Subgroups — C₂×#13129715 #16779806

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719059	C₂	1	1	yes	maximal, characteristic
3	#13129715	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊#261	—	2	1	no	—
6	C₂²×C₄⋊#261	—	2	1	no	—
7	C₂²×C₄⋊#261	C₄	1	2	yes	—
8	C₂²×D₁₃⋊C₈	—	2	1	no	—
9	C₂²×C₈×D₁₃	—	2	1	no	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88112	C₄	1	2	yes	complemented
12	C₂×C₄⋊#1057	—	2	1	no	—
13	#11719059	—	2	1	no	—
14	#11719059	—	2	1	no	—
15	#11719059	C₄	1	2	yes	—
16	#11719059	C₂²	1	2	yes	—
17	D₁₃⋊(C₄⋊C₈)	—	2	1	no	—
18	D₁₃⋊(C₄⋊C₈)	—	2	1	no	—
19	D₁₃⋊(C₄⋊C₈)	C₄	1	2	yes	complemented
20	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic, complemented
22	C₂×#88054	—	2	1	no	—
23	C₂×C₄⋊#1055	C₄	1	1	yes	characteristic, complemented
24	D₁₃×C₄⋊C₈	—	2	1	no	—
25	D₁₃×C₄⋊C₈	—	2	1	no	—
26	D₁₃×C₄⋊C₈	C₄	1	2	yes	complemented
27	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
28	C₂³×#261	—	2	2	no	—
29	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
32	C₂²×#1057	—	2	2	no	—
33	C₂×C₄⋊#261	—	2	2	no	—
34	C₂×C₄⋊#261	—	2	2	no	—
35	C₂×C₄⋊#261	—	2	2	no	—
36	C₂×C₄⋊#261	—	2	2	no	—
37	C₂×C₄⋊#261	—	2	2	no	—
38	C₂×C₄⋊#261	—	4	4	no	—
39	C₂×C₄⋊#261	—	4	2	no	—
40	C₂×C₄⋊#261	—	4	2	no	—
41	C₂×C₄⋊#261	—	4	2	no	—
42	C₂×C₄⋊#261	—	4	2	no	—
43	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
44	C₂×D₁₃⋊C₈	—	2	2	no	—
45	C₂×D₁₃⋊C₈	—	2	2	no	—
46	C₂×D₁₃⋊C₈	—	4	2	no	—
47	C₂×D₁₃⋊C₈	—	4	2	no	—
48	C₂²×C₈×C₁₃	—	2	1	no	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
53	C₂²×#1055	—	2	1	no	—
54	C₂×C₈×D₁₃	—	2	2	no	—
55	C₂×C₈×D₁₃	—	2	2	no	—
56	C₂×C₈×D₁₃	—	4	2	no	—
57	C₂×C₈×D₁₃	—	4	2	no	—
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₃	D₄	1	1	yes	characteristic
62	C₄²×D₁₃	D₄	1	1	yes	characteristic
63	C₄²×D₁₃	D₄	1	1	yes	characteristic
64	C₄²×D₁₃	Q₈	1	1	yes	characteristic
65	C₄²×D₁₃	C₂³	1	1	yes	characteristic
66	#88112	—	2	2	no	—
67	#88112	C₂×C₄	1	4	yes	complemented
68	C₄⋊#1057	—	2	2	no	—
69	C₄⋊#1057	—	2	2	no	—
70	C₁₃×C₄⋊C₈	—	2	1	no	—
71	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
72	#88054	—	2	2	no	—
73	#88054	—	2	2	no	—
74	C₄⋊#1055	—	2	1	no	—
75	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
76	C₂×#1296	—	13	1	no	maximal, Sylow
77	C₂³×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×#261	—	2	4	no	—
79	C₂²×#261	—	4	4	no	—
80	C₂²×#261	—	4	4	no	—
81	C₂²×#261	—	4	4	no	—
