Subgroups — C₂×#10617980 #13007059

Order 1280.

7430 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#66150	C₂	1	2	yes	maximal, complemented
3	C₂×#66138	C₂	1	2	yes	maximal, complemented
4	#10617980	C₂	1	32	yes	maximal, direct product factor
5	C₂×#66017	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#66013	C₂	1	2	yes	maximal, complemented
7	C₂×#66012	C₂	1	4	yes	maximal, complemented
8	C₂×#66006	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66018	C₂	1	2	yes	maximal, complemented
10	C₂×#66004	C₂	1	2	yes	maximal, complemented
11	C₂×#66003	C₂	1	4	yes	maximal, complemented
12	C₂×#65824	C₂	1	4	yes	maximal, complemented
13	C₂×#65829	C₂	1	4	yes	maximal, complemented
14	C₂×#65813	C₂	1	2	yes	maximal, complemented
15	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂³×C₂²⋊D₅	C₂²	1	2	yes	complemented
18	C₂²×#709	C₂²	1	2	yes	—
19	C₂×C₅×#124	C₂²	1	1	yes	characteristic
20	C₂×C₅×#124	C₂²	1	1	yes	characteristic
21	C₂×C₅×#124	C₂²	1	4	yes	complemented
22	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×#124	C₂²	1	16	yes	complemented
25	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
26	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
27	C₂×#4099	C₂²	1	4	yes	—
28	C₂²×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
29	#66150	C₂²	1	32	yes	complemented
30	C₂×#4093	C₂²	1	2	yes	complemented
31	C₂×#4093	C₂²	1	2	yes	complemented
32	C₂×#4092	C₂²	1	4	yes	complemented
33	C₂×#4092	C₂²	1	4	yes	complemented
34	C₂×#4090	C₂²	1	2	yes	complemented
35	C₂×#4090	C₂²	1	2	yes	complemented
36	#66138	C₂²	1	32	yes	complemented
37	C₂×#4085	C₂²	1	4	yes	—
38	C₂×#4085	C₂²	1	4	yes	complemented
39	C₂×#4083	C₂²	1	2	yes	—
40	C₂×#4083	C₂²	1	2	yes	complemented
41	C₂×#4081	C₂²	1	2	yes	—
42	C₂×#4081	C₂²	1	2	yes	complemented
43	C₂×#4076	C₂²	1	2	yes	—
44	C₂×#4075	C₂²	1	4	yes	complemented
45	C₂×#4075	C₂²	1	4	yes	complemented
46	C₂×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
47	C₂×#4072	C₂²	1	2	yes	complemented
48	C₂×#4070	C₂²	1	2	yes	complemented
49	#66018	C₂²	1	32	yes	complemented
50	#66017	C₂²	1	16	yes	complemented
51	#66013	C₂²	1	32	yes	complemented
52	#66012	C₂²	1	64	yes	complemented
53	#66006	C₂²	1	16	yes	complemented
54	#66004	C₂²	1	32	yes	complemented
55	#66003	C₂²	1	64	yes	complemented
56	#65829	C₂²	1	64	yes	complemented
57	C₂×#4032	C₂²	1	4	yes	complemented
58	C₂×#4031	C₂²	1	4	yes	complemented
59	C₂×#4031	C₂²	1	4	yes	complemented
60	#65824	C₂²	1	64	yes	complemented
61	C₂×#4030	C₂²	1	4	yes	complemented
62	C₂×#4030	C₂²	1	4	yes	complemented
63	C₂×#4029	C₂²	1	4	yes	complemented
64	C₂×#4029	C₂²	1	4	yes	complemented
65	C₂×#4028	C₂²	1	4	yes	complemented
66	C₂×#4027	C₂²	1	4	yes	complemented
67	C₂×#4027	C₂²	1	4	yes	complemented
68	C₂×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
69	C₂×#4025	C₂²	1	4	yes	complemented
70	C₂×#4025	C₂²	1	4	yes	complemented
71	C₂×#4024	C₂²	1	4	yes	complemented
72	C₂×#4024	C₂²	1	4	yes	complemented
73	C₂×#4023	C₂²	1	4	yes	complemented
74	#65813	C₂²	1	32	yes	complemented
75	C₂×#4022	C₂²	1	4	yes	complemented
76	C₂×#4021	C₂²	1	2	yes	complemented
77	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
78	C₂×#4018	C₂²	1	4	yes	complemented
79	C₂×#4016	C₂²	1	2	yes	complemented
80	C₂×C₄×Dic₁₀	C₂²	1	2	yes	complemented
81	C₂×#3545	—	5	1	no	maximal, Sylow
