Subgroups — C₂×#10601491 #12099474

Order 1280.

786 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#65395	C₂	1	1	yes	maximal, characteristic
3	C₂×#65390	C₂	1	1	yes	maximal, characteristic
4	C₂×#64779	C₂	1	2	yes	maximal
5	C₂×#64777	C₂	1	2	yes	maximal
6	#10601491	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
8	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×#4072	C₂²	1	2	yes	—
10	C₂×#4072	C₂²	1	1	yes	characteristic
11	C₂²×#681	C₂²	1	1	yes	characteristic
12	C₂×C₅×#108	—	2	1	no	—
13	C₂×C₅×#108	—	2	1	no	—
14	C₂×C₅×#108	—	2	2	no	—
15	C₂×C₅×#108	C₂²	1	4	yes	—
16	#65395	—	2	2	no	—
17	#65395	C₂²	1	4	yes	—
18	C₂×#3950	—	2	1	no	—
19	C₂×#3949	—	2	1	no	—
20	#65390	C₄	1	4	yes	complemented
21	#65390	C₂²	1	4	yes	—
22	C₂×#3947	C₄	1	2	yes	complemented
23	C₂×C₈×Dic₅	C₄	1	2	yes	complemented
24	#64779	C₂²	1	8	yes	—
25	#64777	C₂²	1	8	yes	—
26	C₂×#1833	—	5	1	no	maximal, Sylow
27	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
28	C₂×C₅×M₁₆	—	2	2	no	—
29	C₂×C₅×M₁₆	—	2	2	no	—
30	C₂×C₅×M₁₆	—	2	2	no	—
31	C₂×C₅×M₁₆	—	2	2	no	—
32	C₂×C₅×M₁₆	—	2	2	no	—
33	C₂×C₅×M₁₆	C₂³	1	4	yes	—
34	C₂²×C₅×C₈	—	2	2	no	—
35	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
38	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
39	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
40	C₂²×C₅×C₈	D₄	1	2	yes	—
41	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
42	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
43	C₂²×C₅×C₈	Q₈	1	2	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₂×C₂²⋊Dic₅	—	2	1	no	—
46	C₂×C₂²⋊Dic₅	—	2	2	no	—
47	#4072	—	2	1	no	—
48	#4072	—	2	1	no	—
49	#4072	—	2	2	no	—
50	#4072	—	2	2	no	—
51	#4072	—	2	2	no	—
52	#4072	C₂×C₄	1	2	yes	—
53	#4072	C₂³	1	4	yes	—
54	#4072	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₅	—	2	1	no	—
56	C₂×C₄⋊Dic₅	—	2	2	no	—
57	C₂×C₄×Dic₅	—	2	2	no	—
58	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
59	C₂×#681	—	2	1	no	—
60	C₂×#681	—	2	1	no	—
61	C₂×#681	—	2	1	no	—
62	C₂×#681	—	2	1	no	—
63	C₂×#681	C₂×C₄	1	2	yes	—
64	C₂×#681	C₂³	1	2	yes	—
65	C₂²×#168	C₂×C₄	1	2	yes	—
66	C₅×#108	—	2	4	no	—
67	C₅×#108	—	2	4	no	—
68	#3950	—	2	4	no	—
69	#3949	—	2	4	no	—
70	#3947	C₂×C₄	1	8	yes	complemented
71	C₈×Dic₅	C₂×C₄	1	8	yes	complemented
72	C₂²×#108	D₅	1	1	yes	characteristic
73	C₂×#427	—	5	1	no	—
74	C₂×#405	—	5	1	no	—
75	#1833	—	5	8	no	—
76	C₂×#344	—	5	2	no	—
77	C₂×H(3,ℤ/4)	—	5	2	no	—
78	C₂⁴×C₅	#41	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₅	#41	1	1	yes	characteristic
86	C₂²×C₄×C₅	#41	1	1	yes	characteristic
87	C₂²×C₄×C₅	#41	1	1	yes	characteristic
88	C₂²×C₄×C₅	#41	1	1	yes	characteristic
89	C₂²×C₄×C₅	#41	1	1	yes	characteristic
