Subgroups — #13129279

Order 1664.

1004 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719522	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719521	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88198	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719440	C₂	1	2	yes	maximal, complemented
7	#11719434	C₂	1	2	yes	maximal, complemented
8	#11719429	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719426	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719351	C₂	1	2	yes	maximal, complemented
11	#11719350	C₂	1	2	yes	maximal, complemented
12	#11719345	C₂	1	2	yes	maximal, complemented
13	#11719341	C₂	1	2	yes	maximal, complemented
14	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719336	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719330	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719329	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719288	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719269	C₂	1	2	yes	maximal, complemented
21	#11719257	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719245	C₂	1	2	yes	maximal, complemented
23	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×#6131	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
28	C₂×#6127	C₂²	1	1	yes	characteristic
29	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
32	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	#88201	C₂²	1	1	yes	characteristic
40	#88201	C₂²	1	2	yes	—
41	#88201	C₂²	1	1	yes	characteristic
42	#88200	C₂²	1	2	yes	—
43	#88200	C₂²	1	2	yes	—
44	#88200	C₂²	1	2	yes	—
45	#88200	C₂²	1	2	yes	—
46	#88200	C₂²	1	1	yes	characteristic
47	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
48	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
49	#88198	C₂²	1	1	yes	characteristic
50	#88198	C₂²	1	1	yes	characteristic
51	#88198	C₂²	1	1	yes	characteristic
52	#88198	C₂²	1	2	yes	—
53	#88198	C₂²	1	2	yes	—
54	#88198	C₂²	1	2	yes	—
55	#88198	C₂²	1	1	yes	characteristic
56	#88198	C₂²	1	1	yes	characteristic
57	#88193	C₂²	1	1	yes	characteristic
58	#88193	C₂²	1	2	yes	—
59	#88189	C₂²	1	1	yes	characteristic
60	#88184	C₂²	1	2	yes	—
61	#88184	C₂²	1	1	yes	characteristic
62	#88183	C₂²	1	2	yes	—
63	#88183	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
67	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
68	#88180	C₂²	1	1	yes	characteristic
69	#88178	C₂²	1	1	yes	characteristic
70	#88178	C₂²	1	2	yes	—
71	C₂×#6101	C₂²	1	2	yes	—
72	C₂×#6101	C₂²	1	2	yes	—
73	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
74	#88152	C₂²	1	1	yes	characteristic
75	#88152	C₂²	1	2	yes	—
76	#88152	C₂²	1	2	yes	—
77	#88152	C₂²	1	2	yes	—
78	#88151	C₂²	1	1	yes	characteristic
79	#88150	C₂²	1	2	yes	—
80	#88150	C₂²	1	2	yes	—
81	#88150	C₂²	1	2	yes	—
82	#88150	C₂²	1	2	yes	—
83	#88150	C₂²	1	2	yes	—
84	#88148	C₂²	1	2	yes	—
