Subgroups — C₂×C₅×#3178 #11983403

Order 1280.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#542	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3178	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#468	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#465	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₅×#542	—	2	4	no	—
24	C₅×#542	C₂²	1	8	yes	—
25	C₅×#541	—	2	4	no	—
26	C₅×#541	C₂²	1	8	yes	complemented
27	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×#126	—	2	1	no	—
30	C₂×C₅×#126	—	2	1	no	—
31	C₂×C₅×#126	—	2	1	no	—
32	C₂×C₅×#125	—	2	1	no	—
33	C₂×C₅×#125	—	2	1	no	—
34	C₂×C₅×#125	C₂²	1	1	yes	characteristic
35	C₂×C₅×#124	—	2	1	no	—
36	C₂×C₅×#124	C₂²	1	1	yes	characteristic
37	C₂×C₅×#123	—	2	1	no	—
38	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₅×#121	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₅×#117	C₂²	1	1	yes	characteristic
48	C₅×#501	C₂²	1	8	yes	complemented
49	C₅×#497	C₂²	1	8	yes	complemented
50	C₅×#488	C₂²	1	8	yes	complemented
51	C₅×#487	C₂²	1	8	yes	complemented
52	C₅×#470	C₂²	1	8	yes	complemented
53	C₅×#468	C₂²	1	8	yes	—
54	C₅×#467	C₂²	1	8	yes	complemented
55	C₅×#465	C₂²	1	8	yes	—
56	C₅×#441	C₂²	1	8	yes	complemented
57	C₅×#440	C₂²	1	8	yes	complemented
58	C₄×C₅×Q₁₆	C₂²	1	8	yes	complemented
59	C₄×C₅×SD₁₆	C₂²	1	8	yes	complemented
60	C₂×C₅×#107	C₂²	1	1	yes	characteristic
61	C₂×C₅×#107	C₂²	1	1	yes	characteristic
62	C₂×C₅×#106	C₂²	1	1	yes	characteristic
63	C₂×C₅×#106	C₂²	1	1	yes	characteristic
64	C₂×C₅×#103	C₂²	1	1	yes	characteristic
65	C₂×C₅×#103	C₂²	1	1	yes	characteristic
66	C₂×C₅×#103	C₂²	1	1	yes	characteristic
67	C₂×C₅×#103	C₂²	1	1	yes	characteristic
68	C₂×C₅×#103	C₂²	1	1	yes	characteristic
69	C₂×C₅×#103	C₂²	1	1	yes	characteristic
70	C₂×C₅×#102	C₂²	1	1	yes	characteristic
71	C₂×C₅×#102	C₂²	1	1	yes	characteristic
72	C₅×#405	C₂²	1	8	yes	complemented
73	C₂×C₅×#97	C₂²	1	1	yes	characteristic
74	C₂×C₅×#97	C₂²	1	1	yes	characteristic
75	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
77	C₂×#3178	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂²×C₅×Q₈	—	2	1	no	—
79	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×D₄	—	2	1	no	—
83	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₅	—	2	1	no	—
85	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂×C₅×Q₁₆	—	2	4	no	—
87	C₂×C₅×Q₁₆	—	2	4	no	—
88	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
89	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
90	C₂×C₅×SD₁₆	—	2	4	no	—
91	C₂×C₅×SD₁₆	—	2	4	no	—
92	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
93	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
94	C₂×C₅×M₁₆	—	2	4	no	—
95	C₂×C₅×M₁₆	C₂³	1	4	yes	—
96	C₂²×C₅×C₈	—	2	4	no	—
97	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₂²×C₅×C₈	C₂³	1	4	yes	—
100	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₅×C₄⋊Q₈	—	2	2	no	—
103	C₅×C₄⋊Q₈	—	2	2	no	—
104	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
