Subgroups — C₂×C₅×#2148 #11956111

Order 1280.

1154 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2148	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#362	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#361	C₂	1	2	yes	maximal, complemented
7	C₂²×C₅×#41	—	2	1	no	—
8	C₂×C₅×#135	—	2	2	no	—
9	C₂×C₅×#135	—	2	1	no	—
10	C₂×C₅×#135	—	2	1	no	—
11	C₂×C₅×#135	—	2	2	no	—
12	C₂×C₅×#135	C₄	1	2	yes	—
13	C₂×C₅×#135	C₄	1	4	yes	—
14	C₂×C₅×#135	C₄	1	2	yes	—
15	C₂×C₅×#135	C₂²	1	4	yes	—
16	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	—	2	1	no	—
18	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₅×M₁₆	—	2	1	no	—
20	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×M₃₂	—	2	1	no	—
22	C₂×C₅×M₃₂	—	2	2	no	—
23	C₂×C₅×M₃₂	C₂²	1	2	yes	—
24	C₂×C₅×M₃₂	C₂²	1	4	yes	complemented
25	C₂²×C₅×C₁₆	—	2	1	no	—
26	C₂×C₅×#108	—	2	1	no	—
27	C₂×C₅×#108	—	2	2	no	—
28	C₂×C₅×#108	C₂²	1	2	yes	—
29	C₂×C₅×#108	C₂²	1	4	yes	complemented
30	C₅×#362	C₂²	1	8	yes	complemented
31	C₅×#361	C₂²	1	8	yes	complemented
32	C₂×#2148	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₅×#41	—	2	2	no	—
34	C₂×C₅×#41	—	2	4	no	—
35	C₂×C₅×#41	—	2	2	no	—
36	C₂×C₅×#41	—	2	4	no	—
37	C₂×C₅×#41	—	4	1	no	—
38	C₂×C₅×#41	—	4	2	no	—
39	C₂×C₅×#41	—	4	1	no	—
40	C₂×C₅×#41	—	4	2	no	—
41	C₂²×C₅×Q₈	—	2	1	no	—
42	C₂²×C₅×D₄	—	2	1	no	—
43	C₂²×C₅×D₄	—	4	1	no	—
44	C₂³×C₄×C₅	—	4	1	no	—
45	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
46	C₅×#135	—	2	4	no	—
47	C₅×#135	—	2	4	no	—
48	C₅×#135	—	2	4	no	—
49	C₅×#135	—	2	4	no	—
50	C₅×#135	—	2	4	no	—
51	C₅×#135	—	2	4	no	—
52	C₅×#135	C₂×C₄	1	8	yes	—
53	C₅×#135	C₂×C₄	1	8	yes	—
54	C₂×C₅×Q₁₆	—	2	1	no	—
55	C₂×C₅×Q₁₆	—	2	1	no	—
56	C₂×C₅×Q₁₆	—	2	1	no	—
57	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
60	C₂×C₅×SD₁₆	—	2	2	no	—
61	C₂×C₅×SD₁₆	—	2	4	no	—
62	C₂×C₅×SD₁₆	—	2	2	no	—
63	C₂×C₅×SD₁₆	—	2	4	no	—
64	C₂×C₅×D₈	—	2	1	no	—
65	C₂×C₅×D₈	—	2	1	no	—
66	C₂×C₅×D₈	—	2	1	no	—
67	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
68	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
69	C₂×C₅×D₈	C₂³	1	2	yes	—
70	C₂×C₅×M₁₆	—	2	2	no	—
71	C₂×C₅×M₁₆	—	2	4	no	—
72	C₂×C₅×M₁₆	—	4	1	no	—
73	C₂×C₅×M₁₆	—	4	2	no	—
74	C₂²×C₅×C₈	—	4	1	no	—
75	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
77	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
79	C₂²×C₅×C₈	D₄	1	2	yes	—
80	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
81	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
82	C₂²×C₅×C₈	D₄	1	2	yes	—
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	2	yes	—
85	C₅×M₃₂	—	2	2	no	—
86	C₅×M₃₂	—	2	4	no	—
87	C₅×M₃₂	C₂³	1	4	yes	—
88	C₂×C₅×C₁₆	—	2	2	no	—
89	C₂×C₅×C₁₆	—	2	4	no	—
90	C₅×#108	—	2	2	no	—
91	C₅×#108	—	2	4	no	—
92	C₅×#108	C₂³	1	4	yes	—
93	C₂²×#135	C₂×C₅	1	1	yes	characteristic
94	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂²×#108	C₂×C₅	1	1	yes	characteristic, complemented
96	#2148	C₂×C₅	1	8	yes	direct product factor
97	C₂×#362	C₂×C₅	1	2	yes	complemented
98	C₂×#361	C₂×C₅	1	2	yes	complemented
99	C₂⁴×C₅	—	4	1	no	—
100	C₂⁴×C₅	SD₁₆	1	1	yes	characteristic
101	C₅×#41	—	2	8	no	—
102	C₅×#41	—	2	8	no	—
