Subgroups — C₂×#13113701 #15832475

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718673	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113701	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718049	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718046	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×D₈	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×#6099	—	2	1	no	—
13	C₂³×#1055	—	2	1	no	—
14	C₄×C₁₃×D₈	C₄	1	4	yes	—
15	C₄×C₁₃×D₈	C₂²	1	4	yes	—
16	C₂×C₁₃×#107	C₄	1	1	yes	characteristic
17	C₂×C₁₃×#102	C₄	1	1	yes	characteristic
18	C₂×C₁₃×#102	C₄	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊#1055	—	2	1	no	—
21	C₂×C₂²⋊#1055	—	2	1	no	—
22	#11718673	—	2	2	no	—
23	#11718673	C₂²	1	4	yes	complemented
24	D₄×#1055	—	2	2	no	—
25	D₄×#1055	C₂²	1	4	yes	complemented
26	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
28	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
29	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
30	D₄⋊#1055	C₂²	1	4	yes	complemented
31	D₄⋊#1055	C₂²	1	4	yes	complemented
32	#11718049	C₂²	1	4	yes	complemented
33	#11718046	C₂²	1	4	yes	complemented
34	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	—	2	1	no	—
37	C₂³×C₄×C₁₃	—	2	1	no	—
38	C₂×C₁₃×D₈	—	2	4	no	—
39	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₄×D₄×C₁₃	—	2	1	no	—
43	C₄×D₄×C₁₃	—	2	1	no	—
44	C₄×D₄×C₁₃	—	2	1	no	—
45	C₄×D₄×C₁₃	—	2	1	no	—
46	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
47	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₁₃	C₂³	1	2	yes	—
49	C₄×D₄×C₁₃	C₂³	1	2	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×#6099	—	2	4	no	—
56	C₂×#6099	—	4	4	no	—
57	C₂²×#1055	—	2	1	no	—
58	C₂²×#1055	—	2	1	no	—
59	C₂²×#1055	—	2	1	no	—
60	C₂²×#1055	—	2	4	no	—
61	C₂²×#1055	—	4	4	no	—
62	C₂²×#1055	D₄	1	1	yes	characteristic
63	C₂²×#1055	D₄	1	1	yes	characteristic
64	C₁₃×#107	C₂×C₄	1	4	yes	—
65	C₁₃×#102	C₂×C₄	1	4	yes	—
66	C₁₃×#102	C₂×C₄	1	4	yes	—
67	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₁₃	C₂³	1	2	yes	—
69	C₂²⋊#1055	—	2	4	no	—
70	C₂²⋊#1055	—	2	4	no	—
71	C₄⋊#1055	—	2	1	no	—
72	C₄⋊#1055	—	2	1	no	—
73	C₄⋊#1055	C₂³	1	2	yes	—
74	C₄⋊#1055	C₂³	1	2	yes	—
75	C₄×#1055	—	2	1	no	—
76	C₄×#1055	D₄	1	2	yes	—
77	C₄×#1055	C₂³	1	2	yes	—
78	C₄×#1055	C₂³	1	2	yes	—
79	C₂×#1586	—	13	1	no	maximal, Sylow
80	C₂⁴×C₁₃	—	2	1	no	—
81	C₂⁴×C₁₃	—	2	1	no	—
82	C₂×D₄×C₁₃	—	2	1	no	—
83	C₂×D₄×C₁₃	—	2	1	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	2	2	no	—
87	C₂×D₄×C₁₃	M₁₆	1	4	yes	complemented
88	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	—	4	2	no	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
103	C₁₃×D₈	—	2	8	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
108	C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
111	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
112	C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₁₃×C₂²⋊C₄	—	2	2	no	—
114	C₁₃×C₂²⋊C₄	—	2	2	no	—
115	C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₃	#41	1	1	yes	characteristic
119	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
120	#6099	—	4	8	no	—
121	C₂×#1055	—	2	4	no	—
122	C₂×#1055	—	2	2	no	—
123	C₂×#1055	—	2	2	no	—
124	C₂×#1055	—	2	2	no	—
125	C₂×#1055	—	2	2	no	—
126	C₂×#1055	—	2	2	no	—
127	C₂×#1055	—	4	8	no	—
128	C₂×#1055	—	4	2	no	—
129	C₂×#1055	—	4	2	no	—
130	C₂×#1055	C₂×D₄	1	2	yes	—
131	C₂×#1055	C₂×D₄	1	2	yes	—
132	C₂×C₄×D₈	D₁₃	1	1	yes	characteristic
133	C₂×#436	—	13	1	no	—
134	C₂×C₈×D₄	—	13	1	no	—
135	#1586	—	13	8	no	—
136	C₂×#334	—	13	1	no	—
137	C₂×D₄⋊C₈	—	13	1	no	—
138	C₂×D₄⋊C₈	—	13	1	no	—