105	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
106	C₅×#126	—	2	8	no	—
107	C₅×#126	—	2	8	no	—
108	C₅×#126	—	2	8	no	—
109	C₅×#125	—	2	8	no	—
110	C₅×#125	—	2	8	no	—
111	C₅×#125	—	2	2	no	—
112	C₅×#125	C₂³	1	4	yes	—
113	C₅×#124	—	2	8	no	—
114	C₅×#124	—	2	2	no	—
115	C₅×#124	C₂³	1	4	yes	—
116	C₅×#123	—	2	8	no	—
117	C₅×C₂²⋊Q₈	—	2	2	no	—
118	C₅×C₂²⋊Q₈	—	2	2	no	—
119	C₅×C₂²⋊Q₈	—	2	2	no	—
120	C₅×C₂²⋊Q₈	—	2	8	no	—
121	C₅×C₂²⋊Q₈	C₂³	1	4	yes	—
122	C₅×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₅×C₂²⋊Q₈	C₂³	1	4	yes	—
124	C₅×#121	—	2	2	no	—
125	C₅×#121	C₂³	1	4	yes	—
126	C₄×C₅×Q₈	—	2	2	no	—
127	C₄×C₅×Q₈	—	2	2	no	—
128	C₄×C₅×Q₈	—	2	2	no	—
129	C₄×C₅×Q₈	C₂³	1	4	yes	—
130	C₄×C₅×Q₈	C₂³	1	4	yes	—
131	C₄×C₅×Q₈	C₂³	1	4	yes	—
132	C₄×C₅×D₄	—	2	2	no	—
133	C₄×C₅×D₄	C₂³	1	4	yes	—
134	C₅×#117	D₄	1	4	yes	—
135	C₅×#117	C₂³	1	4	yes	—
136	C₂×C₅×C₄⋊C₄	—	2	1	no	—
137	C₂×C₅×C₄⋊C₄	—	2	1	no	—
138	C₂×C₅×C₄⋊C₄	—	2	1	no	—
139	C₂×C₅×C₄⋊C₄	—	2	1	no	—
140	C₂×C₅×C₄⋊C₄	—	2	1	no	—
141	C₂×C₅×C₄⋊C₄	—	2	1	no	—
142	C₂×C₅×C₄⋊C₄	—	2	1	no	—
143	C₂×C₅×C₄⋊C₄	—	2	1	no	—
144	C₂×C₅×C₄⋊C₄	—	2	1	no	—
145	C₂×C₅×C₄⋊C₄	—	2	1	no	—
146	C₂×C₅×C₄⋊C₄	—	2	1	no	—
147	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
148	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
158	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
161	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₅	—	2	1	no	—
163	C₂×C₄²×C₅	—	2	1	no	—
164	C₂×C₄²×C₅	—	2	1	no	—
165	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
167	C₅×#107	C₂³	1	4	yes	—
168	C₅×#107	C₂³	1	4	yes	—
169	C₅×#106	C₂³	1	4	yes	—
170	C₅×#106	C₂³	1	4	yes	—
171	C₅×#103	C₂³	1	4	yes	—
172	C₅×#103	C₂³	1	4	yes	—
173	C₅×#103	C₂³	1	4	yes	—
174	C₅×#103	C₂³	1	4	yes	—
175	C₅×#103	C₂³	1	4	yes	—
176	C₅×#103	C₂³	1	4	yes	—
177	C₅×#102	C₂³	1	4	yes	—
178	C₅×#102	C₂³	1	4	yes	—
179	C₅×#97	C₂³	1	4	yes	—
180	C₅×#97	C₂³	1	4	yes	—
181	C₄×C₅×C₈	C₂³	1	4	yes	—
182	C₄×C₅×C₈	C₂³	1	4	yes	—
183	C₂×#542	C₂×C₅	1	1	yes	characteristic
184	C₂×#541	C₂×C₅	1	1	yes	characteristic, complemented
185	#3178	C₂×C₅	1	16	yes	direct product factor
186	C₂×#501	C₂×C₅	1	1	yes	characteristic, complemented
187	C₂×#497	C₂×C₅	1	1	yes	characteristic, complemented
188	C₂×#488	C₂×C₅	1	1	yes	characteristic, complemented
189	C₂×#487	C₂×C₅	1	1	yes	characteristic, complemented
190	C₂×#470	C₂×C₅	1	1	yes	characteristic, complemented
191	C₂×#468	C₂×C₅	1	1	yes	characteristic
192	C₂×#467	C₂×C₅	1	1	yes	characteristic, complemented
193	C₂×#465	C₂×C₅	1	1	yes	characteristic
194	C₂×#441	C₂×C₅	1	1	yes	characteristic, complemented
195	C₂×#440	C₂×C₅	1	1	yes	characteristic, complemented
196	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
197	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
198	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
199	C₂⁴×C₅	—	2	1	no	—
200	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂×C₅×Q₈	—	2	1	no	—
202	C₂×C₅×Q₈	—	2	1	no	—
203	C₂×C₅×Q₈	—	2	1	no	—