103	C₅×#41	—	4	4	no	—
104	C₅×#41	—	4	4	no	—
105	C₅×#41	—	4	4	no	—
106	C₅×#41	—	4	4	no	—
107	C₅×#41	—	4	4	no	—
108	C₅×#41	—	4	4	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	4	1	no	—
113	C₂×C₅×Q₈	—	4	1	no	—
114	C₂×C₅×Q₈	—	4	1	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	4	2	no	—
119	C₂×C₅×D₄	—	4	2	no	—
120	C₂×C₅×D₄	—	4	4	no	—
121	C₂×C₅×D₄	—	4	4	no	—
122	C₂×C₅×D₄	—	4	1	no	—
123	C₂×C₅×D₄	—	4	1	no	—
124	C₂×C₅×D₄	—	4	1	no	—
125	C₂²×C₄×C₅	—	4	1	no	—
126	C₂²×C₄×C₅	—	4	4	no	—
127	C₂²×C₄×C₅	—	4	2	no	—
128	C₂²×C₄×C₅	—	4	2	no	—
129	C₂²×C₄×C₅	—	4	4	no	—
130	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
132	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
134	C₂²×C₄×C₅	D₈	1	2	yes	—
135	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
136	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
137	C₂²×C₄×C₅	SD₁₆	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₅×Q₁₆	—	2	2	no	—
141	C₅×Q₁₆	—	2	2	no	—
142	C₅×Q₁₆	—	2	2	no	—
143	C₅×Q₁₆	C₂²×C₄	1	4	yes	—
144	C₅×SD₁₆	—	2	8	no	—
145	C₅×SD₁₆	—	2	8	no	—
146	C₅×D₈	—	2	2	no	—
147	C₅×D₈	—	2	2	no	—
148	C₅×D₈	—	2	2	no	—
149	C₅×D₈	C₂²×C₄	1	4	yes	—
150	C₅×M₁₆	—	2	4	no	—
151	C₅×M₁₆	—	4	2	no	—
152	C₅×M₁₆	—	4	4	no	—
153	C₂×C₅×C₈	—	4	2	no	—
154	C₂×C₅×C₈	—	4	4	no	—
155	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
157	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
159	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
160	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
161	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
162	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
165	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
166	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
168	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
171	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
172	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
173	C₅×C₁₆	—	2	4	no	—
174	C₂²×#41	—	2	1	no	—
175	C₂×#135	—	2	2	no	—
176	C₂×#135	—	2	1	no	—
177	C₂×#135	—	2	1	no	—
178	C₂×#135	—	2	2	no	—
179	C₂×#135	C₄×C₅	1	2	yes	—
180	C₂×#135	C₄×C₅	1	4	yes	—
181	C₂×#135	C₄×C₅	1	2	yes	—
182	C₂×#135	C₂²×C₅	1	4	yes	—
183	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
184	C₂²×SD₁₆	—	2	1	no	—
185	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
186	C₂²×M₁₆	—	2	1	no	—
187	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
188	C₂×M₃₂	—	2	1	no	—
189	C₂×M₃₂	—	2	2	no	—
190	C₂×M₃₂	C₂²×C₅	1	2	yes	—
191	C₂×M₃₂	C₂²×C₅	1	4	yes	complemented
192	C₂²×C₁₆	—	2	1	no	—
193	C₂×#108	—	2	2	no	—
194	C₂×#108	—	2	1	no	—
195	C₂×#108	C₂²×C₅	1	2	yes	—
196	C₂×#108	C₂²×C₅	1	4	yes	complemented
197	#362	C₂²×C₅	1	8	yes	complemented
198	#361	C₂²×C₅	1	8	yes	complemented
199	C₂³×C₅	—	4	2	no	—
200	C₂³×C₅	—	4	2	no	—
201	C₂³×C₅	—	4	2	no	—
202	C₂³×C₅	—	4	2	no	—
203	C₂³×C₅	—	8	4	no	—
204	C₂³×C₅	#102	1	1	yes	characteristic
205	C₂³×C₅	#102	1	1	yes	characteristic
206	C₂³×C₅	#102	1	2	yes	—
207	C₂³×C₅	C₂×SD₁₆	1	1	yes	characteristic
208	C₂³×C₅	C₂×SD₁₆	1	2	yes	—
209	C₅×Q₈	—	2	4	no	—
210	C₅×Q₈	—	4	2	no	—
211	C₅×Q₈	—	4	2	no	—
212	C₅×Q₈	—	4	2	no	—
