Subgroups — #13129077

Order 1664.

1014 conjugacy classes of subgroups.

The subgroup lattice has 656 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	#11719521	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88200	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719440	C₂	1	2	yes	maximal, complemented
7	#11719436	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719434	C₂	1	2	yes	maximal, complemented
9	#11719432	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719351	C₂	1	2	yes	maximal, complemented
11	#11719347	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719344	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719343	C₂	1	2	yes	maximal, complemented
14	#11719342	C₂	1	2	yes	maximal, complemented
15	#11719333	C₂	1	1	yes	maximal, characteristic, complemented
16	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719328	C₂	1	2	yes	maximal, complemented
18	#11719288	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719286	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719269	C₂	1	2	yes	maximal, complemented
21	#11719261	C₂	1	2	yes	maximal, complemented
22	#11719252	C₂	1	1	yes	maximal, characteristic
23	#11719246	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, complemented
26	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#6127	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	#88201	C₂²	1	2	yes	—
40	#88200	C₂²	1	1	yes	characteristic
41	#88200	C₂²	1	2	yes	—
42	#88200	C₂²	1	2	yes	—
43	#88200	C₂²	1	1	yes	characteristic
44	#88200	C₂²	1	1	yes	characteristic
45	#88200	C₂²	1	2	yes	—
46	#88200	C₂²	1	1	yes	characteristic
47	#88200	C₂²	1	1	yes	characteristic
48	#88200	C₂²	1	1	yes	characteristic, complemented
49	#88200	C₂²	1	2	yes	complemented
50	#88200	C₂²	1	1	yes	characteristic, complemented
51	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
52	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
53	#88198	C₂²	1	2	yes	complemented
54	#88198	C₂²	1	2	yes	complemented
55	#88198	C₂²	1	2	yes	complemented
56	#88198	C₂²	1	1	yes	characteristic, complemented
57	#88193	C₂²	1	1	yes	characteristic
58	#88191	C₂²	1	1	yes	characteristic
59	#88189	C₂²	1	2	yes	—
60	#88183	C₂²	1	2	yes	—
61	#88183	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
65	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
66	C₂×#6103	C₂²	1	2	yes	—
67	#88180	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
69	#88178	C₂²	1	1	yes	characteristic
70	#88178	C₂²	1	2	yes	—
71	#88178	C₂²	1	1	yes	characteristic, complemented
72	#88178	C₂²	1	2	yes	complemented
73	C₂×#6101	C₂²	1	2	yes	—
74	#88152	C₂²	1	2	yes	—
75	#88152	C₂²	1	2	yes	—
76	#88152	C₂²	1	2	yes	—
77	#88152	C₂²	1	2	yes	complemented
78	#88151	C₂²	1	1	yes	characteristic
79	#88150	C₂²	1	2	yes	—
80	#88150	C₂²	1	1	yes	characteristic
81	#88150	C₂²	1	2	yes	—
82	#88150	C₂²	1	2	yes	complemented
83	#88148	C₂²	1	1	yes	characteristic
84	#88148	C₂²	1	2	yes	—
85	#88148	C₂²	1	2	yes	—
86	#88147	C₂²	1	2	yes	—