204	C₂×C₅×Q₈	—	2	4	no	—
205	C₂×C₅×Q₈	—	2	2	no	—
206	C₂×C₅×Q₈	—	2	2	no	—
207	C₂×C₅×Q₈	—	2	2	no	—
208	C₂×C₅×Q₈	—	2	2	no	—
209	C₂×C₅×Q₈	—	2	2	no	—
210	C₂×C₅×Q₈	—	2	2	no	—
211	C₂×C₅×Q₈	—	8	2	no	—
212	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
213	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
214	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
215	C₂×C₅×D₄	—	2	4	no	—
216	C₂×C₅×D₄	—	2	1	no	—
217	C₂×C₅×D₄	—	2	2	no	—
218	C₂×C₅×D₄	—	2	2	no	—
219	C₂×C₅×D₄	—	8	2	no	—
220	C₂×C₅×D₄	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅	—	2	2	no	—
222	C₂²×C₄×C₅	—	2	2	no	—
223	C₂²×C₄×C₅	—	2	1	no	—
224	C₂²×C₄×C₅	—	2	1	no	—
225	C₂²×C₄×C₅	—	2	1	no	—
226	C₂²×C₄×C₅	—	2	1	no	—
227	C₂²×C₄×C₅	—	2	1	no	—
228	C₂²×C₄×C₅	—	2	1	no	—
229	C₂²×C₄×C₅	—	2	1	no	—
230	C₂²×C₄×C₅	—	2	4	no	—
231	C₂²×C₄×C₅	—	8	2	no	—
232	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
240	C₅×Q₁₆	—	2	8	no	—
241	C₅×Q₁₆	—	2	8	no	—
242	C₅×SD₁₆	—	2	8	no	—
243	C₅×SD₁₆	—	2	8	no	—
244	C₅×M₁₆	—	2	8	no	—
245	C₂×C₅×C₈	—	2	2	no	—
246	C₂×C₅×C₈	—	2	2	no	—
247	C₂×C₅×C₈	—	2	8	no	—
248	C₂×C₅×C₈	#41	1	4	yes	—
249	C₂×C₅×C₈	#41	1	4	yes	—
250	C₂×C₅×C₈	C₂⁴	1	2	yes	—
251	C₂×C₅×C₈	C₂⁴	1	2	yes	—
252	C₂×C₅×C₈	C₂⁴	1	2	yes	—
253	C₂×C₅×C₈	C₂⁴	1	2	yes	—
254	C₅×C₄⋊C₄	—	2	4	no	—
255	C₅×C₄⋊C₄	—	2	4	no	—
256	C₅×C₄⋊C₄	—	2	4	no	—
257	C₅×C₄⋊C₄	—	2	4	no	—
258	C₅×C₄⋊C₄	—	2	4	no	—
259	C₅×C₄⋊C₄	—	2	4	no	—
260	C₅×C₄⋊C₄	—	2	4	no	—
261	C₅×C₄⋊C₄	—	2	4	no	—
262	C₅×C₄⋊C₄	—	2	4	no	—
263	C₅×C₄⋊C₄	—	2	4	no	—
264	C₅×C₄⋊C₄	—	2	4	no	—
265	C₅×C₄⋊C₄	—	2	1	no	—
266	C₅×C₄⋊C₄	—	2	1	no	—
267	C₅×C₄⋊C₄	—	2	1	no	—
268	C₅×C₄⋊C₄	—	2	1	no	—
269	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
270	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
271	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
272	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
273	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
274	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
275	C₅×C₂²⋊C₄	—	2	4	no	—
276	C₅×C₂²⋊C₄	—	2	4	no	—
277	C₅×C₂²⋊C₄	—	2	4	no	—
278	C₅×C₂²⋊C₄	—	2	4	no	—
279	C₅×C₂²⋊C₄	—	2	4	no	—
280	C₅×C₂²⋊C₄	—	2	4	no	—
281	C₅×C₂²⋊C₄	—	2	4	no	—
282	C₅×C₂²⋊C₄	C₂×D₄	1	4	yes	—
283	C₅×C₂²⋊C₄	C₂×D₄	1	4	yes	—
284	C₄²×C₅	—	2	4	no	—
285	C₄²×C₅	—	2	4	no	—
286	C₄²×C₅	—	2	4	no	—
287	C₄²×C₅	C₂×D₄	1	2	yes	—
288	C₄²×C₅	C₂×D₄	1	2	yes	—
289	C₄²×C₅	C₂⁴	1	2	yes	—
290	C₄²×C₅	C₂⁴	1	2	yes	—
291	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
292	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
293	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
294	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
296	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
297	#542	—	2	4	no	—
298	#542	C₂²×C₅	1	8	yes	—
299	#541	—	2	4	no	—
300	#541	C₂²×C₅	1	8	yes	complemented
301	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
302	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
303	C₂×#126	—	2	1	no	—
