Subgroups — C₄×#91156 #14295615

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6772	C₂	1	1	yes	maximal, characteristic
2	C₄×#6758	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄²×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91156	C₂	1	2	yes	maximal
5	#11746526	C₂	1	2	yes	maximal, complemented
6	C₄×#4008	—	3	1	no	maximal, Hall
7	C₂×#6772	C₂²	1	1	yes	characteristic
8	C₂×#6758	C₂²	1	2	yes	—
9	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
10	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
11	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
12	C₄×Dic₃₀	C₄	1	1	yes	characteristic, complemented
13	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic, complemented
14	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
15	#91440	—	2	1	no	—
16	C₄×#1201	—	2	1	no	—
17	Dic₅×D₁₂	C₄	1	1	yes	characteristic, complemented
18	#91398	—	2	1	no	—
19	C₄×D₃×Dic₅	—	2	1	no	—
20	#91358	C₂²	1	1	yes	characteristic
21	#91333	C₄	1	1	yes	characteristic, complemented
22	#91231	—	2	1	no	—
23	C₄×C₃⋊#170	—	2	1	no	—
24	#91156	C₄	1	8	yes	direct product factor
25	C₄×#805	—	5	1	no	maximal, Hall
26	C₄×#711	—	3	1	no	—
27	C₂×#4008	—	3	2	no	—
28	C₄²×AGL(1,𝔽₅)	D₃	1	1	yes	characteristic, complemented
29	C₄×#700	—	3	1	no	—
30	#64875	—	3	2	no	—
31	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
32	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
33	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×C₅×D₃	—	2	1	no	—
35	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
36	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
38	C₂×#1201	—	2	1	no	—
39	C₂×D₃×Dic₅	—	2	1	no	—
40	C₂×D₃×Dic₅	—	2	1	no	—
41	#6772	—	2	2	no	—
42	#6772	C₂×C₄	1	4	yes	—
43	C₂×C₃⋊#170	—	2	2	no	—
44	#6758	—	2	2	no	—
45	#6758	C₂×C₄	1	4	yes	complemented
46	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
47	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
48	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
49	C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	complemented
50	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
52	#6712	—	2	1	no	—
53	C₄×Dic₁₅	—	2	1	no	—
54	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
55	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
58	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
59	#6669	—	2	1	no	—
60	(C₂×D₃)⋊Dic₅	—	2	1	no	—
61	#6665	—	2	1	no	—
62	Dic₃×Dic₅	—	2	1	no	—
63	Dic₃×Dic₅	—	2	1	no	—
64	C₄×#235	—	5	1	no	—
65	C₃×C₄³	—	5	1	no	—
66	C₂×#805	—	5	2	no	—
67	C₄×#208	—	5	1	no	—
68	#4523	—	5	2	no	—
69	C₂×#711	—	3	1	no	—
70	C₂×C₄×AGL(1,𝔽₅)	—	2	1	no	—
71	C₂×C₄×AGL(1,𝔽₅)	—	2	1	no	—
72	C₂×C₄×AGL(1,𝔽₅)	C₂×D₃	1	2	yes	—
73	C₂×#700	—	3	2	no	—
74	C₄×C₅×D₄	—	3	1	no	—
75	D₄×Dic₅	—	3	1	no	—
