×D₅	—	6	1	no	—
152	C₈×D₅	—	6	1	no	—
153	C₂×#97	—	15	1	no	—
154	C₂×#97	—	15	1	no	—
155	C₄³	—	15	1	no	—
156	#336	—	5	1	no	—
157	#336	—	15	1	no	—
158	#336	—	15	1	no	—
159	#336	—	15	1	no	—
160	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₃×D₅	#117	1	1	yes	characteristic
162	C₂×C₃×D₅	#117	1	1	yes	characteristic
163	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
164	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
165	ΓL(1,𝔽₁₆)	—	2	4	no	—
166	C₃×AGL(1,𝔽₅)	—	2	4	no	—
167	C₃×C₄×C₅	#117	1	1	yes	characteristic
168	C₃×C₄×C₅	#117	1	1	yes	characteristic
169	Dic₁₅	—	2	1	no	—
170	Dic₁₅	—	2	1	no	—
171	C₃×Dic₅	#117	1	1	yes	characteristic
172	C₃×Dic₅	#117	1	1	yes	characteristic
173	C₅×Dic₃	—	2	1	no	—
174	C₅×Dic₃	—	2	1	no	—
175	C₂²×C₃×C₄	—	5	1	no	—
176	C₂²×C₃×C₄	—	5	2	no	—
177	C₂²×Dic₃	—	5	2	no	—
178	C₂²×Dic₃	—	5	1	no	—
179	C₂²×Dic₃	—	5	1	no	—
180	C₂×C₃×C₈	—	5	2	no	—
181	C₂×C₃×C₈	—	5	1	no	—
182	C₂×C₃×C₈	—	10	1	no	—
183	C₂×C₃×C₈	—	10	1	no	—
184	C₂×C₃×C₈	—	10	1	no	—
185	C₂×C₃×C₈	—	10	1	no	—
186	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
187	C₃×C₄²	—	10	1	no	—
188	C₃×C₄²	—	10	1	no	—
189	C₄×Dic₃	—	5	1	no	—
190	C₄×Dic₃	—	5	1	no	—
191	C₄×Dic₃	—	5	1	no	—
192	C₄×Dic₃	—	10	4	no	—
193	C₄×Dic₃	—	10	4	no	—
194	C₄×Dic₃	—	10	1	no	—
195	C₄×Dic₃	—	10	1	no	—
196	C₄×Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
197	C₂×C₃⋊C₈	—	5	2	no	—
198	C₂×C₃⋊C₈	—	5	1	no	—
199	C₂×C₃⋊C₈	—	10	1	no	—
200	C₂×C₃⋊C₈	—	10	1	no	—
201	C₂×C₃⋊C₈	—	10	1	no	—
202	C₂×C₃⋊C₈	—	10	1	no	—
203	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
204	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
205	C₂×AGL(1,𝔽₅)	—	2	2	no	—
206	C₂×AGL(1,𝔽₅)	—	2	2	no	—
207	C₂×AGL(1,𝔽₅)	—	3	4	no	—
208	C₂×AGL(1,𝔽₅)	—	6	2	no	—
209	C₂×AGL(1,𝔽₅)	—	6	2	no	—
210	C₂×AGL(1,𝔽₅)	ΓL(1,𝔽₂₅)	1	4	yes	—
211	C₂×C₄×C₅	—	3	1	no	—
212	C₂×C₄×C₅	—	3	1	no	—
213	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
214	C₂×Dic₅	—	3	1	no	—
215	C₂×Dic₅	—	3	1	no	—
216	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
217	C₄×D₅	—	6	2	no	—
218	C₄×D₅	—	6	2	no	—
219	C₄×D₅	#237	1	1	yes	characteristic
220	C₄×D₅	#237	1	1	yes	characteristic
221	C₄×D₅	#237	1	1	yes	characteristic
222	C₄×D₅	#239	1	1	yes	characteristic
223	#170	—	2	2	no	—
224	#170	—	6	2	no	—
225	C₅×C₈	—	2	1	no	—
226	C₅×C₈	—	6	1	no	—
227	#168	—	2	1	no	—
228	#168	—	6	1	no	—
229	C₂²×C₈	—	5	1	no	—
230	C₂²×C₈	—	5	1	no	—
231	C₂²×C₈	—	15	1	no	—
232	C₂²×C₈	—	15	1	no	—
233	C₂×C₄²	—	5	1	no	—
234	C₂×C₄²	—	15	1	no	—
235	C₂×C₄²	—	15	1	no	—
