Subgroups — C₅×#83900 #14426214

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5832	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5233	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5185	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5182	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5166	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5163	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5153	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5150	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5113	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3035	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂×C₅×#235	C₂²	1	1	yes	characteristic
20	C₃×C₅×#135	—	2	4	no	—
21	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₅×#950	—	2	4	no	—
27	C₅×#947	C₂²	1	1	yes	characteristic
28	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
29	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
30	C₅×#944	C₂²	1	1	yes	characteristic
31	C₂×C₅×#216	C₂²	1	1	yes	characteristic
32	C₂×C₅×#215	C₂²	1	1	yes	characteristic
33	C₅×#940	C₂²	1	1	yes	characteristic
34	C₅×#939	—	2	1	no	—
35	C₅×#939	—	2	1	no	—
36	C₅×#936	C₂²	1	1	yes	characteristic
37	C₅×D₄×Dic₃	—	2	1	no	—
38	C₅×D₄×Dic₃	—	2	1	no	—
39	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
40	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
41	C₂×C₅×#214	C₂²	1	1	yes	characteristic
42	C₂×C₅×#213	C₂²	1	1	yes	characteristic
43	C₄×C₅×#67	—	2	1	no	—
44	C₄×C₅×#67	—	2	1	no	—
45	C₅×#926	—	2	1	no	—
46	C₅×#926	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₅×Dic₃	—	2	1	no	—
48	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
49	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
50	C₅×#835	C₂²	1	1	yes	characteristic
51	C₅×#835	C₂²	1	1	yes	characteristic
52	C₅×#832	C₂²	1	1	yes	characteristic
53	C₅×#832	C₂²	1	1	yes	characteristic
54	C₅×#821	C₂²	1	1	yes	characteristic
55	C₅×#821	C₂²	1	1	yes	characteristic
56	C₅×#816	C₂²	1	1	yes	characteristic
57	C₅×#816	C₂²	1	1	yes	characteristic
58	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
59	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
60	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
61	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
62	#83900	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×#135	—	3	1	no	—
64	C₂×C₅×#135	D₃	1	1	yes	characteristic, complemented
65	C₅×#532	—	3	1	no	—
66	C₄×C₅×#41	—	3	1	no	—
67	C₅×#464	—	3	1	no	—
68	C₅×#464	—	3	1	no	—
69	C₅×#463	—	3	1	no	—
70	C₅×#463	—	3	1	no	—
71	C₅×#462	—	3	1	no	—
72	C₅×#461	—	3	1	no	—
73	C₅×#460	—	3	1	no	—
74	C₅×#459	—	3	1	no	—
75	C₂×C₅×C₄⋊C₈	—	3	1	no	—
76	C₅×#416	—	3	1	no	—
77	C₅×#416	—	3	1	no	—
78	C₃×C₅×#41	—	2	2	no	—
79	C₃×C₅×#41	—	2	2	no	—
80	C₃×C₅×#41	—	2	2	no	—
81	C₃×C₅×#41	D₄	1	4	yes	complemented
82	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	—	2	1	no	—
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	—	2	1	no	—
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₅×#67	—	2	1	no	—
92	C₂×C₅×#67	—	2	1	no	—
93	C₂×C₅×#67	—	2	1	no	—
94	C₂²×C₅×Dic₃	—	2	1	no	—
95	C₂²×C₅×Dic₃	—	2	1	no	—
96	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