82	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₁₃	—	2	2	no	—
89	C₂×C₄×D₁₃	—	2	2	no	—
90	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	D₈	1	2	yes	—
100	C₂×C₄×D₁₃	D₈	1	2	yes	—
101	C₂×C₄×D₁₃	SD₁₆	1	2	yes	—
102	C₂×C₄×D₁₃	SD₁₆	1	2	yes	—
103	C₂×C₄×D₁₃	SD₁₆	1	2	yes	—
104	C₂×C₄×D₁₃	SD₁₆	1	2	yes	—
105	C₂×C₄×D₁₃	Q₁₆	1	2	yes	—
106	C₂×C₄×D₁₃	Q₁₆	1	2	yes	—
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×#1057	—	2	4	no	—
111	C₂×#1057	—	4	4	no	—
112	C₄⋊#261	—	4	4	no	—
113	C₄⋊#261	—	4	4	no	—
114	C₄⋊#261	—	4	4	no	—
115	C₄⋊#261	—	4	4	no	—
116	C₄⋊#261	—	4	2	no	—
117	C₄⋊#261	—	4	2	no	—
118	C₄⋊#261	—	4	2	no	—
119	C₄⋊#261	—	4	2	no	—
120	D₁₃⋊C₈	—	4	4	no	—
121	D₁₃⋊C₈	—	4	2	no	—
122	D₁₃⋊C₈	—	4	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	4	2	no	—
125	C₄²×C₁₃	C₄²	1	1	yes	characteristic
126	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
128	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	—	4	2	no	—
143	C₈×D₁₃	—	4	4	no	—
144	C₈×D₁₃	—	4	2	no	—
145	C₈×D₁₃	—	4	2	no	—
146	C₂²×C₄⋊C₈	—	13	1	no	—
147	C₂²×C₄⋊C₈	—	13	1	no	—
148	C₂×#384	—	13	1	no	—
149	#1296	—	13	4	no	—
150	C₂³×C₁₃	#95	1	1	yes	characteristic
151	C₂²×D₁₃	#95	1	1	yes	characteristic
152	C₂²×D₁₃	#100	1	2	yes	—
153	C₂²×D₁₃	#101	1	2	yes	—
154	C₂²×D₁₃	#102	1	2	yes	—
155	C₂²×D₁₃	#102	1	2	yes	—
156	C₂²×D₁₃	#103	1	2	yes	—
157	C₂²×D₁₃	#103	1	2	yes	—
158	C₂²×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#261	—	4	4	no	—
160	C₂×#261	—	4	4	no	—
161	C₂×#261	—	4	4	no	—
162	C₂×#261	—	8	8	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
165	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
166	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
167	C₂×C₄×C₁₃	#102	1	2	yes	—
168	C₂×C₄×C₁₃	#103	1	2	yes	—
169	C₂×C₄×C₁₃	#106	1	2	yes	—
170	C₂×C₄×C₁₃	#107	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₁₃	—	2	2	no	—
175	C₂×Dic₁₃	#95	1	1	yes	characteristic
176	C₂×Dic₁₃	#95	1	1	yes	characteristic
177	C₂×Dic₁₃	#95	1	1	yes	characteristic
178	C₂×Dic₁₃	#102	1	2	yes	—
179	C₂×Dic₁₃	#103	1	2	yes	—
180	C₂×Dic₁₃	#106	1	2	yes	—
181	C₂×Dic₁₃	#107	1	2	yes	—
182	C₂×Dic₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	1	no	—
188	C₄×D₁₃	—	2	1	no	—
189	C₄×D₁₃	—	2	1	no	—
190	C₄×D₁₃	—	2	1	no	—
191	C₄×D₁₃	#102	1	2	yes	—
192	C₄×D₁₃	#102	1	2	yes	—
193	C₄×D₁₃	#102	1	2	yes	—
194	C₄×D₁₃	#102	1	2	yes	—
195	C₄×D₁₃	#103	1	2	yes	—
196	C₄×D₁₃	#103	1	2	yes	—
197	C₄×D₁₃	#103	1	2	yes	—
