Subgroups — C₄×#11719100 #16797216

Order 3328.

1034 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719100	C₂	1	2	yes	maximal
2	C₂×C₄×#6118	C₂	1	1	yes	maximal, characteristic
3	C₄×D₁₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
4	#13130656	C₂	1	4	yes	maximal, complemented
5	C₄×#88104	C₂	1	2	yes	maximal, complemented
6	C₄×#88103	C₂	1	2	yes	maximal, complemented
7	#13130530	C₂	1	2	yes	maximal
8	C₄×M₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
10	C₂²×#6118	C₂²	1	2	yes	—
11	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
12	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
14	C₄×#6122	—	2	1	no	—
15	C₄×#6122	—	2	1	no	—
16	C₂×#88110	—	2	1	no	—
17	C₂×C₄×#1057	—	2	1	no	—
18	#11719100	C₄	1	16	yes	direct product factor
19	C₂×#88104	C₂²	1	4	yes	—
20	C₂×#88103	C₂²	1	4	yes	—
21	C₄×#6118	—	2	1	no	—
22	C₄×#6118	—	2	1	no	—
23	C₄×#6118	C₂²	1	1	yes	characteristic
24	C₄×#6118	C₂²	1	1	yes	characteristic
25	C₄×#6118	C₂²	1	2	yes	—
26	C₄×#6118	C₂²	1	2	yes	—
27	C₄×#6118	C₂²	1	2	yes	—
28	#11719047	—	2	1	no	—
29	C₄×D₁₃⋊C₈	—	2	1	no	—
30	C₄×C₁₃×M₁₆	C₄	1	1	yes	characteristic
31	M₁₆×Dic₁₃	C₄	1	1	yes	characteristic
32	M₁₆×Dic₁₃	C₄	1	1	yes	characteristic
33	C₄×#6099	C₄	1	1	yes	characteristic
34	#11718368	C₄	1	2	yes	—
35	D₁₃×#97	C₂²	1	2	yes	—
36	C₄×#6094	C₄	1	2	yes	—
37	C₄×C₈×D₁₃	C₂²	1	2	yes	—
38	#11718268	C₂²	1	4	yes	—
39	#11718268	C₂²	1	4	yes	—
40	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
42	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
43	C₂×#6122	—	2	2	no	—
44	C₂²×#1057	—	2	2	no	—
45	D₁₃⋊M₁₆	—	2	4	no	—
46	D₁₃⋊M₁₆	C₂×C₄	1	8	yes	—
47	C₂×#6118	—	2	2	no	—
48	C₂×#6118	—	2	4	no	—
49	C₂×#6118	C₂×C₄	1	8	yes	—
50	C₂×#6118	C₂³	1	2	yes	—
51	C₂×#6118	C₂³	1	4	yes	—
52	C₂×#6118	C₂³	1	2	yes	—
53	C₂×D₁₃⋊C₈	—	2	2	no	—
54	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
60	C₂×#6099	C₂×C₄	1	1	yes	characteristic
61	C₂×#6099	C₂×C₄	1	1	yes	characteristic
62	M₁₆×D₁₃	—	2	4	no	—
63	M₁₆×D₁₃	C₂×C₄	1	8	yes	—
64	C₂×#6094	C₂×C₄	1	2	yes	—
65	C₂×#6094	C₂×C₄	1	2	yes	—
66	C₂×C₈×D₁₃	C₂³	1	2	yes	—
67	C₂×C₈×D₁₃	C₂³	1	2	yes	—
68	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₁₃	D₄	1	1	yes	characteristic
71	C₄²×D₁₃	D₄	1	1	yes	characteristic
72	C₄²×D₁₃	Q₈	1	1	yes	characteristic
73	C₄²×D₁₃	Q₈	1	1	yes	characteristic
74	C₄²×D₁₃	C₂³	1	1	yes	characteristic
75	C₄²×D₁₃	C₂³	1	1	yes	characteristic
76	#88110	—	2	2	no	—
77	#88110	—	2	1	no	—
78	#88110	—	2	1	no	—
79	#88110	—	2	2	no	—
80	#88110	—	2	2	no	—
81	C₄×#1057	—	2	1	no	—
82	C₄×#1057	—	2	1	no	—
83	C₄×#1057	—	2	2	no	—
84	C₄×#1057	—	2	2	no	—
85	C₄×#1057	—	2	2	no	—
86	#88104	C₂×C₄	1	16	yes	complemented
87	#88103	C₂×C₄	1	16	yes	complemented
88	C₁₃×#97	C₂×C₄	1	2	yes	—
89	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
90	#88055	C₂×C₄	1	2	yes	—
91	#88055	C₂×C₄	1	2	yes	—
92	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
93	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
94	#88043	C₂×C₄	1	2	yes	—
95	C₄×#1055	C₂×C₄	1	2	yes	—
96	C₄×#430	—	13	1	no	maximal, Sylow
97	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	—	4	2	no	—