82	C₂⁵×C₅	C₂³	1	2	yes	—
83	C₂⁴×D₅	C₂³	1	2	yes	—
84	C₂²×C₅×Q₈	—	4	4	no	—
85	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×Q₈	C₂³	1	2	yes	—
87	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
88	C₂²×C₅×Q₈	C₂³	1	8	yes	complemented
89	C₂²×C₅×D₄	—	4	4	no	—
90	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
91	C₂²×C₅×D₄	C₂³	1	2	yes	—
92	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
93	C₂²×C₅×D₄	C₂³	1	8	yes	—
94	C₂³×C₄×C₅	C₂³	1	2	yes	—
95	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₅	C₂³	1	2	yes	—
97	C₂²×C₂²⋊D₅	—	4	8	no	—
98	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
99	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
100	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
101	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
102	C₂²×C₂²⋊D₅	C₂³	1	16	yes	complemented
103	C₂³×Dic₅	C₂³	1	4	yes	—
104	C₂³×Dic₅	C₂³	1	2	yes	—
105	C₂×#709	—	4	8	no	—
106	C₂×#709	C₂³	1	16	yes	—
107	C₂²×D₂₀	C₂³	1	2	yes	—
108	C₂²×D₂₀	C₂³	1	2	yes	—
109	C₂²×C₄×D₅	C₂³	1	4	yes	—
110	C₂²×C₄×D₅	C₂³	1	4	yes	—
111	C₂²×Dic₁₀	C₂³	1	2	yes	—
112	C₂²×Dic₁₀	C₂³	1	2	yes	—
113	C₅×#124	C₂³	1	8	yes	—
114	C₅×#124	C₂³	1	8	yes	—
115	C₅×#124	C₂³	1	32	yes	complemented
116	C₅×#124	C₂³	1	8	yes	complemented
117	C₅×#124	C₂³	1	8	yes	complemented
118	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
123	C₂×C₄²×C₅	C₂³	1	2	yes	—
124	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
127	#4099	C₂³	1	32	yes	—
128	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
129	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
130	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
131	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
132	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
133	C₂×C₂²⋊Dic₅	C₂³	1	16	yes	complemented
134	#4093	C₂³	1	16	yes	complemented
135	#4093	C₂³	1	16	yes	complemented
136	#4092	C₂³	1	32	yes	complemented
137	#4092	C₂³	1	32	yes	complemented
138	#4090	C₂³	1	16	yes	complemented
139	#4090	C₂³	1	16	yes	complemented
140	#4085	C₂³	1	32	yes	—
141	#4085	C₂³	1	32	yes	complemented
142	#4083	C₂³	1	16	yes	—
143	#4083	C₂³	1	16	yes	complemented
144	#4081	C₂³	1	16	yes	—
145	#4081	C₂³	1	16	yes	complemented
146	#4076	C₂³	1	16	yes	—
147	#4075	C₂³	1	32	yes	complemented
148	#4075	C₂³	1	32	yes	complemented
149	C₄×C₂²⋊D₅	C₂³	1	32	yes	complemented
150	C₂×#685	C₂³	1	4	yes	—
151	C₂×#685	C₂³	1	4	yes	—
152	C₂×#685	C₂³	1	4	yes	—
153	C₂×#685	C₂³	1	4	yes	—
154	C₂×#685	C₂³	1	4	yes	—
155	C₂×#685	C₂³	1	4	yes	—
156	#4072	C₂³	1	16	yes	complemented
157	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
158	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
159	C₂×C₄⋊Dic₅	C₂³	1	4	yes	—
160	#4070	C₂³	1	16	yes	complemented
161	C₂×#683	C₂³	1	4	yes	—
162	C₂×#683	C₂³	1	4	yes	—
163	C₂×#683	C₂³	1	4	yes	—
164	C₂×#683	C₂³	1	4	yes	—
165	C₂×#683	C₂³	1	4	yes	—
166	C₂×#683	C₂³	1	4	yes	—
167	C₂×C₄×Dic₅	C₂³	1	4	yes	—
168	C₂×C₄×Dic₅	C₂³	1	2	yes	—
169	C₂×C₄×Dic₅	C₂³	1	2	yes	—
170	#4032	C₂³	1	32	yes	complemented
171	#4031	C₂³	1	32	yes	complemented
172	#4031	C₂³	1	32	yes	complemented
173	#4030	C₂³	1	32	yes	complemented
174	#4030	C₂³	1	32	yes	complemented
175	#4029	C₂³	1	32	yes	complemented
176	#4029	C₂³	1	32	yes	complemented
177	#4028	C₂³	1	32	yes	complemented
