Subgroups — C₂×#13129670 #16779076

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊#261	C₂	1	1	yes	maximal, characteristic
3	#13129670	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊#261	C₄	1	2	yes	—
6	C₂²×C₄×#261	—	2	1	no	—
7	C₂²×D₁₃⋊C₈	—	2	1	no	—
8	C₂²×C₈×D₁₃	—	2	1	no	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×(C₂×#261)⋊C₄	—	2	1	no	—
11	C₂×C₄×#1057	—	2	1	no	—
12	C₂×C₄×#1057	C₄	1	2	yes	complemented
13	C₄×C₄⋊#261	—	2	1	no	—
14	C₄×C₄⋊#261	—	2	1	no	—
15	C₄×C₄⋊#261	C₄	1	2	yes	—
16	C₄×C₄⋊#261	C₂²	1	2	yes	—
17	C₄×D₁₃⋊C₈	—	2	1	no	—
18	C₄×D₁₃⋊C₈	—	2	1	no	—
19	C₄×D₁₃⋊C₈	C₄	1	2	yes	complemented
20	C₄×D₁₃⋊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	4	no	—
35	C₂×C₄⋊#261	C₈	1	8	yes	complemented
36	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
37	C₂×C₄×#261	—	2	2	no	—
38	C₂×C₄×#261	—	2	2	no	—
39	C₂×C₄×#261	—	4	2	no	—
40	C₂×C₄×#261	—	4	2	no	—
41	C₂×D₁₃⋊C₈	—	2	8	no	—
42	C₂×D₁₃⋊C₈	—	2	2	no	—
43	C₂×D₁₃⋊C₈	—	2	2	no	—
44	C₂²×C₈×C₁₃	—	2	1	no	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
49	C₂²×#1055	—	2	1	no	—
50	C₂×C₈×D₁₃	—	2	2	no	—
51	C₂×C₈×D₁₃	—	2	2	no	—
52	C₂×C₈×D₁₃	—	4	2	no	—
53	C₂×C₈×D₁₃	—	4	2	no	—
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	D₄	1	1	yes	characteristic
58	C₄²×D₁₃	D₄	1	1	yes	characteristic
59	C₄²×D₁₃	D₄	1	1	yes	characteristic
60	C₄²×D₁₃	Q₈	1	1	yes	characteristic
61	C₄²×D₁₃	C₂³	1	1	yes	characteristic
62	(C₂×#261)⋊C₄	—	2	2	no	—
63	(C₂×#261)⋊C₄	—	2	2	no	—
64	C₄×#1057	—	2	2	no	—
65	C₄×#1057	—	2	2	no	—
66	C₄×#1057	—	2	2	no	—
67	C₄×#1057	C₂×C₄	1	4	yes	complemented
68	C₁₃×C₄⋊C₈	—	2	1	no	—
69	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
70	#88054	—	2	2	no	—
71	#88054	—	2	2	no	—
72	C₄⋊#1055	—	2	1	no	—
73	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
74	C₂×#1279	—	13	1	no	maximal, Sylow
75	C₂³×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×#261	—	2	8	no	—
77	C₂²×#261	—	2	4	no	—
78	C₂²×#261	—	4	4	no	—
79	C₂²×#261	—	4	4	no	—
80	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	—	2	4	no	—
87	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
97	C₂×C₄×D₁₃	M₁₆	1	4	yes	—
98	C₂×C₄×D₁₃	D₈	1	2	yes	—
99	C₂×C₄×D₁₃	SD₁₆	1	2	yes	—
100	C₂×C₄×D₁₃	SD₁₆	1	2	yes	—
101	C₂×C₄×D₁₃	Q₁₆	1	2	yes	—
102	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×#1057	—	2	8	no	—
106	C₂×#1057	—	2	4	no	—
107	C₄⋊#261	—	2	8	no	—
108	C₄⋊#261	—	2	4	no	—
109	C₄⋊#261	C₂×C₈	1	8	yes	complemented
110	C₄×#261	—	4	4	no	—
111	C₄×#261	—	4	2	no	—
112	C₄×#261	—	4	2	no	—
113	D₁₃⋊C₈	—	2	8	no	—
114	D₁₃⋊C₈	—	2	8	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	4	2	no	—
117	C₄²×C₁₃	C₄²	1	1	yes	characteristic
118	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
122	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
133	C₂×#1055	—	2	2	no	—
134	C₂×#1055	—	4	2	no	—
135	C₈×D₁₃	—	4	4	no	—
136	C₈×D₁₃	—	4	2	no	—
137	C₈×D₁₃	—	4	2	no	—
138	C₂²×C₄⋊C₈	—	13	1	no	—
139	C₂²×C₄×C₈	—	13	1	no	—
140	C₂×C₄×C₄⋊C₄	—	13	1	no	—
141	#1279	—	13	4	no	—
142	C₂³×C₁₃	#95	1	1	yes	characteristic
143	C₂²×D₁₃	#95	1	1	yes	characteristic
