Subgroups — #16794954

Order 3328.

756 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131514	C₂	1	1	yes	maximal, characteristic
2	D₁₃⋊#423	C₂	1	1	yes	maximal, characteristic
3	#13130402	C₂	1	2	yes	maximal, complemented
4	#13130401	C₂	1	2	yes	maximal, complemented
5	#13130393	C₂	1	2	yes	maximal, complemented
6	#13130390	C₂	1	2	yes	maximal, complemented
7	#13130388	C₂	1	4	yes	maximal, complemented
8	C₂×#11718368	C₂	1	1	yes	maximal, characteristic
9	C₂×D₁₃⋊M₁₆	—	2	1	no	—
10	C₂²×#6094	C₄	1	2	yes	—
11	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	#11719129	—	2	1	no	—
13	#11719129	C₂²	1	1	yes	characteristic
14	#11719129	C₂²	1	2	yes	—
15	#11719129	C₂²	1	1	yes	characteristic
16	#11719126	—	2	1	no	—
17	C₄×#6122	—	2	1	no	—
18	#11719055	—	2	1	no	—
19	#11719054	C₂²	1	2	yes	—
20	#11719053	—	2	1	no	—
21	#11719052	C₂²	1	2	yes	—
22	#11719051	C₂²	1	2	yes	—
23	D₁₃⋊(C₄⋊C₈)	—	2	1	no	—
24	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
25	#11719049	—	2	1	no	—
26	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
27	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
28	C₂×#88043	C₄	1	1	yes	characteristic
29	#11718368	C₄	1	1	yes	characteristic
30	#11718368	C₄	1	2	yes	—
31	#11718368	C₄	1	1	yes	characteristic
32	#11718368	C₂²	1	2	yes	—
33	#11718368	C₂²	1	1	yes	characteristic
34	#11718368	C₂²	1	1	yes	characteristic
35	#11718256	C₂²	1	4	yes	complemented
36	#11718255	C₂²	1	4	yes	complemented
37	#11718254	C₂²	1	4	yes	complemented
38	#11718253	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
42	C₂×#6122	—	2	2	no	—
43	C₂×#6122	—	2	1	no	—
44	C₂×#6122	—	2	1	no	—
45	D₁₃⋊M₁₆	—	4	4	no	—
46	C₂×#6118	—	2	2	no	—
47	C₂×D₁₃⋊C₈	—	2	2	no	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
53	C₂²×#1055	C₂×C₄	1	2	yes	—
54	C₂×#6094	—	2	8	no	—
55	C₂×#6094	C₂×C₄	1	2	yes	—
56	C₂×#6094	C₂×C₄	1	2	yes	—
57	C₂×#6094	C₂×C₄	1	2	yes	—
58	C₂×#6094	C₂×C₄	1	2	yes	—
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	Q₈	1	1	yes	characteristic
64	C₄²×D₁₃	Q₈	1	1	yes	characteristic
65	C₄²×D₁₃	C₂³	1	1	yes	characteristic
66	C₄²×D₁₃	C₂³	1	1	yes	characteristic
67	#88112	—	2	1	no	—
68	#88112	—	2	1	no	—
69	#88112	—	2	2	no	—
70	#88112	—	2	2	no	—
71	#88111	—	2	2	no	—
72	#88111	—	2	2	no	—
73	#88110	—	2	2	no	—
74	C₄⋊#1057	—	2	2	no	—
75	C₄⋊#1057	C₂³	1	2	yes	—
76	C₄⋊#1057	C₂³	1	4	yes	—
77	C₄⋊#1057	C₂³	1	2	yes	—
78	C₄×#1057	—	2	2	no	—
79	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
80	C₁₃×#97	C₂×C₄	1	2	yes	—
81	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
83	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
84	C₈×Dic₁₃	C₂³	1	2	yes	—
85	C₈×Dic₁₃	C₂³	1	2	yes	—
86	#88043	C₂×C₄	1	1	yes	characteristic
87	#88043	C₂×C₄	1	2	yes	—
88	#88043	C₂×C₄	1	1	yes	characteristic
