Subgroups — C₂×C₅×#2223 #11956336

Order 1280.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#473	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#472	C₂	1	1	yes	maximal, characteristic
5	C₅×#2223	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#361	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#137	—	2	1	no	—
10	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#131	C₂²	1	1	yes	characteristic
14	C₂×C₅×SD₃₂	—	2	1	no	—
15	C₂×C₅×SD₃₂	—	2	1	no	—
16	C₂×C₅×SD₃₂	—	2	2	no	—
17	C₂×C₅×SD₃₂	C₂²	1	4	yes	complemented
18	C₅×#504	—	2	2	no	—
19	C₅×#504	C₂²	1	4	yes	complemented
20	C₂×C₅×M₃₂	—	2	1	no	—
21	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₁₆	—	2	1	no	—
23	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
24	C₅×#473	—	2	2	no	—
25	C₅×#473	C₂²	1	4	yes	complemented
26	C₅×#472	—	2	2	no	—
27	C₅×#472	C₂²	1	4	yes	—
28	C₂×C₅×#108	C₂²	1	1	yes	characteristic
29	C₂×C₅×#108	C₂²	1	1	yes	characteristic
30	C₂×C₅×#101	—	2	1	no	—
31	C₂×C₅×#100	—	2	1	no	—
32	C₅×#368	C₂²	1	4	yes	complemented
33	C₅×#362	C₂²	1	4	yes	complemented
34	C₅×#361	C₂²	1	4	yes	complemented
35	C₂×#2223	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂×C₅×#41	D₄	1	1	yes	characteristic
37	C₂²×C₅×Q₈	—	2	1	no	—
38	C₂²×C₅×D₄	—	2	1	no	—
39	C₅×#137	—	2	4	no	—
40	C₅×#137	—	4	2	no	—
41	C₅×AGL(1,ℤ/8)	—	2	4	no	—
42	C₅×AGL(1,ℤ/8)	—	4	2	no	—
43	C₂×C₅×Q₁₆	—	2	1	no	—
44	C₂×C₅×Q₁₆	—	2	1	no	—
45	C₂×C₅×Q₁₆	—	2	1	no	—
46	C₂×C₅×Q₁₆	—	2	1	no	—
47	C₂×C₅×Q₁₆	—	2	1	no	—
48	C₂×C₅×Q₁₆	—	4	1	no	—
49	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
50	C₂×C₅×SD₁₆	—	4	1	no	—
51	C₂×C₅×SD₁₆	—	4	1	no	—
52	C₂×C₅×D₈	—	2	1	no	—
53	C₂×C₅×D₈	—	2	1	no	—
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×D₈	—	2	1	no	—
56	C₂×C₅×D₈	—	2	1	no	—
57	C₂×C₅×D₈	—	4	1	no	—
58	C₂×C₅×D₈	C₂³	1	2	yes	—
59	C₅×#131	—	2	1	no	—
60	C₅×#131	—	2	1	no	—
61	C₅×#131	D₄	1	2	yes	—
62	C₅×#131	C₂³	1	2	yes	—
63	C₂×C₅×M₁₆	—	2	1	no	—
64	C₂×C₅×M₁₆	—	2	1	no	—
65	C₂×C₅×M₁₆	—	2	1	no	—
66	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
67	C₂²×C₅×C₈	—	2	1	no	—
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₅×SD₃₂	—	2	4	no	—
70	C₅×SD₃₂	—	2	4	no	—
71	C₅×M₃₂	—	2	1	no	—
72	C₅×M₃₂	—	2	4	no	—
73	C₅×M₃₂	C₂³	1	2	yes	—
74	C₂×C₅×C₁₆	—	2	1	no	—
75	C₂×C₅×C₁₆	—	2	4	no	—
76	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
77	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
78	C₂×C₅×C₁₆	D₄	1	2	yes	—
79	C₂×C₅×C₁₆	C₂³	1	2	yes	—
80	C₅×#108	—	2	1	no	—
81	C₅×#108	—	2	1	no	—
82	C₅×#108	C₂³	1	2	yes	—
83	C₅×#108	C₂³	1	2	yes	—
84	C₅×#101	—	2	4	no	—
85	C₅×#100	—	2	4	no	—
86	C₂²×SD₃₂	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×#504	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×#473	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×#472	C₂×C₅	1	1	yes	characteristic
90	#2223	C₂×C₅	1	8	yes	direct product factor
91	C₂×#368	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#362	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×#361	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂⁴×C₅	—	4	1	no	—
