Subgroups — #15832953

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124901	C₂	1	1	yes	maximal, characteristic
2	C₈×#6127	C₂	1	1	yes	maximal, characteristic
3	#13113684	C₂	1	2	yes	maximal, complemented
4	#13113670	C₂	1	2	yes	maximal, complemented
5	#13113653	C₂	1	2	yes	maximal, complemented
6	#13113646	C₂	1	2	yes	maximal, complemented
7	#13113627	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113273	C₂	1	1	yes	maximal, characteristic
9	#13113257	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₄×#6127	C₂²	1	1	yes	characteristic
14	C₁₃×#446	—	2	1	no	—
15	C₁₃×#446	C₂²	1	2	yes	—
16	C₈×Q₈×C₁₃	—	2	1	no	—
17	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#424	—	2	1	no	—
19	C₁₃×#423	C₂²	1	1	yes	characteristic
20	C₁₃×#405	—	2	1	no	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₁₃	—	2	1	no	—
23	C₈×C₂²⋊D₁₃	—	2	1	no	—
24	#11718755	C₄	1	1	yes	characteristic
25	#11718751	C₄	1	1	yes	characteristic
26	#11718748	C₄	1	1	yes	characteristic
27	#11718744	C₄	1	1	yes	characteristic
28	#11718708	C₄	1	2	yes	—
29	#11718706	C₄	1	2	yes	—
30	C₄×#6107	C₂²	1	2	yes	—
31	C₄×#6106	C₂²	1	2	yes	—
32	#11718586	C₂²	1	1	yes	characteristic
33	#11718586	C₂²	1	1	yes	characteristic
34	C₄×#6099	C₂²	1	1	yes	characteristic
35	C₈×D₅₂	C₂²	1	1	yes	characteristic
36	C₈×D₅₂	C₂²	1	1	yes	characteristic
37	#11718346	—	2	1	no	—
38	C₄×C₈×D₁₃	—	2	1	no	—
39	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
40	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
41	Q₈⋊#1055	C₂²	1	2	yes	—
42	Q₈⋊#1055	C₂²	1	2	yes	—
43	#11718076	C₂²	1	2	yes	—
44	#11718075	C₂²	1	2	yes	—
45	#11718072	C₂²	1	2	yes	—
46	#11718071	C₂²	1	2	yes	—
47	#11718047	C₂²	1	2	yes	—
48	#11718046	C₂²	1	2	yes	—
49	C₂×#6127	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#125	—	2	1	no	—
56	C₁₃×C₂²⋊Q₈	—	2	1	no	—
57	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
58	C₄×Q₈×C₁₃	—	2	1	no	—
59	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₁₃×#117	—	2	1	no	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×#6107	C₂×C₄	1	2	yes	—
63	C₂×#6106	C₂×C₄	1	2	yes	—
64	C₄×C₂²⋊D₁₃	—	2	1	no	—
65	C₄×C₂²⋊D₁₃	—	2	1	no	—
66	#88180	C₂×C₄	1	1	yes	characteristic
67	C₂×#6099	—	2	1	no	—
68	C₂×C₈×D₁₃	—	2	1	no	—
69	C₂×C₈×D₁₃	—	2	1	no	—
70	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
71	C₄×D₅₂	C₂³	1	1	yes	characteristic
72	#88126	—	2	1	no	—
73	C₄²×D₁₃	—	2	1	no	—
74	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	1	no	—
79	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₃×#97	—	2	2	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	#88075	C₂×C₄	1	2	yes	—
87	#88075	C₂×C₄	1	2	yes	—
88	C₂²⋊#1055	—	2	1	no	—
89	C₂²⋊#1055	C₂×C₄	1	2	yes	—
90	#88060	—	2	1	no	—
91	#88060	—	2	1	no	—
92	#88054	—	2	1	no	—
93	#88054	—	2	1	no	—
94	C₈×Dic₁₃	—	2	1	no	—
95	C₈×Dic₁₃	—	2	1	no	—
96	#88050	C₂×C₄	1	2	yes	—
97	#88049	C₂×C₄	1	2	yes	—
98	#88048	C₂×C₄	1	2	yes	—
99	#88047	C₂×C₄	1	2	yes	—
100	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