87	#88146	C₂²	1	2	yes	—
88	#88146	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
90	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
91	#88144	C₂²	1	2	yes	complemented
92	#88144	C₂²	1	1	yes	characteristic, complemented
93	#88143	C₂²	1	2	yes	complemented
94	#88143	C₂²	1	2	yes	complemented
95	#88143	C₂²	1	2	yes	complemented
96	#88143	C₂²	1	2	yes	complemented
97	#88143	C₂²	1	2	yes	complemented
98	#88143	C₂²	1	2	yes	complemented
99	#88142	C₂²	1	2	yes	complemented
100	#88142	C₂²	1	2	yes	complemented
101	#88140	C₂²	1	2	yes	—
102	#88139	C₂²	1	2	yes	—
103	#88138	C₂²	1	1	yes	characteristic
104	#88137	C₂²	1	1	yes	characteristic
105	#88137	C₂²	1	2	yes	—
106	#88137	C₂²	1	2	yes	complemented
107	#88136	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
109	#88133	C₂²	1	2	yes	complemented
110	#88133	C₂²	1	2	yes	complemented
111	#88132	C₂²	1	1	yes	characteristic
112	#88132	C₂²	1	2	yes	—
113	#88131	C₂²	1	2	yes	—
114	#88131	C₂²	1	2	yes	—
115	#88130	C₂²	1	2	yes	—
116	#88130	C₂²	1	2	yes	complemented
117	C₄×D₅₂	C₂²	1	1	yes	characteristic
118	#88126	C₂²	1	2	yes	—
119	#88126	C₂²	1	1	yes	characteristic
120	#88124	C₂²	1	2	yes	complemented
121	#88124	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	—	4	2	no	—
125	C₂×Q₈×C₁₃	—	4	2	no	—
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
130	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
131	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₃	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	1	yes	characteristic
139	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₃	C₂³	1	2	yes	—
141	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
142	Q₈×D₁₃	—	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	1	yes	characteristic
147	C₂×C₄×D₁₃	—	4	2	no	—
148	C₂×C₄×D₁₃	C₂³	1	2	yes	—
149	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
156	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
157	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
158	C₂×Dic₂₆	C₂³	1	2	yes	—
159	C₂×Dic₂₆	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	1	yes	characteristic
163	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
178	#6103	C₂³	1	1	yes	characteristic
179	#6103	C₂³	1	1	yes	characteristic
180	#6103	C₂³	1	1	yes	characteristic
181	#6103	C₂³	1	2	yes	—
182	#6103	C₂³	1	1	yes	characteristic
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	2	yes	—
188	#6103	C₂³	1	1	yes	characteristic
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	1	yes	characteristic
191	#6103	C₂³	1	2	yes	—
192	#6103	C₂³	1	2	yes	—
193	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₃	C₂³	1	2	yes	—
195	C₄⋊Dic₁₃	C₂³	1	2	yes	—
196	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₃	C₂³	1	2	yes	—
200	C₄⋊Dic₁₃	C₂³	1	2	yes	—
201	C₄⋊Dic₁₃	C₂³	1	2	yes	—
202	#6101	C₂³	1	2	yes	—
203	#6101	C₂³	1	1	yes	characteristic
204	#6101	C₂³	1	2	yes	—
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	2	yes	—
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	2	yes	—