198	C₄×D₁₃	#103	1	2	yes	—
199	C₄×D₁₃	#106	1	2	yes	—
200	C₄×D₁₃	#106	1	2	yes	—
201	C₄×D₁₃	#107	1	2	yes	—
202	C₄×D₁₃	#107	1	2	yes	—
203	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
204	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
205	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
206	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
207	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
208	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
209	C₄×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
210	C₄×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
211	#1057	—	4	4	no	—
212	C₈×C₁₃	—	4	2	no	—
213	#1055	—	4	2	no	—
214	C₂³×C₈	—	26	1	no	—
215	C₂³×C₈	—	26	1	no	—
216	C₂²×C₄⋊C₄	—	13	2	no	—
217	C₂²×C₄⋊C₄	—	26	1	no	—
218	C₂²×C₄⋊C₄	—	26	1	no	—
219	C₂²×C₄²	—	13	1	no	—
220	C₂×C₄⋊C₈	—	13	2	no	—
221	C₂×C₄⋊C₈	—	13	2	no	—
222	C₂×C₄⋊C₈	—	13	2	no	—
223	C₂×C₄⋊C₈	—	13	1	no	—
224	C₂×C₄⋊C₈	—	13	2	no	—
225	C₂×C₄⋊C₈	—	13	2	no	—
226	C₂×C₄⋊C₈	—	26	1	no	—
227	C₂×C₄⋊C₈	—	26	1	no	—
228	C₂×C₄⋊C₈	—	26	1	no	—
229	C₂×C₄⋊C₈	—	26	1	no	—
230	C₂×C₄⋊C₈	—	26	1	no	—
231	C₂×C₄⋊C₈	—	26	1	no	—
232	C₂×C₄⋊C₈	#261	1	1	yes	characteristic, complemented
233	#384	—	13	2	no	—
234	#384	—	13	2	no	—
235	#384	—	26	1	no	—
236	#384	—	26	1	no	—
237	C₂²×C₁₃	#340	1	2	yes	—
238	C₂²×C₁₃	#340	1	2	yes	—
239	C₂²×C₁₃	#343	1	2	yes	—
240	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
241	C₂×D₁₃	#331	1	4	yes	—
242	C₂×D₁₃	#332	1	4	yes	—
243	C₂×D₁₃	#332	1	4	yes	—
244	C₂×D₁₃	#333	1	4	yes	—
245	C₂×D₁₃	#340	1	2	yes	—
246	C₂×D₁₃	#340	1	2	yes	—
247	C₂×D₁₃	#343	1	2	yes	—
248	C₂×D₁₃	C₂×#100	1	1	yes	characteristic
249	C₂×D₁₃	C₂×#101	1	1	yes	characteristic
250	C₂×D₁₃	C₂×#102	1	1	yes	characteristic
251	C₂×D₁₃	C₂×#102	1	1	yes	characteristic
252	C₂×D₁₃	C₂×#103	1	1	yes	characteristic
253	C₂×D₁₃	C₂×#103	1	1	yes	characteristic
254	#261	—	8	4	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	#340	1	2	yes	—
258	C₄×C₁₃	#340	1	2	yes	—
259	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
260	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
261	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
262	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
263	Dic₁₃	—	2	1	no	—
264	Dic₁₃	—	2	1	no	—
265	Dic₁₃	#340	1	2	yes	—
266	Dic₁₃	#340	1	2	yes	—
267	Dic₁₃	C₂×#102	1	1	yes	characteristic
268	Dic₁₃	C₂×#103	1	1	yes	characteristic
269	Dic₁₃	C₂×#106	1	1	yes	characteristic