85	#88148	C₂²	1	2	yes	—
86	#88148	C₂²	1	2	yes	—
87	#88147	C₂²	1	1	yes	characteristic
88	#88146	C₂²	1	2	yes	—
89	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
90	#88144	C₂²	1	2	yes	—
91	#88144	C₂²	1	2	yes	—
92	#88144	C₂²	1	1	yes	characteristic
93	#88143	C₂²	1	2	yes	—
94	#88143	C₂²	1	2	yes	—
95	#88143	C₂²	1	1	yes	characteristic
96	#88143	C₂²	1	2	yes	—
97	#88143	C₂²	1	2	yes	—
98	#88142	C₂²	1	2	yes	—
99	#88141	C₂²	1	2	yes	—
100	#88141	C₂²	1	1	yes	characteristic
101	#88140	C₂²	1	1	yes	characteristic
102	#88140	C₂²	1	2	yes	—
103	#88139	C₂²	1	1	yes	characteristic
104	#88139	C₂²	1	2	yes	—
105	#88138	C₂²	1	2	yes	—
106	#88137	C₂²	1	2	yes	—
107	#88135	C₂²	1	2	yes	—
108	#88135	C₂²	1	2	yes	—
109	#88135	C₂²	1	2	yes	—
110	#88133	C₂²	1	1	yes	characteristic
111	#88133	C₂²	1	2	yes	—
112	#88133	C₂²	1	2	yes	—
113	#88132	C₂²	1	1	yes	characteristic
114	#88132	C₂²	1	2	yes	—
115	#88130	C₂²	1	2	yes	—
116	#88130	C₂²	1	2	yes	—
117	#88129	C₂²	1	1	yes	characteristic
118	#88126	C₂²	1	1	yes	characteristic
119	#88126	C₂²	1	2	yes	—
120	#88124	C₂²	1	2	yes	—
121	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₁₃	—	4	2	no	—
124	C₂×Q₈×C₁₃	—	4	2	no	—
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
129	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
130	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
139	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₃	C₂³	1	2	yes	—
142	#6131	—	4	2	no	—
143	Q₈×D₁₃	—	4	2	no	—
144	#6127	—	4	2	no	—
145	C₂×D₅₂	C₂³	1	1	yes	characteristic
146	C₂×D₅₂	C₂³	1	2	yes	—
147	C₂×C₄×D₁₃	C₂³	1	2	yes	—
148	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₃	C₂³	1	2	yes	—
150	C₂×C₄×D₁₃	C₂³	1	2	yes	—
151	C₂×C₄×D₁₃	C₂³	1	2	yes	—
152	C₂×Dic₂₆	—	4	2	no	—
153	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
154	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
155	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
156	C₂×Dic₂₆	C₂³	1	2	yes	—
157	C₂×Dic₂₆	C₂³	1	2	yes	—
158	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
176	#6103	C₂³	1	2	yes	—
177	#6103	C₂³	1	1	yes	characteristic
178	#6103	C₂³	1	1	yes	characteristic
179	#6103	C₂³	1	2	yes	—
180	#6103	C₂³	1	2	yes	—
181	#6103	C₂³	1	2	yes	—
182	#6103	C₂³	1	2	yes	—
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	2	yes	—
185	#6103	C₂³	1	2	yes	—
186	#6103	C₂³	1	2	yes	—
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	2	yes	—
189	#6103	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₃	C₂³	1	2	yes	—
193	C₄⋊Dic₁₃	C₂³	1	2	yes	—
194	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₃	C₂³	1	2	yes	—
196	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₃	C₂³	1	2	yes	—
198	#6101	C₂³	1	2	yes	—
199	#6101	C₂³	1	1	yes	characteristic
200	#6101	C₂³	1	1	yes	characteristic
201	#6101	C₂³	1	1	yes	characteristic
202	#6101	C₂³	1	2	yes	—