89	#17796	—	13	1	no	maximal, Sylow
90	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₄×D₁₃	—	2	2	no	—
98	C₂×C₄×D₁₃	—	2	2	no	—
99	C₂×C₄×D₁₃	—	2	4	no	—
100	C₂×C₄×D₁₃	—	4	2	no	—
101	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
113	#6122	—	4	4	no	—
114	#6122	—	4	2	no	—
115	#6122	—	4	2	no	—
116	C₂×#1057	—	2	2	no	—
117	C₂×#1057	—	2	2	no	—
118	C₂×#1057	—	2	4	no	—
119	#6118	—	4	4	no	—
120	D₁₃⋊C₈	—	4	4	no	—
121	C₂×C₈×C₁₃	—	2	4	no	—
122	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂²×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	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
140	C₂×#1055	—	2	4	no	—
141	C₂×#1055	C₂²×C₄	1	2	yes	—
142	C₂×#1055	C₂²×C₄	1	2	yes	—
143	#6094	—	2	4	no	—
144	#6094	—	2	4	no	—
145	#6094	—	2	4	no	—
146	#6094	M₁₆	1	8	yes	complemented
147	#2920	—	13	1	no	—
148	C₂×#423	—	13	1	no	—
149	C₂×C₄×M₁₆	—	13	1	no	—
150	#1569	—	13	2	no	—
151	#1569	—	13	2	no	—
152	#1567	—	13	2	no	—
153	#1566	—	13	2	no	—
154	#1565	—	13	4	no	—
155	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×D₁₃	—	2	2	no	—
157	C₂²×D₁₃	—	2	2	no	—
158	C₂²×D₁₃	—	4	1	no	—
159	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×Dic₁₃	—	2	2	no	—
171	C₂×Dic₁₃	—	2	2	no	—
172	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×Dic₁₃	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×Dic₁₃	#137	1	2	yes	—
178	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	2	2	no	—
182	C₄×D₁₃	—	2	1	no	—
183	C₄×D₁₃	—	2	1	no	—
184	C₄×D₁₃	—	2	1	no	—
185	C₄×D₁₃	—	2	1	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	2	2	no	—
191	C₄×D₁₃	—	4	1	no	—
192	C₄×D₁₃	—	4	1	no	—
193	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
194	#1057	—	4	4	no	—
195	#1057	—	4	2	no	—
196	#1057	—	4	2	no	—
197	C₈×C₁₃	—	2	2	no	—
198	C₈×C₁₃	C₂×M₁₆	1	4	yes	complemented
199	#1055	—	2	2	no	—
200	#1055	C₂×M₁₆	1	4	yes	complemented
201	C₂²×M₁₆	—	13	2	no	—
202	C₂²×M₁₆	—	26	1	no	—
203	C₂²×C₄²	—	13	1	no	—
204	#432	—	13	2	no	—
205	#432	—	26	1	no	—
206	#431	—	13	2	no	—
207	#431	—	26	1	no	—
208	#423	—	13	1	no	—
209	#423	—	13	2	no	—
210	#423	—	13	1	no	—
211	#423	—	13	2	no	—
212	#423	—	26	1	no	—
213	#423	—	26	1	no	—
214	C₂×C₄⋊C₈	—	13	2	no	—
215	C₂×C₄⋊C₈	—	26	1	no	—
216	#407	—	26	1	no	—
217	C₄×M₁₆	—	13	2	no	—
218	C₄×M₁₆	—	13	1	no	—
219	C₄×M₁₆	—	13	1	no	—
220	C₄×M₁₆	—	13	1	no	—
221	C₄×M₁₆	—	13	2	no	—
222	C₄×M₁₆	—	13	1	no	—
223	C₄×M₁₆	—	26	1	no	—
224	C₂×#97	—	13	1	no	—
225	C₂×#97	#261	1	1	yes	characteristic
226	C₂×C₄×C₈	—	13	2	no	—
227	#335	—	13	4	no	—
228	#335	—	13	4	no	—
229	#334	—	13	4	no	—
230	#334	—	13	4	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	#428	1	2	yes	—
234	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
235	C₂×D₁₃	—	2	1	no	—