236	C₂×C₄²	—	15	2	no	—
237	C₂×C₄²	—	15	2	no	—
238	#97	—	3	1	no	—
239	#97	—	15	1	no	—
240	#97	—	15	1	no	—
241	#97	—	15	2	no	—
242	#97	—	15	2	no	—
243	#97	—	15	1	no	—
244	C₂×C₃×C₅	#376	1	1	yes	characteristic
245	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
246	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
247	C₃×D₅	#432	1	2	yes	—
248	C₃×D₅	#432	1	2	yes	—
249	C₂³×C₃	—	5	1	no	—
250	C₂×C₃×C₄	—	5	1	no	—
251	C₂×C₃×C₄	—	5	1	no	—
252	C₂×C₃×C₄	—	5	1	no	—
253	C₂×C₃×C₄	—	5	1	no	—
254	C₂×C₃×C₄	—	5	1	no	—
255	C₂×C₃×C₄	—	5	4	no	—
256	C₂×C₃×C₄	—	10	2	no	—
257	C₂×C₃×C₄	—	10	2	no	—
258	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
259	C₂×Dic₃	—	5	4	no	—
260	C₂×Dic₃	—	5	1	no	—
261	C₂×Dic₃	—	5	1	no	—
262	C₂×Dic₃	—	10	2	no	—
263	C₂×Dic₃	—	10	2	no	—
264	C₂×Dic₃	—	10	2	no	—
265	C₂×Dic₃	—	10	2	no	—
266	C₂×Dic₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
267	C₂×Dic₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
268	C₃×C₈	—	2	1	no	—
269	C₃×C₈	—	10	2	no	—
270	C₃×C₈	—	10	1	no	—
271	C₃⋊C₈	—	2	1	no	—
272	C₃⋊C₈	—	10	2	no	—
273	C₃⋊C₈	—	10	1	no	—
274	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
275	C₂×D₅	#877	1	1	yes	characteristic
276	C₂×D₅	#892	1	1	yes	characteristic
277	C₂×D₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
278	C₂×D₅	D₃×M₁₆	1	2	yes	—
279	AGL(1,𝔽₅)	—	2	4	no	—
280	AGL(1,𝔽₅)	—	6	4	no	—
281	C₄×C₅	—	6	1	no	—
282	C₄×C₅	—	6	1	no	—
283	C₄×C₅	#877	1	1	yes	characteristic
284	C₄×C₅	#892	1	1	yes	characteristic
285	Dic₅	—	6	1	no	—
286	Dic₅	—	6	1	no	—
287	Dic₅	#877	1	1	yes	characteristic
288	Dic₅	#892	1	1	yes	characteristic
289	C₂²×C₄	—	5	1	no	—
290	C₂²×C₄	—	5	2	no	—
291	C₂²×C₄	—	15	1	no	—
292	C₂²×C₄	—	15	1	no	—
293	C₂²×C₄	—	15	2	no	—
294	C₂×C₈	—	3	1	no	—
295	C₂×C₈	—	5	2	no	—
296	C₂×C₈	—	5	1	no	—
297	C₂×C₈	—	10	1	no	—
298	C₂×C₈	—	10	1	no	—
299	C₂×C₈	—	10	1	no	—
300	C₂×C₈	—	10	1	no	—
301	C₂×C₈	—	15	2	no	—
302	C₂×C₈	—	15	1	no	—
303	C₂×C₈	—	30	1	no	—
304	C₂×C₈	—	30	1	no	—
305	C₂×C₈	—	30	1	no	—
306	C₂×C₈	—	30	1	no	—
307	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
308	C₄²	—	3	1	no	—
309	C₄²	—	10	1	no	—
310	C₄²	—	10	1	no	—
311	C₄²	—	15	1	no	—
312	C₄²	—	15	1	no	—
313	C₄²	—	15	1	no	—
314	C₄²	—	30	1	no	—
315	C₄²	—	30	1	no	—
316	C₄²	—	30	4	no	—
317	C₄²	—	30	4	no	—
318	C₃×C₅	#1745	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	5	1	no	—
320	C₂²×C₃	—	5	1	no	—
321	C₂²×C₃	—	5	2	no	—
322	C₂²×C₃	—	5	2	no	—
323	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
324	C₃×C₄	—	5	1	no	—
325	C₃×C₄	—	5	1	no	—