95	C₅×#41	—	2	1	no	—
96	C₅×#41	—	2	1	no	—
97	C₅×#41	D₈	1	2	yes	—
98	C₅×#41	C₂×D₄	1	2	yes	—
99	C₂×C₅×Q₈	—	2	2	no	—
100	C₂×C₅×Q₈	—	4	1	no	—
101	C₂×C₅×Q₈	—	4	1	no	—
102	C₂×C₅×Q₈	—	4	1	no	—
103	C₂×C₅×Q₈	—	4	1	no	—
104	C₂×C₅×Q₈	—	4	1	no	—
105	C₂×C₅×Q₈	D₈	1	1	yes	characteristic
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	4	1	no	—
109	C₂×C₅×D₄	—	4	1	no	—
110	C₂×C₅×D₄	—	4	1	no	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	1	no	—
113	C₂×C₅×D₄	D₈	1	1	yes	characteristic
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	4	1	no	—
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₅×Q₁₆	—	2	2	no	—
118	C₅×Q₁₆	—	2	2	no	—
119	C₅×Q₁₆	—	4	4	no	—
120	C₅×Q₁₆	—	4	1	no	—
121	C₅×Q₁₆	—	4	1	no	—
122	C₅×SD₁₆	—	4	4	no	—
123	C₅×SD₁₆	—	4	4	no	—
124	C₅×D₈	—	2	2	no	—
125	C₅×D₈	—	2	2	no	—
126	C₅×D₈	—	4	4	no	—
127	C₅×D₈	—	4	1	no	—
128	C₅×D₈	—	4	1	no	—
129	C₅×M₁₆	—	2	1	no	—
130	C₅×M₁₆	—	2	2	no	—
131	C₅×M₁₆	—	2	2	no	—
132	C₅×M₁₆	—	2	2	no	—
133	C₅×M₁₆	—	2	2	no	—
134	C₅×M₁₆	—	4	1	no	—
135	C₅×M₁₆	—	4	1	no	—
136	C₅×M₁₆	C₂×D₄	1	2	yes	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	4	1	no	—
141	C₂×C₅×C₈	—	4	1	no	—
142	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅×C₈	#41	1	1	yes	characteristic
146	C₂×C₅×C₈	#41	1	1	yes	characteristic
147	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
148	C₅×C₁₆	—	2	2	no	—
149	C₅×C₁₆	C₂×D₄	1	2	yes	—
150	C₅×C₁₆	C₂×D₄	1	2	yes	—
151	C₂×#137	—	2	1	no	—
152	C₂×AGL(1,ℤ/8)	—	2	1	no	—
153	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
154	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
155	C₂×#131	C₂²×C₅	1	1	yes	characteristic
156	C₂×SD₃₂	—	2	1	no	—
157	C₂×SD₃₂	—	2	1	no	—
158	C₂×SD₃₂	—	2	2	no	—
159	C₂×SD₃₂	C₂²×C₅	1	4	yes	complemented
160	#504	—	2	2	no	—
161	#504	C₂²×C₅	1	4	yes	complemented
162	C₂×M₃₂	—	2	1	no	—
163	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
164	C₂²×C₁₆	—	2	1	no	—
165	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
166	#473	—	2	2	no	—
167	#473	C₂²×C₅	1	4	yes	complemented
168	#472	—	2	2	no	—
169	#472	C₂²×C₅	1	4	yes	—
170	C₂×#108	C₂²×C₅	1	1	yes	characteristic
171	C₂×#108	C₂²×C₅	1	1	yes	characteristic
172	C₂×#101	—	2	1	no	—
173	C₂×#100	—	2	1	no	—
174	#368	C₂²×C₅	1	4	yes	complemented
175	#362	C₂²×C₅	1	4	yes	complemented
176	#361	C₂²×C₅	1	4	yes	complemented
177	C₂³×C₅	—	2	1	no	—
178	C₂³×C₅	—	4	2	no	—
179	C₂³×C₅	—	8	1	no	—
180	C₂³×C₅	—	8	1	no	—
181	C₂³×C₅	—	16	2	no	—
182	C₂³×C₅	#135	1	1	yes	characteristic
183	C₅×Q₈	—	2	1	no	—
184	C₅×Q₈	—	4	2	no	—
185	C₅×Q₈	—	4	2	no	—
186	C₅×Q₈	—	8	1	no	—
187	C₅×Q₈	—	8	1	no	—
188	C₅×Q₈	C₂×D₈	1	2	yes	—
189	C₅×D₄	—	2	2	no	—
190	C₅×D₄	—	2	2	no	—
191	C₅×D₄	—	2	1	no	—
192	C₅×D₄	—	4	2	no	—
193	C₅×D₄	—	4	2	no	—
194	C₅×D₄	—	8	1	no	—
195	C₅×D₄	—	8	1	no	—
196	C₅×D₄	C₂×D₈	1	2	yes	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	8	1	no	—
202	C₂×C₄×C₅	—	8	1	no	—
203	C₂×C₄×C₅	#121	1	1	yes	characteristic
204	C₂×C₄×C₅	#121	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