97	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
98	C₅×#235	—	2	2	no	—
99	C₅×#235	—	2	2	no	—
100	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
101	C₂×C₄×C₅×D₃	—	2	1	no	—
102	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
103	C₃×C₅×Q₁₆	—	2	2	no	—
104	C₃×C₅×SD₁₆	—	2	2	no	—
105	C₃×C₅×SD₁₆	—	2	2	no	—
106	C₃×C₅×D₈	—	2	2	no	—
107	C₂×C₃×C₅×C₈	—	2	2	no	—
108	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₅×#217	—	2	1	no	—
111	C₅×#217	—	2	1	no	—
112	C₅×#217	—	2	1	no	—
113	C₅×#217	—	2	1	no	—
114	C₅×#217	—	2	1	no	—
115	C₅×#216	—	2	2	no	—
116	C₅×#215	—	2	2	no	—
117	C₅×#214	—	2	2	no	—
118	C₅×#213	—	2	2	no	—
119	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
120	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
121	C₅×C₄⋊Dic₃	—	2	1	no	—
122	C₅×C₄⋊Dic₃	—	2	1	no	—
123	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
124	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
125	C₅×Dic₃⋊C₄	—	2	1	no	—
126	C₅×Dic₃⋊C₄	—	2	1	no	—
127	C₄×C₅×Dic₃	—	2	1	no	—
128	C₄×C₅×Dic₃	—	2	1	no	—
129	C₄×C₅×Dic₃	—	2	1	no	—
130	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
131	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
132	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
133	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
134	C₂×C₅×C₃⋊C₈	—	2	2	no	—
135	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
136	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
137	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
138	#5832	C₂×C₅	1	1	yes	characteristic, complemented
139	Dic₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×#950	C₂×C₅	1	1	yes	characteristic, complemented
141	#5233	C₂×C₅	1	1	yes	characteristic, complemented
142	#5185	C₂×C₅	1	1	yes	characteristic, complemented
143	#5182	C₂×C₅	1	1	yes	characteristic, complemented
144	#5166	C₂×C₅	1	1	yes	characteristic, complemented
145	#5165	C₂×C₅	1	1	yes	characteristic, complemented
146	#5163	C₂×C₅	1	1	yes	characteristic, complemented
147	#5162	C₂×C₅	1	1	yes	characteristic, complemented
148	#5153	C₂×C₅	1	1	yes	characteristic, complemented
149	#5150	C₂×C₅	1	1	yes	characteristic, complemented
150	#5113	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×C₅×#41	—	3	1	no	—
153	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
154	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
155	C₅×#135	—	2	4	no	—
156	C₅×#135	—	6	4	no	—
157	C₂×C₅×Q₁₆	—	3	1	no	—
158	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
159	C₂×C₅×SD₁₆	—	3	1	no	—
160	C₂×C₅×SD₁₆	—	3	1	no	—
161	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
162	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
163	C₂×C₅×D₈	—	3	1	no	—
164	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
165	C₂²×C₅×C₈	—	3	1	no	—
166	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
167	C₅×C₄⋊Q₈	—	3	1	no	—
168	C₅×#127	—	3	1	no	—
169	C₅×#124	—	3	1	no	—
170	C₅×#124	—	3	1	no	—
171	C₅×#121	—	6	1	no	—
172	C₅×#121	—	6	1	no	—
173	C₄×C₅×Q₈	—	3	1	no	—
174	C₄×C₅×Q₈	—	3	1	no	—
175	C₄×C₅×D₄	—	3	1	no	—
176	C₄×C₅×D₄	—	3	1	no	—
177	C₄×C₅×D₄	—	6	1	no	—
178	C₄×C₅×D₄	—	6	1	no	—
179	C₄×C₅×D₄	—	6	1	no	—