139	C₂×#322	—	13	1	no	—
140	C₂³×C₁₃	—	2	2	no	—
141	C₂³×C₁₃	—	2	4	no	—
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	4	2	no	—
144	C₂³×C₁₃	—	4	2	no	—
145	C₂³×C₁₃	—	4	2	no	—
146	C₂³×C₁₃	—	4	2	no	—
147	C₂³×C₁₃	—	4	2	no	—
148	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
149	D₄×C₁₃	—	2	2	no	—
150	D₄×C₁₃	—	2	2	no	—
151	D₄×C₁₃	—	2	2	no	—
152	D₄×C₁₃	—	2	4	no	—
153	D₄×C₁₃	—	4	2	no	—
154	D₄×C₁₃	C₂×M₁₆	1	4	yes	complemented
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	4	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
170	C₂×C₄×C₁₃	#131	1	2	yes	—
171	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
172	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
176	C₈×C₁₃	—	2	2	no	—
177	C₈×C₁₃	—	2	2	no	—
178	#1055	—	2	4	no	—
179	#1055	—	2	2	no	—
180	#1055	—	2	2	no	—
181	#1055	—	4	2	no	—
182	#1055	—	4	2	no	—
183	C₂²×D₈	Dic₁₃	1	1	yes	characteristic
184	C₂²×M₁₆	—	26	1	no	—
185	C₂³×C₈	—	26	1	no	—
186	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
187	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
188	C₄×D₈	Dic₁₃	1	4	yes	—
189	C₄×D₈	C₂×D₁₃	1	4	yes	—
190	#436	—	13	4	no	—
191	#436	—	26	2	no	—
192	C₈×D₄	—	13	4	no	—
193	C₈×D₄	—	26	2	no	—
194	C₂×#107	Dic₁₃	1	1	yes	characteristic
195	C₂×C₄⋊C₈	—	13	1	no	—
196	C₂×C₄⋊C₈	—	13	1	no	—
197	C₂×#102	Dic₁₃	1	1	yes	characteristic
198	C₂×#102	Dic₁₃	1	1	yes	characteristic
199	C₂×C₂²⋊C₈	—	26	1	no	—
200	C₂×C₂²⋊C₈	—	26	1	no	—
201	C₂×C₄×C₈	—	13	1	no	—
202	C₂×C₄×C₈	—	13	1	no	—
203	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
204	#334	—	13	4	no	—
205	D₄⋊C₈	—	13	4	no	—
206	D₄⋊C₈	—	13	4	no	—
207	#322	—	13	4	no	—
208	C₂²×C₁₃	—	2	4	no	—
209	C₂²×C₁₃	—	4	8	no	—
210	C₂²×C₁₃	—	4	2	no	—
211	C₂²×C₁₃	—	4	2	no	—
212	C₂²×C₁₃	—	4	2	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	8	4	no	—
216	C₂²×C₁₃	#435	1	2	yes	—
217	C₂²×C₁₃	#442	1	2	yes	—
218	C₂²×C₁₃	#443	1	2	yes	—
219	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	4	2	no	—
223	C₄×C₁₃	—	4	2	no	—
224	C₄×C₁₃	#435	1	2	yes	—
225	C₄×C₁₃	#442	1	2	yes	—
226	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
227	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
228	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
231	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	—	2	1	no	—
234	C₂×D₈	—	2	4	no	—
235	C₂×D₈	C₂×Dic₁₃	1	4	yes	—
236	C₂×M₁₆	—	26	4	no	—
237	C₂×M₁₆	—	52	4	no	—
238	C₂²×C₈	—	13	1	no	—
239	C₂²×C₈	—	13	1	no	—
240	C₂²×C₈	—	26	4	no	—
241	C₂²×C₈	—	26	1	no	—
242	C₂²×C₈	—	26	1	no	—
243	C₂²×C₈	—	26	1	no	—
244	C₂²×C₈	—	52	4	no	—
245	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
246	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
252	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
253	C₄×D₄	C₂²×D₁₃	1	2	yes	—
254	C₄×D₄	C₂²×D₁₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
260	#107	C₂×Dic₁₃	1	4	yes	—
261	C₄⋊C₈	—	13	2	no	—
262	C₄⋊C₈	—	13	2	no	—
263	C₄⋊C₈	—	26	1	no	—
264	C₄⋊C₈	—	26	1	no	—
265	#102	C₂×Dic₁₃	1	4	yes	—
266	#102	C₂×Dic₁₃	1	4	yes	—
267	C₂²⋊C₈	—	26	4	no	—
268	C₂²⋊C₈	—	26	4	no	—
269	C₄×C₈	—	13	2	no	—
270	C₄×C₈	—	13	2	no	—
271	C₄×C₈	—	13	2	no	—
272	C₄×C₈	—	26	1	no	—
273	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
274	C₄×C₈	C₂²×D₁₃	1	2	yes	—
275	C₂×C₁₃	—	4	4	no	—
276	C₂×C₁₃	—	8	2	no	—
277	C₂×C₁₃	#1586	1	4	yes	complemented
278	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
279	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
280	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
281	C₂⁴	—	2	1	no	—