178	#4027	C₂³	1	32	yes	complemented
179	#4027	C₂³	1	32	yes	complemented
180	D₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
181	#4025	C₂³	1	32	yes	complemented
182	#4025	C₂³	1	32	yes	complemented
183	#4024	C₂³	1	32	yes	complemented
184	#4024	C₂³	1	32	yes	complemented
185	#4023	C₂³	1	32	yes	complemented
186	#4022	C₂³	1	32	yes	complemented
187	#4021	C₂³	1	16	yes	complemented
188	C₄×D₂₀	C₂³	1	16	yes	complemented
189	#4018	C₂³	1	32	yes	complemented
190	#4016	C₂³	1	16	yes	complemented
191	C₄×Dic₁₀	C₂³	1	16	yes	complemented
192	#3545	—	5	32	no	—
193	C₂×#563	—	5	1	no	—
194	C₂×#562	—	5	2	no	—
195	C₂×H(3,𝔽₄)	—	5	1	no	—
196	C₂×#555	—	5	2	no	—
197	C₂×#551	—	5	2	no	—
198	C₂×#551	—	5	4	no	—
199	C₂×#546	—	5	4	no	—
200	C₂×#542	—	5	4	no	—
201	C₂×#538	—	5	4	no	—
202	C₂×#536	—	5	2	no	—
203	C₂×#534	—	5	2	no	—
204	C₂×#529	—	5	2	no	—
205	C₂²×#124	D₅	1	1	yes	characteristic, complemented
206	C₂⁴×C₅	—	2	8	no	—
207	C₂⁴×C₅	—	4	8	no	—
208	C₂⁴×C₅	C₂⁴	1	2	yes	—
209	C₂⁴×C₅	C₂⁴	1	2	yes	—
210	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
211	C₂⁴×C₅	C₂⁴	1	8	yes	—
212	C₂³×D₅	—	4	4	no	—
213	C₂³×D₅	—	4	8	no	—
214	C₂³×D₅	C₂⁴	1	4	yes	—
215	C₂³×D₅	C₂⁴	1	8	yes	—
216	C₂×C₅×Q₈	—	4	2	no	—
217	C₂×C₅×Q₈	—	4	4	no	—
218	C₂×C₅×Q₈	—	4	2	no	—
219	C₂×C₅×Q₈	—	4	16	no	—
220	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
221	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
222	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
223	C₂×C₅×D₄	—	4	2	no	—
224	C₂×C₅×D₄	—	4	4	no	—
225	C₂×C₅×D₄	—	4	2	no	—
226	C₂×C₅×D₄	—	4	16	no	—
227	C₂×C₅×D₄	C₂⁴	1	4	yes	—
228	C₂×C₅×D₄	C₂⁴	1	8	yes	—
229	C₂×C₅×D₄	C₂⁴	1	4	yes	—
230	C₂²×C₄×C₅	—	2	8	no	—
231	C₂²×C₄×C₅	—	2	4	no	—
232	C₂²×C₄×C₅	—	4	4	no	—
233	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
241	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
242	C₂×C₂²⋊D₅	—	2	16	no	—
243	C₂×C₂²⋊D₅	—	4	8	no	—
244	C₂×C₂²⋊D₅	—	4	8	no	—
245	C₂×C₂²⋊D₅	—	4	8	no	—
246	C₂×C₂²⋊D₅	—	4	32	no	—
247	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
248	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
249	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
250	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
251	C₂²×Dic₅	—	4	8	no	—
252	C₂²×Dic₅	—	4	4	no	—
253	C₂²×Dic₅	C₂⁴	1	4	yes	—
254	C₂²×Dic₅	C₂⁴	1	4	yes	—
255	C₂²×Dic₅	C₂⁴	1	4	yes	—
256	C₂²×Dic₅	C₂⁴	1	16	yes	—
257	C₂²×Dic₅	C₂⁴	1	8	yes	—
258	#709	—	4	32	no	—
259	C₂×D₂₀	—	4	4	no	—
260	C₂×D₂₀	—	4	4	no	—
261	C₂×D₂₀	C₂⁴	1	8	yes	—
262	C₂×D₂₀	C₂⁴	1	8	yes	—
263	C₂×C₄×D₅	—	4	8	no	—
264	C₂×C₄×D₅	—	4	8	no	—
265	C₂×C₄×D₅	C₂⁴	1	16	yes	—
266	C₂×C₄×D₅	C₂⁴	1	16	yes	—
267	C₂×Dic₁₀	—	4	4	no	—
268	C₂×Dic₁₀	—	4	4	no	—
269	C₂×Dic₁₀	C₂⁴	1	8	yes	—
270	C₂×Dic₁₀	C₂⁴	1	8	yes	—
271	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
272	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
273	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
274	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
275	C₄²×C₅	C₂⁴	1	4	yes	—
276	C₄²×C₅	C₂⁴	1	4	yes	—
277	C₄²×C₅	C₂⁴	1	8	yes	—
278	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
279	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
280	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
281	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
282	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
