Subgroups — C₅×Dic₃×#104 #14295577

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	C₅×Dic₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#837	C₂	1	1	yes	maximal, characteristic
4	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4555	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×#104	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₅×Q₈×Dic₃	C₄	1	2	yes	complemented
13	C₅×D₄×Dic₃	—	2	2	no	—
14	C₅×D₄×Dic₃	C₄	1	2	yes	complemented
15	C₅×#926	—	2	1	no	—
16	C₅×#926	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Dic₃	—	2	2	no	—
18	C₂×C₄×C₅×Dic₃	—	2	1	no	—
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×#208	C₂²	1	1	yes	characteristic
22	C₃×C₅×#104	C₄	1	4	yes	complemented
23	C₅×#837	C₄	1	4	yes	complemented
24	C₅×#815	—	2	1	no	—
25	C₅×C₈×Dic₃	—	2	1	no	—
26	Dic₃×#104	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₄×C₅×#41	—	3	1	no	—
28	C₂×C₅×#104	—	3	1	no	—
29	C₂×C₅×#104	D₃	1	1	yes	characteristic
30	C₄×C₅×M₁₆	—	3	1	no	—
31	C₄³×C₅	—	3	1	no	—
32	C₅×#339	—	3	1	no	—
33	C₅×#339	—	3	1	no	—
34	C₃×C₅×#41	—	2	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	C₂×C₄	1	2	yes	—
37	C₃×C₅×#41	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	—	2	2	no	—
46	C₂²×C₅×Dic₃	D₄	1	2	yes	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
52	C₅×#217	—	2	1	no	—
53	C₅×#217	—	2	2	no	—
54	C₅×C₄⋊Dic₃	—	2	2	no	—
55	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
56	C₄×C₅×Dic₃	—	2	8	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₄×C₅×Dic₃	—	2	1	no	—
59	C₄×C₅×Dic₃	—	2	2	no	—
60	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
61	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	complemented
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
64	C₅×#208	—	2	1	no	—
65	C₅×#208	C₂×C₄	1	2	yes	complemented
66	C₂×C₅×C₃⋊C₈	—	2	1	no	—
67	Dic₃×#41	C₂×C₅	1	1	yes	characteristic
68	C₂×C₃×#104	C₂×C₅	1	1	yes	characteristic
69	C₂×#837	C₂×C₅	1	1	yes	characteristic
70	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
71	C₄²×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
72	#4555	C₂×C₅	1	1	yes	characteristic, complemented
73	#4523	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
75	C₂×C₅×M₁₆	—	3	1	no	—
76	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
77	C₄×C₅×Q₈	—	3	2	no	—
78	C₄×C₅×D₄	—	3	2	no	—
79	C₄×C₅×D₄	—	6	2	no	—
80	C₅×#117	—	3	1	no	—
81	C₅×#117	—	6	1	no	—
82	C₂×C₄²×C₅	—	3	1	no	—
83	C₂×C₄²×C₅	—	3	1	no	—
84	C₂×C₄²×C₅	—	6	1	no	—
85	C₂×C₄²×C₅	—	6	2	no	—
86	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
87	C₅×#104	—	3	4	no	—
88	C₅×#104	Dic₃	1	4	yes	direct product factor
89	C₅×#97	—	6	1	no	—
90	C₄×C₅×C₈	—	6	1	no	—
91	C₄×#104	—	3	1	no	Sylow
92	C₂³×C₃×C₅	—	2	1	no	—
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₃×C₅×Q₈	—	2	1	no	—
95	C₃×C₅×Q₈	C₄²	1	2	yes	complemented
96	C₃×C₅×D₄	—	2	2	no	—
97	C₃×C₅×D₄	—	2	2	no	—
98	C₃×C₅×D₄	—	2	1	no	—
99	C₃×C₅×D₄	C₄²	1	2	yes	complemented
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₂×C₅×Dic₃	—	2	4	no	—
112	C₂×C₅×Dic₃	—	2	2	no	—
113	C₂×C₅×Dic₃	—	2	4	no	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	4	4	no	—
116	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
117	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
118	C₃×C₅×C₈	—	2	2	no	—
119	C₅×C₃⋊C₈	—	2	2	no	—
120	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
121	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
122	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
123	Q₈×Dic₃	C₄×C₅	1	2	yes	complemented
124	D₄×Dic₃	—	2	2	no	—
125	D₄×Dic₃	C₄×C₅	1	2	yes	complemented
126	#926	—	2	1	no	—
127	#926	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₄×Dic₃	—	2	2	no	—
129	C₂×C₄×Dic₃	—	2	1	no	—
130	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
132	C₂×#208	C₂²×C₅	1	1	yes	characteristic
133	C₃×#104	C₄×C₅	1	4	yes	complemented
134	#837	C₄×C₅	1	4	yes	complemented
135	#815	—	2	1	no	—
136	C₈×Dic₃	—	2	1	no	—
137	C₅×#41	—	2	1	no	—
138	C₅×#41	—	2	1	no	—
139	C₅×#41	C₄×D₃	1	2	yes	—
140	C₅×#41	C₂×Dic₃	1	2	yes	—
141	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	3	2	no	—
