Subgroups — #15832111

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123464	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718498	C₂	1	1	yes	maximal, characteristic
4	#13113622	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113621	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113619	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113609	C₂	1	2	yes	maximal, complemented
8	#13113605	C₂	1	2	yes	maximal, complemented
9	#13113602	C₂	1	2	yes	maximal, complemented
10	#13113600	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1573	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#6094	—	2	1	no	—
13	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#432	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×#88054	—	2	1	no	—
18	#11718587	C₂²	1	1	yes	characteristic
19	#11718586	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
21	#11718498	—	2	1	no	—
22	#11718498	—	2	1	no	—
23	#11718498	C₄	1	2	yes	—
24	#11718498	C₂²	1	2	yes	—
25	#11718498	C₂²	1	2	yes	—
26	#11718496	C₄	1	2	yes	—
27	#11718496	C₂²	1	1	yes	characteristic
28	#11718496	C₂²	1	1	yes	characteristic
29	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	#11718387	C₄	1	2	yes	—
32	D₁₃×C₂²⋊C₈	—	2	1	no	—
33	#11718380	—	2	1	no	—
34	#11718380	C₄	1	2	yes	—
35	#11718366	—	2	1	no	—
36	D₁₃×#97	—	2	1	no	—
37	C₄×#6094	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	C₂²×C₈×C₁₃	—	2	1	no	—
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
55	C₂²×#1055	—	2	1	no	—
56	C₂×#6094	—	2	2	no	—
57	C₂×#6094	—	2	2	no	—
58	C₂×#6094	—	4	4	no	—
59	C₂×#6094	C₂×C₄	1	4	yes	—
60	C₂×C₈×D₁₃	—	2	1	no	—
61	C₂×C₈×D₁₃	—	2	1	no	—
62	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₁₃	D₄	1	1	yes	characteristic
65	C₄²×D₁₃	D₄	1	1	yes	characteristic
66	C₄²×D₁₃	Q₈	1	1	yes	characteristic
67	C₄²×D₁₃	Q₈	1	1	yes	characteristic
68	C₄²×D₁₃	C₂³	1	1	yes	characteristic
69	C₄²×D₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊C₈	—	2	1	no	—
71	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
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×C₂²⋊C₈	C₂×C₄	1	2	yes	—
77	C₁₃×#97	—	2	1	no	—
78	C₄×C₈×C₁₃	C₂³	1	2	yes	—
79	C₂²⋊#1055	—	2	1	no	—
80	C₂²⋊#1055	C₂×C₄	1	2	yes	—
81	#88060	—	2	1	no	—
82	#88060	—	2	1	no	—
83	#88060	C₂×C₄	1	4	yes	—
84	#88055	—	2	1	no	—
85	#88055	—	2	1	no	—
86	#88055	C₂×C₄	1	4	yes	—
87	#88054	—	2	1	no	—
88	#88054	—	2	1	no	—
89	#88054	—	2	2	no	—
90	#88054	—	2	2	no	—
91	#88054	C₂×C₄	1	4	yes	—
92	C₄⋊#1055	—	2	1	no	—
93	C₄⋊#1055	C₂×C₄	1	2	yes	—
94	C₄⋊#1055	C₂³	1	1	yes	characteristic
95	C₄⋊#1055	C₂³	1	1	yes	characteristic
96	C₄⋊#1055	C₂³	1	2	yes	—
97	#88043	—	2	1	no	—
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	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	4	2	no	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
128	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
131	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₄×Dic₁₃	C₄⋊C₄	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	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
143	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
144	C₂×#1055	—	2	1	no	—
145	C₂×#1055	—	2	1	no	—
146	C₂×#1055	—	2	2	no	—
147	C₂×#1055	—	4	2	no	—
148	C₂×#1055	C₂²×C₄	1	4	yes	—
149	#6094	—	4	4	no	—
150	#6094	—	4	4	no	—
151	#6094	—	4	4	no	—
152	C₈×D₁₃	—	4	2	no	—
153	C₈×D₁₃	—	4	2	no	—
154	#2920	—	13	1	no	—
155	C₂×#432	—	13	1	no	—
156	C₂×#423	—	13	1	no	—
157	#1573	—	13	1	no	—
158	#1573	—	13	1	no	—
159	#1573	—	13	1	no	—
160	#1573	D₁₃	1	1	yes	characteristic, complemented
