Subgroups — #15832110

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123467	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#432	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#423	C₂	1	1	yes	maximal, characteristic
4	#13113620	C₂	1	2	yes	maximal, complemented
5	#13113618	C₂	1	2	yes	maximal, complemented
6	#13113609	C₂	1	2	yes	maximal, complemented
7	#13113605	C₂	1	2	yes	maximal, complemented
8	#13113604	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113603	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113601	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1569	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₃	—	2	1	no	—
13	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#432	C₂²	1	1	yes	characteristic
15	C₁₃×#423	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	#11718787	C₄	1	2	yes	—
18	#11718779	—	2	1	no	—
19	#11718779	C₄	1	2	yes	—
20	#11718587	C₂²	1	1	yes	characteristic
21	#11718585	C₂²	1	1	yes	characteristic
22	C₄×#6099	C₂²	1	1	yes	characteristic
23	#11718498	—	2	1	no	—
24	#11718498	C₂²	1	2	yes	—
25	#11718496	C₂²	1	1	yes	characteristic
26	#11718496	C₂²	1	1	yes	characteristic
27	D₁₃×C₄⋊C₈	—	2	1	no	—
28	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
31	D₁₃×C₂²⋊C₈	—	2	1	no	—
32	#11718380	—	2	1	no	—
33	#11718366	—	2	1	no	—
34	#11718366	C₄	1	2	yes	—
35	#11718366	C₄	1	2	yes	—
36	D₁₃×#97	—	2	1	no	—
37	#11718346	C₂²	1	2	yes	—
38	#11718346	C₂²	1	2	yes	—
39	C₁₃×#335	C₂²	1	2	yes	complemented
40	C₁₃×#334	C₂²	1	2	yes	complemented
41	#11718072	C₂²	1	2	yes	complemented
42	#11718072	C₂²	1	2	yes	complemented
43	#11718071	C₂²	1	2	yes	complemented
44	#11718071	C₂²	1	2	yes	complemented
45	#11718050	C₂²	1	2	yes	complemented
46	#11718049	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
56	C₂×#6099	—	2	1	no	—
57	C₂×#6099	C₂×C₄	1	2	yes	—
58	M₁₆×D₁₃	—	4	4	no	—
59	C₂×#6094	—	2	2	no	—
60	C₂×C₈×D₁₃	—	2	2	no	—
61	C₂×C₈×D₁₃	—	2	1	no	—
62	C₂×C₈×D₁₃	—	2	1	no	—
63	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₁₃	D₄	1	1	yes	characteristic
66	C₄²×D₁₃	D₄	1	1	yes	characteristic
67	C₄²×D₁₃	Q₈	1	1	yes	characteristic
68	C₄²×D₁₃	Q₈	1	1	yes	characteristic
69	C₄²×D₁₃	C₂³	1	1	yes	characteristic
70	C₄²×D₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊C₈	—	2	1	no	—
72	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
75	C₁₃×C₂²⋊C₈	—	2	1	no	—
76	C₁₃×#97	—	2	1	no	—
77	C₁₃×#97	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₁₃	C₂³	1	2	yes	—
79	C₂²⋊#1055	—	2	1	no	—
80	#88060	—	2	1	no	—
81	#88060	—	2	1	no	—
82	#88060	C₂×C₄	1	4	yes	—
83	#88060	C₂×C₄	1	4	yes	—
84	#88055	—	2	1	no	—
85	#88055	—	2	1	no	—
86	#88054	—	2	2	no	—
87	#88054	—	2	2	no	—
88	#88054	—	2	1	no	—
89	#88054	—	2	1	no	—
90	#88054	C₂×C₄	1	4	yes	—
91	#88054	C₂×C₄	1	4	yes	—
92	C₄⋊#1055	—	2	1	no	—
93	C₄⋊#1055	C₂³	1	1	yes	characteristic
94	C₄⋊#1055	C₂³	1	1	yes	characteristic
95	C₄⋊#1055	C₂³	1	2	yes	—
96	#88043	—	2	1	no	—
97	#88043	C₂×C₄	1	2	yes	—
98	C₄×#1055	C₂³	1	2	yes	—