304	C₂×#126	—	2	1	no	—
305	C₂×#126	—	2	1	no	—
306	C₂×#125	—	2	1	no	—
307	C₂×#125	—	2	1	no	—
308	C₂×#125	C₂²×C₅	1	1	yes	characteristic
309	C₂×#124	—	2	1	no	—
310	C₂×#124	C₂²×C₅	1	1	yes	characteristic
311	C₂×#123	—	2	1	no	—
312	C₂×C₂²⋊Q₈	—	2	1	no	—
313	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
314	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
315	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
316	C₂×#121	C₂²×C₅	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
319	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
321	C₂×#117	C₂²×C₅	1	1	yes	characteristic
322	#501	C₂²×C₅	1	8	yes	complemented
323	#497	C₂²×C₅	1	8	yes	complemented
324	#488	C₂²×C₅	1	8	yes	complemented
325	#487	C₂²×C₅	1	8	yes	complemented
326	#470	C₂²×C₅	1	8	yes	complemented
327	#468	C₂²×C₅	1	8	yes	—
328	#467	C₂²×C₅	1	8	yes	complemented
329	#465	C₂²×C₅	1	8	yes	—
330	#441	C₂²×C₅	1	8	yes	complemented
331	#440	C₂²×C₅	1	8	yes	complemented
332	C₄×Q₁₆	C₂²×C₅	1	8	yes	complemented
333	C₄×SD₁₆	C₂²×C₅	1	8	yes	complemented
334	C₂×#107	C₂²×C₅	1	1	yes	characteristic
335	C₂×#107	C₂²×C₅	1	1	yes	characteristic
336	C₂×#106	C₂²×C₅	1	1	yes	characteristic
337	C₂×#106	C₂²×C₅	1	1	yes	characteristic
338	C₂×#103	C₂²×C₅	1	1	yes	characteristic
339	C₂×#103	C₂²×C₅	1	1	yes	characteristic
340	C₂×#103	C₂²×C₅	1	1	yes	characteristic
341	C₂×#103	C₂²×C₅	1	1	yes	characteristic
342	C₂×#103	C₂²×C₅	1	1	yes	characteristic
343	C₂×#103	C₂²×C₅	1	1	yes	characteristic
344	C₂×#102	C₂²×C₅	1	1	yes	characteristic
345	C₂×#102	C₂²×C₅	1	1	yes	characteristic
346	#405	C₂²×C₅	1	8	yes	complemented
347	C₂×#97	C₂²×C₅	1	1	yes	characteristic
348	C₂×#97	C₂²×C₅	1	1	yes	characteristic
349	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
350	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
351	C₂³×C₅	—	2	2	no	—
352	C₂³×C₅	—	2	2	no	—
353	C₂³×C₅	—	2	2	no	—
354	C₂³×C₅	—	2	2	no	—
355	C₂³×C₅	—	4	2	no	—
356	C₂³×C₅	—	4	2	no	—
357	C₂³×C₅	—	4	2	no	—
358	C₂³×C₅	C₂²×D₄	1	2	yes	—
359	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
360	C₅×Q₈	—	2	2	no	—
361	C₅×Q₈	—	2	2	no	—
362	C₅×Q₈	—	2	2	no	—
363	C₅×Q₈	—	2	2	no	—
364	C₅×Q₈	—	2	2	no	—
365	C₅×Q₈	—	2	2	no	—
366	C₅×Q₈	—	4	2	no	—
367	C₅×Q₈	—	4	2	no	—
368	C₅×Q₈	—	4	2	no	—
369	C₅×Q₈	—	8	4	no	—
370	C₅×D₄	—	2	2	no	—
371	C₅×D₄	—	2	2	no	—
372	C₅×D₄	—	4	2	no	—
373	C₅×D₄	—	8	4	no	—
374	C₂×C₄×C₅	—	2	2	no	—
375	C₂×C₄×C₅	—	2	2	no	—
376	C₂×C₄×C₅	—	2	2	no	—
377	C₂×C₄×C₅	—	2	2	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	4	no	—
380	C₂×C₄×C₅	—	2	2	no	—
381	C₂×C₄×C₅	—	2	2	no	—
382	C₂×C₄×C₅	—	2	2	no	—
383	C₂×C₄×C₅	—	2	2	no	—
384	C₂×C₄×C₅	—	2	2	no	—
385	C₂×C₄×C₅	—	2	2	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	2	no	—
388	C₂×C₄×C₅	—	2	2	no	—
389	C₂×C₄×C₅	—	4	2	no	—
390	C₂×C₄×C₅	—	4	2	no	—
391	C₂×C₄×C₅	—	4	2	no	—
392	C₂×C₄×C₅	—	4	2	no	—
393	C₂×C₄×C₅	—	4	2	no	—
394	C₂×C₄×C₅	—	4	2	no	—
395	C₂×C₄×C₅	—	4	2	no	—
396	C₂×C₄×C₅	—	8	4	no	—
