Subgroups — #13128635

Order 1664.

1100 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719434	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719432	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719395	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719395	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719394	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719393	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719341	C₂	1	2	yes	maximal, complemented
9	#11719341	C₂	1	2	yes	maximal, complemented
10	#11719339	C₂	1	2	yes	maximal, complemented
11	#11719339	C₂	1	2	yes	maximal, complemented
12	#11719337	C₂	1	2	yes	maximal, complemented
13	D₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	#11719284	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719250	C₂	1	1	yes	maximal, characteristic
17	#11719250	C₂	1	1	yes	maximal, characteristic
18	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
19	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719216	C₂	1	2	yes	maximal, complemented
23	C₂×#88150	C₂	1	2	yes	maximal, complemented
24	C₂×Q₈×D₁₃	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
27	C₂²×Dic₂₆	C₂²	1	2	yes	complemented
28	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
39	#88200	C₂²	1	2	yes	—
40	#88200	C₂²	1	1	yes	characteristic
41	#88200	C₂²	1	2	yes	complemented
42	#88200	C₂²	1	2	yes	complemented
43	#88198	C₂²	1	2	yes	complemented
44	#88198	C₂²	1	1	yes	characteristic, complemented
45	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
46	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
47	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
51	C₂×#6103	C₂²	1	2	yes	—
52	C₂×#6103	C₂²	1	2	yes	—
53	#88178	C₂²	1	2	yes	complemented
54	#88178	C₂²	1	2	yes	complemented
55	#88178	C₂²	1	2	yes	complemented
56	C₂×#6101	C₂²	1	2	yes	complemented
57	C₂×#6101	C₂²	1	2	yes	complemented
58	#88151	C₂²	1	1	yes	characteristic
59	#88151	C₂²	1	2	yes	—
60	#88151	C₂²	1	2	yes	complemented
61	#88151	C₂²	1	2	yes	complemented
62	#88150	C₂²	1	2	yes	—
63	#88150	C₂²	1	1	yes	characteristic
64	#88150	C₂²	1	2	yes	—
65	#88150	C₂²	1	2	yes	—
66	#88150	C₂²	1	1	yes	characteristic
67	#88150	C₂²	1	2	yes	—
68	#88150	C₂²	1	2	yes	complemented
69	#88150	C₂²	1	2	yes	complemented
70	#88150	C₂²	1	2	yes	complemented
71	#88150	C₂²	1	2	yes	complemented
72	#88150	C₂²	1	2	yes	complemented
73	#88150	C₂²	1	2	yes	complemented
74	#88150	C₂²	1	2	yes	complemented
75	#88150	C₂²	1	2	yes	complemented
76	#88147	C₂²	1	1	yes	characteristic
77	#88147	C₂²	1	1	yes	characteristic
78	#88147	C₂²	1	1	yes	characteristic
79	#88146	C₂²	1	1	yes	characteristic
80	#88146	C₂²	1	1	yes	characteristic
81	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
82	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
83	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
84	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
85	#88144	C₂²	1	1	yes	characteristic, complemented
86	#88144	C₂²	1	1	yes	characteristic, complemented
87	#88143	C₂²	1	2	yes	complemented
88	#88143	C₂²	1	1	yes	characteristic, complemented