144	C₂²×D₁₃	C₂²⋊C₈	1	4	yes	—
145	C₂²×D₁₃	#102	1	2	yes	—
146	C₂²×D₁₃	#103	1	2	yes	—
147	C₂²×D₁₃	#104	1	4	yes	—
148	C₂²×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×#261	—	2	8	no	—
150	C₂×#261	—	4	16	no	—
151	C₂×#261	—	4	4	no	—
152	C₂×#261	—	4	4	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
155	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
156	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
158	C₂×C₄×C₁₃	#97	1	2	yes	—
159	C₂×C₄×C₁₃	#102	1	2	yes	—
160	C₂×C₄×C₁₃	#103	1	2	yes	—
161	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×Dic₁₃	—	2	2	no	—
165	C₂×Dic₁₃	#95	1	1	yes	characteristic
166	C₂×Dic₁₃	#95	1	1	yes	characteristic
167	C₂×Dic₁₃	#95	1	1	yes	characteristic
168	C₂×Dic₁₃	C₄⋊C₈	1	4	yes	—
169	C₂×Dic₁₃	#106	1	2	yes	—
170	C₂×Dic₁₃	#107	1	2	yes	—
171	C₂×Dic₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₄×D₁₃	—	2	2	no	—
175	C₄×D₁₃	—	2	2	no	—
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	2	2	no	—
178	C₄×D₁₃	C₄×C₈	1	2	yes	—
179	C₄×D₁₃	#97	1	2	yes	—
180	C₄×D₁₃	C₂²⋊C₈	1	4	yes	—
181	C₄×D₁₃	#102	1	2	yes	—
182	C₄×D₁₃	#102	1	2	yes	—
183	C₄×D₁₃	#103	1	2	yes	—
184	C₄×D₁₃	#103	1	2	yes	—
185	C₄×D₁₃	C₄⋊C₈	1	4	yes	—
186	C₄×D₁₃	#106	1	2	yes	—
187	C₄×D₁₃	#107	1	2	yes	—
188	C₄×D₁₃	C₂²×C₈	1	2	yes	—
189	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
190	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
191	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
192	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
193	C₄×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
194	#1057	—	2	8	no	—
195	C₈×C₁₃	—	4	2	no	—
196	#1055	—	4	2	no	—
197	C₂³×C₈	—	26	1	no	—
198	C₂³×C₈	—	26	1	no	—
199	C₂²×C₄⋊C₄	—	13	2	no	—
200	C₂²×C₄²	—	13	1	no	—
201	C₂²×C₄²	—	26	1	no	—
202	C₂×C₄⋊C₈	—	13	1	no	—
203	C₂×C₄⋊C₈	—	13	2	no	—
204	C₂×C₄⋊C₈	—	13	2	no	—
205	C₂×C₄⋊C₈	—	26	1	no	—
206	C₂×C₄⋊C₈	—	26	1	no	—
207	C₂×C₄⋊C₈	—	26	1	no	—
208	C₂×C₄⋊C₈	#261	1	1	yes	characteristic, complemented
209	C₂×C₄×C₈	—	13	2	no	—
210	C₂×C₄×C₈	—	13	2	no	—
211	C₂×C₄×C₈	—	13	2	no	—
212	C₂×C₄×C₈	—	26	1	no	—
213	C₂×C₄×C₈	—	26	1	no	—
214	C₂×C₄×C₈	—	26	1	no	—
215	C₄×C₄⋊C₄	—	13	2	no	—
216	C₄×C₄⋊C₄	—	13	2	no	—
217	C₄×C₄⋊C₄	—	26	1	no	—
218	C₄×C₄⋊C₄	—	26	1	no	—
219	C₂×#95	—	26	1	no	—
220	C₂²×C₁₃	#336	1	2	yes	—
221	C₂²×C₁₃	#339	1	2	yes	—
222	C₂²×C₁₃	#340	1	2	yes	—
223	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
224	C₂×D₁₃	D₄⋊C₈	1	8	yes	—
225	C₂×D₁₃	Q₈⋊C₈	1	8	yes	—
226	C₂×D₁₃	#336	1	2	yes	—
227	C₂×D₁₃	#339	1	2	yes	—
228	C₂×D₁₃	#340	1	2	yes	—
229	C₂×D₁₃	C₂×C₂²⋊C₈	1	2	yes	—
230	C₂×D₁₃	C₂×#102	1	1	yes	characteristic
231	C₂×D₁₃	C₂×#103	1	1	yes	characteristic
232	C₂×D₁₃	C₂×#104	1	2	yes	—
233	#261	—	4	8	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	#336	1	2	yes	—
237	C₄×C₁₃	#340	1	2	yes	—
238	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
239	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
240	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
241	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