283	#685	C₂⁴	1	16	yes	—
284	#685	C₂⁴	1	16	yes	—
285	#685	C₂⁴	1	16	yes	—
286	#685	C₂⁴	1	16	yes	—
287	#685	C₂⁴	1	16	yes	—
288	#685	C₂⁴	1	16	yes	—
289	C₄⋊Dic₅	C₂⁴	1	8	yes	—
290	C₄⋊Dic₅	C₂⁴	1	8	yes	—
291	C₄⋊Dic₅	C₂⁴	1	16	yes	—
292	#683	C₂⁴	1	16	yes	—
293	#683	C₂⁴	1	16	yes	—
294	#683	C₂⁴	1	16	yes	—
295	#683	C₂⁴	1	16	yes	—
296	#683	C₂⁴	1	16	yes	—
297	#683	C₂⁴	1	16	yes	—
298	C₄×Dic₅	C₂⁴	1	16	yes	—
299	C₄×Dic₅	C₂⁴	1	8	yes	—
300	C₄×Dic₅	C₂⁴	1	8	yes	—
301	C₂²×#41	—	5	2	no	—
302	C₂³×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
303	C₂³×D₄	—	5	2	no	—
304	C₂³×D₄	C₂×D₅	1	1	yes	characteristic
305	#563	—	5	16	no	—
306	#562	—	5	32	no	—
307	H(3,𝔽₄)	—	5	16	no	—
308	#555	—	5	32	no	—
309	#551	—	5	32	no	—
310	#551	—	5	64	no	—
311	#546	—	5	64	no	—
312	#542	—	5	64	no	—
313	#538	—	5	64	no	—
314	#536	—	5	32	no	—
315	#534	—	5	32	no	—
316	C₂×C₄⋊Q₈	—	5	2	no	—
317	C₂×C₄⋊Q₈	—	5	2	no	—
318	#529	—	5	32	no	—
319	C₂×#126	—	5	4	no	—
320	C₂×#126	—	5	4	no	—
321	C₂×#126	—	5	4	no	—
322	C₂×#125	—	5	2	no	—
323	C₂×#124	—	5	2	no	—
324	C₂×#124	—	5	2	no	—
325	C₂×#124	—	5	4	no	—
326	C₂×#124	—	5	4	no	—
327	C₂×#124	—	5	2	no	—
328	C₂×#124	C₂×D₅	1	1	yes	characteristic
329	C₂×#124	C₂×D₅	1	1	yes	characteristic
330	C₂×#124	C₂×D₅	1	4	yes	complemented
331	C₂×#124	C₂×D₅	1	1	yes	characteristic, complemented
332	C₂×#124	C₂×D₅	1	1	yes	characteristic, complemented
333	C₂×#124	C₂×D₅	1	16	yes	complemented
334	C₂×#123	—	5	2	no	—
335	C₂×#123	—	5	2	no	—
336	C₂×#123	—	5	4	no	—
337	C₂×#123	—	5	4	no	—
338	C₂×#123	—	5	4	no	—
339	C₂×#123	—	5	4	no	—
340	C₂×#123	—	5	4	no	—
341	C₂×C₂²⋊Q₈	—	5	4	no	—
342	C₂×C₂²⋊Q₈	—	5	4	no	—
343	C₂×C₂²⋊Q₈	—	5	2	no	—
344	C₂×C₂²⋊Q₈	—	5	4	no	—
345	C₂×C₂²⋊Q₈	—	5	4	no	—
346	C₂×#121	—	5	4	no	—
347	C₂×#121	—	5	4	no	—
348	C₂×#121	—	5	2	no	—
349	C₂×#121	—	5	4	no	—
350	C₂×#121	—	5	4	no	—
351	C₂×#120	—	5	4	no	—
352	C₂×#120	—	5	2	no	—
353	C₂×#120	—	5	2	no	—
354	C₂×#120	—	5	4	no	—
355	C₂×C₄×Q₈	—	5	2	no	—
356	C₂×C₄×D₄	—	5	4	no	—
357	C₂×C₄×D₄	—	5	4	no	—
358	C₂×C₄×D₄	—	5	4	no	—
359	C₂×C₄×D₄	—	5	2	no	—
360	C₂×#117	—	5	2	no	—
361	C₂×#117	—	5	4	no	—
362	C₂×#117	—	5	4	no	—
363	C₂²×C₂²⋊C₄	—	5	2	no	—
364	C₂²×C₂²⋊C₄	—	5	4	no	—
365	C₂²×C₂²⋊C₄	C₂×D₅	1	4	yes	complemented
366	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
367	C₂³×C₅	—	2	4	no	—
368	C₂³×C₅	—	2	4	no	—
369	C₂³×C₅	—	2	4	no	—
370	C₂³×C₅	—	2	8	no	—
371	C₂³×C₅	—	2	8	no	—
372	C₂³×C₅	—	2	16	no	—
373	C₂³×C₅	—	4	16	no	—
374	C₂³×C₅	—	8	16	no	—
375	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
376	C₂³×C₅	C₂⁵	1	4	yes	—
377	C₂³×C₅	C₂⁵	1	4	yes	—
378	C₂³×C₅	C₂⁵	1	2	yes	—
379	C₂³×C₅	C₂⁵	1	1	yes	characteristic
380	C₂²×D₅	—	2	8	no	—
381	C₂²×D₅	—	2	8	no	—
382	C₂²×D₅	—	2	8	no	—
383	C₂²×D₅	—	4	8	no	—
384	C₂²×D₅	—	4	16	no	—
385	C₂²×D₅	—	8	16	no	—
386	C₂²×D₅	C₂⁵	1	8	yes	—
387	C₅×Q₈	—	4	4	no	—
388	C₅×Q₈	—	4	8	no	—
389	C₅×Q₈	—	4	4	no	—
390	C₅×D₄	—	4	4	no	—
391	C₅×D₄	—	4	8	no	—
392	C₅×D₄	—	4	4	no	—
393	C₂×C₄×C₅	—	2	4	no	—
394	C₂×C₄×C₅	—	2	4	no	—
395	C₂×C₄×C₅	—	2	16	no	—
396	C₂×C₄×C₅	—	2	8	no	—
397	C₂×C₄×C₅	—	2	2	no	—
398	C₂×C₄×C₅	—	2	2	no	—
399	C₂×C₄×C₅	—	2	4	no	—
400	C₂×C₄×C₅	—	2	4	no	—
401	C₂×C₄×C₅	—	4	8	no	—
402	C₂×C₄×C₅	C₂⁵	1	4	yes	—
403	C₂×C₄×C₅	C₂⁵	1	4	yes	—
404	C₂×C₄×C₅	C₂⁵	1	2	yes	—
405	C₂×C₄×C₅	C₂⁵	1	2	yes	—
406	C₂×C₄×C₅	C₂⁵	1	4	yes	—