270	Dic₁₃	C₂×#107	1	1	yes	characteristic
271	C₂³×C₄	—	13	1	no	—
272	C₂³×C₄	—	13	1	no	—
273	C₂³×C₄	—	13	1	no	—
274	C₂³×C₄	—	26	2	no	—
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	—	26	2	no	—
277	C₂²×C₈	—	26	2	no	—
278	C₂²×C₈	—	26	2	no	—
279	C₂²×C₈	—	26	2	no	—
280	C₂²×C₈	—	26	2	no	—
281	C₂²×C₈	—	26	1	no	—
282	C₂²×C₈	—	52	2	no	—
283	C₂²×C₈	—	52	2	no	—
284	C₂²×C₈	—	52	2	no	—
285	C₂²×C₈	—	52	2	no	—
286	C₂×C₄⋊C₄	—	13	4	no	—
287	C₂×C₄⋊C₄	—	26	2	no	—
288	C₂×C₄⋊C₄	—	26	2	no	—
289	C₂×C₄⋊C₄	—	26	2	no	—
290	C₂×C₄⋊C₄	—	26	2	no	—
291	C₂×C₄⋊C₄	—	26	2	no	—
292	C₂×C₄⋊C₄	—	52	2	no	—
293	C₂×C₄⋊C₄	—	52	2	no	—
294	C₂×C₄⋊C₄	—	52	2	no	—
295	C₂×C₄⋊C₄	—	52	2	no	—
296	C₂×C₄⋊C₄	—	52	4	no	—
297	C₂×C₄²	—	13	1	no	—
298	C₂×C₄²	—	13	1	no	—
299	C₂×C₄²	—	13	1	no	—
300	C₂×C₄²	—	13	1	no	—
301	C₂×C₄²	—	13	1	no	—
302	C₂×C₄²	—	13	1	no	—
303	C₂×C₄²	—	13	1	no	—
304	C₂×C₄²	—	13	1	no	—
305	C₂×C₄²	—	13	1	no	—
306	C₂×C₄²	—	13	1	no	—
307	C₂×C₄²	—	13	1	no	—
308	C₂×C₄²	C₂×#261	1	1	yes	characteristic
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	13	4	no	—
311	C₄⋊C₈	—	13	2	no	—
312	C₄⋊C₈	—	26	2	no	—
313	C₄⋊C₈	—	26	2	no	—
314	C₄⋊C₈	—	26	2	no	—
315	C₄⋊C₈	—	26	2	no	—
316	C₄⋊C₈	—	26	2	no	—
317	C₄⋊C₈	—	26	1	no	—
318	C₄⋊C₈	C₂×#261	1	2	yes	complemented
319	C₂×C₁₃	#1296	1	4	yes	complemented
320	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
321	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
322	C₂×C₁₃	C₂×#343	1	1	yes	characteristic
323	D₁₃	#1296	1	4	yes	complemented
324	D₁₃	C₂×#331	1	1	yes	characteristic
325	D₁₃	C₂×#332	1	1	yes	characteristic
326	D₁₃	C₂×#332	1	1	yes	characteristic
327	D₁₃	C₂×#333	1	1	yes	characteristic
328	C₂⁴	—	13	1	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	13	1	no	—
331	C₂²×C₄	—	13	2	no	—
332	C₂²×C₄	—	13	2	no	—
333	C₂²×C₄	—	13	2	no	—
334	C₂²×C₄	—	13	2	no	—
335	C₂²×C₄	—	13	1	no	—
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	1	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	2	no	—
340	C₂²×C₄	—	13	2	no	—
341	C₂²×C₄	—	13	2	no	—
342	C₂²×C₄	—	13	2	no	—
343	C₂²×C₄	—	13	1	no	—
344	C₂²×C₄	—	13	1	no	—
345	C₂²×C₄	—	13	1	no	—
346	C₂²×C₄	—	13	1	no	—
347	C₂²×C₄	—	13	1	no	—
348	C₂²×C₄	—	13	1	no	—
349	C₂²×C₄	—	13	1	no	—
350	C₂²×C₄	—	13	1	no	—
351	C₂²×C₄	—	13	1	no	—
352	C₂²×C₄	—	26	2	no	—
353	C₂²×C₄	—	26	2	no	—
354	C₂²×C₄	—	26	4	no	—
355	C₂²×C₄	—	52	4	no	—
356	C₂²×C₄	—	52	4	no	—
357	C₂²×C₄	—	52	4	no	—