89	#88143	C₂²	1	1	yes	characteristic, complemented
90	#88143	C₂²	1	2	yes	complemented
91	#88142	C₂²	1	1	yes	characteristic, complemented
92	#88142	C₂²	1	1	yes	characteristic, complemented
93	#88142	C₂²	1	1	yes	characteristic, complemented
94	#88142	C₂²	1	2	yes	complemented
95	#88142	C₂²	1	1	yes	characteristic, complemented
96	#88142	C₂²	1	1	yes	characteristic, complemented
97	#88141	C₂²	1	2	yes	complemented
98	#88141	C₂²	1	2	yes	complemented
99	#88135	C₂²	1	2	yes	—
100	#88135	C₂²	1	2	yes	—
101	#88135	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
103	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
104	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
105	#88132	C₂²	1	2	yes	complemented
106	#88132	C₂²	1	2	yes	complemented
107	#88132	C₂²	1	2	yes	complemented
108	#88132	C₂²	1	2	yes	complemented
109	#88132	C₂²	1	2	yes	complemented
110	#88132	C₂²	1	2	yes	complemented
111	C₄×D₅₂	C₂²	1	1	yes	characteristic
112	C₄×D₅₂	C₂²	1	1	yes	characteristic
113	C₄×D₅₂	C₂²	1	1	yes	characteristic
114	#88126	C₂²	1	1	yes	characteristic
115	#88126	C₂²	1	1	yes	characteristic
116	C₄²×D₁₃	C₂²	1	1	yes	characteristic
117	#88124	C₂²	1	1	yes	characteristic, complemented
118	#88124	C₂²	1	1	yes	characteristic, complemented
119	#88123	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
131	C₂²×Dic₁₃	C₂³	1	2	yes	—
132	C₂²×Dic₁₃	C₂³	1	2	yes	—
133	C₂²×Dic₁₃	C₂³	1	2	yes	—
134	Q₈×D₁₃	—	4	4	no	—
135	D₄×D₁₃	Q₈	1	8	yes	complemented
136	C₂×D₅₂	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₃	—	4	4	no	—
138	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₃	C₂³	1	2	yes	—
140	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₃	C₂³	1	2	yes	—
142	C₂×C₄×D₁₃	C₂³	1	2	yes	—
143	C₂×C₄×D₁₃	C₂³	1	2	yes	—
144	C₂×C₄×D₁₃	C₂³	1	2	yes	—
145	C₂×C₄×D₁₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₃	C₂³	1	2	yes	—
147	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
148	C₂×Dic₂₆	—	4	4	no	—
149	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
150	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
151	C₂×Dic₂₆	C₂³	1	2	yes	—
152	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
153	C₂×Dic₂₆	C₂³	1	2	yes	—
154	C₂×Dic₂₆	C₂³	1	2	yes	—
155	C₂×Dic₂₆	C₂³	1	2	yes	—
156	C₂×Dic₂₆	C₂³	1	2	yes	—
157	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	#6103	C₂³	1	1	yes	characteristic
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	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	2	yes	—
188	#6103	C₂³	1	2	yes	—
189	C₄⋊Dic₁₃	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	1	yes	characteristic
193	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₃	C₂³	1	2	yes	—
195	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₃	C₂³	1	2	yes	—
197	C₄⋊Dic₁₃	C₂³	1	2	yes	—
198	#6101	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
210	#6101	C₂³	1	1	yes	characteristic
211	#6101	C₂³	1	1	yes	characteristic
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	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	#3501	—	13	1	no	maximal, Sylow
227	C₂³×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×D₁₃	—	4	2	no	—
229	C₂²×D₁₃	—	4	2	no	—