76	C₄×C₂²⋊D₅	—	6	1	no	—
77	C₂×C₄×Dic₅	—	6	1	no	—
78	#4038	—	3	1	no	—
79	#4033	—	3	1	no	—
80	#4027	—	6	1	no	—
81	#4023	—	6	1	no	—
82	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
83	C₄×Dic₁₀	—	3	1	no	—
84	#4008	—	3	8	no	—
85	#4002	—	6	1	no	—
86	C₄×#170	—	6	1	no	—
87	C₄×#104	—	15	1	no	Sylow
88	C₂²×C₅×D₃	—	2	1	no	—
89	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
91	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
92	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×Dic₁₅	—	2	1	no	—
97	C₂×Dic₁₅	—	2	1	no	—
98	Dic₃₀	—	2	1	no	—
99	Dic₃₀	C₄²	1	2	yes	complemented
100	C₂×C₅×Dic₃	—	2	1	no	—
101	C₅×D₁₂	—	2	1	no	—
102	C₅×D₁₂	C₄²	1	2	yes	complemented
103	C₄×C₅×D₃	—	4	2	no	—
104	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
107	C₃×C₄×D₅	—	2	2	no	—
108	C₃×C₄×D₅	—	2	2	no	—
109	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
110	C₃×C₄×D₅	#41	1	2	yes	—
111	#1201	—	2	4	no	—
112	D₃×Dic₅	—	2	4	no	—
113	D₃×Dic₅	—	4	2	no	—
114	C₃⋊#170	—	2	4	no	—
115	C₂×#235	—	5	1	no	—
116	C₂×C₃×C₄²	—	5	1	no	—
117	C₂×C₃×C₄²	—	5	2	no	—
118	C₂×C₃×C₄²	—	10	1	no	—
119	C₂×C₃×C₄²	—	10	1	no	—
120	C₄×#67	—	10	1	no	—
121	C₄×#67	—	10	1	no	—
122	#926	—	5	1	no	—
123	C₂×#208	—	5	2	no	—
124	C₄×D₁₂	—	5	1	no	—
125	C₄×D₁₂	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
126	#872	—	10	1	no	—
127	C₄²×D₃	—	10	1	no	—
128	C₄×Dic₆	—	5	1	no	—
129	C₄×Dic₆	—	5	1	no	—
130	#805	—	5	8	no	—
131	#803	—	10	1	no	—
132	C₄×C₃⋊C₈	—	10	1	no	—
133	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
134	C₂×C₅×D₄	—	3	1	no	—
135	C₂²×C₄×C₅	—	6	1	no	—
136	C₂×C₂²⋊D₅	—	6	1	no	—
137	C₂²×Dic₅	—	6	1	no	—
138	C₂²×Dic₅	—	6	1	no	—
139	#711	—	3	4	no	—
140	#711	—	6	2	no	—
141	C₂×C₄×D₅	#67	1	1	yes	characteristic
142	C₂×C₄×D₅	#67	1	1	yes	characteristic
143	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
144	C₂×Dic₁₀	—	3	1	no	—
145	C₂×#170	—	6	2	no	—
146	C₄×AGL(1,𝔽₅)	—	2	4	no	—
147	C₄×AGL(1,𝔽₅)	—	2	4	no	—
148	C₄×AGL(1,𝔽₅)	—	2	2	no	—
149	C₄×AGL(1,𝔽₅)	C₄×D₃	1	4	yes	complemented
150	#700	—	3	4	no	—
151	#700	—	6	2	no	—
152	C₅×C₄⋊C₄	—	3	1	no	—
153	C₅×C₂²⋊C₄	—	6	1	no	—
154	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
155	C₂²⋊Dic₅	—	6	1	no	—
156	#685	—	6	1	no	—
157	C₄⋊Dic₅	—	3	1	no	—
158	#683	—	6	1	no	—
159	#683	—	6	1	no	—
160	C₄×Dic₅	—	6	1	no	—
161	C₄×Dic₅	—	6	1	no	—
162	C₄×Dic₅	—	6	1	no	—
163	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
164	C₄×Dic₅	D₁₂	1	1	yes	characteristic
165	C₄×Dic₅	D₁₂	1	1	yes	characteristic
166	C₄×#41	—	15	1	no	—
167	C₂×#104	—	15	2	no	—
168	C₄×M₁₆	—	15	1	no	—
169	C₄³	—	5	1	no	—
170	#339	—	15	2	no	—
171	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₅×D₃	—	2	2	no	—
173	C₂×C₅×D₃	—	4	1	no	—
174	C₂×C₅×D₃	—	4	1	no	—
175	C₂×C₃×D₅	—	2	1	no	—
176	C₂×C₃×D₅	—	2	1	no	—