147	C₂²×C₄×C₅	—	6	2	no	—
148	C₂²×C₄×C₅	—	6	1	no	—
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₅×M₁₆	—	2	1	no	—
151	C₅×M₁₆	—	3	2	no	—
152	C₅×M₁₆	—	6	1	no	—
153	C₅×M₁₆	C₂×Dic₃	1	2	yes	complemented
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	6	1	no	—
156	C₅×C₄⋊C₄	—	3	2	no	—
157	C₅×C₄⋊C₄	—	6	2	no	—
158	C₅×C₂²⋊C₄	—	6	2	no	—
159	C₅×C₂²⋊C₄	—	6	1	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	3	2	no	—
162	C₄²×C₅	—	3	1	no	—
163	C₄²×C₅	—	3	1	no	—
164	C₄²×C₅	—	3	2	no	—
165	C₄²×C₅	—	6	2	no	—
166	C₄²×C₅	—	6	8	no	—
167	C₄²×C₅	—	6	1	no	—
168	C₄²×C₅	—	6	1	no	—
169	C₄²×C₅	C₂×Dic₃	1	2	yes	complemented
170	C₄×#41	—	3	1	no	—
171	C₂×#104	—	3	1	no	—
172	C₂×#104	C₅×D₃	1	1	yes	characteristic
173	C₄×M₁₆	—	3	1	no	—
174	C₄³	—	3	1	no	—
175	#339	—	3	1	no	—
176	#339	—	3	1	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	—	2	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
183	C₃×C₄×C₅	—	2	4	no	—
184	C₃×C₄×C₅	—	2	2	no	—
185	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
186	C₃×C₄×C₅	#117	1	1	yes	characteristic
187	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
188	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
189	C₅×Dic₃	—	2	4	no	—
190	C₅×Dic₃	—	2	2	no	—
191	C₅×Dic₃	—	4	2	no	—
192	C₅×Dic₃	#104	1	4	yes	direct product factor
193	C₃×#41	—	2	1	no	—
194	C₃×#41	—	2	1	no	—
195	C₃×#41	C₂×C₄×C₅	1	2	yes	—
196	C₃×#41	C₂×C₄×C₅	1	2	yes	—
197	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂×C₃×D₄	—	2	1	no	—
199	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
203	C₂²×Dic₃	—	2	1	no	—
204	C₂²×Dic₃	—	2	2	no	—
205	C₂²×Dic₃	C₅×D₄	1	2	yes	—
206	C₃×M₁₆	—	2	1	no	—
207	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	complemented
208	C₂×C₃×C₈	—	2	1	no	—
209	C₃×C₄²	—	2	1	no	—
210	C₃×C₄²	C₂×C₄×C₅	1	2	yes	complemented
211	#217	—	2	1	no	—
212	#217	—	2	2	no	—
213	C₄⋊Dic₃	—	2	2	no	—
214	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
215	C₄×Dic₃	—	2	8	no	—
216	C₄×Dic₃	—	2	1	no	—
217	C₄×Dic₃	—	2	1	no	—
218	C₄×Dic₃	—	2	2	no	—
219	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
220	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	complemented
221	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
222	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
223	#208	—	2	1	no	—
224	#208	C₂×C₄×C₅	1	2	yes	complemented
225	C₂×C₃⋊C₈	—	2	1	no	—
226	C₂³×C₅	—	2	1	no	—
227	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
228	C₅×Q₈	—	2	1	no	—
229	C₅×Q₈	C₄×Dic₃	1	2	yes	complemented
230	C₅×D₄	—	2	2	no	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	—	2	1	no	—
233	C₅×D₄	C₄×Dic₃	1	2	yes	complemented
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	3	2	no	—
240	C₂×C₄×C₅	—	3	2	no	—
241	C₂×C₄×C₅	—	6	4	no	—
242	C₂×C₄×C₅	—	6	4	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	—	6	2	no	—
245	C₂×C₄×C₅	—	12	4	no	—
246	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
248	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	#237	1	1	yes	characteristic
250	C₂×C₄×C₅	#237	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	—	6	2	no	—
254	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
255	C₂×M₁₆	—	3	1	no	—
256	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
257	C₄×Q₈	—	3	2	no	—
258	C₄×D₄	—	3	2	no	—
259	C₄×D₄	—	6	2	no	—
260	#117	—	3	1	no	—
261	#117	—	6	1	no	—
262	C₂×C₄²	—	3	1	no	—
263	C₂×C₄²	—	3	1	no	—
264	C₂×C₄²	—	6	1	no	—
265	C₂×C₄²	—	6	2	no	—
266	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
267	#104	—	3	4	no	—
268	#104	C₅×Dic₃	1	4	yes	direct product factor
269	#97	—	6	1	no	—
270	C₄×C₈	—	6	1	no	—
271	C₂×C₃×C₅	—	2	1	no	—
272	C₂×C₃×C₅	—	2	1	no	—
273	C₂×C₃×C₅	—	4	2	no	—
274	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂×#104	1	2	yes	—
276	C₂³×C₃	—	2	1	no	—
277	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
278	C₃×Q₈	—	2	1	no	—
279	C₃×Q₈	C₄²×C₅	1	2	yes	complemented
280	C₃×D₄	—	2	2	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	2	1	no	—
283	C₃×D₄	C₄²×C₅	1	2	yes	complemented
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