207	C₂×C₄×C₅	#135	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₅×C₈	—	2	2	no	—
210	C₅×C₈	—	4	2	no	—
211	C₅×C₈	—	4	2	no	—
212	C₅×C₈	#121	1	1	yes	characteristic
213	C₅×C₈	#121	1	1	yes	characteristic
214	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
215	C₅×C₈	C₂×#41	1	1	yes	characteristic
216	C₂×#41	C₅×D₄	1	1	yes	characteristic
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×D₄	—	2	1	no	—
219	#137	—	2	4	no	—
220	#137	—	4	2	no	—
221	AGL(1,ℤ/8)	—	2	4	no	—
222	AGL(1,ℤ/8)	—	4	2	no	—
223	C₂×Q₁₆	—	2	1	no	—
224	C₂×Q₁₆	—	2	1	no	—
225	C₂×Q₁₆	—	2	1	no	—
226	C₂×Q₁₆	—	2	1	no	—
227	C₂×Q₁₆	—	2	1	no	—
228	C₂×Q₁₆	—	4	1	no	—
229	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
230	C₂×SD₁₆	—	4	1	no	—
231	C₂×SD₁₆	—	4	1	no	—
232	C₂×D₈	—	2	1	no	—
233	C₂×D₈	—	2	1	no	—
234	C₂×D₈	—	2	1	no	—
235	C₂×D₈	—	2	1	no	—
236	C₂×D₈	—	2	1	no	—
237	C₂×D₈	—	4	1	no	—
238	C₂×D₈	C₂³×C₅	1	2	yes	—
239	#131	—	2	1	no	—
240	#131	—	2	1	no	—
241	#131	C₅×D₄	1	2	yes	—
242	#131	C₂³×C₅	1	2	yes	—
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
249	SD₃₂	—	2	4	no	—
250	SD₃₂	—	2	4	no	—
251	M₃₂	—	2	1	no	—
252	M₃₂	—	2	4	no	—
253	M₃₂	C₂³×C₅	1	2	yes	—
254	C₂×C₁₆	—	2	1	no	—
255	C₂×C₁₆	—	2	4	no	—
256	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
257	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
258	C₂×C₁₆	C₅×D₄	1	2	yes	—
259	C₂×C₁₆	C₂³×C₅	1	2	yes	—
260	#108	—	2	1	no	—
261	#108	—	2	1	no	—
262	#108	C₂³×C₅	1	2	yes	—
263	#108	C₂³×C₅	1	2	yes	—
264	#101	—	2	4	no	—
265	#100	—	2	4	no	—
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	—	2	2	no	—
268	C₂²×C₅	—	4	2	no	—
269	C₂²×C₅	—	8	2	no	—
270	C₂²×C₅	—	16	2	no	—
271	C₂²×C₅	—	16	2	no	—
272	C₂²×C₅	—	16	2	no	—
273	C₂²×C₅	#466	1	1	yes	characteristic
274	C₂²×C₅	#466	1	1	yes	characteristic
275	C₂²×C₅	C₂×#135	1	1	yes	characteristic
276	C₄×C₅	—	2	2	no	—
277	C₄×C₅	—	8	2	no	—
278	C₄×C₅	#466	1	1	yes	characteristic
279	C₄×C₅	#466	1	1	yes	characteristic
280	C₄×C₅	C₂×#121	1	1	yes	characteristic
281	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
282	C₂⁴	—	4	1	no	—
283	#41	—	2	1	no	—
284	#41	—	2	1	no	—
285	#41	C₅×D₈	1	2	yes	—
286	#41	C₂×C₅×D₄	1	2	yes	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×Q₈	—	4	1	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×Q₈	C₅×D₈	1	1	yes	characteristic
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	C₅×D₈	1	1	yes	characteristic
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	Q₁₆	—	2	2	no	—
306	Q₁₆	—	2	2	no	—
307	Q₁₆	—	4	4	no	—
308	Q₁₆	—	4	1	no	—
309	Q₁₆	—	4	1	no	—
310	SD₁₆	—	4	4	no	—
311	SD₁₆	—	4	4	no	—
312	D₈	—	2	2	no	—
313	D₈	—	2	2	no	—
314	D₈	—	4	4	no	—
315	D₈	—	4	1	no	—
316	D₈	—	4	1	no	—
317	M₁₆	—	2	1	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	4	1	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	C₂×C₅×D₄	1	2	yes	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂×C₈	C₅×#41	1	1	yes	characteristic
334	C₂×C₈	C₅×#41	1	1	yes	characteristic
335	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