105	C₂×C₄×D₁₃	—	4	2	no	—
106	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
112	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
118	C₂×C₄×D₁₃	#41	1	4	yes	—
119	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
120	#6122	—	2	8	no	—
121	C₂×#1057	—	2	8	no	—
122	C₂×#1057	—	2	2	no	—
123	C₂×#1057	—	2	2	no	—
124	C₂×#1057	—	2	4	no	—
125	#6118	—	2	8	no	—
126	#6118	—	2	4	no	—
127	#6118	—	2	2	no	—
128	#6118	—	2	2	no	—
129	#6118	C₂²×C₄	1	4	yes	—
130	#6118	C₂²×C₄	1	8	yes	—
131	#6118	C₂²×C₄	1	4	yes	—
132	D₁₃⋊C₈	—	2	8	no	—
133	C₁₃×M₁₆	—	2	2	no	—
134	C₁₃×M₁₆	C₄²	1	4	yes	—
135	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
138	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
143	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
144	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
147	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
153	#6099	—	2	2	no	—
154	#6099	C₄²	1	4	yes	—
155	C₂×#1055	C₂²×C₄	1	2	yes	—
156	C₂×#1055	C₂²×C₄	1	2	yes	—
157	#6094	—	2	4	no	—
158	#6094	C₄²	1	8	yes	—
159	C₈×D₁₃	—	2	4	no	—
160	C₈×D₁₃	C₂²×C₄	1	8	yes	—
161	C₂×#430	—	13	2	no	—
162	C₂×C₄×M₁₆	—	13	1	no	—
163	C₂×C₄×M₁₆	—	13	1	no	—
164	C₂×C₄×M₁₆	—	13	1	no	—
165	#1778	—	13	4	no	—
166	C₄×#108	—	13	2	no	—
167	C₄×#108	—	13	2	no	—
168	#1738	—	13	2	no	—
169	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×D₁₃	—	4	1	no	—
171	C₂²×D₁₃	—	4	1	no	—
172	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×D₁₃	C₄×Q₈	1	4	yes	—
174	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#117	1	2	yes	—
184	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×Dic₁₃	—	2	2	no	—
186	C₂×Dic₁₃	—	4	1	no	—
187	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×Dic₁₃	C₄×D₄	1	4	yes	—
193	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₄×D₁₃	—	2	2	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	—	2	2	no	—
197	C₄×D₁₃	—	2	2	no	—
198	C₄×D₁₃	—	4	1	no	—
199	C₄×D₁₃	—	4	1	no	—
200	C₄×D₁₃	—	4	1	no	—
201	C₄×D₁₃	—	4	1	no	—
202	C₄×D₁₃	C₂×C₄²	1	2	yes	—
203	C₄×D₁₃	#117	1	2	yes	—
204	C₄×D₁₃	C₄×D₄	1	4	yes	—
205	C₄×D₁₃	C₄×Q₈	1	4	yes	—
206	C₄×D₁₃	C₂³×C₄	1	2	yes	—
207	C₄×D₁₃	C₂×#41	1	2	yes	—
208	#1057	—	2	4	no	—
209	#1057	—	2	4	no	—
210	#1057	—	2	8	no	—
211	C₈×C₁₃	—	2	2	no	—
212	C₈×C₁₃	C₂×C₄²	1	4	yes	—
213	#1055	—	2	2	no	—
214	#1055	C₂×C₄²	1	4	yes	—
215	C₂²×M₁₆	—	13	1	no	—
216	C₂²×M₁₆	—	13	1	no	—
217	C₂²×M₁₆	—	13	2	no	—
218	C₂²×M₁₆	—	13	2	no	—
219	C₂²×C₄²	—	13	1	no	—
220	#430	—	13	16	no	—
221	C₂×#108	—	13	4	no	—
222	C₂×#108	—	13	4	no	—
223	C₄×M₁₆	—	13	1	no	—
224	C₄×M₁₆	—	13	1	no	—
225	C₄×M₁₆	—	13	1	no	—
226	C₄×M₁₆	—	13	2	no	—
227	C₄×M₁₆	—	13	2	no	—
228	C₄×M₁₆	—	13	1	no	—
229	C₄×M₁₆	—	13	1	no	—
230	C₄×M₁₆	—	13	2	no	—
231	C₄×M₁₆	—	13	2	no	—
232	C₄×M₁₆	—	13	2	no	—
233	C₄×M₁₆	—	26	1	no	—
234	C₄×M₁₆	—	26	1	no	—
235	C₄×M₁₆	—	26	1	no	—
236	C₄×M₁₆	—	26	1	no	—
237	C₄×M₁₆	#261	1	1	yes	characteristic
238	C₂×#97	—	13	2	no	—
239	C₂×#97	—	26	1	no	—
240	C₂×#97	—	26	1	no	—
241	C₂×C₄×C₈	—	13	2	no	—
242	C₂×C₄×C₈	—	26	1	no	—
243	C₂×C₄×C₈	—	26	1	no	—
244	#341	—	13	4	no	—