397	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₅	C₂×#41	1	2	yes	—
404	C₂×C₄×C₅	C₂×#41	1	2	yes	—
405	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
406	C₅×C₈	—	2	2	no	—
407	C₅×C₈	—	2	2	no	—
408	C₅×C₈	C₂×#41	1	4	yes	—
409	C₅×C₈	C₂×#41	1	4	yes	—
410	C₂²×Q₈	—	2	1	no	—
411	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
412	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
416	C₂³×C₄	—	2	1	no	—
417	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
418	C₂×Q₁₆	—	2	4	no	—
419	C₂×Q₁₆	—	2	4	no	—
420	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
421	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
422	C₂×SD₁₆	—	2	4	no	—
423	C₂×SD₁₆	—	2	4	no	—
424	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
425	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
426	C₂×M₁₆	—	2	4	no	—
427	C₂×M₁₆	C₂³×C₅	1	4	yes	—
428	C₂²×C₈	—	2	4	no	—
429	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₅	1	4	yes	—
431	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
434	C₄⋊Q₈	—	2	2	no	—
435	C₄⋊Q₈	—	2	2	no	—
436	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
437	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
438	#126	—	2	8	no	—
439	#126	—	2	8	no	—
440	#126	—	2	8	no	—
441	#125	—	2	8	no	—
442	#125	—	2	8	no	—
443	#125	—	2	2	no	—
444	#125	C₂³×C₅	1	4	yes	—
445	#124	—	2	8	no	—
446	#124	—	2	2	no	—
447	#124	C₂³×C₅	1	4	yes	—
448	#123	—	2	8	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	8	no	—
453	C₂²⋊Q₈	C₂³×C₅	1	4	yes	—
454	C₂²⋊Q₈	C₂³×C₅	1	4	yes	—
455	C₂²⋊Q₈	C₂³×C₅	1	4	yes	—
456	#121	—	2	2	no	—
457	#121	C₂³×C₅	1	4	yes	—
458	C₄×Q₈	—	2	2	no	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	C₂³×C₅	1	4	yes	—
462	C₄×Q₈	C₂³×C₅	1	4	yes	—
463	C₄×Q₈	C₂³×C₅	1	4	yes	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	C₂³×C₅	1	4	yes	—
466	#117	C₅×D₄	1	4	yes	—
467	#117	C₂³×C₅	1	4	yes	—
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
494	C₂×C₄²	—	2	1	no	—
495	C₂×C₄²	—	2	1	no	—
496	C₂×C₄²	—	2	1	no	—
497	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
499	#107	C₂³×C₅	1	4	yes	—
500	#107	C₂³×C₅	1	4	yes	—
501	#106	C₂³×C₅	1	4	yes	—
502	#106	C₂³×C₅	1	4	yes	—
503	#103	C₂³×C₅	1	4	yes	—
504	#103	C₂³×C₅	1	4	yes	—
505	#103	C₂³×C₅	1	4	yes	—
506	#103	C₂³×C₅	1	4	yes	—
507	#103	C₂³×C₅	1	4	yes	—
508	#103	C₂³×C₅	1	4	yes	—
509	#102	C₂³×C₅	1	4	yes	—
510	#102	C₂³×C₅	1	4	yes	—
511	#97	C₂³×C₅	1	4	yes	—
512	#97	C₂³×C₅	1	4	yes	—
513	C₄×C₈	C₂³×C₅	1	4	yes	—
514	C₄×C₈	C₂³×C₅	1	4	yes	—
515	C₂²×C₅	—	2	2	no	—
516	C₂²×C₅	—	2	2	no	—
517	C₂²×C₅	—	2	2	no	—
518	C₂²×C₅	—	4	4	no	—
519	C₂²×C₅	—	4	2	no	—
520	C₂²×C₅	—	4	2	no	—
521	C₂²×C₅	—	4	2	no	—
522	C₂²×C₅	—	8	4	no	—
523	C₂²×C₅	#532	1	2	yes	—
524	C₂²×C₅	#577	1	2	yes	—
525	C₂²×C₅	#578	1	2	yes	—
526	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
527	C₄×C₅	—	2	2	no	—
528	C₄×C₅	—	2	2	no	—
529	C₄×C₅	—	2	2	no	—
530	C₄×C₅	—	2	2	no	—
531	C₄×C₅	—	2	2	no	—
532	C₄×C₅	—	4	2	no	—
533	C₄×C₅	—	4	2	no	—
534	C₄×C₅	—	4	2	no	—