326	C₃×C₄	—	10	4	no	—
327	C₃×C₄	#4130	1	1	yes	characteristic
328	C₃×C₄	#4130	1	1	yes	characteristic
329	Dic₃	—	2	1	no	—
330	Dic₃	—	2	1	no	—
331	Dic₃	—	10	4	no	—
332	Dic₃	—	10	1	no	—
333	Dic₃	—	10	1	no	—
334	C₂×C₅	#4648	1	1	yes	characteristic
335	C₂×C₅	C₄×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
336	C₂×C₅	#4707	1	1	yes	characteristic
337	D₅	#4719	1	2	yes	—
338	D₅	#4835	1	2	yes	—
339	C₂³	—	5	1	no	—
340	C₂×C₄	—	3	1	no	—
341	C₂×C₄	—	3	1	no	—
342	C₂×C₄	—	5	1	no	—
343	C₂×C₄	—	5	1	no	—
344	C₂×C₄	—	5	1	no	—
345	C₂×C₄	—	5	1	no	—
346	C₂×C₄	—	5	1	no	—
347	C₂×C₄	—	5	4	no	—
348	C₂×C₄	—	10	2	no	—
349	C₂×C₄	—	10	2	no	—
350	C₂×C₄	—	15	4	no	—
351	C₂×C₄	—	15	1	no	—
352	C₂×C₄	—	15	1	no	—
353	C₂×C₄	—	30	2	no	—
354	C₂×C₄	—	30	2	no	—
355	C₂×C₄	—	30	2	no	—
356	C₂×C₄	—	30	2	no	—
357	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	6	1	no	—
360	C₈	—	10	2	no	—
361	C₈	—	10	1	no	—
362	C₈	—	30	2	no	—
363	C₈	—	30	1	no	—
364	C₂×C₃	—	5	2	no	—
365	C₂×C₃	—	5	2	no	—
366	C₂×C₃	#65686	1	1	yes	characteristic
367	C₂×C₃	M₁₆×AGL(1,𝔽₅)	1	1	yes	characteristic
368	C₂×C₃	M₁₆×AGL(1,𝔽₅)	1	1	yes	characteristic
369	C₅	#68597	1	1	yes	characteristic, complemented, Sylow
370	C₂²	—	5	1	no	—
371	C₂²	—	5	1	no	—
372	C₂²	—	5	2	no	—
373	C₂²	—	5	2	no	—
374	C₂²	C₄×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
375	C₄	—	5	1	no	—
376	C₄	—	5	1	no	—
377	C₄	—	6	1	no	—
378	C₄	—	6	1	no	—
379	C₄	—	10	4	no	—
380	C₄	—	30	4	no	—
381	C₄	—	30	1	no	—
382	C₄	—	30	1	no	—
383	C₄	#91907	1	1	yes	characteristic
384	C₄	#91923	1	1	yes	characteristic
385	C₃	#10603878	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	5	2	no	—
387	C₂	—	5	2	no	—
388	C₂	AGL(1,𝔽₅)×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
389	C₂	#11751650	1	1	yes	characteristic
390	C₂	#11751832	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
commutator, socle	C₂²×C₃×C₅	C₂×C₄²
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
prime radical	C₂²×C₃×D₅	C₂²×C₄
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#1745
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
18. #91169	C₄	semidirect
19. #91169	C₄	semidirect
20. #91099	C₄	semidirect
21. C₅×#815	C₄	semidirect
22. #90954	C₄	semidirect
23. #90953	C₄	semidirect
123. #815	AGL(1,𝔽₅)	semidirect
318. C₃×C₅	#1745	semidirect
369. C₅	#68597	semidirect
385. C₃	#10603878	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₃×AGL(1,𝔽₅)	2
#11751788	2
D₅×#815	2
#11746763	2
C₃×(C₂×AGL(1,𝔽₅))⋊C₈	2
#11746517	2
(C₂×AGL(1,𝔽₅))⋊(C₃⋊C₈)	2
#10603878	3
#68597	5