245	#341	—	13	4	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
249	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
250	C₂×D₁₃	—	2	1	no	—
251	C₂×D₁₃	—	2	1	no	—
252	C₂×D₁₃	—	2	1	no	—
253	C₂×D₁₃	—	2	1	no	—
254	C₂×D₁₃	—	4	4	no	—
255	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
256	C₂×D₁₃	C₂×C₄×Q₈	1	2	yes	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
261	C₄×C₁₃	#430	1	2	yes	complemented
262	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
263	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
264	Dic₁₃	—	2	1	no	—
265	Dic₁₃	—	2	1	no	—
266	Dic₁₃	—	2	1	no	—
267	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
268	Dic₁₃	#430	1	2	yes	complemented
269	Dic₁₃	C₂×C₄×D₄	1	2	yes	—
270	C₂³×C₄	—	13	1	no	—
271	C₂³×C₄	—	13	1	no	—
272	C₂³×C₄	—	13	1	no	—
273	C₂×M₁₆	—	13	1	no	—
274	C₂×M₁₆	—	13	8	no	—
275	C₂×M₁₆	—	13	1	no	—
276	C₂×M₁₆	—	13	2	no	—
277	C₂×M₁₆	—	13	2	no	—
278	C₂×M₁₆	—	13	4	no	—
279	C₂×M₁₆	—	13	2	no	—
280	C₂×M₁₆	—	13	2	no	—
281	C₂×M₁₆	—	13	8	no	—
282	C₂×M₁₆	—	13	8	no	—
283	C₂×M₁₆	—	26	4	no	—
284	C₂×M₁₆	—	26	2	no	—
285	C₂×M₁₆	—	26	2	no	—
286	C₂×M₁₆	—	26	4	no	—
287	C₂×M₁₆	—	26	4	no	—
288	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
289	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
290	C₂²×C₈	—	13	2	no	—
291	C₂²×C₈	—	13	2	no	—
292	C₂²×C₈	—	26	2	no	—
293	C₂²×C₈	—	26	2	no	—
294	C₂×C₄²	—	13	1	no	—
295	C₂×C₄²	—	13	1	no	—
296	C₂×C₄²	—	13	1	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	C₂×#261	1	1	yes	characteristic
306	#108	—	13	16	no	—
307	#108	—	13	16	no	—
308	#97	—	13	2	no	—
309	#97	—	13	2	no	—
310	#97	—	13	2	no	—
311	#97	—	26	2	no	—
312	#97	—	26	2	no	—
313	#97	—	26	1	no	—
314	#97	—	26	1	no	—
315	#97	—	26	2	no	—
316	#97	C₂×#261	1	2	yes	—
317	C₄×C₈	—	13	2	no	—
318	C₄×C₈	—	13	2	no	—
319	C₄×C₈	—	13	2	no	—
320	C₄×C₈	—	26	2	no	—
321	C₄×C₈	—	26	2	no	—
322	C₄×C₈	—	26	1	no	—
323	C₄×C₈	—	26	1	no	—
324	C₄×C₈	—	26	2	no	—
325	C₄×C₈	C₂×#261	1	2	yes	—
326	C₂×C₁₃	—	2	2	no	—
327	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
328	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
329	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
330	D₁₃	—	2	2	no	—
331	D₁₃	—	2	2	no	—
332	C₂⁴	—	13	1	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	4	no	—
335	C₂²×C₄	—	13	1	no	—
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	4	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	1	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	1	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	—	52	2	no	—
351	C₂²×C₄	—	52	2	no	—
352	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
353	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
354	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
355	M₁₆	—	2	2	no	—
356	M₁₆	—	13	4	no	—
357	M₁₆	—	13	8	no	—
358	M₁₆	—	13	4	no	—
359	M₁₆	—	13	8	no	—
360	M₁₆	—	13	4	no	—
361	M₁₆	—	26	4	no	—
362	M₁₆	—	26	8	no	—
363	M₁₆	—	26	4	no	—
364	M₁₆	—	26	2	no	—
365	M₁₆	—	26	2	no	—
366	M₁₆	—	26	8	no	—
367	M₁₆	—	26	2	no	—
368	M₁₆	C₄×#261	1	4	yes	—
369	C₂×C₈	—	13	2	no	—
370	C₂×C₈	—	13	8	no	—
371	C₂×C₈	—	13	2	no	—