294	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
295	C₂×Dic₃	—	2	4	no	—
296	C₂×Dic₃	—	2	2	no	—
297	C₂×Dic₃	—	2	4	no	—
298	C₂×Dic₃	—	2	2	no	—
299	C₂×Dic₃	—	4	4	no	—
300	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
301	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
302	C₃×C₈	—	2	2	no	—
303	C₃⋊C₈	—	2	2	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	4	2	no	—
307	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
309	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
310	C₄×C₅	—	2	4	no	—
311	C₄×C₅	—	2	2	no	—
312	C₄×C₅	—	3	4	no	—
313	C₄×C₅	—	6	4	no	—
314	C₄×C₅	—	6	2	no	—
315	C₄×C₅	—	12	2	no	—
316	C₄×C₅	#877	1	1	yes	characteristic
317	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
318	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
319	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
320	#41	—	2	1	no	—
321	#41	—	2	1	no	—
322	#41	C₄×C₅×D₃	1	2	yes	—
323	#41	C₂×C₅×Dic₃	1	2	yes	—
324	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	3	2	no	—
330	C₂²×C₄	—	6	2	no	—
331	C₂²×C₄	—	6	1	no	—
332	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
333	M₁₆	—	2	1	no	—
334	M₁₆	—	3	2	no	—
335	M₁₆	—	6	1	no	—
336	M₁₆	C₂×C₅×Dic₃	1	2	yes	complemented
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	6	1	no	—
339	C₄⋊C₄	—	3	2	no	—
340	C₄⋊C₄	—	6	2	no	—
341	C₂²⋊C₄	—	6	2	no	—
342	C₂²⋊C₄	—	6	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	3	2	no	—
345	C₄²	—	3	1	no	—
346	C₄²	—	3	1	no	—
347	C₄²	—	3	2	no	—
348	C₄²	—	6	2	no	—
349	C₄²	—	6	8	no	—
350	C₄²	—	6	1	no	—
351	C₄²	—	6	1	no	—
352	C₄²	C₂×C₅×Dic₃	1	2	yes	complemented
353	C₃×C₅	C₄×#104	1	1	yes	characteristic, complemented, Hall
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
358	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
359	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
360	C₃×C₄	—	2	4	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
363	C₃×C₄	C₅×#117	1	1	yes	characteristic
364	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
365	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
366	Dic₃	—	2	4	no	—
367	Dic₃	—	2	2	no	—
368	Dic₃	—	4	2	no	—
369	Dic₃	C₅×#104	1	4	yes	direct product factor
370	C₂×C₅	—	2	1	no	—
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	—	4	2	no	—
373	C₂×C₅	D₃×#104	1	2	yes	—
374	C₂×C₅	Dic₃×C₂²⋊C₄	1	1	yes	characteristic
375	C₂³	—	2	1	no	—
376	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
377	Q₈	—	2	1	no	—
378	Q₈	C₄×C₅×Dic₃	1	2	yes	complemented
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	1	no	—
382	D₄	C₄×C₅×Dic₃	1	2	yes	complemented
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	3	2	no	—
389	C₂×C₄	—	3	2	no	—
390	C₂×C₄	—	6	4	no	—
391	C₂×C₄	—	6	4	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	—	6	2	no	—
394	C₂×C₄	—	12	4	no	—
395	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
396	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
397	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
398	C₂×C₄	C₅×#237	1	1	yes	characteristic
399	C₂×C₄	C₅×#237	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	6	2	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	—	4	2	no	—
406	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
407	C₂×C₃	C₂×C₅×#104	1	2	yes	—
408	C₅	Dic₃×#104	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
413	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
414	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
415	C₄	—	2	4	no	—
416	C₄	—	2	2	no	—
417	C₄	—	3	4	no	—
418	C₄	—	6	4	no	—
419	C₄	—	6	2	no	—
420	C₄	—	12	2	no	—
421	C₄	C₅×#877	1	1	yes	characteristic
422	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
423	C₄	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
424	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
425	C₃	C₄×C₅×#104	1	1	yes	characteristic, complemented, Sylow
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	4	2	no	—
429	C₂	C₅×D₃×#104	1	2	yes	—
430	C₂	C₅×Dic₃×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#104	D₃
hypocenter	C₃	C₄×C₅×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#104