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	1	yes	characteristic
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	1	yes	characteristic
221	#6101	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3538	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₃	—	2	2	no	—
232	C₂²×D₁₃	—	2	2	no	—
233	C₂²×D₁₃	—	4	1	no	—
234	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	2	2	no	—
240	Q₈×C₁₃	—	4	2	no	—
241	Q₈×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₁₃	—	2	2	no	—
257	C₂²⋊D₁₃	—	2	2	no	—
258	C₂²⋊D₁₃	—	4	1	no	—
259	C₂²⋊D₁₃	—	4	1	no	—
260	C₂×Dic₁₃	—	2	4	no	—
261	C₂×Dic₁₃	—	4	1	no	—
262	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₃	C₂⁴	1	2	yes	—
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	2	yes	—
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	D₅₂	—	2	2	no	—
272	D₅₂	—	4	1	no	—
273	C₄×D₁₃	—	2	4	no	—
274	C₄×D₁₃	—	2	2	no	—
275	C₄×D₁₃	—	2	2	no	—
276	C₄×D₁₃	—	2	2	no	—
277	C₄×D₁₃	—	4	1	no	—
278	C₄×D₁₃	—	4	1	no	—
279	C₄×D₁₃	—	4	2	no	—
280	C₄×D₁₃	—	4	2	no	—
281	Dic₂₆	—	2	2	no	—
282	Dic₂₆	—	4	1	no	—
283	Dic₂₆	—	4	2	no	—
284	Dic₂₆	—	4	2	no	—
285	#563	—	13	2	no	—
286	#563	—	13	2	no	—
287	#552	—	13	1	no	—
288	#552	—	13	1	no	—
289	#552	—	13	1	no	—
290	#552	—	13	1	no	—
291	#551	—	13	2	no	—
292	#551	—	13	2	no	—
293	D₄×Q₈	—	13	1	no	—
294	D₄×Q₈	—	13	1	no	—
295	D₄×Q₈	—	13	1	no	—
296	D₄×Q₈	D₁₃	1	1	yes	characteristic, complemented
297	#544	—	13	2	no	—
298	#544	—	13	2	no	—
299	#541	—	13	1	no	—
300	#541	—	13	1	no	—
301	#539	—	13	2	no	—
302	#539	—	13	2	no	—
303	#536	—	13	1	no	—
304	#536	—	13	1	no	—
305	#525	—	13	1	no	—
306	C₂×C₂²⋊Q₈	—	13	1	no	—
307	C₂×C₂²⋊Q₈	—	13	1	no	—
308	C₂²×C₁₃	—	2	1	no	—
309	C₂²×C₁₃	—	2	1	no	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
314	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
315	C₂×D₁₃	—	2	1	no	—
316	C₂×D₁₃	—	2	1	no	—
317	C₂×D₁₃	—	2	1	no	—
318	C₂×D₁₃	—	2	1	no	—
319	C₂×D₁₃	—	2	1	no	—
320	C₂×D₁₃	—	2	1	no	—
321	C₂×D₁₃	—	2	1	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	4	4	no	—
324	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
334	Dic₁₃	—	2	2	no	—
335	Dic₁₃	—	2	1	no	—
336	Dic₁₃	—	2	1	no	—
337	Dic₁₃	—	2	1	no	—
338	Dic₁₃	—	2	2	no	—
339	Dic₁₃	—	2	2	no	—
340	Dic₁₃	—	2	2	no	—
341	Dic₁₃	—	2	1	no	—
342	Dic₁₃	—	2	1	no	—
343	C₂×#41	—	13	1	no	—
344	C₂²×Q₈	—	13	1	no	—
345	C₂²×Q₈	—	13	1	no	—
346	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic
347	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
348	C₂³×C₄	—	13	1	no	—
349	C₄⋊Q₈	—	13	2	no	—
350	C₄⋊Q₈	—	13	1	no	—
351	C₄⋊Q₈	—	13	2	no	—
352	C₄⋊Q₈	—	13	2	no	—
353	C₄⋊Q₈	—	13	2	no	—
354	C₄⋊Q₈	—	13	2	no	—
355	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
356	C₄⋊Q₈	C₂×D₁₃	1	2	yes	complemented
357	#126	—	13	2	no	—
358	#126	—	13	2	no	—
359	#126	—	13	2	no	—
360	#126	—	13	2	no	—
361	#126	—	13	2	no	—
362	#126	—	13	2	no	—
363	#126	—	13	2	no	—
364	#126	—	13	2	no	—
365	#125	—	13	2	no	—
366	#125	—	13	2	no	—
367	#125	—	13	2	no	—
368	#125	—	13	1	no	—