180	C₄×C₅×D₄	—	6	1	no	—
181	C₅×#117	—	3	1	no	—
182	C₅×#117	—	6	1	no	—
183	C₂×C₄²×C₅	—	3	1	no	—
184	C₂×C₄²×C₅	—	6	1	no	—
185	C₅×C₄⋊C₈	—	3	1	no	—
186	C₅×C₄⋊C₈	—	3	1	no	—
187	C₅×C₄⋊C₈	—	3	1	no	—
188	C₅×C₄⋊C₈	—	3	1	no	—
189	C₅×#103	—	3	1	no	—
190	C₅×#103	—	3	1	no	—
191	C₅×#103	—	3	1	no	—
192	C₅×#103	—	3	1	no	—
193	C₅×#102	—	3	1	no	—
194	C₅×#102	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	—	3	1	no	—
197	#3035	—	3	1	no	Sylow
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂³×C₃×C₅	—	2	1	no	—
200	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₅×D₃	—	2	1	no	—
202	C₃×C₅×Q₈	—	2	1	no	—
203	C₃×C₅×Q₈	—	2	1	no	—
204	C₃×C₅×Q₈	—	2	1	no	—
205	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
206	C₃×C₅×D₄	—	2	4	no	—
207	C₃×C₅×D₄	—	2	1	no	—
208	C₃×C₅×D₄	—	2	1	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₃×C₅×D₄	—	4	2	no	—
211	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	4	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	4	2	no	—
216	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
218	C₂×C₃×C₄×C₅	#41	1	2	yes	—
219	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₅×#67	—	4	2	no	—
221	C₅×#67	—	4	2	no	—
222	C₅×#67	—	4	2	no	—
223	C₂×C₅×Dic₃	—	2	2	no	—
224	C₂×C₅×Dic₃	—	2	1	no	—
225	C₂×C₅×Dic₃	—	2	1	no	—
226	C₂×C₅×Dic₃	—	2	1	no	—
227	C₂×C₅×Dic₃	—	4	1	no	—
228	C₂×C₅×Dic₃	—	4	2	no	—
229	C₂×C₅×Dic₃	—	4	2	no	—
230	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
231	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
232	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
233	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
234	C₅×D₁₂	—	2	1	no	—
235	C₅×D₁₂	—	2	1	no	—
236	C₄×C₅×D₃	—	4	2	no	—
237	C₅×Dic₆	—	2	1	no	—
238	C₅×Dic₆	—	2	1	no	—
239	C₃×C₅×C₈	—	2	1	no	—
240	C₃×C₅×C₈	—	2	1	no	—
241	C₅×C₃⋊C₈	—	2	1	no	—
242	C₅×C₃⋊C₈	—	2	1	no	—
243	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
245	C₂×#235	C₂²×C₅	1	1	yes	characteristic
246	C₃×#135	—	2	4	no	—
247	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
251	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
252	#950	—	2	4	no	—
253	#947	C₂²×C₅	1	1	yes	characteristic
254	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
255	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
256	#944	C₂²×C₅	1	1	yes	characteristic
257	C₂×#216	C₂²×C₅	1	1	yes	characteristic
258	C₂×#215	C₂²×C₅	1	1	yes	characteristic
259	#940	C₂²×C₅	1	1	yes	characteristic
260	#939	—	2	1	no	—
261	#939	—	2	1	no	—
262	#936	C₂²×C₅	1	1	yes	characteristic
263	D₄×Dic₃	—	2	1	no	—
264	D₄×Dic₃	—	2	1	no	—
265	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
266	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
267	C₂×#214	C₂²×C₅	1	1	yes	characteristic
268	C₂×#213	C₂²×C₅	1	1	yes	characteristic
269	C₄×#67	—	2	1	no	—
270	C₄×#67	—	2	1	no	—
271	#926	—	2	1	no	—
272	#926	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₄×Dic₃	—	2	1	no	—
274	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
275	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
276	#835	C₂²×C₅	1	1	yes	characteristic
277	#835	C₂²×C₅	1	1	yes	characteristic
278	#832	C₂²×C₅	1	1	yes	characteristic
279	#832	C₂²×C₅	1	1	yes	characteristic