407	C₂×C₄×C₅	C₂⁵	1	4	yes	—
408	C₂²⋊D₅	—	2	32	no	—
409	C₂²⋊D₅	—	4	16	no	—
410	C₂²⋊D₅	—	4	16	no	—
411	C₂²⋊D₅	—	4	16	no	—
412	C₂×Dic₅	—	2	8	no	—
413	C₂×Dic₅	—	2	8	no	—
414	C₂×Dic₅	—	2	8	no	—
415	C₂×Dic₅	—	4	16	no	—
416	C₂×Dic₅	—	4	8	no	—
417	C₂×Dic₅	C₂⁵	1	8	yes	—
418	C₂×Dic₅	C₂⁵	1	8	yes	—
419	C₂×Dic₅	C₂⁵	1	8	yes	—
420	D₂₀	—	4	8	no	—
421	D₂₀	—	4	8	no	—
422	C₄×D₅	—	4	16	no	—
423	C₄×D₅	—	4	16	no	—
424	Dic₁₀	—	4	8	no	—
425	Dic₁₀	—	4	8	no	—
426	C₂⁵	—	5	2	no	—
427	C₂⁵	C₂²×D₅	1	2	yes	—
428	C₂×#41	—	5	16	no	—
429	C₂×#41	—	20	8	no	—
430	C₂²×Q₈	—	4	4	no	—
431	C₂²×Q₈	—	5	2	no	—
432	C₂²×Q₈	—	5	2	no	—
433	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
434	C₂²×Q₈	C₂²×D₅	1	2	yes	—
435	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
436	C₂²×Q₈	C₂²×D₅	1	8	yes	complemented
437	C₂²×D₄	—	4	4	no	—
438	C₂²×D₄	—	5	4	no	—
439	C₂²×D₄	—	5	4	no	—
440	C₂²×D₄	—	5	4	no	—
441	C₂²×D₄	—	5	4	no	—
442	C₂²×D₄	—	5	16	no	—
443	C₂²×D₄	—	5	2	no	—
444	C₂²×D₄	—	5	2	no	—
445	C₂²×D₄	—	20	8	no	—
446	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
447	C₂²×D₄	C₂²×D₅	1	2	yes	—
448	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
449	C₂²×D₄	C₂²×D₅	1	8	yes	—
450	C₂³×C₄	—	5	4	no	—
451	C₂³×C₄	—	5	2	no	—
452	C₂³×C₄	—	5	4	no	—
453	C₂³×C₄	—	5	4	no	—
454	C₂³×C₄	C₂²×D₅	1	2	yes	—
455	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
456	C₂³×C₄	C₂²×D₅	1	2	yes	—
457	C₄⋊Q₈	—	5	16	no	—
458	C₄⋊Q₈	—	5	16	no	—
459	#126	—	5	32	no	—
460	#126	—	5	32	no	—
461	#126	—	5	32	no	—
462	#125	—	5	16	no	—
463	#124	—	5	16	no	—
464	#124	—	5	16	no	—
465	#124	—	5	32	no	—
466	#124	—	5	32	no	—
467	#124	—	5	16	no	—
468	#124	C₂²×D₅	1	8	yes	—
469	#124	C₂²×D₅	1	8	yes	—
470	#124	C₂²×D₅	1	32	yes	complemented
471	#124	C₂²×D₅	1	8	yes	complemented
472	#124	C₂²×D₅	1	8	yes	complemented
473	#123	—	5	16	no	—
474	#123	—	5	16	no	—
475	#123	—	5	32	no	—
476	#123	—	5	32	no	—
477	#123	—	5	32	no	—
478	#123	—	5	32	no	—
479	#123	—	5	32	no	—
480	C₂²⋊Q₈	—	5	32	no	—
481	C₂²⋊Q₈	—	5	32	no	—
482	C₂²⋊Q₈	—	5	16	no	—
483	C₂²⋊Q₈	—	5	32	no	—
484	C₂²⋊Q₈	—	5	32	no	—
485	#121	—	5	32	no	—
486	#121	—	5	32	no	—
487	#121	—	5	16	no	—
488	#121	—	5	32	no	—
489	#121	—	5	32	no	—
490	#120	—	5	32	no	—
491	#120	—	5	16	no	—
492	#120	—	5	16	no	—
493	#120	—	5	32	no	—
494	C₄×Q₈	—	5	16	no	—
495	C₄×D₄	—	5	32	no	—
496	C₄×D₄	—	5	32	no	—
497	C₄×D₄	—	5	32	no	—
498	C₄×D₄	—	5	16	no	—
499	#117	—	5	16	no	—
500	#117	—	5	32	no	—
501	#117	—	5	32	no	—
502	C₂×C₄⋊C₄	—	5	4	no	—
503	C₂×C₄⋊C₄	—	5	4	no	—
504	C₂×C₄⋊C₄	—	5	4	no	—
505	C₂×C₄⋊C₄	—	5	4	no	—
506	C₂×C₄⋊C₄	—	5	4	no	—
507	C₂×C₄⋊C₄	—	5	4	no	—
508	C₂×C₄⋊C₄	—	5	2	no	—
509	C₂×C₄⋊C₄	—	5	2	no	—
510	C₂×C₄⋊C₄	—	5	4	no	—
511	C₂×C₂²⋊C₄	—	5	4	no	—
512	C₂×C₂²⋊C₄	—	5	4	no	—
513	C₂×C₂²⋊C₄	—	5	2	no	—
514	C₂×C₂²⋊C₄	—	5	2	no	—
515	C₂×C₂²⋊C₄	—	5	16	no	—
516	C₂×C₂²⋊C₄	—	5	4	no	—
517	C₂×C₂²⋊C₄	—	5	4	no	—
518	C₂×C₂²⋊C₄	—	5	4	no	—
519	C₂×C₂²⋊C₄	—	5	4	no	—
520	C₂×C₂²⋊C₄	—	5	4	no	—
521	C₂×C₂²⋊C₄	—	5	4	no	—
522	C₂×C₂²⋊C₄	—	5	4	no	—
523	C₂×C₂²⋊C₄	—	5	32	no	—
524	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂²×D₅	1	32	yes	complemented
529	C₂×C₄²	—	5	2	no	—
530	C₂×C₄²	—	5	4	no	—
531	C₂×C₄²	—	5	2	no	—
532	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
533	C₂×C₄²	C₂²×D₅	1	2	yes	—
534	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