358	C₂²×C₄	C₄×#261	1	1	yes	characteristic
359	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
360	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	26	4	no	—
364	C₂×C₈	—	26	2	no	—
365	C₂×C₈	—	52	2	no	—
366	C₂×C₈	—	52	4	no	—
367	C₂×C₈	—	52	2	no	—
368	C₂×C₈	—	52	4	no	—
369	C₂×C₈	—	52	2	no	—
370	C₂×C₈	—	52	2	no	—
371	C₂×C₈	—	52	4	no	—
372	C₂×C₈	—	52	2	no	—
373	C₄⋊C₄	—	52	4	no	—
374	C₄⋊C₄	—	52	4	no	—
375	C₄⋊C₄	—	52	2	no	—
376	C₄⋊C₄	—	52	2	no	—
377	C₄⋊C₄	—	52	2	no	—
378	C₄⋊C₄	—	52	2	no	—
379	C₄⋊C₄	—	52	4	no	—
380	C₄⋊C₄	—	52	4	no	—
381	C₄²	—	13	1	no	—
382	C₄²	—	13	1	no	—
383	C₄²	—	13	1	no	—
384	C₄²	—	13	1	no	—
385	C₄²	—	13	1	no	—
386	C₄²	—	13	1	no	—
387	C₄²	—	13	1	no	—
388	C₄²	—	13	1	no	—
389	C₄²	—	13	1	no	—
390	C₄²	—	13	1	no	—
391	C₄²	—	13	1	no	—
392	C₄²	—	13	1	no	—
393	C₄²	C₄×#261	1	1	yes	characteristic
394	C₄²	C₄⋊#261	1	1	yes	characteristic
395	C₄²	C₂²⋊#261	1	1	yes	characteristic
396	C₄²	C₂²×#261	1	1	yes	characteristic
397	C₁₃	C₂×#1296	1	1	yes	characteristic, complemented, Sylow
398	C₂³	—	13	2	no	—
399	C₂³	—	13	2	no	—
400	C₂³	—	13	2	no	—
401	C₂³	—	13	2	no	—
402	C₂³	—	13	2	no	—
403	C₂³	—	13	2	no	—
404	C₂³	—	13	1	no	—
405	C₂³	—	13	1	no	—
406	C₂³	(C₂×#261)⋊C₄	1	1	yes	characteristic
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	13	2	no	—
409	C₂×C₄	—	13	2	no	—
410	C₂×C₄	—	13	2	no	—
411	C₂×C₄	—	13	2	no	—
412	C₂×C₄	—	13	1	no	—
413	C₂×C₄	—	13	1	no	—
414	C₂×C₄	—	13	1	no	—
415	C₂×C₄	—	13	1	no	—
416	C₂×C₄	—	13	2	no	—
417	C₂×C₄	—	13	2	no	—
418	C₂×C₄	—	13	2	no	—
419	C₂×C₄	—	13	2	no	—
420	C₂×C₄	—	13	2	no	—
421	C₂×C₄	—	13	2	no	—
422	C₂×C₄	—	13	2	no	—
423	C₂×C₄	—	13	2	no	—
424	C₂×C₄	—	13	1	no	—
425	C₂×C₄	—	13	1	no	—
426	C₂×C₄	—	13	2	no	—
427	C₂×C₄	—	13	1	no	—
428	C₂×C₄	—	13	2	no	—
429	C₂×C₄	—	13	1	no	—
430	C₂×C₄	—	13	1	no	—
431	C₂×C₄	—	13	2	no	—
432	C₂×C₄	—	13	1	no	—
433	C₂×C₄	—	13	1	no	—
434	C₂×C₄	—	13	2	no	—
435	C₂×C₄	—	13	1	no	—
436	C₂×C₄	—	13	1	no	—
437	C₂×C₄	—	13	1	no	—
438	C₂×C₄	—	26	1	no	—
439	C₂×C₄	—	26	1	no	—
440	C₂×C₄	—	26	2	no	—
441	C₂×C₄	—	26	1	no	—
442	C₂×C₄	—	26	2	no	—
443	C₂×C₄	—	26	1	no	—
444	C₂×C₄	—	26	2	no	—
445	C₂×C₄	—	52	4	no	—
446	C₂×C₄	—	52	4	no	—
447	C₂×C₄	—	52	4	no	—
448	C₂×C₄	—	104	8	no	—
449	C₂×C₄	#88101	1	2	yes	—
450	C₂×C₄	#88102	1	2	yes	—
451	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
452	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