230	C₂²×D₁₃	C₂×Q₈	1	8	yes	complemented
231	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₃	C₂⁴	1	2	yes	—
233	Q₈×C₁₃	—	4	2	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	D₄×C₁₃	C₂×Q₈	1	4	yes	complemented
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²⋊D₁₃	C₂×Q₈	1	8	yes	complemented
250	C₂×Dic₁₃	—	2	4	no	—
251	C₂×Dic₁₃	—	4	2	no	—
252	C₂×Dic₁₃	—	4	2	no	—
253	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃	C₂⁴	1	2	yes	—
256	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₃	C₂⁴	1	2	yes	—
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	D₅₂	C₂×Q₈	1	4	yes	complemented
264	C₄×D₁₃	—	2	2	no	—
265	C₄×D₁₃	—	2	4	no	—
266	C₄×D₁₃	—	4	2	no	—
267	C₄×D₁₃	—	4	2	no	—
268	C₄×D₁₃	—	4	1	no	—
269	C₄×D₁₃	—	4	2	no	—
270	C₄×D₁₃	—	4	2	no	—
271	C₄×D₁₃	—	4	2	no	—
272	C₄×D₁₃	—	4	2	no	—
273	C₄×D₁₃	C₂×Q₈	1	4	yes	complemented
274	Dic₂₆	—	2	2	no	—
275	Dic₂₆	—	2	4	no	—
276	Dic₂₆	—	2	2	no	—
277	Dic₂₆	—	4	2	no	—
278	Dic₂₆	—	4	2	no	—
279	Dic₂₆	—	4	2	no	—
280	Dic₂₆	—	4	1	no	—
281	Dic₂₆	—	4	2	no	—
282	#554	—	13	1	no	—
283	#554	—	13	1	no	—
284	#554	—	13	2	no	—
285	#554	—	13	2	no	—
286	#554	—	13	1	no	—
287	#554	—	13	1	no	—
288	#554	—	13	1	no	—
289	#554	—	13	2	no	—
290	#554	D₁₃	1	1	yes	characteristic, complemented
291	D₄×Q₈	—	13	1	no	—
292	D₄×Q₈	—	13	2	no	—
293	D₄×Q₈	—	13	1	no	—
294	#544	—	13	1	no	—
295	#544	—	13	1	no	—
296	#543	—	13	2	no	—
297	#543	—	13	2	no	—
298	#533	—	13	1	no	—
299	#533	—	13	1	no	—
300	C₂×C₂²⋊Q₈	—	13	2	no	—
301	C₂×C₂²⋊Q₈	—	13	2	no	—
302	#518	—	13	1	no	—
303	#518	—	13	1	no	—
304	C₂×C₄×D₄	—	13	1	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	2	2	no	—
307	C₂²×C₁₃	C₂²×Q₈	1	4	yes	—
308	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
309	C₂×D₁₃	—	2	2	no	—
310	C₂×D₁₃	—	2	1	no	—
311	C₂×D₁₃	—	2	2	no	—
312	C₂×D₁₃	—	2	1	no	—
313	C₂×D₁₃	—	4	8	no	—
314	C₂×D₁₃	C₂²×Q₈	1	2	yes	—
315	C₂×D₁₃	C₂²×Q₈	1	4	yes	—
316	C₄×C₁₃	—	2	1	no	—
317	C₄×C₁₃	—	2	2	no	—
318	C₄×C₁₃	—	2	1	no	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	—	2	1	no	—
324	C₄×C₁₃	—	2	1	no	—
325	C₄×C₁₃	C₂²×Q₈	1	2	yes	—
326	Dic₁₃	—	2	1	no	—
327	Dic₁₃	—	2	2	no	—
328	Dic₁₃	—	2	1	no	—
329	Dic₁₃	—	2	2	no	—
330	Dic₁₃	—	2	1	no	—
331	Dic₁₃	—	2	1	no	—
332	Dic₁₃	—	2	2	no	—
333	Dic₁₃	—	2	1	no	—
334	Dic₁₃	C₂²×Q₈	1	2	yes	—
335	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
336	C₂²×Q₈	—	13	2	no	—
337	C₂²×Q₈	—	13	2	no	—
338	C₂²×D₄	—	13	1	no	—
339	C₂³×C₄	—	13	2	no	—
340	C₄⋊Q₈	—	13	1	no	—
341	C₄⋊Q₈	—	13	2	no	—
342	C₄⋊Q₈	—	13	1	no	—
343	C₄⋊Q₈	—	13	1	no	—
344	C₄⋊Q₈	—	13	1	no	—
345	C₄⋊Q₈	—	13	2	no	—
346	C₄⋊Q₈	—	13	1	no	—
347	C₄⋊Q₈	—	13	1	no	—
348	C₄⋊Q₈	—	13	1	no	—
349	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
350	#125	—	13	1	no	—
351	#125	—	13	1	no	—
352	#125	—	13	2	no	—
353	#125	—	13	2	no	—
354	#125	—	13	1	no	—
355	#125	—	13	1	no	—
356	#125	—	13	1	no	—
357	#125	—	13	1	no	—
358	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
359	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
360	C₂²⋊Q₈	—	13	2	no	—
361	C₂²⋊Q₈	—	13	1	no	—
362	C₂²⋊Q₈	—	13	2	no	—
363	C₂²⋊Q₈	—	13	2	no	—
364	C₂²⋊Q₈	—	13	2	no	—
365	C₂²⋊Q₈	—	13	2	no	—
366	C₂²⋊Q₈	—	13	2	no	—