101	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
102	C₄⋊#1055	C₂³	1	1	yes	characteristic
103	C₄⋊#1055	C₂³	1	1	yes	characteristic
104	#88043	—	2	1	no	—
105	C₄×#1055	—	2	1	no	—
106	C₄×#1055	C₂³	1	2	yes	—
107	C₄×#1055	C₂³	1	2	yes	—
108	#17916	—	13	1	no	maximal, Sylow
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₁₃	—	2	1	no	—
115	#6127	—	2	2	no	—
116	#6127	—	2	2	no	—
117	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	—	2	1	no	—
119	C₂×C₄×D₁₃	—	2	1	no	—
120	C₂×C₄×D₁₃	—	2	1	no	—
121	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
122	C₁₃×M₁₆	—	4	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	4	1	no	—
126	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
136	C₁₃×C₂²⋊C₄	—	2	2	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	#41	1	1	yes	characteristic
141	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂²⋊Dic₁₃	—	2	1	no	—
143	#6107	—	2	4	no	—
144	#6106	—	2	4	no	—
145	#6103	—	2	1	no	—
146	#6103	—	2	1	no	—
147	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
149	#6101	—	2	1	no	—
150	#6101	—	2	1	no	—
151	C₄×Dic₁₃	—	2	1	no	—
152	C₄×Dic₁₃	—	2	1	no	—
153	C₄×Dic₁₃	—	2	1	no	—
154	#6099	—	4	2	no	—
155	C₂×#1055	—	2	1	no	—
156	C₂×#1055	—	2	1	no	—
157	C₂×#1055	—	2	2	no	—
158	C₂×#1055	C₂²×C₄	1	2	yes	—
159	C₂×#1055	C₂²×C₄	1	2	yes	—
160	C₈×D₁₃	—	4	2	no	—
161	C₈×D₁₃	—	4	2	no	—
162	#3107	—	13	1	no	—
163	C₈×#41	—	13	1	no	—
164	#2960	D₁₃	1	1	yes	characteristic, complemented
165	#1584	—	13	2	no	—
166	#1582	—	13	2	no	—
167	#1579	—	13	2	no	—
168	SD₁₆⋊C₈	—	13	2	no	—
169	#1574	—	13	1	no	—
170	#1489	—	13	1	no	—
171	#1485	—	13	1	no	—
172	#1451	—	13	1	no	—
173	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
174	C₂²×D₁₃	—	2	1	no	—
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₂²⋊D₁₃	—	2	4	no	—
192	C₂×Dic₁₃	—	2	1	no	—
193	C₂×Dic₁₃	—	2	1	no	—
194	C₂×Dic₁₃	—	2	1	no	—
195	D₅₂	—	2	1	no	—
196	D₅₂	#131	1	2	yes	—
197	C₄×D₁₃	—	2	4	no	—
198	C₄×D₁₃	—	4	1	no	—
199	C₄×D₁₃	—	4	1	no	—
200	C₄×D₁₃	—	4	2	no	—
201	Dic₂₆	—	2	1	no	—
202	Dic₂₆	#131	1	2	yes	—
203	C₈×C₁₃	—	2	1	no	—
204	C₈×C₁₃	—	2	1	no	—
205	C₈×C₁₃	—	2	1	no	—
206	C₈×C₁₃	—	4	2	no	—
207	C₈×C₁₃	#137	1	2	yes	—
208	#1055	—	2	2	no	—
209	#1055	—	2	2	no	—
210	#1055	—	4	2	no	—
211	#1055	—	4	1	no	—
212	#1055	—	4	1	no	—
213	#533	C₂×D₁₃	1	1	yes	characteristic
214	C₄×#41	—	13	1	no	—
215	#485	—	13	2	no	—
216	#475	—	13	1	no	—
217	#474	—	13	1	no	—
218	#462	—	13	1	no	—
219	#461	—	13	1	no	—
220	#452	—	13	2	no	—
221	#446	—	2	1	no	—
222	#446	C₂×D₁₃	1	2	yes	—
223	C₈×Q₈	—	2	1	no	—
224	C₈×Q₈	—	13	1	no	—
225	C₈×Q₈	—	13	1	no	—
226	C₈×Q₈	C₂×D₁₃	1	2	yes	—
227	C₄×Q₁₆	—	13	2	no	—
228	C₄×SD₁₆	—	13	2	no	—
229	C₈×D₄	—	13	1	no	—
230	C₈×D₄	—	13	1	no	—
231	C₈×D₄	—	26	1	no	—
232	C₈×D₄	—	26	1	no	—
233	#431	—	13	1	no	—
234	#431	—	13	1	no	—
235	#431	—	26	1	no	—
236	#424	—	2	1	no	—
237	#423	C₂×D₁₃	1	1	yes	characteristic
238	#405	—	2	1	no	—
239	C₄×M₁₆	—	13	1	no	—
240	C₂×C₄×C₈	—	26	1	no	—
241	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
242	#335	—	13	2	no	—
243	#334	—	13	2	no	—