90	C₂²×C₄×C₅	#41	1	1	yes	characteristic
91	C₂²×C₄×C₅	#41	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₅	—	2	2	no	—
94	C₂²×Dic₅	—	4	2	no	—
95	C₅×M₁₆	—	2	4	no	—
96	C₅×M₁₆	—	2	4	no	—
97	C₅×M₁₆	—	4	2	no	—
98	C₅×M₁₆	—	4	2	no	—
99	C₂×C₅×C₈	—	2	4	no	—
100	C₂×C₅×C₈	—	4	2	no	—
101	C₂×C₅×C₈	—	4	2	no	—
102	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
105	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
108	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
109	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
110	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
111	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
112	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
113	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
115	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
116	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
117	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
118	C₂²⋊Dic₅	—	2	2	no	—
119	C₂²⋊Dic₅	—	2	2	no	—
120	C₂²⋊Dic₅	—	2	4	no	—
121	C₂²⋊Dic₅	—	4	2	no	—
122	C₄⋊Dic₅	—	2	2	no	—
123	C₄⋊Dic₅	—	2	2	no	—
124	C₄⋊Dic₅	—	2	4	no	—
125	C₄⋊Dic₅	—	4	2	no	—
126	C₄×Dic₅	—	2	2	no	—
127	C₄×Dic₅	—	2	4	no	—
128	C₄×Dic₅	—	4	2	no	—
129	C₄×Dic₅	C₂²×C₄	1	4	yes	—
130	#681	—	2	2	no	—
131	#681	—	2	2	no	—
132	#681	—	2	2	no	—
133	#681	—	2	2	no	—
134	C₂×#168	—	2	2	no	—
135	C₂×#168	—	2	2	no	—
136	C₂×#168	C₂²×C₄	1	4	yes	—
137	C₂²×M₁₆	—	5	1	no	—
138	C₂²×M₁₆	C₂×D₅	1	2	yes	—
139	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
140	C₂×#117	—	5	1	no	—
141	C₂×#117	—	5	2	no	—
142	C₂×#108	—	2	1	no	—
143	C₂×#108	—	2	1	no	—
144	C₂×#108	—	2	2	no	—
145	C₂×#108	C₂×D₅	1	4	yes	—
146	#427	—	5	4	no	—
147	#427	—	10	2	no	—
148	C₂×#107	—	10	1	no	—
149	C₂×#106	—	10	1	no	—
150	#405	—	5	4	no	—
151	#405	—	5	4	no	—
152	C₂×#97	—	5	2	no	—
153	C₂×C₄×C₈	—	5	2	no	—
154	#344	—	5	8	no	—
155	H(3,ℤ/4)	—	5	8	no	—
156	C₂³×C₅	—	4	2	no	—
157	C₂³×C₅	#117	1	1	yes	characteristic
158	C₂³×C₅	#117	1	1	yes	characteristic
159	C₂³×C₅	#124	1	1	yes	characteristic
160	C₂³×C₅	#124	1	1	yes	characteristic
161	C₂³×C₅	#125	1	1	yes	characteristic
162	C₂³×C₅	#125	1	1	yes	characteristic
163	C₂³×C₅	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₅	#117	1	1	yes	characteristic
169	C₂×C₄×C₅	#117	1	1	yes	characteristic
170	C₂×C₄×C₅	#117	1	1	yes	characteristic
171	C₂×C₄×C₅	#117	1	1	yes	characteristic
172	C₂×C₄×C₅	#117	1	1	yes	characteristic
173	C₂×C₄×C₅	#117	1	1	yes	characteristic
174	C₂×C₄×C₅	#124	1	1	yes	characteristic
175	C₂×C₄×C₅	#124	1	1	yes	characteristic
176	C₂×C₄×C₅	#124	1	1	yes	characteristic
177	C₂×C₄×C₅	#124	1	1	yes	characteristic
178	C₂×C₄×C₅	#124	1	1	yes	characteristic