213	C₅×D₄	—	2	4	no	—
214	C₅×D₄	—	4	8	no	—
215	C₅×D₄	—	4	8	no	—
216	C₅×D₄	—	4	2	no	—
217	C₅×D₄	—	4	2	no	—
218	C₅×D₄	—	4	2	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	8	no	—
223	C₂×C₄×C₅	—	4	8	no	—
224	C₂×C₄×C₅	#102	1	1	yes	characteristic
225	C₂×C₄×C₅	#102	1	2	yes	—
226	C₂×C₄×C₅	#102	1	2	yes	—
227	C₂×C₄×C₅	#102	1	2	yes	—
228	C₂×C₄×C₅	#102	1	2	yes	—
229	C₂×C₄×C₅	#102	1	2	yes	—
230	C₂×C₄×C₅	#102	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
234	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
235	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
237	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
239	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
240	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₅×C₈	—	4	4	no	—
243	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
246	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
247	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
248	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
249	C₂×#41	—	2	2	no	—
250	C₂×#41	—	2	4	no	—
251	C₂×#41	—	2	2	no	—
252	C₂×#41	—	2	4	no	—
253	C₂×#41	—	4	1	no	—
254	C₂×#41	—	4	1	no	—
255	C₂×#41	—	4	2	no	—
256	C₂×#41	—	4	2	no	—
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	—	4	1	no	—
260	C₂³×C₄	—	4	1	no	—
261	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
262	#135	—	2	4	no	—
263	#135	—	2	4	no	—
264	#135	—	2	4	no	—
265	#135	—	2	4	no	—
266	#135	—	2	4	no	—
267	#135	—	2	4	no	—
268	#135	C₂×C₄×C₅	1	8	yes	—
269	#135	C₂×C₄×C₅	1	8	yes	—
270	C₂×Q₁₆	—	2	1	no	—
271	C₂×Q₁₆	—	2	1	no	—
272	C₂×Q₁₆	—	2	1	no	—
273	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
274	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
275	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	4	no	—
278	C₂×SD₁₆	—	2	2	no	—
279	C₂×SD₁₆	—	2	4	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	—	2	1	no	—
283	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
284	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
285	C₂×D₈	C₂³×C₅	1	2	yes	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	4	no	—
288	C₂×M₁₆	—	4	1	no	—
289	C₂×M₁₆	—	4	2	no	—
290	C₂²×C₈	—	4	1	no	—
291	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
292	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
293	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
294	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
295	C₂²×C₈	C₅×D₄	1	2	yes	—
296	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
297	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
298	C₂²×C₈	C₅×D₄	1	2	yes	—
299	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₅	1	2	yes	—
301	M₃₂	—	2	2	no	—
302	M₃₂	—	2	4	no	—
303	M₃₂	C₂³×C₅	1	4	yes	—
304	C₂×C₁₆	—	2	2	no	—
305	C₂×C₁₆	—	2	4	no	—
306	#108	—	2	2	no	—
307	#108	—	2	4	no	—
308	#108	C₂³×C₅	1	4	yes	—
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	4	2	no	—
313	C₂²×C₅	—	4	2	no	—
314	C₂²×C₅	—	4	4	no	—
315	C₂²×C₅	—	8	4	no	—
316	C₂²×C₅	—	8	4	no	—
317	C₂²×C₅	—	8	4	no	—
318	C₂²×C₅	C₂×#102	1	1	yes	characteristic
319	C₂²×C₅	C₂×#102	1	2	yes	—
320	C₂²×C₅	C₂×#102	1	2	yes	—