369	#125	—	13	2	no	—
370	#125	—	13	2	no	—
371	#125	—	13	2	no	—
372	#125	—	13	2	no	—
373	#125	—	13	2	no	—
374	#125	—	13	1	no	—
375	#124	—	13	2	no	—
376	#124	—	13	2	no	—
377	#123	—	13	2	no	—
378	#123	—	13	2	no	—
379	#123	—	13	2	no	—
380	#123	—	13	1	no	—
381	#123	—	13	2	no	—
382	#123	—	13	2	no	—
383	#123	—	13	1	no	—
384	#123	—	13	2	no	—
385	#123	—	13	2	no	—
386	#123	—	13	2	no	—
387	C₂²⋊Q₈	—	13	1	no	—
388	C₂²⋊Q₈	—	13	1	no	—
389	C₂²⋊Q₈	—	13	1	no	—
390	C₂²⋊Q₈	—	13	2	no	—
391	C₂²⋊Q₈	—	13	1	no	—
392	C₂²⋊Q₈	—	13	1	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	C₂²⋊Q₈	—	13	1	no	—
395	C₂²⋊Q₈	—	13	1	no	—
396	C₂²⋊Q₈	—	13	2	no	—
397	C₂²⋊Q₈	—	13	2	no	—
398	C₂²⋊Q₈	—	13	1	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	2	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	—	13	1	no	—
403	C₂²⋊Q₈	—	13	2	no	—
404	C₂²⋊Q₈	—	13	1	no	—
405	C₂²⋊Q₈	—	13	2	no	—
406	C₂²⋊Q₈	—	13	2	no	—
407	C₂²⋊Q₈	—	13	2	no	—
408	C₂²⋊Q₈	—	13	1	no	—
409	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
410	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
411	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
412	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
413	#121	—	13	1	no	—
414	#121	—	13	1	no	—
415	#120	—	13	1	no	—
416	#120	—	13	1	no	—
417	C₄×Q₈	—	13	1	no	—
418	C₄×Q₈	—	13	1	no	—
419	C₄×Q₈	—	13	1	no	—
420	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
421	C₄×D₄	—	13	1	no	—
422	C₄×D₄	—	13	1	no	—
423	C₄×D₄	—	13	2	no	—
424	C₄×D₄	—	13	2	no	—
425	C₄×D₄	—	13	2	no	—
426	C₄×D₄	—	13	1	no	—
427	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
428	C₄×D₄	C₂×D₁₃	1	2	yes	—
429	#117	—	13	1	no	—
430	#117	—	13	1	no	—
431	#117	—	13	2	no	—
432	#117	—	13	2	no	—
433	#117	—	13	2	no	—
434	#117	—	13	1	no	—
435	#117	—	13	2	no	—
436	C₂×C₄⋊C₄	—	13	2	no	—
437	C₂×C₄⋊C₄	—	13	1	no	—
438	C₂×C₄⋊C₄	—	13	2	no	—
439	C₂×C₄⋊C₄	—	13	1	no	—
440	C₂×C₂²⋊C₄	—	13	2	no	—
441	C₂×C₂²⋊C₄	—	13	2	no	—
442	C₂×C₁₃	—	2	2	no	—
443	C₂×C₁₃	—	4	1	no	—
444	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
446	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
447	D₁₃	—	2	2	no	—
448	D₁₃	—	4	1	no	—
449	D₁₃	—	4	1	no	—
450	C₂⁴	—	13	1	no	—
451	#41	—	52	2	no	—
452	C₂×Q₈	—	4	2	no	—
453	C₂×Q₈	—	4	2	no	—
454	C₂×Q₈	—	13	1	no	—
455	C₂×Q₈	—	13	2	no	—
456	C₂×Q₈	—	13	2	no	—
457	C₂×Q₈	—	13	1	no	—
458	C₂×Q₈	—	52	2	no	—
459	C₂×Q₈	—	52	2	no	—
460	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
461	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
462	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
464	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
465	C₂×D₄	—	13	1	no	—
466	C₂×D₄	—	13	1	no	—
467	C₂×D₄	—	13	1	no	—
468	C₂×D₄	—	13	1	no	—
469	C₂×D₄	—	13	1	no	—
470	C₂×D₄	—	13	1	no	—
471	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
472	C₂²×C₄	—	13	2	no	—
473	C₂²×C₄	—	13	1	no	—
474	C₂²×C₄	—	13	2	no	—
475	C₂²×C₄	—	13	1	no	—
476	C₂²×C₄	—	13	1	no	—
477	C₂²×C₄	—	13	1	no	—
478	C₂²×C₄	—	13	2	no	—
479	C₂²×C₄	—	13	1	no	—