453	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
454	C₂×C₄	#88115	1	2	yes	—
455	C₂×C₄	#88117	1	2	yes	—
456	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
457	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
458	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
459	C₈	—	4	2	no	—
460	C₈	—	52	4	no	—
461	C₈	—	52	2	no	—
462	C₂²	—	13	2	no	—
463	C₂²	—	13	1	no	—
464	C₂²	—	13	1	no	—
465	C₂²	—	13	2	no	—
466	C₂²	—	13	1	no	—
467	C₂²	—	13	1	no	—
468	C₂²	—	13	2	no	—
469	C₂²	—	13	1	no	—
470	C₂²	—	13	1	no	—
471	C₂²	—	13	4	no	—
472	C₂²	—	13	4	no	—
473	C₂²	—	13	4	no	—
474	C₂²	—	13	4	no	—
475	C₂²	#11718246	1	2	yes	—
476	C₂²	#11718265	1	2	yes	—
477	C₂²	#11718271	1	2	yes	—
478	C₂²	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	13	2	no	—
482	C₄	—	13	1	no	—
483	C₄	—	13	1	no	—
484	C₄	—	13	2	no	—
485	C₄	—	13	1	no	—
486	C₄	—	13	1	no	—
487	C₄	—	26	1	no	—
488	C₄	—	26	1	no	—
489	C₄	—	104	4	no	—
490	C₄	#11718246	1	2	yes	—
491	C₄	#11718265	1	2	yes	—
492	C₄	C₂×#88101	1	1	yes	characteristic
493	C₄	C₂×#88102	1	1	yes	characteristic
494	C₄	C₂×#88115	1	1	yes	characteristic
495	C₄	C₂×#88117	1	1	yes	characteristic
496	C₂	—	13	1	no	—
497	C₂	—	13	1	no	—
498	C₂	—	13	1	no	—
499	C₂	—	13	1	no	—
500	C₂	—	13	4	no	—
501	C₂	#13129715	1	4	yes	direct product factor
502	C₂	C₂×#11718246	1	1	yes	characteristic
503	C₂	C₂×#11718265	1	1	yes	characteristic
504	C₂	C₂×#11718271	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	(C₂×#261)⋊C₄
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₄²	C₂²×#261
Fitting	C₂×C₁₃×C₄⋊C₈	C₄
socle	C₂³×C₁₃	#95
prime radical	C₂³×D₁₃	C₂²⋊C₄
cosocle	C₄²×D₁₃	C₂³
hypercenter	C₂×C₄⋊C₈	#261
hypocenter	C₁₃	C₂×#1296
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13129715	C₂	direct (N × H)
11. C₂×#88112	C₄	semidirect
19. D₁₃⋊(C₄⋊C₈)	C₄	semidirect
21. C₂×C₁₃×C₄⋊C₈	C₄	semidirect
23. C₂×C₄⋊#1055	C₄	semidirect
26. D₁₃×C₄⋊C₈	C₄	semidirect
67. #88112	C₂×C₄	semidirect
71. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
75. C₄⋊#1055	C₂×C₄	semidirect
232. C₂×C₄⋊C₈	#261	semidirect
318. C₄⋊C₈	C₂×#261	semidirect
319. C₂×C₁₃	#1296	semidirect
323. D₁₃	#1296	semidirect
397. C₁₃	C₂×#1296	semidirect
501. C₂	#13129715	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×D₁₃⋊(C₄⋊C₈)	2
C₂×#11719059	2
#13129715	2
C₂×D₁₃×C₄⋊C₈	2
C₂×#1296	13

Subgroups — C2×#13129715 #16779806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129715 #16779806