203	#6101	C₂³	1	2	yes	—
204	#6101	C₂³	1	1	yes	characteristic
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	2	yes	—
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	1	yes	characteristic
212	#6101	C₂³	1	1	yes	characteristic
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	C₄×Dic₁₃	C₂³	1	2	yes	—
220	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
228	#3552	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₃	C₂⁴	1	2	yes	—
233	Q₈×C₁₃	—	2	2	no	—
234	Q₈×C₁₃	—	2	2	no	—
235	Q₈×C₁₃	—	2	2	no	—
236	Q₈×C₁₃	—	4	2	no	—
237	Q₈×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₁₃	—	2	4	no	—
253	C₂²⋊D₁₃	—	2	2	no	—
254	C₂²⋊D₁₃	—	2	2	no	—
255	C₂²⋊D₁₃	—	4	2	no	—
256	C₂×Dic₁₃	—	2	2	no	—
257	C₂×Dic₁₃	—	2	2	no	—
258	C₂×Dic₁₃	—	4	2	no	—
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃	C₂⁴	1	2	yes	—
261	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₃	C₂⁴	1	2	yes	—
266	C₂×Dic₁₃	C₂⁴	1	2	yes	—
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	D₅₂	—	2	2	no	—
270	D₅₂	—	4	2	no	—
271	C₄×D₁₃	—	2	2	no	—
272	C₄×D₁₃	—	2	4	no	—
273	C₄×D₁₃	—	4	2	no	—
274	C₄×D₁₃	—	4	2	no	—
275	C₄×D₁₃	—	4	2	no	—
276	Dic₂₆	—	2	2	no	—
277	Dic₂₆	—	2	2	no	—
278	Dic₂₆	—	2	2	no	—
279	Dic₂₆	—	4	2	no	—
280	Dic₂₆	—	4	2	no	—
281	#563	—	13	2	no	—
282	#563	—	13	2	no	—
283	#557	—	13	1	no	—
284	#556	—	13	1	no	—
285	#554	—	13	2	no	—
286	#553	—	13	2	no	—
287	D₄×Q₈	—	13	1	no	—
288	D₄×Q₈	—	13	1	no	—
289	D₄×Q₈	D₁₃	1	1	yes	characteristic, complemented
290	#548	—	13	1	no	—
291	#548	—	13	1	no	—
292	#547	—	13	1	no	—
293	#544	—	13	2	no	—
294	#542	—	13	2	no	—
295	#541	—	13	1	no	—
296	#541	—	13	1	no	—
297	#539	—	13	2	no	—
298	#539	—	13	2	no	—
299	#536	—	13	1	no	—
300	#536	—	13	1	no	—
301	C₂×C₄⋊Q₈	—	13	1	no	—
302	#529	—	13	1	no	—
303	#529	—	13	1	no	—
304	C₂²×C₁₃	—	2	1	no	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	—	2	1	no	—
307	C₂²×C₁₃	—	2	1	no	—
308	C₂²×C₁₃	—	2	1	no	—
309	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
310	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
311	C₂×D₁₃	—	2	1	no	—
312	C₂×D₁₃	—	2	2	no	—
313	C₂×D₁₃	—	2	2	no	—
314	C₂×D₁₃	—	2	1	no	—
315	C₂×D₁₃	—	2	2	no	—
316	C₂×D₁₃	—	2	1	no	—
317	C₄×C₁₃	—	2	1	no	—
318	C₄×C₁₃	—	2	2	no	—
319	C₄×C₁₃	—	2	1	no	—
320	C₄×C₁₃	—	2	2	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	—	2	2	no	—
324	C₄×C₁₃	—	2	1	no	—
325	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
326	Dic₁₃	—	2	2	no	—
327	Dic₁₃	—	2	2	no	—
328	Dic₁₃	—	2	1	no	—
329	Dic₁₃	—	2	1	no	—
330	Dic₁₃	—	2	1	no	—
331	Dic₁₃	—	2	1	no	—
332	Dic₁₃	—	2	1	no	—
333	Dic₁₃	—	2	2	no	—
334	Dic₁₃	—	2	1	no	—
335	Dic₁₃	2₋¹⁺⁴	1	2	yes	—
336	C₂×#41	—	13	1	no	—
337	C₂×#41	—	13	1	no	—
338	C₂²×Q₈	—	13	1	no	—
339	C₂²×Q₈	—	13	1	no	—
340	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic
341	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic
342	C₄⋊Q₈	—	13	1	no	—
343	C₄⋊Q₈	—	13	1	no	—
344	C₄⋊Q₈	—	13	2	no	—
345	C₄⋊Q₈	—	13	1	no	—
346	C₄⋊Q₈	—	13	1	no	—
347	C₄⋊Q₈	—	13	2	no	—
348	C₄⋊Q₈	—	13	1	no	—
349	C₄⋊Q₈	—	13	2	no	—
350	C₄⋊Q₈	—	13	2	no	—
351	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
352	C₄⋊Q₈	C₂×D₁₃	1	2	yes	—
353	#126	—	13	2	no	—
354	#126	—	13	1	no	—
355	#126	—	13	2	no	—
356	#126	—	13	2	no	—
357	#126	—	13	1	no	—
358	#126	—	13	2	no	—
359	#126	—	13	2	no	—
360	#126	—	13	2	no	—
361	#126	—	13	2	no	—
362	#125	—	13	1	no	—
363	#125	—	13	1	no	—
364	#125	—	13	2	no	—
365	#125	—	13	2	no	—
366	#125	—	13	2	no	—
367	#125	—	13	2	no	—
368	#125	—	13	2	no	—
369	#125	—	13	2	no	—
370	#125	—	13	2	no	—
371	#124	—	13	1	no	—
372	#124	—	13	1	no	—
373	#124	—	13	2	no	—
374	#124	—	13	1	no	—
375	#124	—	13	2	no	—
376	#124	—	13	1	no	—
377	#123	—	13	1	no	—
378	#123	—	13	2	no	—
379	#123	—	13	2	no	—
380	#123	—	13	2	no	—
381	#123	—	13	2	no	—
382	#123	—	13	2	no	—
383	#123	—	13	2	no	—
384	#123	—	13	1	no	—
385	#123	—	13	2	no	—
386	C₂²⋊Q₈	—	13	2	no	—
387	C₂²⋊Q₈	—	13	2	no	—
388	C₂²⋊Q₈	—	13	2	no	—
389	C₂²⋊Q₈	—	13	1	no	—
390	C₂²⋊Q₈	—	13	2	no	—
391	C₂²⋊Q₈	—	13	2	no	—
392	C₂²⋊Q₈	—	13	1	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	C₂²⋊Q₈	—	13	2	no	—
395	C₂²⋊Q₈	—	13	1	no	—
396	C₂²⋊Q₈	—	13	2	no	—
397	C₂²⋊Q₈	—	13	2	no	—
398	C₂²⋊Q₈	—	13	2	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	2	no	—
401	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
402	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
403	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
404	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
405	#121	—	13	1	no	—
406	#121	—	13	2	no	—
407	#121	—	13	1	no	—
408	#121	—	13	2	no	—
409	#121	—	13	2	no	—
410	C₄×Q₈	—	13	1	no	—
411	C₄×Q₈	—	13	1	no	—
412	C₄×Q₈	—	13	1	no	—
413	C₄×Q₈	—	13	2	no	—
414	C₄×Q₈	—	13	1	no	—
415	C₄×Q₈	—	13	1	no	—
416	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
417	C₄×D₄	—	13	1	no	—
418	C₄×D₄	—	13	1	no	—
419	C₄×D₄	—	13	2	no	—
420	C₄×D₄	—	13	2	no	—
421	C₄×D₄	—	13	1	no	—
422	C₄×D₄	—	13	2	no	—
423	C₄×D₄	—	13	2	no	—
424	C₄×D₄	—	13	2	no	—
425	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
426	C₄×D₄	C₂×D₁₃	1	2	yes	—
427	#117	—	13	1	no	—
428	#117	—	13	2	no	—
429	#117	—	13	1	no	—
430	#117	—	13	2	no	—
431	C₂×C₄⋊C₄	—	13	2	no	—
432	C₂×C₄⋊C₄	—	13	2	no	—
433	C₂×C₄⋊C₄	—	13	2	no	—
434	C₂×C₄²	—	13	1	no	—
435	C₂×C₁₃	—	2	2	no	—
436	C₂×C₁₃	—	4	1	no	—
437	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
439	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
440	D₁₃	—	4	1	no	—
441	D₁₃	—	4	2	no	—
442	#41	—	52	2	no	—
443	#41	—	52	2	no	—
444	C₂×Q₈	—	4	2	no	—
445	C₂×Q₈	—	4	2	no	—
446	C₂×Q₈	—	13	1	no	—
447	C₂×Q₈	—	13	1	no	—
448	C₂×Q₈	—	13	1	no	—
449	C₂×Q₈	—	13	2	no	—
450	C₂×Q₈	—	13	2	no	—
451	C₂×Q₈	—	52	2	no	—