177	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
178	C₃×AGL(1,𝔽₅)	—	2	8	no	—
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	#104	1	2	yes	complemented
181	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
182	C₃×C₄×C₅	#117	1	1	yes	characteristic
183	Dic₁₅	—	2	2	no	—
184	Dic₁₅	—	4	1	no	—
185	C₃×Dic₅	—	2	1	no	—
186	C₃×Dic₅	#104	1	2	yes	complemented
187	C₃×Dic₅	C₄×D₄	1	2	yes	—
188	C₅×Dic₃	—	4	1	no	—
189	C₂²×C₃×C₄	—	5	1	no	—
190	C₂²×C₃×C₄	—	5	1	no	—
191	C₂²×C₃×C₄	—	5	1	no	—
192	C₂²×C₃×C₄	—	10	2	no	—
193	C₂×#67	—	10	1	no	—
194	#235	—	5	4	no	—
195	#235	—	10	2	no	—
196	C₂×D₁₂	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
197	C₂×C₄×D₃	—	2	1	no	—
198	C₂×C₄×D₃	—	10	1	no	—
199	C₂×C₄×D₃	—	10	1	no	—
200	C₂×Dic₆	—	5	1	no	—
201	C₃×C₄²	—	5	1	no	—
202	C₃×C₄²	—	5	1	no	—
203	C₃×C₄²	—	5	1	no	—
204	C₃×C₄²	—	5	4	no	—
205	C₃×C₄²	—	10	2	no	—
206	C₃×C₄²	—	10	4	no	—
207	C₃×C₄²	—	10	4	no	—
208	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
209	#217	—	10	1	no	—
210	(C₂×D₃)⋊C₄	—	2	1	no	—
211	(C₂×D₃)⋊C₄	—	10	1	no	—
212	C₄⋊Dic₃	—	5	1	no	—
213	C₄⋊Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
214	Dic₃⋊C₄	—	10	1	no	—
215	Dic₃⋊C₄	—	10	1	no	—
216	C₄×Dic₃	—	10	1	no	—
217	C₄×Dic₃	—	10	1	no	—
218	C₄×Dic₃	—	10	1	no	—
219	#208	—	5	4	no	—
220	#208	—	10	2	no	—
221	C₂×C₃⋊C₈	—	10	2	no	—
222	C₂³×C₅	—	6	1	no	—
223	C₂²×D₅	C₂×#67	1	1	yes	characteristic
224	C₂×AGL(1,𝔽₅)	—	2	4	no	—
225	C₂×AGL(1,𝔽₅)	—	2	4	no	—
226	C₂×AGL(1,𝔽₅)	—	2	4	no	—
227	C₅×D₄	—	3	2	no	—
228	C₅×D₄	—	6	1	no	—
229	C₂×C₄×C₅	—	6	1	no	—
230	C₂×C₄×C₅	—	12	2	no	—
231	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
234	C₂²⋊D₅	—	6	4	no	—
235	C₂×Dic₅	—	6	1	no	—
236	C₂×Dic₅	—	6	4	no	—
237	C₂×Dic₅	—	6	1	no	—
238	C₂×Dic₅	—	12	2	no	—
239	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
240	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
241	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
242	C₄×D₅	—	2	2	no	—
243	C₄×D₅	—	2	2	no	—
244	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
245	C₄×D₅	#235	1	2	yes	—
246	Dic₁₀	—	3	2	no	—
247	Dic₁₀	—	6	1	no	—
248	#170	—	6	4	no	—
249	C₂×#41	—	15	1	no	—
250	C₂×M₁₆	—	15	2	no	—
251	C₄×Q₈	—	15	1	no	—
252	C₄×Q₈	—	15	1	no	—
253	C₄×D₄	—	3	1	no	—
254	C₄×D₄	—	15	1	no	—
255	C₄×D₄	—	30	1	no	—
256	C₄×D₄	—	30	1	no	—
257	#117	—	15	1	no	—
258	#117	—	30	1	no	—
259	C₂×C₄²	—	5	1	no	—
260	C₂×C₄²	—	5	2	no	—
261	C₂×C₄²	—	10	1	no	—
262	C₂×C₄²	—	10	1	no	—
263	C₂×C₄²	—	30	1	no	—
264	#104	—	15	8	no	—
265	#97	—	30	1	no	—
266	C₄×C₈	—	30	1	no	—
267	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
270	C₃×D₅	—	2	2	no	—
271	C₅×D₃	—	4	2	no	—
272	C₂³×C₃	—	5	1	no	—
273	C₂²×D₃	—	2	1	no	—
274	C₂×C₃×C₄	—	5	1	no	—
275	C₂×C₃×C₄	—	5	1	no	—
276	C₂×C₃×C₄	—	5	2	no	—