179	C₂×C₄×C₅	#124	1	1	yes	characteristic
180	C₂×C₄×C₅	#125	1	1	yes	characteristic
181	C₂×C₄×C₅	#125	1	1	yes	characteristic
182	C₂×C₄×C₅	#125	1	1	yes	characteristic
183	C₂×C₄×C₅	#125	1	1	yes	characteristic
184	C₂×C₄×C₅	#125	1	1	yes	characteristic
185	C₂×C₄×C₅	#125	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
192	C₂×Dic₅	—	2	4	no	—
193	C₂×Dic₅	—	4	4	no	—
194	C₂×Dic₅	—	4	4	no	—
195	C₂×Dic₅	—	8	4	no	—
196	C₅×C₈	—	4	4	no	—
197	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
198	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
199	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
200	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
201	#168	—	2	4	no	—
202	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	—	2	2	no	—
205	C₂×M₁₆	—	2	2	no	—
206	C₂×M₁₆	—	2	2	no	—
207	C₂×M₁₆	—	2	2	no	—
208	C₂×M₁₆	—	5	2	no	—
209	C₂×M₁₆	—	5	2	no	—
210	C₂×M₁₆	—	10	1	no	—
211	C₂×M₁₆	—	10	1	no	—
212	C₂×M₁₆	—	10	1	no	—
213	C₂×M₁₆	—	10	1	no	—
214	C₂×M₁₆	C₂²×D₅	1	4	yes	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	5	2	no	—
217	C₂²×C₈	Dic₁₀	1	1	yes	characteristic
218	C₂²×C₈	Dic₁₀	1	1	yes	characteristic
219	C₂²×C₈	Dic₁₀	1	2	yes	—
220	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
221	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
222	C₂²×C₈	C₄×D₅	1	2	yes	—
223	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
224	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
225	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
226	C₂²×C₈	C₂²×D₅	1	2	yes	—
227	#117	—	5	2	no	—
228	#117	—	5	2	no	—
229	#117	—	5	4	no	—
230	#117	—	10	1	no	—
231	#117	—	10	1	no	—
232	#117	—	10	2	no	—
233	#117	—	10	2	no	—
234	#117	—	10	2	no	—
235	C₂×C₄⋊C₄	—	10	1	no	—
236	C₂×C₄⋊C₄	—	10	2	no	—
237	C₂×C₂²⋊C₄	—	10	1	no	—
238	C₂×C₂²⋊C₄	—	10	2	no	—
239	C₂×C₄²	—	5	2	no	—
240	C₂×C₄²	—	10	2	no	—
241	#108	—	2	4	no	—
242	#108	—	2	4	no	—
243	#107	—	10	4	no	—
244	#106	—	10	4	no	—
245	#97	—	5	8	no	—
246	C₄×C₈	—	5	8	no	—
247	C₂²×C₅	—	2	2	no	—
248	C₂²×C₅	—	2	2	no	—
249	C₂²×C₅	—	2	2	no	—
250	C₂²×C₅	—	4	1	no	—
251	C₂²×C₅	—	4	1	no	—
252	C₂²×C₅	—	4	1	no	—
253	C₂²×C₅	—	4	1	no	—
254	C₂²×C₅	#382	1	1	yes	characteristic
255	C₂²×C₅	#382	1	1	yes	characteristic
256	C₂²×C₅	#382	1	1	yes	characteristic
257	C₂²×C₅	#382	1	1	yes	characteristic
258	C₂²×C₅	C₂×#117	1	1	yes	characteristic
259	C₂²×C₅	C₂×#124	1	1	yes	characteristic
260	C₂²×C₅	C₂×#125	1	1	yes	characteristic
261	C₄×C₅	#382	1	1	yes	characteristic
262	C₄×C₅	#382	1	1	yes	characteristic
263	C₄×C₅	#382	1	1	yes	characteristic
264	C₄×C₅	#382	1	1	yes	characteristic
265	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
266	C₄×C₅	C₂×#117	1	1	yes	characteristic