452	C₂×Q₈	—	52	2	no	—
453	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
454	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
455	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
456	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
457	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
458	C₂×D₄	—	13	1	no	—
459	C₂×D₄	—	13	2	no	—
460	C₂×D₄	—	13	1	no	—
461	C₂×D₄	—	13	2	no	—
462	C₂×D₄	—	13	1	no	—
463	C₂×D₄	—	13	2	no	—
464	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
465	C₂²×C₄	—	13	1	no	—
466	C₂²×C₄	—	13	1	no	—
467	C₂²×C₄	—	13	2	no	—
468	C₂²×C₄	—	13	2	no	—
469	C₂²×C₄	—	13	1	no	—
470	C₂²×C₄	—	13	2	no	—
471	C₂²×C₄	—	13	2	no	—
472	C₂²×C₄	—	13	2	no	—
473	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
476	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
477	C₄⋊C₄	—	13	1	no	—
478	C₄⋊C₄	—	13	2	no	—
479	C₄⋊C₄	—	13	2	no	—
480	C₄⋊C₄	—	13	2	no	—
481	C₄⋊C₄	—	13	2	no	—
482	C₄⋊C₄	—	13	2	no	—
483	C₄⋊C₄	—	13	2	no	—
484	C₄⋊C₄	—	13	2	no	—
485	C₄⋊C₄	—	13	2	no	—
486	C₄⋊C₄	—	13	2	no	—
487	C₄⋊C₄	—	13	1	no	—
488	C₄⋊C₄	—	13	1	no	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	1	no	—
491	C₄⋊C₄	—	13	1	no	—
492	C₄⋊C₄	—	13	2	no	—
493	C₄⋊C₄	—	13	2	no	—
494	C₄⋊C₄	—	13	2	no	—
495	C₄⋊C₄	—	13	1	no	—
496	C₄⋊C₄	—	13	2	no	—
497	C₄⋊C₄	—	13	2	no	—
498	C₄⋊C₄	—	13	1	no	—
499	C₄⋊C₄	—	13	2	no	—
500	C₄⋊C₄	—	13	2	no	—
501	C₄⋊C₄	—	13	2	no	—
502	C₄⋊C₄	—	13	2	no	—
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	—	13	1	no	—
505	C₄⋊C₄	—	13	1	no	—
506	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
508	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
511	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
512	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
513	C₂²⋊C₄	—	13	1	no	—
514	C₂²⋊C₄	—	13	1	no	—
515	C₂²⋊C₄	—	13	1	no	—
516	C₂²⋊C₄	—	13	2	no	—
517	C₂²⋊C₄	—	13	1	no	—
518	C₂²⋊C₄	—	13	2	no	—
519	C₂²⋊C₄	—	13	2	no	—
520	C₂²⋊C₄	—	13	2	no	—
521	C₂²⋊C₄	—	13	1	no	—
522	C₂²⋊C₄	—	13	2	no	—
523	C₂²⋊C₄	—	13	1	no	—
524	C₂²⋊C₄	—	13	2	no	—
525	C₂²⋊C₄	—	13	2	no	—
526	C₂²⋊C₄	—	13	1	no	—
527	C₂²⋊C₄	—	13	2	no	—
528	C₂²⋊C₄	—	13	2	no	—
529	C₂²⋊C₄	—	13	2	no	—
530	C₂²⋊C₄	—	13	1	no	—
531	C₂²⋊C₄	—	13	2	no	—
532	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
533	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
536	C₄²	—	13	1	no	—
537	C₄²	—	13	1	no	—
538	C₄²	—	13	1	no	—
539	C₄²	—	13	1	no	—
540	C₄²	—	13	2	no	—
541	C₄²	—	13	1	no	—
542	C₄²	—	13	2	no	—
543	C₄²	—	13	2	no	—
544	C₄²	—	13	2	no	—
545	C₄²	C₂²×D₁₃	1	1	yes	characteristic
546	C₄²	C₂²×D₁₃	1	2	yes	—
547	C₁₃	#3552	1	1	yes	characteristic, complemented, Sylow
548	C₂³	—	13	1	no	—
549	C₂³	—	13	2	no	—
550	C₂³	C₂³×D₁₃	1	1	yes	characteristic
551	C₂³	C₂³×D₁₃	1	1	yes	characteristic
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	2	2	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	26	2	no	—