244	Q₈⋊C₈	—	13	2	no	—
245	Q₈⋊C₈	—	13	2	no	—
246	Q₈⋊C₈	—	13	2	no	—
247	D₄⋊C₈	—	13	2	no	—
248	#322	—	13	2	no	—
249	#322	—	13	2	no	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	1	no	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂×D₁₃	—	2	2	no	—
255	C₂×D₁₃	—	4	1	no	—
256	C₂×D₁₃	—	4	1	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	#444	1	2	yes	—
263	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
264	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
265	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
266	C₄×C₁₃	#575	1	1	yes	characteristic
267	Dic₁₃	—	2	2	no	—
268	Dic₁₃	—	4	1	no	—
269	Dic₁₃	—	4	1	no	—
270	C₂×#41	—	13	1	no	—
271	C₂×Q₁₆	—	13	2	no	—
272	C₂×SD₁₆	—	13	2	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	26	1	no	—
275	C₂²×C₈	—	26	1	no	—
276	C₂²×C₈	—	26	1	no	—
277	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
278	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
279	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
280	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
281	#125	—	2	1	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	C₂²⋊Q₈	C₄×D₁₃	1	2	yes	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	—	13	1	no	—
286	C₄×Q₈	—	13	1	no	—
287	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
288	C₄×D₄	—	13	1	no	—
289	C₄×D₄	—	13	1	no	—
290	C₄×D₄	—	26	1	no	—
291	C₄×D₄	—	26	1	no	—
292	#117	—	2	1	no	—
293	#117	—	13	1	no	—
294	#117	—	26	1	no	—
295	C₂×C₄²	—	26	1	no	—
296	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
297	#107	—	13	2	no	—
298	#106	—	13	2	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	13	1	no	—
303	C₄⋊C₈	—	13	1	no	—
304	C₄⋊C₈	—	13	1	no	—
305	C₄⋊C₈	—	13	1	no	—
306	C₄⋊C₈	—	26	1	no	—
307	C₄⋊C₈	—	26	1	no	—
308	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
309	#103	—	13	2	no	—
310	#103	—	13	2	no	—
311	#103	—	13	2	no	—
312	#102	—	13	2	no	—
313	C₂²⋊C₈	—	13	2	no	—
314	C₂²⋊C₈	—	26	1	no	—
315	C₂²⋊C₈	—	26	1	no	—
316	C₂²⋊C₈	—	26	1	no	—
317	#97	—	2	2	no	—
318	#97	—	26	1	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	13	2	no	—
321	C₄×C₈	—	13	2	no	—
322	C₄×C₈	—	26	1	no	—
323	C₄×C₈	—	26	1	no	—
324	C₄×C₈	—	26	1	no	—
325	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
326	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
327	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
329	C₂×C₁₃	—	4	1	no	—
330	C₂×C₁₃	#2929	1	1	yes	characteristic
331	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
332	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
333	D₁₃	—	4	2	no	—
334	#41	—	26	2	no	—
335	#41	—	26	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	13	1	no	—
338	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
339	C₂×D₄	—	13	1	no	—
340	C₂×D₄	—	26	1	no	—
341	C₂²×C₄	—	26	1	no	—
342	C₂²×C₄	—	26	1	no	—
343	C₂²×C₄	—	26	1	no	—
344	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
345	C₂²×C₄	#6127	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
347	Q₁₆	—	26	4	no	—