535	C₂×C₄²	C₂²×D₅	1	8	yes	complemented
536	C₂²×C₅	—	2	4	no	—
537	C₂²×C₅	—	2	8	no	—
538	C₂²×C₅	—	2	4	no	—
539	C₂²×C₅	—	2	4	no	—
540	C₂²×C₅	—	2	8	no	—
541	C₂²×C₅	—	2	8	no	—
542	C₂²×C₅	—	4	8	no	—
543	C₂²×C₅	—	4	8	no	—
544	C₂²×C₅	—	8	16	no	—
545	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
546	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
547	C₂²×C₅	#585	1	4	yes	—
548	C₂²×C₅	C₂⁶	1	1	yes	characteristic
549	C₂×D₅	—	2	8	no	—
550	C₂×D₅	—	2	8	no	—
551	C₂×D₅	—	2	8	no	—
552	C₂×D₅	—	4	16	no	—
553	C₂×D₅	—	8	16	no	—
554	C₄×C₅	—	2	4	no	—
555	C₄×C₅	—	2	4	no	—
556	C₄×C₅	—	2	2	no	—
557	C₄×C₅	—	2	2	no	—
558	C₄×C₅	—	2	4	no	—
559	C₄×C₅	—	2	4	no	—
560	Dic₅	—	2	8	no	—
561	Dic₅	—	2	8	no	—
562	Dic₅	—	2	8	no	—
563	C₂⁴	—	2	8	no	—
564	C₂⁴	—	4	8	no	—
565	C₂⁴	—	5	4	no	—
566	C₂⁴	—	5	8	no	—
567	C₂⁴	—	20	4	no	—
568	C₂⁴	—	20	8	no	—
569	C₂⁴	C₂³×D₅	1	2	yes	—
570	C₂⁴	C₂³×D₅	1	2	yes	—
571	C₂⁴	C₂³×D₅	1	1	yes	characteristic
572	C₂⁴	C₂³×D₅	1	8	yes	—
573	#41	—	20	32	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂×Q₈	—	4	4	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	—	4	16	no	—
578	C₂×Q₈	—	5	8	no	—
579	C₂×Q₈	—	5	8	no	—
580	C₂×Q₈	—	20	4	no	—
581	C₂×Q₈	—	20	4	no	—
582	C₂×Q₈	C₂³×D₅	1	4	yes	—
583	C₂×Q₈	C₂³×D₅	1	8	yes	—
584	C₂×Q₈	C₂³×D₅	1	4	yes	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	—	4	4	no	—
587	C₂×D₄	—	4	2	no	—
588	C₂×D₄	—	4	16	no	—
589	C₂×D₄	—	5	16	no	—
590	C₂×D₄	—	5	16	no	—
591	C₂×D₄	—	5	16	no	—
592	C₂×D₄	—	5	16	no	—
593	C₂×D₄	—	5	8	no	—
594	C₂×D₄	—	5	8	no	—
595	C₂×D₄	—	10	16	no	—
596	C₂×D₄	—	20	4	no	—
597	C₂×D₄	—	20	4	no	—
598	C₂×D₄	—	20	8	no	—
599	C₂×D₄	—	20	8	no	—
600	C₂×D₄	—	20	8	no	—
601	C₂×D₄	—	20	32	no	—
602	C₂×D₄	C₂³×D₅	1	4	yes	—
603	C₂×D₄	C₂³×D₅	1	8	yes	—
604	C₂×D₄	C₂³×D₅	1	4	yes	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	8	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	—	5	4	no	—
609	C₂²×C₄	—	5	4	no	—
610	C₂²×C₄	—	5	4	no	—
611	C₂²×C₄	—	5	16	no	—
612	C₂²×C₄	—	5	8	no	—
613	C₂²×C₄	—	5	16	no	—
614	C₂²×C₄	—	5	16	no	—
615	C₂²×C₄	—	20	8	no	—
616	C₂²×C₄	—	20	8	no	—
617	C₂²×C₄	—	20	4	no	—
618	C₂²×C₄	—	20	8	no	—
619	C₂²×C₄	C₂³×D₅	1	4	yes	—
620	C₂²×C₄	C₂³×D₅	1	8	yes	—
621	C₂²×C₄	C₂³×D₅	1	2	yes	—
622	C₂²×C₄	C₂³×D₅	1	2	yes	—
623	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
624	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
625	C₂²×C₄	C₂³×D₅	1	2	yes	—
626	C₂²×C₄	C₂³×D₅	1	2	yes	—
627	C₂²×C₄	C₂³×D₅	1	8	yes	—
628	C₄⋊C₄	—	5	16	no	—
629	C₄⋊C₄	—	5	16	no	—
630	C₄⋊C₄	—	5	16	no	—
631	C₄⋊C₄	—	5	16	no	—
632	C₄⋊C₄	—	5	16	no	—
633	C₄⋊C₄	—	5	16	no	—
634	C₄⋊C₄	—	5	8	no	—
635	C₄⋊C₄	—	5	8	no	—
636	C₄⋊C₄	—	5	16	no	—
637	C₂²⋊C₄	—	5	16	no	—
638	C₂²⋊C₄	—	5	16	no	—
639	C₂²⋊C₄	—	5	8	no	—
640	C₂²⋊C₄	—	5	8	no	—
641	C₂²⋊C₄	—	5	16	no	—
642	C₂²⋊C₄	—	5	16	no	—
643	C₂²⋊C₄	—	5	16	no	—
644	C₂²⋊C₄	—	5	16	no	—
645	C₂²⋊C₄	—	5	16	no	—
646	C₂²⋊C₄	—	5	16	no	—
647	C₂²⋊C₄	—	5	16	no	—
648	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
649	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
650	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
651	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
652	C₄²	—	5	8	no	—
653	C₄²	—	5	16	no	—
654	C₄²	—	5	8	no	—
655	C₄²	C₂³×D₅	1	4	yes	—
656	C₄²	C₂³×D₅	1	8	yes	—
657	C₄²	C₂³×D₅	1	4	yes	—
658	C₂×C₅	—	2	4	no	—
659	C₂×C₅	—	4	4	no	—