280	#821	C₂²×C₅	1	1	yes	characteristic
281	#821	C₂²×C₅	1	1	yes	characteristic
282	#816	C₂²×C₅	1	1	yes	characteristic
283	#816	C₂²×C₅	1	1	yes	characteristic
284	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
285	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
286	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
287	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
288	C₅×#41	—	2	2	no	—
289	C₅×#41	—	2	2	no	—
290	C₅×#41	—	2	2	no	—
291	C₅×#41	—	6	2	no	—
292	C₅×#41	—	6	2	no	—
293	C₅×#41	#67	1	4	yes	complemented
294	C₂×C₅×Q₈	—	3	1	no	—
295	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
296	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
297	C₂×C₅×D₄	—	2	1	no	—
298	C₂×C₅×D₄	—	2	1	no	—
299	C₂×C₅×D₄	—	3	1	no	—
300	C₂×C₅×D₄	—	6	1	no	—
301	C₂×C₅×D₄	—	6	1	no	—
302	C₂×C₅×D₄	—	6	1	no	—
303	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
304	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
305	C₂²×C₄×C₅	—	2	1	no	—
306	C₂²×C₄×C₅	—	2	1	no	—
307	C₂²×C₄×C₅	—	3	1	no	—
308	C₂²×C₄×C₅	—	3	1	no	—
309	C₂²×C₄×C₅	—	6	1	no	—
310	C₂²×C₄×C₅	—	6	1	no	—
311	C₂²×C₄×C₅	—	6	1	no	—
312	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
313	C₅×Q₁₆	—	2	2	no	—
314	C₅×Q₁₆	—	6	2	no	—
315	C₅×SD₁₆	—	2	2	no	—
316	C₅×SD₁₆	—	2	2	no	—
317	C₅×SD₁₆	—	6	2	no	—
318	C₅×SD₁₆	—	6	2	no	—
319	C₅×D₈	—	2	2	no	—
320	C₅×D₈	—	6	2	no	—
321	C₂×C₅×C₈	—	2	2	no	—
322	C₂×C₅×C₈	—	3	1	no	—
323	C₂×C₅×C₈	—	3	1	no	—
324	C₂×C₅×C₈	—	6	2	no	—
325	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
326	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
327	C₅×C₄⋊C₄	—	3	1	no	—
328	C₅×C₄⋊C₄	—	3	1	no	—
329	C₅×C₄⋊C₄	—	6	1	no	—
330	C₅×C₄⋊C₄	—	6	1	no	—
331	C₅×C₄⋊C₄	—	6	1	no	—
332	C₅×C₄⋊C₄	—	6	1	no	—
333	C₅×C₂²⋊C₄	—	6	1	no	—
334	C₅×C₂²⋊C₄	—	6	1	no	—
335	C₅×C₂²⋊C₄	—	6	1	no	—
336	C₅×C₂²⋊C₄	—	6	1	no	—
337	C₅×C₂²⋊C₄	—	6	1	no	—
338	C₅×C₂²⋊C₄	—	6	1	no	—
339	C₅×C₂²⋊C₄	—	6	1	no	—
340	C₄²×C₅	—	3	1	no	—
341	C₄²×C₅	—	3	1	no	—
342	C₄²×C₅	—	3	1	no	—
343	C₄²×C₅	—	3	1	no	—
344	C₄²×C₅	—	6	1	no	—
345	C₄²×C₅	—	6	1	no	—
346	C₄²×C₅	—	6	1	no	—
347	C₂×#135	—	3	1	no	—
348	C₂×#135	C₅×D₃	1	1	yes	characteristic, complemented
349	#532	—	3	1	no	—
350	C₄×#41	—	3	1	no	—
351	#464	—	3	1	no	—
352	#464	—	3	1	no	—
353	#463	—	3	1	no	—
354	#463	—	3	1	no	—
355	#462	—	3	1	no	—
356	#461	—	3	1	no	—
357	#460	—	3	1	no	—
358	#459	—	3	1	no	—
359	C₂×C₄⋊C₈	—	3	1	no	—
360	#416	—	3	1	no	—
361	#416	—	3	1	no	—
362	C₂²×C₃×C₅	—	2	1	no	—
363	C₂²×C₃×C₅	—	2	1	no	—
364	C₂²×C₃×C₅	—	2	2	no	—
365	C₂²×C₃×C₅	—	4	1	no	—
366	C₂²×C₃×C₅	—	4	1	no	—
367	C₂²×C₃×C₅	—	4	1	no	—
368	C₂²×C₃×C₅	—	4	1	no	—
369	C₂²×C₃×C₅	—	4	1	no	—
370	C₂²×C₃×C₅	#121	1	2	yes	—
371	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₅×D₃	—	4	1	no	—
373	C₂×C₅×D₃	—	4	1	no	—
374	C₂×C₅×D₃	—	4	1	no	—
375	C₃×C₄×C₅	—	2	2	no	—
376	C₃×C₄×C₅	—	4	1	no	—
377	C₃×C₄×C₅	#121	1	2	yes	—
378	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
379	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
380	C₅×Dic₃	—	2	1	no	—
381	C₅×Dic₃	—	2	1	no	—
382	C₅×Dic₃	—	2	1	no	—
383	C₅×Dic₃	—	4	1	no	—
384	C₅×Dic₃	—	4	1	no	—
385	C₅×Dic₃	—	4	1	no	—
386	C₅×Dic₃	#135	1	2	yes	complemented