535	C₄×C₅	—	4	2	no	—
536	C₄×C₅	—	4	2	no	—
537	C₄×C₅	—	4	2	no	—
538	C₄×C₅	—	4	2	no	—
539	C₄×C₅	#532	1	2	yes	—
540	C₄×C₅	C₂²×#41	1	1	yes	characteristic
541	C₄×C₅	C₂²×#41	1	1	yes	characteristic
542	C₂⁴	—	2	1	no	—
543	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	4	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	2	2	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	8	2	no	—
555	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
556	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
557	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	8	2	no	—
563	C₂×D₄	C₂⁴×C₅	1	2	yes	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	8	2	no	—
575	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
576	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
577	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
578	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
579	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
580	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
583	Q₁₆	—	2	8	no	—
584	Q₁₆	—	2	8	no	—
585	SD₁₆	—	2	8	no	—
586	SD₁₆	—	2	8	no	—
587	M₁₆	—	2	8	no	—
588	C₂×C₈	—	2	2	no	—
589	C₂×C₈	—	2	2	no	—
590	C₂×C₈	—	2	8	no	—
591	C₂×C₈	C₅×#41	1	4	yes	—
592	C₂×C₈	C₅×#41	1	4	yes	—
593	C₂×C₈	C₂⁴×C₅	1	2	yes	—
594	C₂×C₈	C₂⁴×C₅	1	2	yes	—
595	C₂×C₈	C₂⁴×C₅	1	2	yes	—
596	C₂×C₈	C₂⁴×C₅	1	2	yes	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
613	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
614	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
615	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
616	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
617	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	C₂×C₅×D₄	1	4	yes	—
626	C₂²⋊C₄	C₂×C₅×D₄	1	4	yes	—
627	C₄²	—	2	4	no	—
628	C₄²	—	2	4	no	—
629	C₄²	—	2	4	no	—
630	C₄²	C₂×C₅×D₄	1	2	yes	—
631	C₄²	C₂×C₅×D₄	1	2	yes	—
632	C₄²	C₂⁴×C₅	1	2	yes	—
633	C₄²	C₂⁴×C₅	1	2	yes	—
634	C₂×C₅	—	4	2	no	—
635	C₂×C₅	—	8	2	no	—
636	C₂×C₅	#3178	1	4	yes	direct product factor
637	C₂×C₅	C₂×#532	1	1	yes	characteristic
638	C₂×C₅	C₂×#577	1	1	yes	characteristic
639	C₂×C₅	C₂×#578	1	1	yes	characteristic
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	2	no	—
647	C₂³	C₂²×C₅×D₄	1	2	yes	—
648	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
649	Q₈	—	2	2	no	—
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	2	2	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	4	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	8	4	no	—
659	D₄	—	2	2	no	—
660	D₄	—	2	2	no	—
661	D₄	—	4	2	no	—
662	D₄	—	8	4	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	4	2	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	8	4	no	—
686	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
687	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
688	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
689	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