321	C₂²×C₅	C₂×#102	1	1	yes	characteristic
322	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
323	C₄×C₅	—	4	4	no	—
324	C₄×C₅	C₂×#102	1	2	yes	—
325	C₄×C₅	C₂×#102	1	2	yes	—
326	C₄×C₅	C₂×#102	1	1	yes	characteristic
327	C₄×C₅	C₂×#102	1	1	yes	characteristic
328	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
329	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
330	C₂⁴	—	4	1	no	—
331	C₂⁴	C₅×SD₁₆	1	1	yes	characteristic
332	#41	—	2	8	no	—
333	#41	—	2	8	no	—
334	#41	—	4	4	no	—
335	#41	—	4	4	no	—
336	#41	—	4	4	no	—
337	#41	—	4	4	no	—
338	#41	—	4	4	no	—
339	#41	—	4	4	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	4	1	no	—
344	C₂×Q₈	—	4	1	no	—
345	C₂×Q₈	—	4	1	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	4	4	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
362	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
363	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
364	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
365	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
366	C₂²×C₄	C₅×D₈	1	2	yes	—
367	C₂²×C₄	C₅×SD₁₆	1	1	yes	characteristic
368	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
369	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
371	Q₁₆	—	2	2	no	—
372	Q₁₆	—	2	2	no	—
373	Q₁₆	—	2	2	no	—
374	Q₁₆	C₂²×C₄×C₅	1	4	yes	—
375	SD₁₆	—	2	8	no	—
376	SD₁₆	—	2	8	no	—
377	D₈	—	2	2	no	—
378	D₈	—	2	2	no	—
379	D₈	—	2	2	no	—
380	D₈	C₂²×C₄×C₅	1	4	yes	—
381	M₁₆	—	2	4	no	—
382	M₁₆	—	4	2	no	—
383	M₁₆	—	4	4	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	—	4	4	no	—
386	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
387	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
388	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
390	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
391	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
392	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
393	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
394	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
395	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
396	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
397	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
398	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
399	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
400	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
401	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
402	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
403	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
404	C₁₆	—	2	4	no	—
405	C₂×C₅	—	2	1	no	—
406	C₂×C₅	—	2	1	no	—
407	C₂×C₅	—	2	2	no	—
408	C₂×C₅	—	2	2	no	—
409	C₂×C₅	—	8	4	no	—
410	C₂×C₅	#2148	1	2	yes	direct product factor
411	C₂×C₅	C₂²×#102	1	1	yes	characteristic
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	8	4	no	—
417	C₂³	C₅×#102	1	1	yes	characteristic
418	C₂³	C₅×#102	1	1	yes	characteristic
419	C₂³	C₅×#102	1	2	yes	—
420	C₂³	C₂×C₅×SD₁₆	1	1	yes	characteristic
421	C₂³	C₂×C₅×SD₁₆	1	2	yes	—
422	Q₈	—	2	4	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	D₄	—	2	4	no	—
427	D₄	—	4	8	no	—
