Subgroups — #16798320

Order 3328.

982 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	#13131285	C₂	1	2	yes	maximal
2	#13130772	C₂	1	2	yes	maximal, complemented
3	#13130757	C₂	1	2	yes	maximal, complemented
4	#13130713	C₂	1	4	yes	maximal
5	C₄×#88102	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂×#88237	—	2	2	no	—
8	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	#11719136	—	2	2	no	—
11	#11719136	C₂²	1	4	yes	—
12	C₂×#88102	C₂²	1	8	yes	—
13	#11719060	—	2	2	no	—
14	#11719059	C₂²	1	4	yes	—
15	C₄×C₄⋊#261	—	2	2	no	—
16	C₄×C₄⋊#261	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
18	C₂×C₈×Dic₁₃	C₄	1	2	yes	complemented
19	C₂×C₄×#1055	C₄	1	1	yes	characteristic, complemented
20	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
21	C₄×C₈×D₁₃	C₄	1	2	yes	complemented
22	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
23	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
24	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₁₃	C₂²	1	2	yes	—
26	#11718265	C₂²	1	8	yes	—
27	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
30	C₂×C₂²⋊#261	—	2	4	no	—
31	#88237	—	4	8	no	—
32	C₂×C₄⋊#261	—	2	4	no	—
33	C₂×C₄⋊#261	—	2	4	no	—
34	C₂×C₄⋊#261	C₂³	1	8	yes	—
35	C₂×C₄×#261	—	2	4	no	—
36	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
40	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
41	C₂²×#1055	C₂×C₄	1	2	yes	—
42	C₂×C₈×D₁₃	—	2	8	no	—
43	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
44	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
45	C₂×C₈×D₁₃	C₂³	1	2	yes	—
46	C₂×C₈×D₁₃	C₂³	1	2	yes	—
47	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₁₃	D₄	1	1	yes	characteristic
50	C₄²×D₁₃	D₄	1	1	yes	characteristic
51	C₄²×D₁₃	Q₈	1	1	yes	characteristic
52	C₄²×D₁₃	Q₈	1	1	yes	characteristic
53	C₄²×D₁₃	C₂³	1	1	yes	characteristic
54	C₄²×D₁₃	C₂³	1	1	yes	characteristic
55	(C₂×#261)⋊C₄	—	2	4	no	—
56	(C₂×#261)⋊C₄	—	2	4	no	—
57	#88102	—	2	16	no	—
58	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
62	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
63	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
64	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
65	C₄×#1055	C₂×C₄	1	1	yes	characteristic
66	C₄×#1055	C₂×C₄	1	2	yes	—
67	C₄×#1055	C₂×C₄	1	1	yes	characteristic
68	#20817	—	13	1	no	maximal, Sylow
69	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×#261	—	2	8	no	—
71	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
77	C₂×C₄×D₁₃	—	2	4	no	—
78	C₂×C₄×D₁₃	—	2	4	no	—
79	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₃	D₈	1	4	yes	—
84	C₂×C₄×D₁₃	Q₁₆	1	4	yes	—
85	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
93	C₂²⋊#261	—	4	8	no	—
94	C₄⋊#261	—	2	16	no	—
95	C₄⋊#261	—	4	8	no	—
96	C₄⋊#261	—	4	8	no	—
97	C₄×#261	—	4	8	no	—
98	C₂×C₈×C₁₃	—	2	4	no	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