99	#17822	—	13	1	no	maximal, Sylow
100	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
104	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	—	2	2	no	—
108	C₂×C₄×D₁₃	—	2	2	no	—
109	C₂×C₄×D₁₃	—	4	2	no	—
110	C₂×C₄×D₁₃	—	4	2	no	—
111	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
122	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
123	C₁₃×M₁₆	—	4	2	no	—
124	C₁₃×M₁₆	—	4	2	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
129	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
132	C₄²×C₁₃	C₂⁴	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	C₄⋊C₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
144	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
145	#6099	—	4	2	no	—
146	#6099	—	4	2	no	—
147	C₂×#1055	—	2	1	no	—
148	C₂×#1055	—	2	1	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	C₂²×C₄	1	4	yes	—
151	#6094	—	4	4	no	—
152	C₈×D₁₃	—	4	4	no	—
153	C₈×D₁₃	—	4	2	no	—
154	C₈×D₁₃	—	4	2	no	—
155	#2920	—	13	1	no	—
156	C₂×#432	—	13	1	no	—
157	C₂×#423	—	13	1	no	—
158	#1573	—	13	2	no	—
159	#1573	—	13	2	no	—
160	#1571	—	13	2	no	—
161	#1570	—	13	2	no	—
162	#1569	—	13	1	no	—
163	#1569	—	13	1	no	—
164	#1569	—	13	1	no	—
165	#1569	D₁₃	1	1	yes	characteristic, complemented
166	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×D₁₃	—	2	2	no	—
168	C₂²×D₁₃	—	2	2	no	—
169	C₂²×D₁₃	—	4	1	no	—
170	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
182	C₂×Dic₁₃	—	2	2	no	—
183	C₂×Dic₁₃	—	4	1	no	—
184	C₂×Dic₁₃	—	4	1	no	—
185	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₄×D₁₃	—	2	2	no	—
192	C₄×D₁₃	—	2	2	no	—
193	C₄×D₁₃	—	2	2	no	—
194	C₄×D₁₃	—	2	2	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	—	2	1	no	—
197	C₄×D₁₃	—	2	1	no	—
198	C₄×D₁₃	—	2	2	no	—
199	C₄×D₁₃	—	4	1	no	—
200	C₄×D₁₃	—	4	1	no	—
201	C₄×D₁₃	—	4	1	no	—
202	C₄×D₁₃	—	4	1	no	—
203	C₄×D₁₃	AGL(1,ℤ/8)	1	2	yes	—
204	C₄×D₁₃	#137	1	2	yes	—
205	C₈×C₁₃	—	2	4	no	—
206	C₈×C₁₃	—	4	2	no	—
207	C₈×C₁₃	—	4	1	no	—
208	C₈×C₁₃	—	4	1	no	—
209	#1055	—	2	4	no	—
210	#1055	—	4	2	no	—
211	#1055	—	4	1	no	—
212	#1055	—	4	1	no	—
213	C₂²×M₁₆	—	26	1	no	—
214	C₂²×C₄²	—	13	1	no	—
215	#432	—	13	2	no	—
216	#432	—	13	2	no	—
217	#432	—	13	1	no	—
218	#432	—	13	1	no	—
219	#432	—	13	1	no	—
220	#432	—	26	1	no	—
221	#432	—	26	1	no	—
222	#432	C₂×D₁₃	1	1	yes	characteristic
223	#431	—	13	2	no	—
224	#431	—	13	2	no	—
225	#423	—	13	2	no	—
226	#423	—	13	1	no	—
227	#423	—	13	2	no	—
228	#423	—	26	1	no	—
229	#423	—	26	1	no	—
230	#423	C₂×D₁₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	—	13	1	no	—
232	C₂×C₄⋊C₈	—	13	1	no	—
233	C₂×C₄⋊C₈	—	13	2	no	—
234	C₂×C₄⋊C₈	—	26	1	no	—
235	#407	—	13	2	no	—
236	C₂×C₂²⋊C₈	—	26	1	no	—
237	C₄×M₁₆	—	13	1	no	—
238	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
239	C₂×#97	—	26	1	no	—
240	#335	—	13	2	no	—
241	#335	—	13	2	no	—
242	#335	—	13	2	no	—
243	#335	C₂×D₁₃	1	2	yes	complemented
244	#334	—	13	2	no	—
245	#334	—	13	2	no	—
246	#334	—	13	2	no	—
247	#334	C₂×D₁₃	1	2	yes	complemented