242	Dic₁₃	—	2	1	no	—
243	Dic₁₃	—	2	1	no	—
244	Dic₁₃	#336	1	2	yes	—
245	Dic₁₃	#340	1	2	yes	—
246	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
247	Dic₁₃	C₂×#106	1	1	yes	characteristic
248	Dic₁₃	C₂×#107	1	1	yes	characteristic
249	C₂³×C₄	—	13	1	no	—
250	C₂³×C₄	—	13	1	no	—
251	C₂³×C₄	—	13	1	no	—
252	C₂³×C₄	—	26	2	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	26	2	no	—
255	C₂²×C₈	—	26	2	no	—
256	C₂²×C₈	—	26	2	no	—
257	C₂²×C₈	—	26	2	no	—
258	C₂²×C₈	—	26	2	no	—
259	C₂²×C₈	—	26	8	no	—
260	C₂²×C₈	—	26	1	no	—
261	C₂²×C₈	—	52	2	no	—
262	C₂²×C₈	—	52	2	no	—
263	C₂×C₄⋊C₄	—	13	4	no	—
264	C₂×C₄⋊C₄	—	13	8	no	—
265	C₂×C₄⋊C₄	—	26	2	no	—
266	C₂×C₄⋊C₄	—	26	4	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	—	13	1	no	—
272	C₂×C₄²	—	13	1	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	1	no	—
276	C₂×C₄²	—	13	1	no	—
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	—	26	2	no	—
279	C₂×C₄²	—	26	2	no	—
280	C₂×C₄²	—	52	2	no	—
281	C₂×C₄²	—	52	2	no	—
282	C₂×C₄²	C₂×#261	1	1	yes	characteristic
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	13	2	no	—
285	C₄⋊C₈	—	26	2	no	—
286	C₄⋊C₈	—	26	2	no	—
287	C₄⋊C₈	—	26	1	no	—
288	C₄⋊C₈	C₂×#261	1	2	yes	complemented
289	C₄×C₈	—	13	4	no	—
290	C₄×C₈	—	26	2	no	—
291	C₄×C₈	—	26	2	no	—
292	C₄×C₈	—	26	2	no	—
293	#95	—	26	2	no	—
294	#95	—	26	2	no	—
295	C₂×C₁₃	#1279	1	4	yes	complemented
296	C₂×C₁₃	C₂×#336	1	1	yes	characteristic
297	C₂×C₁₃	C₂×#339	1	1	yes	characteristic
298	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
299	D₁₃	#1279	1	4	yes	complemented
300	D₁₃	C₂×D₄⋊C₈	1	2	yes	—
301	D₁₃	C₂×Q₈⋊C₈	1	2	yes	—
302	C₂⁴	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	4	no	—
306	C₂²×C₄	—	13	4	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	2	no	—
312	C₂²×C₄	—	13	2	no	—
313	C₂²×C₄	—	13	2	no	—
314	C₂²×C₄	—	13	2	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	26	4	no	—
325	C₂²×C₄	—	26	4	no	—
326	C₂²×C₄	—	26	8	no	—
327	C₂²×C₄	—	52	4	no	—
328	C₂²×C₄	—	52	4	no	—
329	C₂²×C₄	C₄×#261	1	1	yes	characteristic
330	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
331	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	26	4	no	—
335	C₂×C₈	—	26	8	no	—
336	C₂×C₈	—	26	8	no	—
337	C₂×C₈	—	26	8	no	—
338	C₂×C₈	—	26	2	no	—
339	C₂×C₈	—	52	2	no	—
340	C₂×C₈	—	52	4	no	—
341	C₂×C₈	—	52	2	no	—
342	C₂×C₈	—	52	2	no	—
343	C₄⋊C₄	—	13	8	no	—
344	C₄⋊C₄	—	26	8	no	—
345	C₄⋊C₄	—	26	4	no	—
346	C₄²	—	13	1	no	—
347	C₄²	—	13	1	no	—
348	C₄²	—	13	1	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	—	13	1	no	—
352	C₄²	—	13	1	no	—
353	C₄²	—	13	1	no	—
354	C₄²	—	13	1	no	—
355	C₄²	—	13	1	no	—
356	C₄²	—	13	1	no	—
357	C₄²	—	13	1	no	—
358	C₄²	—	52	4	no	—
359	C₄²	—	52	2	no	—
360	C₄²	—	52	2	no	—
361	C₄²	C₄×#261	1	1	yes	characteristic
362	C₄²	C₄⋊#261	1	1	yes	characteristic
363	C₄²	C₂²⋊#261	1	1	yes	characteristic
364	C₄²	C₂²×#261	1	1	yes	characteristic
365	C₁₃	C₂×#1279	1	1	yes	characteristic, complemented, Sylow
366	C₂³	—	13	2	no	—
367	C₂³	—	13	2	no	—
368	C₂³	—	13	4	no	—
369	C₂³	—	13	4	no	—
370	C₂³	—	13	1	no	—
371	C₂³	—	13	1	no	—