101	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
108	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
109	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
110	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
111	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
114	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
115	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
116	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
117	C₂×#1055	—	2	4	no	—
118	C₂×#1055	C₂²×C₄	1	2	yes	—
119	C₂×#1055	C₂²×C₄	1	2	yes	—
120	C₈×D₁₃	—	2	4	no	—
121	C₈×D₁₃	—	2	4	no	—
122	C₈×D₁₃	—	2	4	no	—
123	C₈×D₁₃	#41	1	8	yes	—
124	C₂²×C₄×C₈	—	13	1	no	—
125	#2285	—	13	2	no	—
126	#1845	—	13	2	no	—
127	#1834	—	13	2	no	—
128	#1808	—	13	4	no	—
129	C₄×#107	—	13	4	no	—
130	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂²×D₁₃	—	2	2	no	—
132	C₂²×D₁₃	—	2	2	no	—
133	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂²×D₁₃	C₂×D₈	1	2	yes	—
135	C₂²×D₁₃	C₂×Q₁₆	1	2	yes	—
136	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
137	C₂×#261	—	4	8	no	—
138	C₂×#261	—	4	8	no	—
139	C₂×#261	—	4	8	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	#107	1	4	yes	complemented
143	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
149	C₂×Dic₁₃	—	2	2	no	—
150	C₂×Dic₁₃	—	2	2	no	—
151	C₂×Dic₁₃	#107	1	4	yes	complemented
152	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
158	C₄×D₁₃	—	2	2	no	—
159	C₄×D₁₃	—	2	2	no	—
160	C₄×D₁₃	—	2	2	no	—
161	C₄×D₁₃	—	2	2	no	—
162	C₄×D₁₃	—	2	2	no	—
163	C₄×D₁₃	—	2	2	no	—
164	C₄×D₁₃	#107	1	4	yes	complemented
165	C₄×D₁₃	#107	1	4	yes	complemented
166	C₄×D₁₃	C₂×D₈	1	2	yes	—
167	C₄×D₁₃	C₂×D₈	1	2	yes	—
168	C₄×D₁₃	C₂×Q₁₆	1	2	yes	—
169	C₄×D₁₃	C₂×Q₁₆	1	2	yes	—
170	C₄×D₁₃	#135	1	4	yes	—
171	C₄×D₁₃	C₂×#41	1	4	yes	—
172	C₈×C₁₃	—	2	2	no	—
173	C₈×C₁₃	#117	1	4	yes	complemented
174	#1055	—	2	2	no	—
175	#1055	#117	1	4	yes	complemented
176	C₂³×C₈	—	13	2	no	—
177	C₂×#117	—	26	2	no	—
178	C₂²×C₄²	—	13	1	no	—
179	C₂×#107	—	13	8	no	—
180	C₂×C₄×C₈	—	13	2	no	—
181	C₂×C₄×C₈	—	13	1	no	—
182	C₂×C₄×C₈	—	13	1	no	—
183	C₂×C₄×C₈	—	13	1	no	—
184	C₂×C₄×C₈	—	13	1	no	—
185	C₂×C₄×C₈	—	13	2	no	—
186	C₂×C₄×C₈	—	13	1	no	—
187	C₂×C₄×C₈	—	13	2	no	—
188	C₂×C₄×C₈	#261	1	1	yes	characteristic, complemented
189	#384	—	13	4	no	—
190	#382	—	26	2	no	—
191	#380	—	13	4	no	—
192	#380	—	26	2	no	—
193	C₄×C₄⋊C₄	—	13	4	no	—
194	C₄×C₄⋊C₄	—	26	2	no	—
195	#340	—	13	8	no	—
196	C₂²×C₁₃	—	2	1	no	—
197	C₂²×C₁₃	—	2	1	no	—
198	C₂²×C₁₃	C₂×#107	1	2	yes	—
199	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
200	C₂×D₁₃	—	2	1	no	—
201	C₂×D₁₃	—	2	1	no	—
202	C₂×D₁₃	—	2	4	no	—
203	C₂×D₁₃	—	2	4	no	—
204	C₂×D₁₃	C₂×#107	1	2	yes	—
205	C₂×D₁₃	#532	1	2	yes	—
206	C₂×D₁₃	C₂²×D₈	1	1	yes	characteristic
207	C₂×D₁₃	C₂²×Q₁₆	1	1	yes	characteristic