660	C₂×C₅	—	4	4	no	—
661	C₂×C₅	#3545	1	4	yes	complemented
662	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂×C₅	C₂×#585	1	2	yes	—
664	D₅	—	4	8	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	8	no	—
669	C₂³	—	2	8	no	—
670	C₂³	—	2	16	no	—
671	C₂³	—	4	16	no	—
672	C₂³	—	5	8	no	—
673	C₂³	—	8	16	no	—
674	C₂³	—	10	8	no	—
675	C₂³	—	10	8	no	—
676	C₂³	—	10	8	no	—
677	C₂³	—	20	8	no	—
678	C₂³	—	20	16	no	—
679	C₂³	—	40	16	no	—
680	C₂³	#4144	1	4	yes	—
681	C₂³	C₂⁴×D₅	1	4	yes	—
682	C₂³	C₂⁴×D₅	1	4	yes	—
683	C₂³	C₂⁴×D₅	1	2	yes	—
684	C₂³	C₂⁴×D₅	1	1	yes	characteristic
685	Q₈	—	4	4	no	—
686	Q₈	—	4	8	no	—
687	Q₈	—	4	4	no	—
688	Q₈	—	20	8	no	—
689	Q₈	—	20	8	no	—
690	D₄	—	4	4	no	—
691	D₄	—	4	8	no	—
692	D₄	—	4	4	no	—
693	D₄	—	10	32	no	—
694	D₄	—	20	8	no	—
695	D₄	—	20	8	no	—
696	D₄	—	20	16	no	—
697	D₄	—	20	16	no	—
698	D₄	—	20	16	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	16	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	5	8	no	—
709	C₂×C₄	—	5	8	no	—
710	C₂×C₄	—	5	8	no	—
711	C₂×C₄	—	10	8	no	—
712	C₂×C₄	—	10	8	no	—
713	C₂×C₄	—	10	8	no	—
714	C₂×C₄	—	20	16	no	—
715	C₂×C₄	—	20	16	no	—
716	C₂×C₄	—	20	8	no	—
717	C₂×C₄	—	20	16	no	—
718	C₂×C₄	C₂⁴×D₅	1	4	yes	—
719	C₂×C₄	C₂⁴×D₅	1	4	yes	—
720	C₂×C₄	C₂⁴×D₅	1	2	yes	—
721	C₂×C₄	C₂⁴×D₅	1	2	yes	—
722	C₂×C₄	C₂⁴×D₅	1	4	yes	—
723	C₂×C₄	C₂⁴×D₅	1	4	yes	—
724	C₅	C₂×#3545	1	1	yes	characteristic, complemented, Sylow
725	C₂²	—	2	4	no	—
726	C₂²	—	2	8	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	8	no	—
730	C₂²	—	2	8	no	—
731	C₂²	—	4	8	no	—
732	C₂²	—	4	8	no	—
733	C₂²	—	8	16	no	—
734	C₂²	—	10	8	no	—
735	C₂²	—	10	8	no	—
736	C₂²	—	10	8	no	—
737	C₂²	—	20	16	no	—
738	C₂²	—	40	16	no	—
739	C₂²	C₂×#4144	1	4	yes	—
740	C₂²	C₂×#4144	1	2	yes	—
741	C₂²	#66283	1	4	yes	—
742	C₂²	C₂⁵×D₅	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	4	no	—
749	C₄	—	10	8	no	—
750	C₄	—	10	8	no	—
751	C₄	—	10	8	no	—
752	C₂	—	2	4	no	—
753	C₂	—	4	4	no	—
754	C₂	—	4	4	no	—
755	C₂	—	20	8	no	—
756	C₂	#10617980	1	4	yes	direct product factor
757	C₂	C₂²×#4144	1	1	yes	characteristic
758	C₂	C₂×#66283	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂²×C₅×#124	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂²×#124	D₅
hypocenter	C₅	C₂×#3545
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×#124

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#124	C₂	semidirect
2. C₂×#66150	C₂	semidirect
3. C₂×#66138	C₂	semidirect
4. #10617980	C₂	direct (N × H)
5. C₂×#66017	C₂	semidirect
6. C₂×#66013	C₂	semidirect
7. C₂×#66012	C₂	semidirect
8. C₂×#66006	C₂	semidirect
9. C₂×#66018	C₂	semidirect
10. C₂×#66004	C₂	semidirect
11. C₂×#66003	C₂	semidirect
12. C₂×#65824	C₂	semidirect
13. C₂×#65829	C₂	semidirect
14. C₂×#65813	C₂	semidirect
15. C₂³×C₅×Q₈	C₂²	semidirect
17. C₂³×C₂²⋊D₅	C₂²	semidirect
21. C₂×C₅×#124	C₂²	semidirect
22. C₂×C₅×#124	C₂²	semidirect
23. C₂×C₅×#124	C₂²	semidirect
24. C₂×C₅×#124	C₂²	semidirect
25. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
26. C₂²×C₄²×C₅	C₂²	semidirect
28. C₂²×C₂²⋊Dic₅	C₂²	semidirect
29. #66150	C₂²	semidirect
30. C₂×#4093	C₂²	semidirect
31. C₂×#4093	C₂²	semidirect
32. C₂×#4092	C₂²	semidirect
33. C₂×#4092	C₂²	semidirect
34. C₂×#4090	C₂²	semidirect
35. C₂×#4090	C₂²	semidirect
36. #66138	C₂²	semidirect
38. C₂×#4085	C₂²	semidirect