480	C₂²×C₄	—	13	2	no	—
481	C₂²×C₄	—	13	1	no	—
482	C₂²×C₄	—	52	2	no	—
483	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
486	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
487	C₄⋊C₄	—	13	1	no	—
488	C₄⋊C₄	—	13	1	no	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	2	no	—
491	C₄⋊C₄	—	13	2	no	—
492	C₄⋊C₄	—	13	2	no	—
493	C₄⋊C₄	—	13	2	no	—
494	C₄⋊C₄	—	13	2	no	—
495	C₄⋊C₄	—	13	2	no	—
496	C₄⋊C₄	—	13	2	no	—
497	C₄⋊C₄	—	13	2	no	—
498	C₄⋊C₄	—	13	2	no	—
499	C₄⋊C₄	—	13	1	no	—
500	C₄⋊C₄	—	13	1	no	—
501	C₄⋊C₄	—	13	2	no	—
502	C₄⋊C₄	—	13	2	no	—
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	—	13	2	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	—	13	2	no	—
509	C₄⋊C₄	—	13	2	no	—
510	C₄⋊C₄	—	13	1	no	—
511	C₄⋊C₄	—	13	1	no	—
512	C₄⋊C₄	—	13	1	no	—
513	C₄⋊C₄	—	13	2	no	—
514	C₄⋊C₄	—	13	2	no	—
515	C₄⋊C₄	—	13	2	no	—
516	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
518	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
521	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
523	C₂²⋊C₄	—	13	2	no	—
524	C₂²⋊C₄	—	13	1	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	2	no	—
531	C₂²⋊C₄	—	13	2	no	—
532	C₂²⋊C₄	—	13	2	no	—
533	C₂²⋊C₄	—	13	2	no	—
534	C₂²⋊C₄	—	13	1	no	—
535	C₂²⋊C₄	—	13	1	no	—
536	C₂²⋊C₄	—	13	1	no	—
537	C₂²⋊C₄	—	13	1	no	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	1	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	—	13	2	no	—
543	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
547	C₄²	—	13	2	no	—
548	C₄²	—	13	2	no	—
549	C₄²	—	13	1	no	—
550	C₄²	—	13	2	no	—
551	C₄²	—	13	2	no	—
552	C₄²	—	13	2	no	—
553	C₄²	C₂²×D₁₃	1	1	yes	characteristic
554	C₄²	C₂²×D₁₃	1	2	yes	—
555	C₁₃	#3538	1	1	yes	characteristic, complemented, Sylow
556	C₂³	—	13	1	no	—
557	C₂³	—	13	1	no	—
558	C₂³	—	13	1	no	—
559	C₂³	—	26	2	no	—
560	C₂³	—	26	2	no	—
561	C₂³	—	52	1	no	—
562	C₂³	C₂³×D₁₃	1	1	yes	characteristic
563	C₂³	C₂³×D₁₃	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	26	2	no	—
570	Q₈	—	52	2	no	—
571	Q₈	—	52	2	no	—
572	Q₈	—	52	1	no	—
573	D₄	—	2	2	no	—
574	D₄	—	26	2	no	—
575	D₄	—	26	2	no	—
576	D₄	—	26	2	no	—
577	D₄	—	52	1	no	—
578	D₄	—	52	1	no	—
579	D₄	—	52	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	13	1	no	—
585	C₂×C₄	—	13	1	no	—
586	C₂×C₄	—	13	2	no	—
587	C₂×C₄	—	13	2	no	—
588	C₂×C₄	—	13	2	no	—
589	C₂×C₄	—	13	1	no	—
590	C₂×C₄	—	13	2	no	—
591	C₂×C₄	—	13	1	no	—
592	C₂×C₄	—	13	1	no	—
593	C₂×C₄	—	26	4	no	—
594	C₂×C₄	—	26	4	no	—
595	C₂×C₄	—	26	2	no	—
596	C₂×C₄	—	26	2	no	—
597	C₂×C₄	—	26	2	no	—
598	C₂×C₄	—	52	1	no	—
599	C₂×C₄	—	52	1	no	—
600	C₂×C₄	—	52	2	no	—
601	C₂×C₄	—	52	2	no	—
602	C₂×C₄	—	52	1	no	—
603	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₁₃	1	2	yes	—
606	C₂×C₄	C₂³×D₁₃	1	2	yes	—
607	C₂×C₄	C₂³×D₁₃	1	2	yes	—
608	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₃	1	2	yes	—
610	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	13	2	no	—
618	C₂²	—	26	1	no	—
619	C₂²	—	26	1	no	—
620	C₂²	—	26	1	no	—
621	C₂²	—	26	1	no	—
622	C₂²	—	26	1	no	—