208	C₂×D₁₃	C₂×#135	1	2	yes	—
209	#261	—	8	8	no	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	C₂×#107	1	2	yes	—
213	C₄×C₁₃	C₂×#107	1	2	yes	—
214	C₄×C₁₃	#427	1	2	yes	—
215	C₄×C₁₃	C₂×#117	1	2	yes	—
216	Dic₁₃	—	2	1	no	—
217	Dic₁₃	—	2	1	no	—
218	Dic₁₃	C₂×#107	1	2	yes	—
219	Dic₁₃	C₂×#107	1	2	yes	—
220	Dic₁₃	#427	1	2	yes	—
221	Dic₁₃	#533	1	2	yes	—
222	C₂³×C₄	—	13	1	no	—
223	C₂³×C₄	—	13	1	no	—
224	C₂³×C₄	—	13	1	no	—
225	C₂²×C₈	—	13	2	no	—
226	C₂²×C₈	—	13	2	no	—
227	C₂²×C₈	—	13	2	no	—
228	C₂²×C₈	—	13	2	no	—
229	C₂²×C₈	—	13	2	no	—
230	C₂²×C₈	—	26	8	no	—
231	C₂²×C₈	C₂×#261	1	2	yes	—
232	#117	—	52	8	no	—
233	C₂×C₄⋊C₄	—	13	8	no	—
234	C₂×C₄⋊C₄	—	26	4	no	—
235	C₂×C₄⋊C₄	—	26	4	no	—
236	C₂×C₂²⋊C₄	—	26	4	no	—
237	C₂×C₄²	—	13	1	no	—
238	C₂×C₄²	—	13	1	no	—
239	C₂×C₄²	—	13	1	no	—
240	C₂×C₄²	—	13	1	no	—
241	C₂×C₄²	—	13	1	no	—
242	C₂×C₄²	—	13	1	no	—
243	C₂×C₄²	—	13	1	no	—
244	C₂×C₄²	—	13	1	no	—
245	C₂×C₄²	—	13	1	no	—
246	C₂×C₄²	—	13	1	no	—
247	C₂×C₄²	—	13	1	no	—
248	C₂×C₄²	—	26	4	no	—
249	C₂×C₄²	C₂×#261	1	1	yes	characteristic
250	#107	—	26	16	no	—
251	C₄×C₈	—	13	2	no	—
252	C₄×C₈	—	13	2	no	—
253	C₄×C₈	—	13	2	no	—
254	C₄×C₈	—	13	2	no	—
255	C₄×C₈	—	13	1	no	—
256	C₄×C₈	—	13	1	no	—
257	C₄×C₈	—	13	2	no	—
258	C₄×C₈	C₂×#261	1	1	yes	characteristic
259	C₄×C₈	C₂×#261	1	1	yes	characteristic
260	C₄×C₈	C₂×#261	1	2	yes	—
261	#95	—	26	4	no	—
262	#95	—	26	4	no	—
263	C₂×C₁₃	—	2	2	no	—
264	C₂×C₁₃	#2285	1	1	yes	characteristic
265	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
266	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
267	D₁₃	—	2	2	no	—
268	D₁₃	#3169	1	2	yes	—
269	D₁₃	#3170	1	2	yes	—
270	C₂⁴	—	13	1	no	—
271	C₂²×C₄	—	13	1	no	—
272	C₂²×C₄	—	13	4	no	—
273	C₂²×C₄	—	13	4	no	—
274	C₂²×C₄	—	13	1	no	—
275	C₂²×C₄	—	13	1	no	—
276	C₂²×C₄	—	13	1	no	—
277	C₂²×C₄	—	13	1	no	—
278	C₂²×C₄	—	13	1	no	—
279	C₂²×C₄	—	13	1	no	—
280	C₂²×C₄	—	13	1	no	—
281	C₂²×C₄	—	13	1	no	—
282	C₂²×C₄	—	13	1	no	—
283	C₂²×C₄	—	13	1	no	—
284	C₂²×C₄	—	13	1	no	—
285	C₂²×C₄	—	13	1	no	—
286	C₂²×C₄	—	13	1	no	—
287	C₂²×C₄	—	13	1	no	—
288	C₂²×C₄	—	26	4	no	—
289	C₂²×C₄	—	26	4	no	—
290	C₂²×C₄	—	26	8	no	—
291	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
292	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
293	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	13	2	no	—
296	C₂×C₈	—	13	8	no	—
297	C₂×C₈	—	13	2	no	—
298	C₂×C₈	—	26	4	no	—
299	C₂×C₈	—	26	4	no	—
300	C₂×C₈	—	26	4	no	—
301	C₂×C₈	—	26	4	no	—
302	C₂×C₈	C₂²×#261	1	2	yes	—
303	C₂×C₈	C₂²×#261	1	2	yes	—
304	C₄⋊C₄	—	26	16	no	—
305	C₄⋊C₄	—	52	8	no	—
306	C₄⋊C₄	—	52	8	no	—
307	C₂²⋊C₄	—	52	8	no	—
308	C₄²	—	13	1	no	—
309	C₄²	—	13	1	no	—
310	C₄²	—	13	1	no	—
311	C₄²	—	13	1	no	—
312	C₄²	—	13	1	no	—
313	C₄²	—	13	1	no	—
314	C₄²	—	13	1	no	—
315	C₄²	—	13	1	no	—
316	C₄²	—	13	1	no	—
317	C₄²	—	13	1	no	—
318	C₄²	—	13	1	no	—