40. C₂×#4083	C₂²	semidirect
42. C₂×#4081	C₂²	semidirect
44. C₂×#4075	C₂²	semidirect
45. C₂×#4075	C₂²	semidirect
46. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
47. C₂×#4072	C₂²	semidirect
48. C₂×#4070	C₂²	semidirect
49. #66018	C₂²	semidirect
50. #66017	C₂²	semidirect
51. #66013	C₂²	semidirect
52. #66012	C₂²	semidirect
53. #66006	C₂²	semidirect
54. #66004	C₂²	semidirect
55. #66003	C₂²	semidirect
56. #65829	C₂²	semidirect
57. C₂×#4032	C₂²	semidirect
58. C₂×#4031	C₂²	semidirect
59. C₂×#4031	C₂²	semidirect
60. #65824	C₂²	semidirect
61. C₂×#4030	C₂²	semidirect
62. C₂×#4030	C₂²	semidirect
63. C₂×#4029	C₂²	semidirect
64. C₂×#4029	C₂²	semidirect
65. C₂×#4028	C₂²	semidirect
66. C₂×#4027	C₂²	semidirect
67. C₂×#4027	C₂²	semidirect
68. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
69. C₂×#4025	C₂²	semidirect
70. C₂×#4025	C₂²	semidirect
71. C₂×#4024	C₂²	semidirect
72. C₂×#4024	C₂²	semidirect
73. C₂×#4023	C₂²	semidirect
74. #65813	C₂²	semidirect
75. C₂×#4022	C₂²	semidirect
76. C₂×#4021	C₂²	semidirect
77. C₂×C₄×D₂₀	C₂²	semidirect
78. C₂×#4018	C₂²	semidirect
79. C₂×#4016	C₂²	semidirect
80. C₂×C₄×Dic₁₀	C₂²	semidirect
88. C₂²×C₅×Q₈	C₂³	semidirect
102. C₂²×C₂²⋊D₅	C₂³	semidirect
115. C₅×#124	C₂³	semidirect
116. C₅×#124	C₂³	semidirect
117. C₅×#124	C₂³	semidirect
122. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
126. C₂×C₄²×C₅	C₂³	semidirect
133. C₂×C₂²⋊Dic₅	C₂³	semidirect
134. #4093	C₂³	semidirect
135. #4093	C₂³	semidirect
136. #4092	C₂³	semidirect
137. #4092	C₂³	semidirect
138. #4090	C₂³	semidirect
139. #4090	C₂³	semidirect
141. #4085	C₂³	semidirect
143. #4083	C₂³	semidirect
145. #4081	C₂³	semidirect
147. #4075	C₂³	semidirect
148. #4075	C₂³	semidirect
149. C₄×C₂²⋊D₅	C₂³	semidirect
156. #4072	C₂³	semidirect
160. #4070	C₂³	semidirect
170. #4032	C₂³	semidirect
171. #4031	C₂³	semidirect
172. #4031	C₂³	semidirect
173. #4030	C₂³	semidirect
174. #4030	C₂³	semidirect
175. #4029	C₂³	semidirect
176. #4029	C₂³	semidirect
177. #4028	C₂³	semidirect
178. #4027	C₂³	semidirect
179. #4027	C₂³	semidirect
180. D₅×C₂²⋊C₄	C₂³	semidirect
181. #4025	C₂³	semidirect
182. #4025	C₂³	semidirect
183. #4024	C₂³	semidirect
184. #4024	C₂³	semidirect
185. #4023	C₂³	semidirect
186. #4022	C₂³	semidirect
187. #4021	C₂³	semidirect
188. C₄×D₂₀	C₂³	semidirect
189. #4018	C₂³	semidirect
190. #4016	C₂³	semidirect
191. C₄×Dic₁₀	C₂³	semidirect
205. C₂²×#124	D₅	semidirect
302. C₂³×Q₈	C₂×D₅	semidirect
330. C₂×#124	C₂×D₅	semidirect
331. C₂×#124	C₂×D₅	semidirect
332. C₂×#124	C₂×D₅	semidirect
333. C₂×#124	C₂×D₅	semidirect
365. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
366. C₂²×C₄²	C₂×D₅	semidirect
436. C₂²×Q₈	C₂²×D₅	semidirect
470. #124	C₂²×D₅	semidirect
471. #124	C₂²×D₅	semidirect
472. #124	C₂²×D₅	semidirect
528. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
535. C₂×C₄²	C₂²×D₅	semidirect
661. C₂×C₅	#3545	semidirect
724. C₅	C₂×#3545	semidirect
756. C₂	#10617980	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#124	2
C₂×#66150	2
C₂×#66138	2
#10617980	2
C₂×#66017	2
C₂×#66013	2
C₂×#66012	2
C₂×#66006	2
C₂×#66018	2
C₂×#66004	2
C₂×#66003	2
C₂×#65824	2
C₂×#65829	2
C₂×#65813	2
C₂×#3545	5

Subgroups — C2×#10617980 #13007059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10617980 #13007059