161	#1571	—	13	2	no	—
162	#1570	—	13	2	no	—
163	#1569	—	13	2	no	—
164	#1569	—	13	2	no	—
165	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂²×D₁₃	—	2	2	no	—
167	C₂²×D₁₃	—	2	2	no	—
168	C₂²×D₁₃	—	4	1	no	—
169	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	—	2	2	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	—	2	2	no	—
183	C₂×Dic₁₃	—	4	1	no	—
184	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₄×D₁₃	—	2	2	no	—
191	C₄×D₁₃	—	2	2	no	—
192	C₄×D₁₃	—	2	2	no	—
193	C₄×D₁₃	—	2	1	no	—
194	C₄×D₁₃	—	2	1	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	—	4	1	no	—
197	C₄×D₁₃	—	4	1	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	AGL(1,ℤ/8)	1	2	yes	—
203	C₄×D₁₃	#137	1	2	yes	—
204	C₈×C₁₃	—	2	4	no	—
205	C₈×C₁₃	—	4	1	no	—
206	C₈×C₁₃	—	4	2	no	—
207	C₈×C₁₃	—	4	1	no	—
208	#1055	—	2	4	no	—
209	#1055	—	4	1	no	—
210	#1055	—	4	2	no	—
211	#1055	—	4	1	no	—
212	C₂²×M₁₆	—	26	1	no	—
213	C₂²×C₄²	—	13	1	no	—
214	#432	—	13	2	no	—
215	#432	—	13	2	no	—
216	#432	—	13	1	no	—
217	#432	—	13	1	no	—
218	#432	—	13	1	no	—
219	#432	—	26	1	no	—
220	#432	—	26	1	no	—
221	#432	C₂×D₁₃	1	1	yes	characteristic
222	#431	—	13	1	no	—
223	#431	—	13	2	no	—
224	#431	C₂×D₁₃	1	1	yes	characteristic
225	#423	—	13	2	no	—
226	#423	—	13	2	no	—
227	#423	—	13	2	no	—
228	#423	—	26	1	no	—
229	#423	—	26	1	no	—
230	C₂×C₄⋊C₈	—	13	1	no	—
231	C₂×C₄⋊C₈	—	13	1	no	—
232	C₂×C₄⋊C₈	—	13	1	no	—
233	C₂×C₄⋊C₈	—	26	1	no	—
234	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
235	#407	—	13	2	no	—
236	C₂×C₂²⋊C₈	—	26	1	no	—
237	C₄×M₁₆	—	13	2	no	—
238	C₂×#97	—	26	1	no	—
239	#335	—	13	2	no	—
240	#335	—	13	2	no	—
241	#335	—	13	2	no	—
242	#335	C₂×D₁₃	1	2	yes	complemented
243	#334	—	13	2	no	—
244	#334	—	13	2	no	—
245	#334	—	13	2	no	—
246	#334	C₂×D₁₃	1	2	yes	complemented
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	2	1	no	—
249	C₂²×C₁₃	#430	1	2	yes	—
250	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
251	C₂×D₁₃	—	2	1	no	—
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	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	2	1	no	—
262	C₄×C₁₃	#568	1	2	yes	—
263	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
264	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
265	Dic₁₃	—	2	1	no	—
266	Dic₁₃	—	2	1	no	—
267	Dic₁₃	—	2	1	no	—
268	Dic₁₃	—	2	1	no	—
269	Dic₁₃	—	2	1	no	—
270	Dic₁₃	#428	1	2	yes	—
271	C₂³×C₄	—	13	1	no	—
272	C₂³×C₄	—	13	1	no	—
273	C₂³×C₄	—	13	1	no	—
274	C₂×M₁₆	—	13	4	no	—
275	C₂×M₁₆	—	26	2	no	—
276	C₂×M₁₆	—	26	2	no	—
277	C₂×M₁₆	—	52	4	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	26	1	no	—
280	C₂²×C₈	—	26	1	no	—
281	C₂²×C₈	—	26	1	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	—	13	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	C₂²×D₁₃	1	1	yes	characteristic
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	13	4	no	—
296	C₄⋊C₈	—	13	2	no	—
297	C₄⋊C₈	—	13	1	no	—
298	C₄⋊C₈	—	13	2	no	—
299	C₄⋊C₈	—	13	1	no	—
300	C₄⋊C₈	—	26	1	no	—
301	C₄⋊C₈	—	26	1	no	—
302	C₄⋊C₈	—	26	2	no	—
303	C₄⋊C₈	—	26	2	no	—
304	C₄⋊C₈	—	26	1	no	—
305	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
306	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
307	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
308	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
309	C₂²⋊C₈	—	2	1	no	—
310	C₂²⋊C₈	—	13	2	no	—
311	C₂²⋊C₈	—	13	4	no	—
312	C₂²⋊C₈	—	26	1	no	—
313	C₂²⋊C₈	—	26	1	no	—
314	C₂²⋊C₈	—	26	1	no	—
315	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
316	#97	—	2	1	no	—
317	#97	—	13	4	no	—