277	C₂×C₃×C₄	—	5	2	no	—
278	C₂×C₃×C₄	—	5	1	no	—
279	C₂×C₃×C₄	—	10	2	no	—
280	C₂×C₃×C₄	—	10	4	no	—
281	C₂×C₃×C₄	—	10	4	no	—
282	C₂×C₃×C₄	—	10	4	no	—
283	C₂×C₃×C₄	—	10	2	no	—
284	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
287	#67	—	10	4	no	—
288	C₂×Dic₃	—	2	1	no	—
289	C₂×Dic₃	—	10	1	no	—
290	C₂×Dic₃	—	10	1	no	—
291	D₁₂	—	2	1	no	—
292	D₁₂	C₄×AGL(1,𝔽₅)	1	2	yes	complemented
293	C₄×D₃	—	4	2	no	—
294	C₄×D₃	—	10	4	no	—
295	C₄×D₃	—	20	2	no	—
296	Dic₆	—	5	2	no	—
297	Dic₆	—	10	1	no	—
298	C₃⋊C₈	—	10	4	no	—
299	C₂²×C₅	—	6	2	no	—
300	C₂²×C₅	—	12	1	no	—
301	C₂²×C₅	—	12	1	no	—
302	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
303	C₂×D₅	—	2	1	no	—
304	C₂×D₅	—	2	1	no	—
305	C₂×D₅	C₄×#67	1	2	yes	—
306	AGL(1,𝔽₅)	—	2	8	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	12	1	no	—
309	C₄×C₅	#805	1	2	yes	complemented
310	C₄×C₅	C₄²×D₃	1	1	yes	characteristic
311	C₄×C₅	#872	1	1	yes	characteristic
312	Dic₅	—	2	1	no	—
313	Dic₅	—	6	2	no	—
314	Dic₅	—	12	1	no	—
315	Dic₅	#805	1	2	yes	complemented
316	Dic₅	C₄×D₁₂	1	2	yes	—
317	#41	—	15	4	no	—
318	#41	—	30	2	no	—
319	C₂×Q₈	—	15	1	no	—
320	C₂×D₄	—	3	1	no	—
321	C₂×D₄	—	30	1	no	—
322	C₂²×C₄	—	5	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	5	1	no	—
325	C₂²×C₄	—	6	1	no	—
326	C₂²×C₄	—	10	2	no	—
327	C₂²×C₄	—	30	1	no	—
328	C₂²×C₄	—	30	1	no	—
329	M₁₆	—	15	4	no	—
330	M₁₆	—	30	2	no	—
331	C₂×C₈	—	30	2	no	—
332	C₄⋊C₄	—	3	1	no	—
333	C₄⋊C₄	—	15	1	no	—
334	C₄⋊C₄	—	30	1	no	—
335	C₄⋊C₄	—	30	1	no	—
336	C₂²⋊C₄	—	6	1	no	—
337	C₂²⋊C₄	—	30	1	no	—
338	C₂²⋊C₄	—	30	1	no	—
339	C₄²	—	5	1	no	—
340	C₄²	—	5	1	no	—
341	C₄²	—	5	1	no	—
342	C₄²	—	5	4	no	—
343	C₄²	—	10	2	no	—
344	C₄²	—	10	4	no	—
345	C₄²	—	10	4	no	—
346	C₄²	—	30	1	no	—
347	C₄²	—	30	1	no	—
348	C₄²	—	30	1	no	—
349	C₄²	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
350	C₃×C₅	C₄×#104	1	1	yes	characteristic, complemented, Hall
351	C₂²×C₃	—	5	2	no	—
352	C₂²×C₃	—	10	1	no	—
353	C₂²×C₃	—	10	1	no	—
354	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
355	C₂×D₃	—	2	2	no	—
356	C₂×D₃	—	4	1	no	—
357	C₂×D₃	—	4	1	no	—
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	5	2	no	—
360	C₃×C₄	—	5	2	no	—
361	C₃×C₄	—	10	8	no	—
362	C₃×C₄	—	10	1	no	—
363	C₃×C₄	#4008	1	2	yes	complemented
364	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
365	C₃×C₄	#4130	1	1	yes	characteristic
366	Dic₃	—	4	1	no	—
367	Dic₃	—	10	2	no	—
368	Dic₃	—	20	1	no	—
369	C₂×C₅	—	12	2	no	—
370	C₂×C₅	C₂×#805	1	1	yes	characteristic
371	C₂×C₅	C₂×#805	1	1	yes	characteristic
372	C₂×C₅	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
373	D₅	—	2	2	no	—
374	C₂³	—	5	1	no	—
375	C₂³	—	6	1	no	—
376	Q₈	—	15	2	no	—
377	Q₈	—	30	1	no	—
378	D₄	—	3	2	no	—
379	D₄	—	6	1	no	—
380	D₄	—	30	4	no	—
381	C₂×C₄	—	5	1	no	—