267	C₄×C₅	C₂×#124	1	1	yes	characteristic
268	C₄×C₅	C₂×#125	1	1	yes	characteristic
269	Dic₅	—	4	4	no	—
270	Dic₅	—	8	4	no	—
271	C₂⁴	#713	1	1	yes	characteristic
272	C₂²×C₄	—	10	2	no	—
273	C₂²×C₄	—	20	2	no	—
274	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
275	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
278	C₂²×C₄	#711	1	1	yes	characteristic
279	C₂²×C₄	#711	1	1	yes	characteristic
280	C₂²×C₄	#711	1	1	yes	characteristic
281	C₂²×C₄	#711	1	1	yes	characteristic
282	C₂²×C₄	#713	1	1	yes	characteristic
283	C₂²×C₄	#713	1	1	yes	characteristic
284	C₂²×C₄	#713	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
287	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
288	M₁₆	—	2	4	no	—
289	M₁₆	—	2	4	no	—
290	M₁₆	—	4	2	no	—
291	M₁₆	—	4	2	no	—
292	M₁₆	—	10	2	no	—
293	M₁₆	—	10	2	no	—
294	M₁₆	—	10	2	no	—
295	M₁₆	—	10	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	5	4	no	—
300	C₂×C₈	—	10	2	no	—
301	C₂×C₈	—	10	2	no	—
302	C₂×C₈	#683	1	1	yes	characteristic
303	C₂×C₈	#683	1	1	yes	characteristic
304	C₂×C₈	#683	1	2	yes	—
305	C₂×C₈	#683	1	1	yes	characteristic
306	C₂×C₈	#683	1	1	yes	characteristic
307	C₂×C₈	#683	1	2	yes	—
308	C₂×C₈	#683	1	2	yes	—
309	C₂×C₈	#683	1	2	yes	—
310	C₂×C₈	#683	1	2	yes	—
311	C₂×C₈	#683	1	2	yes	—
312	C₂×C₈	C₂×Dic₁₀	1	2	yes	—
313	C₂×C₈	C₂×Dic₁₀	1	2	yes	—
314	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
315	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
316	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
317	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
318	C₄⋊C₄	—	10	2	no	—
319	C₄⋊C₄	—	10	2	no	—
320	C₄⋊C₄	—	10	4	no	—
321	C₄⋊C₄	—	20	2	no	—
322	C₂²⋊C₄	—	10	2	no	—
323	C₂²⋊C₄	—	10	2	no	—
324	C₂²⋊C₄	—	10	4	no	—
325	C₂²⋊C₄	—	20	2	no	—
326	C₄²	—	5	4	no	—
327	C₄²	—	10	2	no	—
328	C₄²	—	10	4	no	—
329	C₄²	—	20	2	no	—
330	C₂×C₅	—	2	1	no	—
331	C₂×C₅	—	2	1	no	—
332	C₂×C₅	—	2	1	no	—
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	—	2	1	no	—
335	C₂×C₅	—	2	1	no	—
336	C₂×C₅	#1833	1	2	yes	complemented
337	C₂×C₅	C₂×#382	1	1	yes	characteristic
338	C₂³	—	4	2	no	—
339	C₂³	#4036	1	1	yes	characteristic
340	C₂³	#4036	1	1	yes	characteristic
341	C₂³	#4038	1	1	yes	characteristic
342	C₂³	#4038	1	1	yes	characteristic
343	C₂³	#4093	1	1	yes	characteristic
344	C₂³	#4093	1	1	yes	characteristic
345	C₂³	C₂×#713	1	1	yes	characteristic
346	C₂×C₄	—	10	4	no	—
347	C₂×C₄	—	20	4	no	—
348	C₂×C₄	—	20	4	no	—
349	C₂×C₄	—	40	4	no	—
350	C₂×C₄	#4036	1	1	yes	characteristic
351	C₂×C₄	#4036	1	1	yes	characteristic
352	C₂×C₄	#4036	1	1	yes	characteristic
353	C₂×C₄	#4036	1	1	yes	characteristic
354	C₂×C₄	#4036	1	1	yes	characteristic
355	C₂×C₄	#4036	1	1	yes	characteristic