336	C₁₆	—	2	2	no	—
337	C₁₆	C₂×C₅×D₄	1	2	yes	—
338	C₁₆	C₂×C₅×D₄	1	2	yes	—
339	C₂×C₅	—	2	1	no	—
340	C₂×C₅	—	2	1	no	—
341	C₂×C₅	—	4	2	no	—
342	C₂×C₅	—	16	2	no	—
343	C₂×C₅	#2223	1	2	yes	direct product factor
344	C₂×C₅	C₂×#466	1	1	yes	characteristic
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	16	2	no	—
350	C₂³	C₅×#135	1	1	yes	characteristic
351	Q₈	—	2	1	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	8	1	no	—
355	Q₈	—	8	1	no	—
356	Q₈	C₂×C₅×D₈	1	2	yes	—
357	D₄	—	2	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	2	1	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	8	1	no	—
363	D₄	—	8	1	no	—
364	D₄	C₂×C₅×D₈	1	2	yes	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	C₅×#121	1	1	yes	characteristic
372	C₂×C₄	C₅×#121	1	1	yes	characteristic
373	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
374	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
375	C₂×C₄	C₅×#135	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₈	C₅×#121	1	1	yes	characteristic
381	C₈	C₅×#121	1	1	yes	characteristic
382	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
383	C₈	C₂×C₅×#41	1	1	yes	characteristic
384	C₅	C₂×#2223	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	2	no	—
390	C₂²	—	16	2	no	—
391	C₂²	—	16	2	no	—
392	C₂²	C₅×#466	1	1	yes	characteristic
393	C₂²	C₅×#466	1	1	yes	characteristic
394	C₂²	C₂×C₅×#135	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₅×#466	1	1	yes	characteristic
398	C₄	C₅×#466	1	1	yes	characteristic
399	C₄	C₂×C₅×#121	1	1	yes	characteristic
400	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	4	2	no	—
404	C₂	—	16	2	no	—
405	C₂	C₅×#2223	1	2	yes	direct product factor
406	C₂	C₂×C₅×#466	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	#466
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₂×C₅×#472	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×SD₃₂	C₂	semidirect
2. C₂×C₅×#504	C₂	semidirect
3. C₂×C₅×#473	C₂	semidirect
5. C₅×#2223	C₂	direct (N × H)
6. C₂×C₅×#368	C₂	semidirect
7. C₂×C₅×#362	C₂	semidirect
8. C₂×C₅×#361	C₂	semidirect
17. C₂×C₅×SD₃₂	C₂²	semidirect
19. C₅×#504	C₂²	semidirect
25. C₅×#473	C₂²	semidirect
32. C₅×#368	C₂²	semidirect
33. C₅×#362	C₂²	semidirect
34. C₅×#361	C₂²	semidirect
35. C₂×#2223	C₅	direct (N × H)
86. C₂²×SD₃₂	C₂×C₅	semidirect
87. C₂×#504	C₂×C₅	semidirect
88. C₂×#473	C₂×C₅	semidirect
90. #2223	C₂×C₅	direct (N × H)
91. C₂×#368	C₂×C₅	semidirect
92. C₂×#362	C₂×C₅	semidirect
93. C₂×#361	C₂×C₅	semidirect
159. C₂×SD₃₂	C₂²×C₅	semidirect
161. #504	C₂²×C₅	semidirect
167. #473	C₂²×C₅	semidirect
174. #368	C₂²×C₅	semidirect
175. #362	C₂²×C₅	semidirect
176. #361	C₂²×C₅	semidirect
343. C₂×C₅	#2223	direct (N × H)
384. C₅	C₂×#2223	direct (N × H)
405. C₂	C₅×#2223	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×SD₃₂	2
C₂×C₅×#504	2
C₂×C₅×#473	2
C₂×C₅×#472	2
C₅×#2223	2
C₂×C₅×#368	2
C₂×C₅×#362	2
C₂×C₅×#361	2
C₂×#2223	5

Subgroups — C2×C5×#2223 #11956336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2223 #11956336