248	C₂²×C₁₃	—	2	1	no	—
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
252	C₂×D₁₃	—	2	1	no	—
253	C₂×D₁₃	—	2	1	no	—
254	C₂×D₁₃	—	2	1	no	—
255	C₂×D₁₃	—	2	1	no	—
256	C₂×D₁₃	—	4	4	no	—
257	C₂×D₁₃	#428	1	2	yes	—
258	C₂×D₁₃	#430	1	2	yes	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	2	1	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	#568	1	2	yes	—
264	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
266	Dic₁₃	—	2	1	no	—
267	Dic₁₃	—	2	1	no	—
268	Dic₁₃	—	2	1	no	—
269	Dic₁₃	—	2	1	no	—
270	Dic₁₃	—	2	1	no	—
271	Dic₁₃	#428	1	2	yes	—
272	C₂³×C₄	—	13	1	no	—
273	C₂³×C₄	—	13	1	no	—
274	C₂³×C₄	—	13	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	13	2	no	—
277	C₂×M₁₆	—	26	2	no	—
278	C₂×M₁₆	—	26	1	no	—
279	C₂×M₁₆	—	52	4	no	—
280	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
281	C₂²×C₈	—	26	2	no	—
282	C₂²×C₈	—	26	1	no	—
283	C₂²×C₈	—	26	1	no	—
284	C₂×C₄²	—	13	1	no	—
285	C₂×C₄²	—	13	1	no	—
286	C₂×C₄²	—	13	1	no	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	—	13	1	no	—
290	C₂×C₄²	—	13	1	no	—
291	C₂×C₄²	—	13	1	no	—
292	C₂×C₄²	—	13	1	no	—
293	C₂×C₄²	—	13	1	no	—
294	C₂×C₄²	—	13	1	no	—
295	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	13	4	no	—
298	C₄⋊C₈	—	13	4	no	—
299	C₄⋊C₈	—	13	1	no	—
300	C₄⋊C₈	—	13	2	no	—
301	C₄⋊C₈	—	13	1	no	—
302	C₄⋊C₈	—	26	2	no	—
303	C₄⋊C₈	—	26	1	no	—
304	C₄⋊C₈	—	26	1	no	—
305	C₄⋊C₈	—	26	2	no	—
306	C₄⋊C₈	—	26	1	no	—
307	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
309	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	13	4	no	—
312	C₂²⋊C₈	—	13	4	no	—
313	C₂²⋊C₈	—	26	1	no	—
314	C₂²⋊C₈	—	26	1	no	—
315	C₂²⋊C₈	—	26	1	no	—
316	#97	—	2	1	no	—
317	#97	—	13	2	no	—
318	#97	—	26	1	no	—
319	#97	—	26	1	no	—
320	#97	—	26	1	no	—
321	#97	C₄×D₁₃	1	2	yes	—
322	C₄×C₈	—	13	2	no	—
323	C₄×C₈	C₂²×D₁₃	1	2	yes	—
324	C₂×C₁₃	—	4	1	no	—
325	C₂×C₁₃	#2905	1	1	yes	characteristic
326	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
327	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
328	D₁₃	—	2	2	no	—
329	D₁₃	—	2	2	no	—
330	C₂⁴	—	13	1	no	—
331	C₂²×C₄	—	13	1	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	1	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	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	—	26	2	no	—
347	C₂²×C₄	—	26	2	no	—
348	C₂²×C₄	—	52	2	no	—
349	C₂²×C₄	—	52	2	no	—
350	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
352	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
353	M₁₆	—	4	2	no	—
354	M₁₆	—	4	2	no	—
355	M₁₆	—	52	4	no	—
356	M₁₆	—	52	2	no	—
357	M₁₆	—	52	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	13	4	no	—
362	C₂×C₈	—	26	1	no	—
363	C₂×C₈	—	26	1	no	—
364	C₂×C₈	—	26	2	no	—
365	C₂×C₈	—	52	2	no	—
366	C₂×C₈	—	52	2	no	—
367	C₂×C₈	—	52	4	no	—
368	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
369	C₄²	—	13	1	no	—
370	C₄²	—	13	1	no	—
371	C₄²	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	1	no	—
374	C₄²	—	13	1	no	—
375	C₄²	—	13	1	no	—
376	C₄²	—	13	1	no	—