387	C₃×#41	—	2	2	no	—
388	C₃×#41	—	2	2	no	—
389	C₃×#41	—	2	2	no	—
390	C₃×#41	C₅×D₄	1	4	yes	complemented
391	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
392	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₃×D₄	—	2	1	no	—
394	C₂×C₃×D₄	—	2	1	no	—
395	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
396	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
397	C₂²×C₃×C₄	—	2	1	no	—
398	C₂²×C₃×C₄	—	2	1	no	—
399	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
400	C₂×#67	—	2	1	no	—
401	C₂×#67	—	2	1	no	—
402	C₂×#67	—	2	1	no	—
403	C₂²×Dic₃	—	2	1	no	—
404	C₂²×Dic₃	—	2	1	no	—
405	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
406	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
407	#235	—	2	2	no	—
408	#235	—	2	2	no	—
409	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₄×D₃	—	2	1	no	—
411	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
412	C₃×Q₁₆	—	2	2	no	—
413	C₃×SD₁₆	—	2	2	no	—
414	C₃×SD₁₆	—	2	2	no	—
415	C₃×D₈	—	2	2	no	—
416	C₂×C₃×C₈	—	2	2	no	—
417	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
419	#217	—	2	1	no	—
420	#217	—	2	1	no	—
421	#217	—	2	1	no	—
422	#217	—	2	1	no	—
423	#217	—	2	1	no	—
424	#216	—	2	2	no	—
425	#215	—	2	2	no	—
426	#214	—	2	2	no	—
427	#213	—	2	2	no	—
428	(C₂×D₃)⋊C₄	—	2	1	no	—
429	(C₂×D₃)⋊C₄	—	2	1	no	—
430	C₄⋊Dic₃	—	2	1	no	—
431	C₄⋊Dic₃	—	2	1	no	—
432	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
433	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
434	Dic₃⋊C₄	—	2	1	no	—
435	Dic₃⋊C₄	—	2	1	no	—
436	C₄×Dic₃	—	2	1	no	—
437	C₄×Dic₃	—	2	1	no	—
438	C₄×Dic₃	—	2	1	no	—
439	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
440	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
441	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
442	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
443	C₂×C₃⋊C₈	—	2	2	no	—
444	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
445	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
446	C₂³×C₅	—	2	1	no	—
447	C₂³×C₅	—	2	1	no	—
448	C₂³×C₅	—	6	1	no	—
449	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
450	C₅×Q₈	—	2	1	no	—
451	C₅×Q₈	—	2	1	no	—
452	C₅×Q₈	—	2	1	no	—
453	C₅×Q₈	—	6	1	no	—
454	C₅×Q₈	—	6	1	no	—
455	C₅×Q₈	C₂×#67	1	2	yes	—
456	C₅×D₄	—	2	4	no	—
457	C₅×D₄	—	2	1	no	—
458	C₅×D₄	—	2	1	no	—
459	C₅×D₄	—	2	1	no	—
460	C₅×D₄	—	4	2	no	—
461	C₅×D₄	—	6	1	no	—
462	C₅×D₄	—	6	1	no	—
463	C₅×D₄	—	12	2	no	—
464	C₅×D₄	—	12	2	no	—
465	C₅×D₄	—	12	2	no	—
466	C₅×D₄	C₂×#67	1	2	yes	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	4	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	3	1	no	—
471	C₂×C₄×C₅	—	3	1	no	—
472	C₂×C₄×C₅	—	3	1	no	—
473	C₂×C₄×C₅	—	3	1	no	—
474	C₂×C₄×C₅	—	4	2	no	—
475	C₂×C₄×C₅	—	6	2	no	—
476	C₂×C₄×C₅	—	6	1	no	—
477	C₂×C₄×C₅	—	6	1	no	—
478	C₂×C₄×C₅	—	6	1	no	—
479	C₂×C₄×C₅	—	12	2	no	—
480	C₂×C₄×C₅	—	12	1	no	—
481	C₂×C₄×C₅	—	12	2	no	—
482	C₂×C₄×C₅	—	12	2	no	—
483	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
484	C₂×C₄×C₅	#237	1	2	yes	—
485	C₂×C₄×C₅	C₂×#67	1	2	yes	—
486	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
487	C₅×C₈	—	2	1	no	—
488	C₅×C₈	—	2	1	no	—
489	C₅×C₈	—	6	1	no	—
490	C₅×C₈	—	6	1	no	—