623	C₂²	—	26	1	no	—
624	C₂²	—	26	1	no	—
625	C₂²	—	26	1	no	—
626	C₂²	—	52	4	no	—
627	C₂²	#88254	1	2	yes	—
628	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	26	1	no	—
638	C₄	—	26	1	no	—
639	C₄	—	26	1	no	—
640	C₄	—	26	2	no	—
641	C₄	—	26	2	no	—
642	C₄	—	26	2	no	—
643	C₄	—	26	1	no	—
644	C₄	—	26	2	no	—
645	C₄	—	26	1	no	—
646	C₄	#88251	1	2	yes	—
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	26	2	no	—
650	C₂	—	52	1	no	—
651	C₂	—	52	1	no	—
652	C₂	C₂×#88251	1	1	yes	characteristic
653	C₂	C₂×#88254	1	1	yes	characteristic
654	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
prime radical	#11719252	C₂
hypercenter	D₄×Q₈	D₁₃
hypocenter	C₁₃	#3538
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. #11719521	C₂	semidirect
3. Q₈×C₂²⋊D₁₃	C₂	semidirect
4. Q₈×C₂²⋊D₁₃	C₂	semidirect
5. C₂×#88200	C₂	semidirect
6. #11719440	C₂	semidirect
7. #11719436	C₂	semidirect
8. #11719434	C₂	semidirect
9. #11719432	C₂	semidirect
10. #11719351	C₂	semidirect
11. #11719347	C₂	semidirect
12. #11719344	C₂	semidirect
13. #11719343	C₂	semidirect
14. #11719342	C₂	semidirect
15. #11719333	C₂	semidirect
16. D₁₃×C₂²⋊Q₈	C₂	semidirect
17. #11719328	C₂	semidirect
18. #11719288	C₂	semidirect
19. #11719286	C₂	semidirect
20. #11719269	C₂	semidirect
21. #11719261	C₂	semidirect
23. #11719246	C₂	semidirect
25. C₂²×Q₈×C₁₃	C₂²	semidirect
27. C₂×Q₈×D₁₃	C₂²	semidirect
30. C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₁₃×C₂²⋊Q₈	C₂²	semidirect
35. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₃	C₂²	semidirect
48. #88200	C₂²	semidirect
49. #88200	C₂²	semidirect
50. #88200	C₂²	semidirect
51. Q₈×Dic₁₃	C₂²	semidirect
52. Q₈×Dic₁₃	C₂²	semidirect
53. #88198	C₂²	semidirect
54. #88198	C₂²	semidirect
55. #88198	C₂²	semidirect
56. #88198	C₂²	semidirect
61. #88183	C₂²	semidirect
67. #88180	C₂²	semidirect
71. #88178	C₂²	semidirect
72. #88178	C₂²	semidirect
77. #88152	C₂²	semidirect
82. #88150	C₂²	semidirect
88. #88146	C₂²	semidirect
91. #88144	C₂²	semidirect
92. #88144	C₂²	semidirect
93. #88143	C₂²	semidirect
94. #88143	C₂²	semidirect
95. #88143	C₂²	semidirect
96. #88143	C₂²	semidirect
97. #88143	C₂²	semidirect
98. #88143	C₂²	semidirect
99. #88142	C₂²	semidirect
100. #88142	C₂²	semidirect
106. #88137	C₂²	semidirect
109. #88133	C₂²	semidirect
110. #88133	C₂²	semidirect
116. #88130	C₂²	semidirect
120. #88124	C₂²	semidirect
121. #88124	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
296. D₄×Q₈	D₁₃	semidirect
347. C₂²×Q₈	C₂×D₁₃	semidirect
355. C₄⋊Q₈	C₂×D₁₃	semidirect
356. C₄⋊Q₈	C₂×D₁₃	semidirect
411. C₂²⋊Q₈	C₂×D₁₃	semidirect
412. C₂²⋊Q₈	C₂×D₁₃	semidirect
420. C₄×Q₈	C₂×D₁₃	semidirect
555. C₁₃	#3538	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
#11719521	2
Q₈×C₂²⋊D₁₃	2
C₂×#88200	2
#11719440	2
#11719436	2
#11719434	2
#11719432	2
#11719351	2
#11719347	2
#11719344	2
#11719343	2
#11719342	2
#11719333	2
D₁₃×C₂²⋊Q₈	2
#11719328	2
#11719288	2
#11719286	2
#11719269	2
#11719261	2
#11719252	2
#11719246	2
#3538	13