377	C₄²	—	13	1	no	—
378	C₄²	—	13	1	no	—
379	C₄²	—	13	1	no	—
380	C₄²	—	13	1	no	—
381	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
382	C₄²	D₄×D₁₃	1	1	yes	characteristic
383	C₄²	Q₈×D₁₃	1	1	yes	characteristic
384	C₄²	C₂³×D₁₃	1	1	yes	characteristic
385	C₁₃	#17822	1	1	yes	characteristic, complemented, Sylow
386	C₂³	—	13	1	no	—
387	C₂³	—	13	1	no	—
388	C₂³	—	26	2	no	—
389	C₂³	—	26	2	no	—
390	C₂³	—	52	1	no	—
391	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	2	no	—
398	C₂×C₄	—	13	2	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	1	no	—
401	C₂×C₄	—	13	1	no	—
402	C₂×C₄	—	13	1	no	—
403	C₂×C₄	—	13	1	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	26	2	no	—
406	C₂×C₄	—	26	2	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	26	2	no	—
409	C₂×C₄	—	26	2	no	—
410	C₂×C₄	—	26	2	no	—
411	C₂×C₄	—	26	1	no	—
412	C₂×C₄	—	26	1	no	—
413	C₂×C₄	—	52	1	no	—
414	C₂×C₄	—	52	1	no	—
415	C₂×C₄	—	52	1	no	—
416	C₂×C₄	—	52	1	no	—
417	C₂×C₄	—	52	1	no	—
418	C₂×C₄	—	52	1	no	—
419	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
420	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
421	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
425	C₈	—	2	4	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	2	no	—
428	C₈	—	4	1	no	—
429	C₈	—	26	4	no	—
430	C₈	—	52	1	no	—
431	C₈	—	52	2	no	—
432	C₈	—	52	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	13	2	no	—
437	C₂²	—	13	2	no	—
438	C₂²	—	26	1	no	—
439	C₂²	—	26	1	no	—
440	C₂²	—	26	1	no	—
441	C₂²	—	26	1	no	—
442	C₂²	—	52	4	no	—
443	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	13	2	no	—
449	C₄	—	26	1	no	—
450	C₄	—	26	1	no	—
451	C₄	—	26	1	no	—
452	C₄	—	26	1	no	—
453	C₄	—	26	1	no	—
454	C₄	#11719450	1	2	yes	—
455	C₄	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
456	C₄	D₁₃×#137	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	—	26	2	no	—
459	C₂	—	26	2	no	—
460	C₂	#13123398	1	1	yes	characteristic
461	C₂	D₁₃×#428	1	1	yes	characteristic
462	C₂	D₁₃×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1569	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1569	D₁₃
hypocenter	C₁₃	#17822
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
4. #13113620	C₂	semidirect
5. #13113618	C₂	semidirect
6. #13113609	C₂	semidirect
7. #13113605	C₂	semidirect
8. #13113604	C₂	semidirect
9. #13113603	C₂	semidirect
10. #13113601	C₂	semidirect
11. C₁₃×#1569	C₂	semidirect
39. C₁₃×#335	C₂²	semidirect
40. C₁₃×#334	C₂²	semidirect
41. #11718072	C₂²	semidirect
42. #11718072	C₂²	semidirect
43. #11718071	C₂²	semidirect
44. #11718071	C₂²	semidirect
45. #11718050	C₂²	semidirect
46. #11718049	C₂²	semidirect
165. #1569	D₁₃	semidirect
243. #335	C₂×D₁₃	semidirect
247. #334	C₂×D₁₃	semidirect
385. C₁₃	#17822	semidirect

Maximal subgroups

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

subgroup	index
#13123467	2
D₁₃×#432	2
D₁₃×#423	2
#13113620	2
#13113618	2
#13113609	2
#13113605	2
#13113604	2
#13113603	2
#13113601	2
C₁₃×#1569	2
#17822	13