319	C₄²	—	13	1	no	—
320	C₄²	—	52	8	no	—
321	C₄²	C₄⋊#261	1	1	yes	characteristic
322	C₄²	C₄⋊#261	1	1	yes	characteristic
323	C₄²	C₂²×#261	1	1	yes	characteristic
324	C₄²	C₂²×#261	1	1	yes	characteristic
325	C₁₃	#20817	1	1	yes	characteristic, complemented, Sylow
326	C₂³	—	13	1	no	—
327	C₂³	—	13	2	no	—
328	C₂³	—	13	2	no	—
329	C₂³	—	13	1	no	—
330	C₂³	—	26	2	no	—
331	C₂³	—	26	2	no	—
332	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	13	4	no	—
336	C₂×C₄	—	13	1	no	—
337	C₂×C₄	—	13	1	no	—
338	C₂×C₄	—	13	1	no	—
339	C₂×C₄	—	13	1	no	—
340	C₂×C₄	—	13	2	no	—
341	C₂×C₄	—	13	2	no	—
342	C₂×C₄	—	13	4	no	—
343	C₂×C₄	—	13	4	no	—
344	C₂×C₄	—	13	2	no	—
345	C₂×C₄	—	13	2	no	—
346	C₂×C₄	—	13	4	no	—
347	C₂×C₄	—	13	4	no	—
348	C₂×C₄	—	13	1	no	—
349	C₂×C₄	—	13	1	no	—
350	C₂×C₄	—	26	2	no	—
351	C₂×C₄	—	26	2	no	—
352	C₂×C₄	—	26	2	no	—
353	C₂×C₄	—	26	2	no	—
354	C₂×C₄	—	26	2	no	—
355	C₂×C₄	—	26	2	no	—
356	C₂×C₄	—	26	2	no	—
357	C₂×C₄	—	26	2	no	—
358	C₂×C₄	—	52	8	no	—
359	C₂×C₄	—	52	8	no	—
360	C₂×C₄	—	52	8	no	—
361	C₂×C₄	#88102	1	4	yes	complemented
362	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
365	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
367	C₂×C₄	C₂³×#261	1	1	yes	characteristic
368	C₈	—	2	2	no	—
369	C₈	—	13	4	no	—
370	C₈	—	26	2	no	—
371	C₈	#88237	1	4	yes	complemented
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	13	2	no	—
375	C₂²	—	13	1	no	—
376	C₂²	—	13	1	no	—
377	C₂²	—	13	2	no	—
378	C₂²	—	13	2	no	—
379	C₂²	—	26	4	no	—
380	C₂²	—	26	4	no	—
381	C₂²	—	26	1	no	—
382	C₂²	—	26	1	no	—
383	C₂²	C₂×#88102	1	2	yes	—
384	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	13	2	no	—
388	C₄	—	13	2	no	—
389	C₄	—	13	2	no	—
390	C₄	—	13	2	no	—
391	C₄	—	26	1	no	—
392	C₄	—	26	1	no	—
393	C₄	—	104	8	no	—
394	C₄	C₂×#88102	1	2	yes	—
395	C₄	C₂×#88102	1	2	yes	—
396	C₄	#11719092	1	2	yes	—
397	C₄	C₂×#88237	1	2	yes	—
398	C₂	—	2	2	no	—
399	C₂	—	13	2	no	—
400	C₂	—	13	2	no	—
401	C₂	—	26	2	no	—
402	C₂	#13131285	1	1	yes	characteristic
403	C₂	C₂²×#88102	1	1	yes	characteristic
404	C₂	C₂×#11719092	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#20817
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13130772	C₂	semidirect
3. #13130757	C₂	semidirect
5. C₄×#88102	C₂	semidirect
17. C₂×C₄×C₈×C₁₃	C₄	semidirect
18. C₂×C₈×Dic₁₃	C₄	semidirect
19. C₂×C₄×#1055	C₄	semidirect
20. C₄×C₈×D₁₃	C₄	semidirect
21. C₄×C₈×D₁₃	C₄	semidirect
22. C₄×C₈×D₁₃	C₄	semidirect
142. C₂×C₄×C₁₃	#107	semidirect
151. C₂×Dic₁₃	#107	semidirect
164. C₄×D₁₃	#107	semidirect
165. C₄×D₁₃	#107	semidirect
173. C₈×C₁₃	#117	semidirect
175. #1055	#117	semidirect
188. C₂×C₄×C₈	#261	semidirect
325. C₁₃	#20817	semidirect
361. C₂×C₄	#88102	semidirect
371. C₈	#88237	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13131285	2
#13130772	2
#13130757	2
#13130713	2
C₄×#88102	2
C₂×C₄×C₈×D₁₃	2
#20817	13