Complements

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

N	H ≅ G/N	type
4. C₅×Dic₃×M₁₆	C₂	semidirect
5. C₄²×C₅×Dic₃	C₂	semidirect
6. C₅×#4555	C₂	semidirect
7. C₅×#4523	C₂	semidirect
12. C₅×Q₈×Dic₃	C₄	semidirect
14. C₅×D₄×Dic₃	C₄	semidirect
22. C₃×C₅×#104	C₄	semidirect
23. C₅×#837	C₄	semidirect
26. Dic₃×#104	C₅	direct (N × H)
48. C₃×C₅×M₁₆	C₂×C₄	semidirect
51. C₃×C₄²×C₅	C₂×C₄	semidirect
61. C₄×C₅×Dic₃	C₂×C₄	semidirect
65. C₅×#208	C₂×C₄	semidirect
70. Dic₃×M₁₆	C₂×C₅	semidirect
71. C₄²×Dic₃	C₂×C₅	semidirect
72. #4555	C₂×C₅	semidirect
73. #4523	C₂×C₅	semidirect
88. C₅×#104	Dic₃	direct (N × H)
95. C₃×C₅×Q₈	C₄²	semidirect
99. C₃×C₅×D₄	C₄²	semidirect
123. Q₈×Dic₃	C₄×C₅	semidirect
125. D₄×Dic₃	C₄×C₅	semidirect
133. C₃×#104	C₄×C₅	semidirect
134. #837	C₄×C₅	semidirect
153. C₅×M₁₆	C₂×Dic₃	semidirect
169. C₄²×C₅	C₂×Dic₃	semidirect
192. C₅×Dic₃	#104	direct (N × H)
207. C₃×M₁₆	C₂×C₄×C₅	semidirect
210. C₃×C₄²	C₂×C₄×C₅	semidirect
220. C₄×Dic₃	C₂×C₄×C₅	semidirect
224. #208	C₂×C₄×C₅	semidirect
229. C₅×Q₈	C₄×Dic₃	semidirect
233. C₅×D₄	C₄×Dic₃	semidirect
268. #104	C₅×Dic₃	direct (N × H)
279. C₃×Q₈	C₄²×C₅	semidirect
283. C₃×D₄	C₄²×C₅	semidirect
336. M₁₆	C₂×C₅×Dic₃	semidirect
352. C₄²	C₂×C₅×Dic₃	semidirect
353. C₃×C₅	C₄×#104	semidirect
369. Dic₃	C₅×#104	direct (N × H)
378. Q₈	C₄×C₅×Dic₃	semidirect
382. D₄	C₄×C₅×Dic₃	semidirect
408. C₅	Dic₃×#104	direct (N × H)
425. C₃	C₄×C₅×#104	semidirect

Maximal subgroups

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

subgroup	index
C₅×Dic₃×#41	2
C₂×C₃×C₅×#104	2
C₂×C₅×#837	2
C₅×Dic₃×M₁₆	2
C₄²×C₅×Dic₃	2
C₅×#4555	2
C₅×#4523	2
C₄×C₅×#104	3
Dic₃×#104	5

Subgroups — C5×Dic3×#104 #14295577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₃×#104 #14295577