282	C₂⁴	—	2	1	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	#6099	1	4	yes	complemented
289	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
290	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
302	C₂²×C₄	#6129	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
304	D₈	—	2	8	no	—
305	M₁₆	—	52	8	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	13	2	no	—
309	C₂×C₈	—	13	2	no	—
310	C₂×C₈	—	26	4	no	—
311	C₂×C₈	—	26	2	no	—
312	C₂×C₈	—	26	2	no	—
313	C₂×C₈	—	26	2	no	—
314	C₂×C₈	—	26	2	no	—
315	C₂×C₈	—	26	2	no	—
316	C₂×C₈	—	52	8	no	—
317	C₂×C₈	—	52	2	no	—
318	C₂×C₈	—	52	2	no	—
319	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
320	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
324	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₄²	D₄×D₁₃	1	1	yes	characteristic
330	C₄²	#6129	1	1	yes	characteristic
331	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
332	C₄²	C₂³×D₁₃	1	1	yes	characteristic
333	C₁₃	C₂×#1586	1	1	yes	characteristic, complemented, Sylow
334	C₂³	—	2	4	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
343	D₄	—	2	4	no	—
344	D₄	—	2	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	2	no	—
348	D₄	C₂×#6099	1	4	yes	complemented
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	#88165	1	2	yes	—
361	C₂×C₄	#88165	1	2	yes	—
362	C₂×C₄	C₂×#6099	1	2	yes	—
363	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
364	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
365	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
366	C₂×C₄	#88202	1	2	yes	—
367	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
368	C₂×C₄	C₂×#6129	1	1	yes	characteristic
369	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	2	no	—
372	C₈	—	26	4	no	—
373	C₈	—	26	2	no	—
374	C₈	—	26	2	no	—
375	C₈	—	52	2	no	—
376	C₈	—	52	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	8	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	8	4	no	—
385	C₂²	#11718672	1	2	yes	—
386	C₂²	#11718813	1	2	yes	—
387	C₂²	#11718857	1	2	yes	—
388	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	#11718672	1	2	yes	—
394	C₄	#11718813	1	2	yes	—
395	C₄	C₂×#88165	1	1	yes	characteristic
396	C₄	C₂×#88165	1	1	yes	characteristic
397	C₄	C₂²×#6099	1	1	yes	characteristic
398	C₄	C₂×#88202	1	1	yes	characteristic
399	C₂	—	4	4	no	—
400	C₂	—	8	2	no	—
401	C₂	#13113701	1	4	yes	direct product factor
402	C₂	C₂×#11718672	1	1	yes	characteristic
403	C₂	C₂×#11718813	1	1	yes	characteristic
404	C₂	C₂×#11718857	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×D₈	C₂
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂²×C₁₃×D₈	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×C₄×D₈	D₁₃
hypocenter	C₁₃	C₂×#1586
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11718673	C₂	semidirect
2. C₂×D₄×#1055	C₂	semidirect
3. #13113701	C₂	direct (N × H)
4. C₂×#11718049	C₂	semidirect
5. C₂×D₄⋊#1055	C₂	semidirect
6. C₂×D₄⋊#1055	C₂	semidirect
7. C₂×#11718046	C₂	semidirect
23. #11718673	C₂²	semidirect
25. D₄×#1055	C₂²	semidirect
30. D₄⋊#1055	C₂²	semidirect
31. D₄⋊#1055	C₂²	semidirect
32. #11718049	C₂²	semidirect
33. #11718046	C₂²	semidirect
87. C₂×D₄×C₁₃	M₁₆	semidirect
154. D₄×C₁₃	C₂×M₁₆	semidirect
277. C₂×C₁₃	#1586	semidirect
288. C₂×D₄	#6099	semidirect
333. C₁₃	C₂×#1586	semidirect
348. D₄	C₂×#6099	semidirect
401. C₂	#13113701	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×#11718673	2
C₂×D₄×#1055	2
#13113701	2
C₂×#11718049	2
C₂×D₄⋊#1055	2
C₂×#11718046	2
C₂×C₄×C₁₃×D₈	2
C₂×#1586	13

Subgroups — C2×#13113701 #15832475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13113701 #15832475