372	C₂×C₈	—	26	4	no	—
373	C₂×C₈	—	26	2	no	—
374	C₂×C₈	—	26	2	no	—
375	C₂×C₈	—	26	4	no	—
376	C₂×C₈	—	26	8	no	—
377	C₂×C₈	—	26	8	no	—
378	C₂×C₈	C₂²×#261	1	2	yes	—
379	C₂×C₈	C₂²×#261	1	2	yes	—
380	C₄²	—	13	1	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	C₄⋊#261	1	1	yes	characteristic
393	C₄²	C₄⋊#261	1	1	yes	characteristic
394	C₄²	C₂²×#261	1	1	yes	characteristic
395	C₄²	C₂²×#261	1	1	yes	characteristic
396	C₁₃	C₄×#430	1	1	yes	characteristic, complemented, Sylow
397	C₂³	—	13	1	no	—
398	C₂³	—	13	1	no	—
399	C₂³	—	13	4	no	—
400	C₂³	—	52	1	no	—
401	C₂³	—	52	1	no	—
402	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	13	4	no	—
406	C₂×C₄	—	13	1	no	—
407	C₂×C₄	—	13	1	no	—
408	C₂×C₄	—	13	1	no	—
409	C₂×C₄	—	13	4	no	—
410	C₂×C₄	—	13	4	no	—
411	C₂×C₄	—	13	2	no	—
412	C₂×C₄	—	13	2	no	—
413	C₂×C₄	—	13	2	no	—
414	C₂×C₄	—	13	2	no	—
415	C₂×C₄	—	13	1	no	—
416	C₂×C₄	—	13	1	no	—
417	C₂×C₄	—	13	1	no	—
418	C₂×C₄	—	26	2	no	—
419	C₂×C₄	—	26	2	no	—
420	C₂×C₄	—	26	2	no	—
421	C₂×C₄	—	26	2	no	—
422	C₂×C₄	—	26	2	no	—
423	C₂×C₄	—	52	1	no	—
424	C₂×C₄	—	52	1	no	—
425	C₂×C₄	—	52	1	no	—
426	C₂×C₄	—	52	1	no	—
427	C₂×C₄	—	52	1	no	—
428	C₂×C₄	C₂×C₄×#261	1	2	yes	—
429	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
430	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
431	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
432	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
434	C₂×C₄	#88237	1	2	yes	—
435	C₂×C₄	C₂³×#261	1	1	yes	characteristic
436	C₈	—	2	2	no	—
437	C₈	—	13	4	no	—
438	C₈	—	26	4	no	—
439	C₈	—	26	4	no	—
440	C₈	—	26	8	no	—
441	C₈	—	26	2	no	—
442	C₈	C₂×C₄×#261	1	4	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	13	2	no	—
446	C₂²	—	13	2	no	—
447	C₂²	—	26	1	no	—
448	C₂²	—	26	1	no	—
449	C₂²	—	26	1	no	—
450	C₂²	—	26	1	no	—
451	C₂²	—	52	4	no	—
452	C₂²	C₄×C₄⋊#261	1	2	yes	—
453	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	13	2	no	—
458	C₄	—	13	2	no	—
459	C₄	—	13	2	no	—
460	C₄	—	26	1	no	—
461	C₄	—	26	1	no	—
462	C₄	—	26	1	no	—
463	C₄	C₄×C₄⋊#261	1	2	yes	—
464	C₄	#11719100	1	2	yes	direct product factor
465	C₄	C₂²×C₄×#261	1	1	yes	characteristic
466	C₄	C₂×#88237	1	1	yes	characteristic
467	C₂	—	2	2	no	—
468	C₂	—	26	2	no	—
469	C₂	—	26	2	no	—
470	C₂	C₂×C₄×C₄⋊#261	1	1	yes	characteristic
471	C₂	C₂×#11719100	1	1	yes	characteristic
472	C₂	D₁₃⋊#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₄×C₁₃×M₁₆	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₄×M₁₆	#261
hypocenter	C₁₃	C₄×#430
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. #13130656	C₂	semidirect
5. C₄×#88104	C₂	semidirect
6. C₄×#88103	C₂	semidirect
18. #11719100	C₄	direct (N × H)
86. #88104	C₂×C₄	semidirect
87. #88103	C₂×C₄	semidirect
261. C₄×C₁₃	#430	semidirect
268. Dic₁₃	#430	semidirect
396. C₁₃	C₄×#430	semidirect
464. C₄	#11719100	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×#11719100	2
C₂×C₄×#6118	2
C₄×D₁₃⋊M₁₆	2
#13130656	2
C₄×#88104	2
C₄×#88103	2
#13130530	2
C₄×M₁₆×D₁₃	2
C₄×#430	13

Subgroups — C4×#11719100 #16797216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11719100 #16797216