236	C₂×D₁₃	—	2	1	no	—
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	2	1	no	—
239	C₂×D₁₃	—	2	1	no	—
240	C₂×D₁₃	—	4	4	no	—
241	C₂×D₁₃	#423	1	2	yes	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
248	Dic₁₃	—	2	1	no	—
249	Dic₁₃	—	2	1	no	—
250	Dic₁₃	#423	1	2	yes	—
251	Dic₁₃	#428	1	2	yes	—
252	Dic₁₃	#430	1	2	yes	—
253	Dic₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	Dic₁₃	C₂×#137	1	1	yes	characteristic
255	C₂³×C₄	—	13	1	no	—
256	C₂³×C₄	—	13	1	no	—
257	C₂³×C₄	—	13	1	no	—
258	C₂×M₁₆	—	13	2	no	—
259	C₂×M₁₆	—	13	2	no	—
260	C₂×M₁₆	—	13	2	no	—
261	C₂×M₁₆	—	13	2	no	—
262	C₂×M₁₆	—	26	8	no	—
263	C₂×M₁₆	—	26	2	no	—
264	C₂×M₁₆	—	26	2	no	—
265	C₂×M₁₆	—	26	1	no	—
266	C₂×M₁₆	—	26	1	no	—
267	C₂×M₁₆	—	52	4	no	—
268	C₂²×C₈	—	13	2	no	—
269	C₂²×C₈	—	26	2	no	—
270	C₂²×C₈	C₂×#261	1	2	yes	—
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	—	13	1	no	—
279	C₂×C₄²	—	13	1	no	—
280	C₂×C₄²	—	13	1	no	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	C₂×#261	1	1	yes	characteristic
283	C₄⋊C₈	—	13	2	no	—
284	C₄⋊C₈	—	13	4	no	—
285	C₄⋊C₈	—	13	2	no	—
286	C₄⋊C₈	—	26	2	no	—
287	C₄⋊C₈	—	26	2	no	—
288	C₄⋊C₈	—	26	2	no	—
289	C₄⋊C₈	—	26	1	no	—
290	C₄⋊C₈	—	26	1	no	—
291	C₂²⋊C₈	—	26	2	no	—
292	C₂²⋊C₈	—	26	2	no	—
293	#97	—	13	1	no	—
294	#97	—	13	2	no	—
295	#97	—	13	1	no	—
296	#97	—	26	2	no	—
297	#97	C₂×#261	1	1	yes	characteristic
298	#97	C₂×#261	1	2	yes	—
299	#97	C₂×#261	1	1	yes	characteristic
300	C₄×C₈	—	13	2	no	—
301	C₄×C₈	—	13	2	no	—
302	C₄×C₈	—	13	2	no	—
303	C₄×C₈	—	13	2	no	—
304	C₄×C₈	—	26	2	no	—
305	C₂×C₁₃	—	2	2	no	—
306	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
307	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
308	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
309	D₁₃	—	2	2	no	—
310	D₁₃	—	4	1	no	—
311	C₂⁴	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	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	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	26	4	no	—
328	C₂²×C₄	—	26	2	no	—
329	C₂²×C₄	—	26	2	no	—
330	C₂²×C₄	—	52	2	no	—
331	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
332	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
333	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
334	M₁₆	—	13	8	no	—
335	M₁₆	—	26	4	no	—
336	M₁₆	—	26	4	no	—
337	M₁₆	—	26	4	no	—
338	M₁₆	—	52	4	no	—
339	M₁₆	—	52	2	no	—
340	M₁₆	—	52	2	no	—
341	M₁₆	—	52	4	no	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	—	13	2	no	—
344	C₂×C₈	—	13	2	no	—
345	C₂×C₈	—	26	4	no	—
346	C₂×C₈	—	26	2	no	—
347	C₂×C₈	—	26	2	no	—
348	C₂×C₈	—	26	4	no	—
349	C₂×C₈	—	52	4	no	—
350	C₂×C₈	C₂²×#261	1	2	yes	—
351	C₂×C₈	C₂²×#261	1	2	yes	—
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	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	—	13	1	no	—