428	D₄	—	4	8	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	C₅×#102	1	2	yes	—
438	C₂×C₄	C₅×#102	1	1	yes	characteristic
439	C₂×C₄	C₅×#102	1	1	yes	characteristic
440	C₂×C₄	C₅×#102	1	2	yes	—
441	C₂×C₄	C₅×#102	1	2	yes	—
442	C₂×C₄	C₅×#102	1	2	yes	—
443	C₂×C₄	C₅×#102	1	2	yes	—
444	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
445	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
446	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
447	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
448	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
449	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
450	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
451	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
452	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
453	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
455	C₈	—	4	4	no	—
456	C₈	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
457	C₈	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
458	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
459	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
460	C₈	C₂³×C₄×C₅	1	1	yes	characteristic
461	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
462	C₅	C₂×#2148	1	1	yes	characteristic, direct product factor, Sylow
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	8	4	no	—
470	C₂²	—	8	4	no	—
471	C₂²	—	8	4	no	—
472	C₂²	C₂×C₅×#102	1	1	yes	characteristic
473	C₂²	C₂×C₅×#102	1	2	yes	—
474	C₂²	C₂×C₅×#102	1	2	yes	—
475	C₂²	C₂×C₅×#102	1	1	yes	characteristic
476	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
477	C₄	—	4	4	no	—
478	C₄	C₂×C₅×#102	1	2	yes	—
479	C₄	C₂×C₅×#102	1	2	yes	—
480	C₄	C₂×C₅×#102	1	1	yes	characteristic
481	C₄	C₂×C₅×#102	1	1	yes	characteristic
482	C₄	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
483	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	2	2	no	—
487	C₂	—	2	2	no	—
488	C₂	—	8	4	no	—
489	C₂	C₅×#2148	1	2	yes	direct product factor
490	C₂	C₂²×C₅×#102	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#102
commutator	C₈	C₂³×C₄×C₅
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂×#102
prime radical	C₂²×C₅×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×M₃₂	C₂	semidirect
3. C₂²×C₅×#108	C₂	semidirect
4. C₅×#2148	C₂	direct (N × H)
5. C₂×C₅×#362	C₂	semidirect
6. C₂×C₅×#361	C₂	semidirect
24. C₂×C₅×M₃₂	C₂²	semidirect
29. C₂×C₅×#108	C₂²	semidirect
30. C₅×#362	C₂²	semidirect
31. C₅×#361	C₂²	semidirect
32. C₂×#2148	C₅	direct (N × H)
94. C₂²×M₃₂	C₂×C₅	semidirect
95. C₂²×#108	C₂×C₅	semidirect
96. #2148	C₂×C₅	direct (N × H)
97. C₂×#362	C₂×C₅	semidirect
98. C₂×#361	C₂×C₅	semidirect
191. C₂×M₃₂	C₂²×C₅	semidirect
196. C₂×#108	C₂²×C₅	semidirect
197. #362	C₂²×C₅	semidirect
198. #361	C₂²×C₅	semidirect
410. C₂×C₅	#2148	direct (N × H)
462. C₅	C₂×#2148	direct (N × H)
489. C₂	C₅×#2148	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×#135	2
C₂²×C₅×M₃₂	2
C₂²×C₅×#108	2
C₅×#2148	2
C₂×C₅×#362	2
C₂×C₅×#361	2
C₂×#2148	5

Subgroups — C2×C5×#2148 #11956111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2148 #11956111