491	C₂×#41	—	3	1	no	—
492	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
493	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
494	#135	—	2	4	no	—
495	#135	—	6	4	no	—
496	C₂×Q₁₆	—	3	1	no	—
497	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
498	C₂×SD₁₆	—	3	1	no	—
499	C₂×SD₁₆	—	3	1	no	—
500	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
501	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
502	C₂×D₈	—	3	1	no	—
503	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
504	C₂²×C₈	—	3	1	no	—
505	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
506	C₄⋊Q₈	—	3	1	no	—
507	#127	—	3	1	no	—
508	#124	—	3	1	no	—
509	#124	—	3	1	no	—
510	#121	—	6	1	no	—
511	#121	—	6	1	no	—
512	C₄×Q₈	—	3	1	no	—
513	C₄×Q₈	—	3	1	no	—
514	C₄×D₄	—	3	1	no	—
515	C₄×D₄	—	3	1	no	—
516	C₄×D₄	—	6	1	no	—
517	C₄×D₄	—	6	1	no	—
518	C₄×D₄	—	6	1	no	—
519	C₄×D₄	—	6	1	no	—
520	#117	—	3	1	no	—
521	#117	—	6	1	no	—
522	C₂×C₄²	—	3	1	no	—
523	C₂×C₄²	—	6	1	no	—
524	C₄⋊C₈	—	3	1	no	—
525	C₄⋊C₈	—	3	1	no	—
526	C₄⋊C₈	—	3	1	no	—
527	C₄⋊C₈	—	3	1	no	—
528	#103	—	3	1	no	—
529	#103	—	3	1	no	—
530	#103	—	3	1	no	—
531	#103	—	3	1	no	—
532	#102	—	3	1	no	—
533	#102	—	3	1	no	—
534	#102	—	3	1	no	—
535	#102	—	3	1	no	—
536	C₂×C₃×C₅	—	2	2	no	—
537	C₂×C₃×C₅	—	4	2	no	—
538	C₂×C₃×C₅	—	8	1	no	—
539	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
540	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
541	C₂×C₃×C₅	#575	1	1	yes	characteristic
542	C₅×D₃	—	8	1	no	—
543	C₂³×C₃	—	2	1	no	—
544	C₂³×C₃	—	2	1	no	—
545	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
546	C₂²×D₃	—	2	1	no	—
547	C₃×Q₈	—	2	1	no	—
548	C₃×Q₈	—	2	1	no	—
549	C₃×Q₈	—	2	1	no	—
550	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
551	C₃×D₄	—	2	4	no	—
552	C₃×D₄	—	2	1	no	—
553	C₃×D₄	—	2	1	no	—
554	C₃×D₄	—	2	1	no	—
555	C₃×D₄	—	4	2	no	—
556	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	4	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	4	2	no	—
561	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
563	C₂×C₃×C₄	C₅×#41	1	2	yes	—
564	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
565	#67	—	4	2	no	—
566	#67	—	4	2	no	—
567	#67	—	4	2	no	—
568	C₂×Dic₃	—	2	2	no	—
569	C₂×Dic₃	—	2	1	no	—
570	C₂×Dic₃	—	2	1	no	—
571	C₂×Dic₃	—	2	1	no	—
572	C₂×Dic₃	—	4	1	no	—
573	C₂×Dic₃	—	4	2	no	—
574	C₂×Dic₃	—	4	2	no	—
575	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
576	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
577	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
578	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
579	D₁₂	—	2	1	no	—
580	D₁₂	—	2	1	no	—
581	C₄×D₃	—	4	2	no	—
582	Dic₆	—	2	1	no	—
583	Dic₆	—	2	1	no	—
584	C₃×C₈	—	2	1	no	—
585	C₃×C₈	—	2	1	no	—
586	C₃⋊C₈	—	2	1	no	—
587	C₃⋊C₈	—	2	1	no	—
588	C₂²×C₅	—	2	1	no	—
589	C₂²×C₅	—	2	1	no	—
590	C₂²×C₅	—	2	2	no	—
591	C₂²×C₅	—	4	1	no	—
592	C₂²×C₅	—	4	1	no	—
593	C₂²×C₅	—	4	1	no	—
594	C₂²×C₅	—	4	1	no	—
595	C₂²×C₅	—	4	1	no	—
596	C₂²×C₅	—	12	1	no	—
597	C₂²×C₅	—	12	1	no	—
598	C₂²×C₅	—	12	1	no	—
599	C₂²×C₅	#939	1	2	yes	—
600	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
601	C₄×C₅	—	2	2	no	—
602	C₄×C₅	—	3	2	no	—
603	C₄×C₅	—	4	1	no	—
604	C₄×C₅	—	6	1	no	—