318	#97	—	26	1	no	—
319	#97	—	26	1	no	—
320	#97	—	26	1	no	—
321	C₄×C₈	—	13	2	no	—
322	C₄×C₈	C₂²×D₁₃	1	2	yes	—
323	C₂×C₁₃	—	2	2	no	—
324	C₂×C₁₃	#2905	1	1	yes	characteristic
325	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
326	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
327	D₁₃	—	2	2	no	—
328	D₁₃	—	4	1	no	—
329	C₂⁴	—	13	1	no	—
330	C₂²×C₄	—	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	—	26	2	no	—
346	C₂²×C₄	—	26	2	no	—
347	C₂²×C₄	—	52	2	no	—
348	C₂²×C₄	—	52	2	no	—
349	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
351	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
352	M₁₆	—	52	4	no	—
353	M₁₆	—	52	4	no	—
354	M₁₆	—	52	4	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	2	no	—
359	C₂×C₈	—	13	4	no	—
360	C₂×C₈	—	26	1	no	—
361	C₂×C₈	—	26	1	no	—
362	C₂×C₈	—	26	2	no	—
363	C₂×C₈	—	52	2	no	—
364	C₂×C₈	—	52	2	no	—
365	C₂×C₈	—	52	2	no	—
366	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
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	C₂×C₄×D₁₃	1	1	yes	characteristic
380	C₄²	D₄×D₁₃	1	1	yes	characteristic
381	C₄²	Q₈×D₁₃	1	1	yes	characteristic
382	C₄²	C₂³×D₁₃	1	1	yes	characteristic
383	C₁₃	#17822	1	1	yes	characteristic, complemented, Sylow
384	C₂³	—	13	1	no	—
385	C₂³	—	13	1	no	—
386	C₂³	—	26	2	no	—
387	C₂³	—	26	2	no	—
388	C₂³	—	52	1	no	—
389	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	2	no	—
396	C₂×C₄	—	13	2	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	1	no	—
401	C₂×C₄	—	13	1	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	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	1	no	—
409	C₂×C₄	—	26	1	no	—
410	C₂×C₄	—	52	1	no	—
411	C₂×C₄	—	52	1	no	—
412	C₂×C₄	—	52	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	C₄⋊C₄×D₁₃	1	1	yes	characteristic
418	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
419	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
421	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	1	no	—
427	C₈	—	26	4	no	—
428	C₈	—	52	1	no	—
429	C₈	—	52	2	no	—
430	C₈	—	52	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	13	2	no	—
434	C₂²	—	26	1	no	—
435	C₂²	—	26	1	no	—
436	C₂²	—	26	1	no	—
437	C₂²	—	26	1	no	—
438	C₂²	—	26	1	no	—
439	C₂²	—	52	4	no	—
440	C₂²	#11718554	1	2	yes	—
441	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	13	2	no	—
447	C₄	—	26	1	no	—
448	C₄	—	26	1	no	—
449	C₄	—	26	1	no	—
450	C₄	—	26	1	no	—
451	C₄	—	26	1	no	—
452	C₄	#11719455	1	2	yes	—
453	C₄	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
454	C₄	D₁₃×#137	1	1	yes	characteristic
455	C₂	—	2	2	no	—
456	C₂	—	26	2	no	—
457	C₂	—	52	1	no	—
458	C₂	#13123397	1	1	yes	characteristic
459	C₂	D₁₃×#428	1	1	yes	characteristic
460	C₂	C₂×#11718554	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×#1573	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1573	D₁₃
hypocenter	C₁₃	#17822
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
4. #13113622	C₂	semidirect
5. #13113621	C₂	semidirect
6. #13113619	C₂	semidirect
7. #13113609	C₂	semidirect
8. #13113605	C₂	semidirect
9. #13113602	C₂	semidirect
10. #13113600	C₂	semidirect
11. C₁₃×#1573	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
160. #1573	D₁₃	semidirect
242. #335	C₂×D₁₃	semidirect
246. #334	C₂×D₁₃	semidirect
383. C₁₃	#17822	semidirect

Maximal subgroups

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

subgroup	index
#13123464	2
D₁₃×#432	2
C₂×#11718498	2
#13113622	2
#13113621	2
#13113619	2
#13113609	2
#13113605	2
#13113602	2
#13113600	2
C₁₃×#1573	2
#17822	13