690	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
691	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
692	C₂×C₄	C₂×C₅×#41	1	2	yes	—
693	C₂×C₄	C₂×C₅×#41	1	2	yes	—
694	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
695	C₈	—	2	2	no	—
696	C₈	—	2	2	no	—
697	C₈	C₂×C₅×#41	1	4	yes	—
698	C₈	C₂×C₅×#41	1	4	yes	—
699	C₅	C₂×#3178	1	1	yes	characteristic, direct product factor, Sylow
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	8	4	no	—
708	C₂²	C₅×#532	1	2	yes	—
709	C₂²	C₅×#577	1	2	yes	—
710	C₂²	C₅×#578	1	2	yes	—
711	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	C₅×#532	1	2	yes	—
725	C₄	C₂²×C₅×#41	1	1	yes	characteristic
726	C₄	C₂²×C₅×#41	1	1	yes	characteristic
727	C₂	—	4	2	no	—
728	C₂	—	8	2	no	—
729	C₂	C₅×#3178	1	4	yes	direct product factor
730	C₂	C₂×C₅×#532	1	1	yes	characteristic
731	C₂	C₂×C₅×#577	1	1	yes	characteristic
732	C₂	C₂×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂×C₅×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#541	C₂	semidirect
3. C₅×#3178	C₂	direct (N × H)
4. C₂×C₅×#501	C₂	semidirect
5. C₂×C₅×#497	C₂	semidirect
6. C₂×C₅×#488	C₂	semidirect
7. C₂×C₅×#487	C₂	semidirect
8. C₂×C₅×#470	C₂	semidirect
10. C₂×C₅×#467	C₂	semidirect
12. C₂×C₅×#441	C₂	semidirect
13. C₂×C₅×#440	C₂	semidirect
14. C₂×C₄×C₅×Q₁₆	C₂	semidirect
15. C₂×C₄×C₅×SD₁₆	C₂	semidirect
16. C₂×C₅×#405	C₂	semidirect
26. C₅×#541	C₂²	semidirect
48. C₅×#501	C₂²	semidirect
49. C₅×#497	C₂²	semidirect
50. C₅×#488	C₂²	semidirect
51. C₅×#487	C₂²	semidirect
52. C₅×#470	C₂²	semidirect
54. C₅×#467	C₂²	semidirect
56. C₅×#441	C₂²	semidirect
57. C₅×#440	C₂²	semidirect
58. C₄×C₅×Q₁₆	C₂²	semidirect
59. C₄×C₅×SD₁₆	C₂²	semidirect
72. C₅×#405	C₂²	semidirect
77. C₂×#3178	C₅	direct (N × H)
184. C₂×#541	C₂×C₅	semidirect
185. #3178	C₂×C₅	direct (N × H)
186. C₂×#501	C₂×C₅	semidirect
187. C₂×#497	C₂×C₅	semidirect
188. C₂×#488	C₂×C₅	semidirect
189. C₂×#487	C₂×C₅	semidirect
190. C₂×#470	C₂×C₅	semidirect
192. C₂×#467	C₂×C₅	semidirect
194. C₂×#441	C₂×C₅	semidirect
195. C₂×#440	C₂×C₅	semidirect
196. C₂×C₄×Q₁₆	C₂×C₅	semidirect
197. C₂×C₄×SD₁₆	C₂×C₅	semidirect
198. C₂×#405	C₂×C₅	semidirect
300. #541	C₂²×C₅	semidirect
322. #501	C₂²×C₅	semidirect
323. #497	C₂²×C₅	semidirect
324. #488	C₂²×C₅	semidirect
325. #487	C₂²×C₅	semidirect
326. #470	C₂²×C₅	semidirect
328. #467	C₂²×C₅	semidirect
330. #441	C₂²×C₅	semidirect
331. #440	C₂²×C₅	semidirect
332. C₄×Q₁₆	C₂²×C₅	semidirect
333. C₄×SD₁₆	C₂²×C₅	semidirect
346. #405	C₂²×C₅	semidirect
636. C₂×C₅	#3178	direct (N × H)
699. C₅	C₂×#3178	direct (N × H)
729. C₂	C₅×#3178	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#542	2
C₂×C₅×#541	2
C₅×#3178	2
C₂×C₅×#501	2
C₂×C₅×#497	2
C₂×C₅×#488	2
C₂×C₅×#487	2
C₂×C₅×#470	2
C₂×C₅×#468	2
C₂×C₅×#467	2
C₂×C₅×#465	2
C₂×C₅×#441	2
C₂×C₅×#440	2
C₂×C₄×C₅×Q₁₆	2
C₂×C₄×C₅×SD₁₆	2
C₂×C₅×#405	2
C₂×#3178	5

Subgroups — C2×C5×#3178 #11983403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3178 #11983403