605	C₄×C₅	—	6	1	no	—
606	C₄×C₅	—	6	1	no	—
607	C₄×C₅	—	12	1	no	—
608	C₄×C₅	—	12	1	no	—
609	C₄×C₅	—	12	1	no	—
610	C₄×C₅	#939	1	2	yes	—
611	C₄×C₅	C₂×#237	1	1	yes	characteristic
612	C₄×C₅	C₂²×#67	1	1	yes	characteristic
613	#41	—	2	2	no	—
614	#41	—	2	2	no	—
615	#41	—	2	2	no	—
616	#41	—	6	2	no	—
617	#41	—	6	2	no	—
618	#41	C₅×#67	1	4	yes	complemented
619	C₂×Q₈	—	3	1	no	—
620	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
621	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	3	1	no	—
625	C₂×D₄	—	6	1	no	—
626	C₂×D₄	—	6	1	no	—
627	C₂×D₄	—	6	1	no	—
628	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
629	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	3	1	no	—
633	C₂²×C₄	—	3	1	no	—
634	C₂²×C₄	—	6	1	no	—
635	C₂²×C₄	—	6	1	no	—
636	C₂²×C₄	—	6	1	no	—
637	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
638	Q₁₆	—	2	2	no	—
639	Q₁₆	—	6	2	no	—
640	SD₁₆	—	2	2	no	—
641	SD₁₆	—	2	2	no	—
642	SD₁₆	—	6	2	no	—
643	SD₁₆	—	6	2	no	—
644	D₈	—	2	2	no	—
645	D₈	—	6	2	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	3	1	no	—
648	C₂×C₈	—	3	1	no	—
649	C₂×C₈	—	6	2	no	—
650	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
651	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
652	C₄⋊C₄	—	3	1	no	—
653	C₄⋊C₄	—	3	1	no	—
654	C₄⋊C₄	—	6	1	no	—
655	C₄⋊C₄	—	6	1	no	—
656	C₄⋊C₄	—	6	1	no	—
657	C₄⋊C₄	—	6	1	no	—
658	C₂²⋊C₄	—	6	1	no	—
659	C₂²⋊C₄	—	6	1	no	—
660	C₂²⋊C₄	—	6	1	no	—
661	C₂²⋊C₄	—	6	1	no	—
662	C₂²⋊C₄	—	6	1	no	—
663	C₂²⋊C₄	—	6	1	no	—
664	C₂²⋊C₄	—	6	1	no	—
665	C₄²	—	3	1	no	—
666	C₄²	—	3	1	no	—
667	C₄²	—	3	1	no	—
668	C₄²	—	3	1	no	—
669	C₄²	—	6	1	no	—
670	C₄²	—	6	1	no	—
671	C₄²	—	6	1	no	—
672	C₃×C₅	#3035	1	1	yes	characteristic, complemented, Hall
673	C₂²×C₃	—	2	1	no	—
674	C₂²×C₃	—	2	1	no	—
675	C₂²×C₃	—	2	2	no	—
676	C₂²×C₃	—	4	1	no	—
677	C₂²×C₃	—	4	1	no	—
678	C₂²×C₃	—	4	1	no	—
679	C₂²×C₃	—	4	1	no	—
680	C₂²×C₃	—	4	1	no	—
681	C₂²×C₃	C₅×#121	1	2	yes	—
682	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
683	C₂×D₃	—	4	1	no	—
684	C₂×D₃	—	4	1	no	—
685	C₂×D₃	—	4	1	no	—
686	C₃×C₄	—	2	2	no	—
687	C₃×C₄	—	4	1	no	—
688	C₃×C₄	C₅×#121	1	2	yes	—
689	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
690	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
691	Dic₃	—	2	1	no	—
692	Dic₃	—	2	1	no	—
693	Dic₃	—	2	1	no	—
694	Dic₃	—	4	1	no	—
695	Dic₃	—	4	1	no	—
696	Dic₃	—	4	1	no	—
697	Dic₃	C₅×#135	1	2	yes	complemented
698	C₂×C₅	—	2	2	no	—
699	C₂×C₅	—	4	2	no	—
700	C₂×C₅	—	8	1	no	—
701	C₂×C₅	—	24	1	no	—
702	C₂×C₅	D₃×#135	1	1	yes	characteristic
703	C₂×C₅	#5768	1	1	yes	characteristic
704	C₂×C₅	C₂×#939	1	1	yes	characteristic
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	6	1	no	—
708	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
709	Q₈	—	2	1	no	—
710	Q₈	—	2	1	no	—
711	Q₈	—	2	1	no	—
712	Q₈	—	6	1	no	—
713	Q₈	—	6	1	no	—
714	Q₈	C₂×C₅×#67	1	2	yes	—
715	D₄	—	2	4	no	—
716	D₄	—	2	1	no	—
717	D₄	—	2	1	no	—
718	D₄	—	2	1	no	—
719	D₄	—	4	2	no	—
720	D₄	—	6	1	no	—
721	D₄	—	6	1	no	—
722	D₄	—	12	2	no	—
723	D₄	—	12	2	no	—
724	D₄	—	12	2	no	—
725	D₄	C₂×C₅×#67	1	2	yes	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	3	1	no	—
730	C₂×C₄	—	3	1	no	—
731	C₂×C₄	—	3	1	no	—