356	C₂×C₄	#4038	1	1	yes	characteristic
357	C₂×C₄	#4038	1	1	yes	characteristic
358	C₂×C₄	#4038	1	1	yes	characteristic
359	C₂×C₄	#4038	1	1	yes	characteristic
360	C₂×C₄	#4038	1	1	yes	characteristic
361	C₂×C₄	#4038	1	1	yes	characteristic
362	C₂×C₄	C₂×#683	1	1	yes	characteristic
363	C₂×C₄	C₂×#683	1	1	yes	characteristic
364	C₂×C₄	C₂×#683	1	1	yes	characteristic
365	C₂×C₄	C₂×#683	1	1	yes	characteristic
366	C₂×C₄	#4082	1	1	yes	characteristic
367	C₂×C₄	#4082	1	1	yes	characteristic
368	C₂×C₄	#4082	1	1	yes	characteristic
369	C₂×C₄	#4082	1	1	yes	characteristic
370	C₂×C₄	#4093	1	1	yes	characteristic
371	C₂×C₄	#4093	1	1	yes	characteristic
372	C₂×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
374	C₂×C₄	C₂×#711	1	1	yes	characteristic
375	C₂×C₄	C₂×#711	1	1	yes	characteristic
376	C₂×C₄	C₂×#713	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
378	C₈	—	4	4	no	—
379	C₈	—	10	4	no	—
380	C₈	C₂×#683	1	2	yes	—
381	C₈	C₂×#683	1	2	yes	—
382	C₈	C₂×#683	1	2	yes	—
383	C₈	C₂×#683	1	2	yes	—
384	C₅	C₂×#1833	1	1	yes	characteristic, complemented, Sylow
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	#65266	1	1	yes	characteristic
393	C₂²	#65266	1	1	yes	characteristic
394	C₂²	#65266	1	1	yes	characteristic
395	C₂²	#65266	1	1	yes	characteristic
396	C₂²	C₂×#4036	1	1	yes	characteristic
397	C₂²	C₂×#4038	1	1	yes	characteristic
398	C₂²	C₂×#4093	1	1	yes	characteristic
399	C₄	—	20	4	no	—
400	C₄	—	40	4	no	—
401	C₄	#65266	1	1	yes	characteristic
402	C₄	#65266	1	1	yes	characteristic
403	C₄	#65266	1	1	yes	characteristic
404	C₄	#65266	1	1	yes	characteristic
405	C₄	C₂×#4036	1	1	yes	characteristic
406	C₄	C₂×#4038	1	1	yes	characteristic
407	C₄	C₂²×#683	1	1	yes	characteristic
408	C₄	C₂×#4082	1	1	yes	characteristic
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	#10601491	1	2	yes	direct product factor
416	C₂	C₂×#65266	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#4038
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₂²×C₅×#108	C₂
socle	C₂²×C₅	#382
prime radical	C₂⁴×C₅	#41
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	C₂²×#108	D₅
hypocenter	C₅	C₂×#1833
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
6. #10601491	C₂	direct (N × H)
20. #65390	C₄	semidirect
22. C₂×#3947	C₄	semidirect
23. C₂×C₈×Dic₅	C₄	semidirect
70. #3947	C₂×C₄	semidirect
71. C₈×Dic₅	C₂×C₄	semidirect
336. C₂×C₅	#1833	semidirect
384. C₅	C₂×#1833	semidirect
415. C₂	#10601491	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×#108	2
C₂×#65395	2
C₂×#65390	2
C₂×#64779	2
C₂×#64777	2
#10601491	2
C₂×#1833	5

Subgroups — C2×#10601491 #12099474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10601491 #12099474