364	C₄²	C₄⋊#261	1	1	yes	characteristic
365	C₄²	C₄⋊#261	1	1	yes	characteristic
366	C₄²	C₂²×#261	1	1	yes	characteristic
367	C₄²	C₂²×#261	1	1	yes	characteristic
368	C₁₃	#17796	1	1	yes	characteristic, complemented, Sylow
369	C₂³	—	13	1	no	—
370	C₂³	—	13	1	no	—
371	C₂³	—	26	2	no	—
372	C₂³	—	26	2	no	—
373	C₂³	—	52	1	no	—
374	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	13	2	no	—
379	C₂×C₄	—	13	2	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	13	4	no	—
385	C₂×C₄	—	13	1	no	—
386	C₂×C₄	—	13	1	no	—
387	C₂×C₄	—	26	1	no	—
388	C₂×C₄	—	26	1	no	—
389	C₂×C₄	—	26	2	no	—
390	C₂×C₄	—	26	1	no	—
391	C₂×C₄	—	26	1	no	—
392	C₂×C₄	—	26	2	no	—
393	C₂×C₄	—	26	2	no	—
394	C₂×C₄	—	26	2	no	—
395	C₂×C₄	—	26	2	no	—
396	C₂×C₄	—	26	2	no	—
397	C₂×C₄	—	26	2	no	—
398	C₂×C₄	—	26	2	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	52	1	no	—
401	C₂×C₄	—	52	1	no	—
402	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
403	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
404	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
405	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
406	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
407	C₂×C₄	C₂³×#261	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	13	4	no	—
410	C₈	—	26	2	no	—
411	C₈	—	52	4	no	—
412	C₈	—	52	2	no	—
413	C₈	—	52	2	no	—
414	C₈	D₁₃⋊M₁₆	1	4	yes	complemented
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	13	2	no	—
418	C₂²	—	26	1	no	—
419	C₂²	—	26	1	no	—
420	C₂²	—	26	1	no	—
421	C₂²	—	26	1	no	—
422	C₂²	—	26	1	no	—
423	C₂²	—	52	4	no	—
424	C₂²	#11719098	1	2	yes	—
425	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	13	2	no	—
432	C₄	—	13	1	no	—
433	C₄	—	13	1	no	—
434	C₄	—	13	2	no	—
435	C₄	—	13	2	no	—
436	C₄	—	26	1	no	—
437	C₄	—	26	1	no	—
438	C₄	C₂×D₁₃⋊M₁₆	1	2	yes	—
439	C₂	—	2	2	no	—
440	C₂	—	26	2	no	—
441	C₂	—	52	1	no	—
442	C₂	D₁₃⋊#423	1	1	yes	characteristic
443	C₂	C₂×#11719098	1	1	yes	characteristic
444	C₂	D₁₃⋊#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₁₃×#97	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂×#97	#261
hypocenter	C₁₃	#17796
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
3. #13130402	C₂	semidirect
4. #13130401	C₂	semidirect
5. #13130393	C₂	semidirect
6. #13130390	C₂	semidirect
7. #13130388	C₂	semidirect
35. #11718256	C₂²	semidirect
36. #11718255	C₂²	semidirect
37. #11718254	C₂²	semidirect
38. #11718253	C₂²	semidirect
146. #6094	M₁₆	semidirect
198. C₈×C₁₃	C₂×M₁₆	semidirect
200. #1055	C₂×M₁₆	semidirect
368. C₁₃	#17796	semidirect
414. C₈	D₁₃⋊M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#13131514	2
D₁₃⋊#423	2
#13130402	2
#13130401	2
#13130393	2
#13130390	2
#13130388	2
C₂×#11718368	2
#17796	13