732	C₂×C₄	—	3	1	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	6	2	no	—
735	C₂×C₄	—	6	1	no	—
736	C₂×C₄	—	6	1	no	—
737	C₂×C₄	—	6	1	no	—
738	C₂×C₄	—	12	2	no	—
739	C₂×C₄	—	12	1	no	—
740	C₂×C₄	—	12	2	no	—
741	C₂×C₄	—	12	2	no	—
742	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
743	C₂×C₄	C₅×#237	1	2	yes	—
744	C₂×C₄	C₂×C₅×#67	1	2	yes	—
745	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
746	C₈	—	2	1	no	—
747	C₈	—	2	1	no	—
748	C₈	—	6	1	no	—
749	C₈	—	6	1	no	—
750	C₂×C₃	—	2	2	no	—
751	C₂×C₃	—	4	2	no	—
752	C₂×C₃	—	8	1	no	—
753	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
754	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
755	C₂×C₃	C₅×#575	1	1	yes	characteristic
756	D₃	—	8	1	no	—
757	C₅	#83900	1	1	yes	characteristic, direct product factor, Sylow
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	12	1	no	—
767	C₂²	—	12	1	no	—
768	C₂²	—	12	1	no	—
769	C₂²	C₅×#939	1	2	yes	—
770	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
771	C₄	—	2	2	no	—
772	C₄	—	3	2	no	—
773	C₄	—	4	1	no	—
774	C₄	—	6	1	no	—
775	C₄	—	6	1	no	—
776	C₄	—	6	1	no	—
777	C₄	—	12	1	no	—
778	C₄	—	12	1	no	—
779	C₄	—	12	1	no	—
780	C₄	C₅×#939	1	2	yes	—
781	C₄	C₂×C₅×#237	1	1	yes	characteristic
782	C₄	C₂²×C₅×#67	1	1	yes	characteristic
783	C₃	C₅×#3035	1	1	yes	characteristic, complemented, Sylow
784	C₂	—	2	2	no	—
785	C₂	—	4	2	no	—
786	C₂	—	8	1	no	—
787	C₂	—	24	1	no	—
788	C₂	C₅×D₃×#135	1	1	yes	characteristic
789	C₂	C₅×#5768	1	1	yes	characteristic
790	C₂	C₂×C₅×#939	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₅×#3035
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₅×#5832	C₂	semidirect
3. C₅×Dic₃×#41	C₂	semidirect
4. C₂×C₅×#950	C₂	semidirect
5. C₅×#5233	C₂	semidirect
6. C₅×#5185	C₂	semidirect
7. C₅×#5182	C₂	semidirect
8. C₅×#5166	C₂	semidirect
9. C₅×#5165	C₂	semidirect
10. C₅×#5163	C₂	semidirect
11. C₅×#5162	C₂	semidirect
12. C₅×#5153	C₂	semidirect
13. C₅×#5150	C₂	semidirect
14. C₅×#5113	C₂	semidirect
15. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
62. #83900	C₅	direct (N × H)
64. C₂×C₅×#135	D₃	semidirect
81. C₃×C₅×#41	D₄	semidirect
137. C₂×C₃×#135	C₂×C₅	semidirect
138. #5832	C₂×C₅	semidirect
139. Dic₃×#41	C₂×C₅	semidirect
140. C₂×#950	C₂×C₅	semidirect
141. #5233	C₂×C₅	semidirect
142. #5185	C₂×C₅	semidirect
143. #5182	C₂×C₅	semidirect
144. #5166	C₂×C₅	semidirect
145. #5165	C₂×C₅	semidirect
146. #5163	C₂×C₅	semidirect
147. #5162	C₂×C₅	semidirect
148. #5153	C₂×C₅	semidirect
149. #5150	C₂×C₅	semidirect
150. #5113	C₂×C₅	semidirect
151. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
293. C₅×#41	#67	semidirect
348. C₂×#135	C₅×D₃	semidirect
386. C₅×Dic₃	#135	semidirect
390. C₃×#41	C₅×D₄	semidirect
618. #41	C₅×#67	semidirect
672. C₃×C₅	#3035	semidirect
697. Dic₃	C₅×#135	semidirect
757. C₅	#83900	direct (N × H)
783. C₃	C₅×#3035	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#135	2
C₅×#5832	2
C₅×Dic₃×#41	2
C₂×C₅×#950	2
C₅×#5233	2
C₅×#5185	2
C₅×#5182	2
C₅×#5166	2
C₅×#5165	2
C₅×#5163	2
C₅×#5162	2
C₅×#5153	2
C₅×#5150	2
C₅×#5113	2
C₂×C₅×Dic₃⋊C₈	2
C₅×#3035	3
#83900	5

Subgroups — C5×#83900 #14426214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83900 #14426214