558	Q₈	—	26	2	no	—
559	Q₈	—	26	2	no	—
560	Q₈	—	52	2	no	—
561	Q₈	—	52	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	26	2	no	—
564	D₄	—	26	2	no	—
565	D₄	—	26	4	no	—
566	D₄	—	26	2	no	—
567	D₄	—	52	2	no	—
568	D₄	—	52	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	13	1	no	—
574	C₂×C₄	—	13	1	no	—
575	C₂×C₄	—	13	2	no	—
576	C₂×C₄	—	13	1	no	—
577	C₂×C₄	—	13	1	no	—
578	C₂×C₄	—	13	1	no	—
579	C₂×C₄	—	13	1	no	—
580	C₂×C₄	—	13	2	no	—
581	C₂×C₄	—	13	2	no	—
582	C₂×C₄	—	13	1	no	—
583	C₂×C₄	—	26	4	no	—
584	C₂×C₄	—	26	2	no	—
585	C₂×C₄	—	26	2	no	—
586	C₂×C₄	—	26	2	no	—
587	C₂×C₄	—	52	2	no	—
588	C₂×C₄	—	52	2	no	—
589	C₂×C₄	—	52	2	no	—
590	C₂×C₄	—	52	2	no	—
591	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₃	1	2	yes	—
594	C₂×C₄	C₂³×D₁₃	1	2	yes	—
595	C₂×C₄	C₂³×D₁₃	1	2	yes	—
596	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₃	1	2	yes	—
598	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	26	1	no	—
606	C₂²	—	26	2	no	—
607	C₂²	—	26	1	no	—
608	C₂²	—	26	2	no	—
609	C₂²	—	26	2	no	—
610	C₂²	—	26	1	no	—
611	C₂²	#88254	1	2	yes	—
612	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	1	no	—
621	C₄	—	13	2	no	—
622	C₄	—	26	1	no	—
623	C₄	—	26	2	no	—
624	C₄	—	26	2	no	—
625	C₄	—	26	1	no	—
626	C₄	—	26	1	no	—
627	C₄	—	26	2	no	—
628	C₄	—	26	1	no	—
629	C₄	—	26	1	no	—
630	C₄	—	26	1	no	—
631	C₄	#88251	1	2	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	4	1	no	—
634	C₂	—	52	1	no	—
635	C₂	—	52	2	no	—
636	C₂	C₂×#88251	1	1	yes	characteristic
637	C₂	C₂×#88254	1	1	yes	characteristic
638	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	D₄×Q₈×C₁₃	C₂
hypercenter	D₄×Q₈	D₁₃
hypocenter	C₁₃	#3552
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. D₄×Q₈×C₁₃	C₂	semidirect
2. #11719522	C₂	semidirect
3. #11719521	C₂	semidirect
4. Q₈×C₂²⋊D₁₃	C₂	semidirect
5. C₂×#88198	C₂	semidirect
6. #11719440	C₂	semidirect
7. #11719434	C₂	semidirect
8. #11719429	C₂	semidirect
9. #11719426	C₂	semidirect
10. #11719351	C₂	semidirect
11. #11719350	C₂	semidirect
12. #11719345	C₂	semidirect
13. #11719341	C₂	semidirect
14. #11719337	C₂	semidirect
15. #11719336	C₂	semidirect
16. #11719330	C₂	semidirect
17. #11719329	C₂	semidirect
18. #11719288	C₂	semidirect
19. #11719273	C₂	semidirect
20. #11719269	C₂	semidirect
21. #11719257	C₂	semidirect
22. #11719245	C₂	semidirect
23. #11719243	C₂	semidirect
289. D₄×Q₈	D₁₃	semidirect
547. C₁₃	#3552	semidirect

Maximal subgroups

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

subgroup	index
D₄×Q₈×C₁₃	2
#11719522	2
#11719521	2
Q₈×C₂²⋊D₁₃	2
C₂×#88198	2
#11719440	2
#11719434	2
#11719429	2
#11719426	2
#11719351	2
#11719350	2
#11719345	2
#11719341	2
#11719337	2
#11719336	2
#11719330	2
#11719329	2
#11719288	2
#11719273	2
#11719269	2
#11719257	2
#11719245	2
#11719243	2
#3552	13