382	C₂×C₄	—	5	1	no	—
383	C₂×C₄	—	5	2	no	—
384	C₂×C₄	—	5	2	no	—
385	C₂×C₄	—	5	1	no	—
386	C₂×C₄	—	6	1	no	—
387	C₂×C₄	—	10	2	no	—
388	C₂×C₄	—	10	4	no	—
389	C₂×C₄	—	10	4	no	—
390	C₂×C₄	—	10	4	no	—
391	C₂×C₄	—	10	2	no	—
392	C₂×C₄	—	12	2	no	—
393	C₂×C₄	—	30	4	no	—
394	C₂×C₄	—	30	1	no	—
395	C₂×C₄	—	30	1	no	—
396	C₂×C₄	—	60	2	no	—
397	C₂×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
398	C₂×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
399	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
400	C₈	—	30	4	no	—
401	C₂×C₃	—	10	2	no	—
402	C₂×C₃	C₄×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₂×C₃	C₂×#4008	1	1	yes	characteristic
404	C₂×C₃	D₅⋊#104	1	1	yes	characteristic
405	D₃	—	4	2	no	—
406	C₅	C₄×#805	1	1	yes	characteristic, complemented, Sylow
407	C₂²	—	5	2	no	—
408	C₂²	—	6	2	no	—
409	C₂²	—	10	1	no	—
410	C₂²	—	10	1	no	—
411	C₂²	—	12	1	no	—
412	C₂²	—	12	1	no	—
413	C₂²	C₂×(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	5	2	no	—
416	C₄	—	5	2	no	—
417	C₄	—	10	8	no	—
418	C₄	—	10	1	no	—
419	C₄	—	12	1	no	—
420	C₄	—	30	2	no	—
421	C₄	—	60	1	no	—
422	C₄	#91156	1	2	yes	direct product factor
423	C₄	#91909	1	1	yes	characteristic
424	C₄	C₄×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
425	C₃	C₄×#4008	1	1	yes	characteristic, complemented, Sylow
426	C₂	—	10	2	no	—
427	C₂	—	12	2	no	—
428	C₂	C₂×#91156	1	1	yes	characteristic
429	C₂	D₅⋊#805	1	1	yes	characteristic
430	C₂	C₄×(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
Fitting	C₃×C₄²×C₅	C₂×C₄
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×#6772	C₂²
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₄²	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₄×#104
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₄×#6758	C₂	semidirect
3. C₃×C₄²×AGL(1,𝔽₅)	C₂	semidirect
5. #11746526	C₂	semidirect
12. C₄×Dic₃₀	C₄	semidirect
13. C₄×C₅×D₁₂	C₄	semidirect
17. Dic₅×D₁₂	C₄	semidirect
21. #91333	C₄	semidirect
24. #91156	C₄	direct (N × H)
28. C₄²×AGL(1,𝔽₅)	D₃	semidirect
45. #6758	C₂×C₄	semidirect
49. C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	semidirect
99. Dic₃₀	C₄²	semidirect
102. C₅×D₁₂	C₄²	semidirect
125. C₄×D₁₂	AGL(1,𝔽₅)	semidirect
149. C₄×AGL(1,𝔽₅)	C₄×D₃	semidirect
180. C₃×C₄×C₅	#104	semidirect
186. C₃×Dic₅	#104	semidirect
292. D₁₂	C₄×AGL(1,𝔽₅)	semidirect
309. C₄×C₅	#805	semidirect
315. Dic₅	#805	semidirect
350. C₃×C₅	C₄×#104	semidirect
363. C₃×C₄	#4008	semidirect
406. C₅	C₄×#805	semidirect
422. C₄	#91156	direct (N × H)
425. C₃	C₄×#4008	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6772	2
C₄×#6758	2
C₃×C₄²×AGL(1,𝔽₅)	2
C₂×#91156	2
#11746526	2
C₄×#4008	3
C₄×#805	5

Subgroups — C4×#91156 #14295615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#91156 #14295615