348	SD₁₆	—	26	4	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	52	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	13	2	no	—
355	C₂×C₈	—	13	2	no	—
356	C₂×C₈	—	26	2	no	—
357	C₂×C₈	—	26	1	no	—
358	C₂×C₈	—	26	1	no	—
359	C₂×C₈	—	52	2	no	—
360	C₂×C₈	—	52	2	no	—
361	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
362	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
363	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
364	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	13	1	no	—
371	C₄⋊C₄	—	13	1	no	—
372	C₄⋊C₄	—	26	1	no	—
373	C₄⋊C₄	—	26	1	no	—
374	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	26	1	no	—
377	C₂²⋊C₄	—	26	1	no	—
378	C₂²⋊C₄	—	26	1	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	26	1	no	—
381	C₄²	—	26	1	no	—
382	C₄²	—	26	1	no	—
383	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
384	C₄²	#6127	1	1	yes	characteristic
385	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
386	C₄²	C₂³×D₁₃	1	1	yes	characteristic
387	C₁₃	#17916	1	1	yes	characteristic, complemented, Sylow
388	C₂³	—	26	1	no	—
389	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	13	2	no	—
394	Q₈	—	26	1	no	—
395	D₄	—	13	2	no	—
396	D₄	—	26	4	no	—
397	D₄	—	26	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	26	4	no	—
406	C₂×C₄	—	26	1	no	—
407	C₂×C₄	—	26	1	no	—
408	C₂×C₄	—	26	1	no	—
409	C₂×C₄	—	52	1	no	—
410	C₂×C₄	—	52	1	no	—
411	C₂×C₄	—	52	2	no	—
412	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
413	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
414	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂×#6127	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	26	2	no	—
423	C₈	—	26	2	no	—
424	C₈	—	52	2	no	—
425	C₈	—	52	1	no	—
426	C₈	—	52	1	no	—
427	C₈	#88196	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	26	2	no	—
432	C₂²	—	52	1	no	—
433	C₂²	—	52	1	no	—
434	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	26	2	no	—
441	C₄	—	52	1	no	—
442	C₄	—	52	1	no	—
443	C₄	#11718806	1	2	yes	—
444	C₄	D₁₃×#131	1	1	yes	characteristic
445	C₄	D₁₃×#131	1	1	yes	characteristic
446	C₄	C₂×#88196	1	1	yes	characteristic
447	C₄	#11719527	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	52	2	no	—
450	C₂	#13123528	1	1	yes	characteristic
451	C₂	C₄×#88196	1	1	yes	characteristic
452	C₂	C₂×#11718806	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2960	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2960	D₁₃
hypocenter	C₁₃	#17916
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #13113684	C₂	semidirect
4. #13113670	C₂	semidirect
5. #13113653	C₂	semidirect
6. #13113646	C₂	semidirect
7. #13113627	C₂	semidirect
9. #13113257	C₂	semidirect
10. #13113125	C₂	semidirect
11. C₁₃×#2960	C₂	semidirect
164. #2960	D₁₃	semidirect
387. C₁₃	#17916	semidirect

Maximal subgroups

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

subgroup	index
#13124901	2
C₈×#6127	2
#13113684	2
#13113670	2
#13113653	2
#13113646	2
#13113627	2
#13113273	2
#13113257	2
#13113125	2
C₁₃×#2960	2
#17916	13