372	C₂³	(C₂×#261)⋊C₄	1	1	yes	characteristic
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	13	2	no	—
375	C₂×C₄	—	13	2	no	—
376	C₂×C₄	—	13	4	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	2	no	—
382	C₂×C₄	—	13	2	no	—
383	C₂×C₄	—	13	2	no	—
384	C₂×C₄	—	13	2	no	—
385	C₂×C₄	—	13	4	no	—
386	C₂×C₄	—	13	4	no	—
387	C₂×C₄	—	13	2	no	—
388	C₂×C₄	—	13	2	no	—
389	C₂×C₄	—	13	2	no	—
390	C₂×C₄	—	13	2	no	—
391	C₂×C₄	—	13	1	no	—
392	C₂×C₄	—	13	2	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	2	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	26	8	no	—
405	C₂×C₄	—	52	4	no	—
406	C₂×C₄	—	52	4	no	—
407	C₂×C₄	—	52	16	no	—
408	C₂×C₄	C₈×#261	1	2	yes	—
409	C₂×C₄	#88100	1	2	yes	—
410	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
411	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
412	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
413	C₂×C₄	#88115	1	2	yes	—
414	C₂×C₄	#88117	1	2	yes	—
415	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
416	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
417	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
418	C₈	—	4	2	no	—
419	C₈	—	26	8	no	—
420	C₈	—	52	2	no	—
421	C₂²	—	13	2	no	—
422	C₂²	—	13	2	no	—
423	C₂²	—	13	2	no	—
424	C₂²	—	13	1	no	—
425	C₂²	—	13	1	no	—
426	C₂²	—	13	8	no	—
427	C₂²	—	13	8	no	—
428	C₂²	—	13	2	no	—
429	C₂²	—	13	2	no	—
430	C₂²	#11718246	1	2	yes	—
431	C₂²	(C₂×#261)⋊C₈	1	2	yes	—
432	C₂²	#11718272	1	2	yes	—
433	C₂²	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	13	2	no	—
437	C₄	—	13	1	no	—
438	C₄	—	13	1	no	—
439	C₄	—	13	2	no	—
440	C₄	—	13	2	no	—
441	C₄	—	26	1	no	—
442	C₄	—	26	1	no	—
443	C₄	—	52	8	no	—
444	C₄	#11718246	1	2	yes	—
445	C₄	(C₂×#261)⋊C₈	1	2	yes	—
446	C₄	C₂×C₈×#261	1	1	yes	characteristic
447	C₄	C₂×#88100	1	1	yes	characteristic
448	C₄	C₂×#88115	1	1	yes	characteristic
449	C₄	C₂×#88117	1	1	yes	characteristic
450	C₂	—	13	2	no	—
451	C₂	—	13	2	no	—
452	C₂	—	13	4	no	—
453	C₂	#13129670	1	4	yes	direct product factor
454	C₂	C₂×(C₂×#261)⋊C₈	1	1	yes	characteristic
455	C₂	C₂×#11718272	1	1	yes	characteristic
456	C₂	C₂×#11718246	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊#261
commutator	C₄×C₁₃	C₂×C₄×C₈
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×#1279
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13129670	C₂	direct (N × H)
12. C₂×C₄×#1057	C₄	semidirect
19. C₄×D₁₃⋊C₈	C₄	semidirect
21. C₂×C₁₃×C₄⋊C₈	C₄	semidirect
23. C₂×C₄⋊#1055	C₄	semidirect
26. D₁₃×C₄⋊C₈	C₄	semidirect
35. C₂×C₄⋊#261	C₈	semidirect
67. C₄×#1057	C₂×C₄	semidirect
69. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
73. C₄⋊#1055	C₂×C₄	semidirect
109. C₄⋊#261	C₂×C₈	semidirect
208. C₂×C₄⋊C₈	#261	semidirect
288. C₄⋊C₈	C₂×#261	semidirect
295. C₂×C₁₃	#1279	semidirect
299. D₁₃	#1279	semidirect
365. C₁₃	C₂×#1279	semidirect
453. C₂	#13129670	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×C₄×D₁₃⋊C₈	2
C₂×C₄×C₄⋊#261	2
#13129670	2
C₂×D₁₃×C₄⋊C₈	2
C₂×#1279	13

Subgroups — C2×#13129670 #16779076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129670 #16779076