367	C₂²⋊Q₈	—	13	1	no	—
368	C₂²⋊Q₈	—	13	2	no	—
369	C₂²⋊Q₈	—	13	1	no	—
370	C₂²⋊Q₈	—	13	2	no	—
371	C₂²⋊Q₈	—	13	2	no	—
372	C₂²⋊Q₈	—	13	2	no	—
373	C₂²⋊Q₈	—	13	2	no	—
374	C₂²⋊Q₈	—	13	2	no	—
375	C₂²⋊Q₈	—	13	2	no	—
376	C₂²⋊Q₈	—	13	2	no	—
377	C₂²⋊Q₈	—	13	2	no	—
378	C₂²⋊Q₈	—	13	1	no	—
379	C₂²⋊Q₈	—	13	2	no	—
380	C₂²⋊Q₈	—	13	2	no	—
381	C₂²⋊Q₈	—	13	2	no	—
382	C₂²⋊Q₈	—	13	2	no	—
383	C₂²⋊Q₈	—	13	2	no	—
384	C₂²⋊Q₈	—	13	2	no	—
385	C₂²⋊Q₈	—	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	2	no	—
390	C₂²⋊Q₈	—	13	2	no	—
391	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
392	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
393	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
394	C₄×Q₈	—	13	2	no	—
395	C₄×Q₈	—	13	2	no	—
396	C₄×Q₈	—	13	1	no	—
397	C₄×Q₈	—	13	1	no	—
398	C₄×Q₈	—	13	1	no	—
399	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
400	C₄×D₄	—	13	1	no	—
401	C₄×D₄	—	13	1	no	—
402	C₄×D₄	—	13	1	no	—
403	C₄×D₄	—	13	2	no	—
404	C₄×D₄	—	13	2	no	—
405	C₄×D₄	—	13	2	no	—
406	C₄×D₄	—	13	1	no	—
407	C₄×D₄	—	13	1	no	—
408	C₄×D₄	—	13	1	no	—
409	C₄×D₄	—	13	2	no	—
410	C₄×D₄	—	13	2	no	—
411	C₄×D₄	—	13	2	no	—
412	C₄×D₄	—	13	1	no	—
413	C₄×D₄	—	13	1	no	—
414	C₄×D₄	—	13	1	no	—
415	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
416	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
417	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
418	#117	—	13	1	no	—
419	#117	—	13	1	no	—
420	#117	—	13	1	no	—
421	#117	—	13	1	no	—
422	C₂×C₄⋊C₄	—	13	2	no	—
423	C₂×C₄⋊C₄	—	13	2	no	—
424	C₂×C₄⋊C₄	—	13	1	no	—
425	C₂×C₄⋊C₄	—	13	2	no	—
426	C₂×C₄⋊C₄	—	13	2	no	—
427	C₂×C₄⋊C₄	—	13	2	no	—
428	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
429	C₂×C₂²⋊C₄	—	13	2	no	—
430	C₂×C₂²⋊C₄	—	13	2	no	—
431	C₂×C₂²⋊C₄	—	13	2	no	—
432	C₂×C₂²⋊C₄	—	13	2	no	—
433	C₂×C₂²⋊C₄	—	13	2	no	—
434	C₂×C₄²	—	13	1	no	—
435	C₂×C₁₃	—	2	4	no	—
436	C₂×C₁₃	C₂³×Q₈	1	1	yes	characteristic
437	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₁₃	#585	1	1	yes	characteristic
439	D₁₃	—	2	2	no	—
440	D₁₃	—	2	4	no	—
441	C₂⁴	—	13	2	no	—
442	C₂×Q₈	—	13	2	no	—
443	C₂×Q₈	—	13	1	no	—
444	C₂×Q₈	—	13	1	no	—
445	C₂×Q₈	—	13	2	no	—
446	C₂×Q₈	—	13	1	no	—
447	C₂×Q₈	—	13	2	no	—
448	C₂×Q₈	—	13	2	no	—
449	C₂×Q₈	—	13	2	no	—
450	C₂×Q₈	—	52	4	no	—
451	C₂×Q₈	—	52	4	no	—
452	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
453	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
454	C₂×D₄	—	13	2	no	—
455	C₂×D₄	—	13	8	no	—
456	C₂×D₄	—	13	1	no	—
457	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
458	C₂²×C₄	—	13	1	no	—
459	C₂²×C₄	—	13	2	no	—
460	C₂²×C₄	—	13	2	no	—
461	C₂²×C₄	—	13	2	no	—
462	C₂²×C₄	—	13	1	no	—
463	C₂²×C₄	—	13	2	no	—
464	C₂²×C₄	—	13	1	no	—
465	C₂²×C₄	—	13	2	no	—
466	C₂²×C₄	—	13	2	no	—
467	C₂²×C₄	—	13	2	no	—
468	C₂²×C₄	—	13	2	no	—
469	C₂²×C₄	—	13	2	no	—
470	C₂²×C₄	—	13	2	no	—
471	C₂²×C₄	—	52	4	no	—
472	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
473	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
474	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
475	C₄⋊C₄	—	13	1	no	—
476	C₄⋊C₄	—	13	2	no	—
477	C₄⋊C₄	—	13	1	no	—
478	C₄⋊C₄	—	13	2	no	—
479	C₄⋊C₄	—	13	1	no	—
480	C₄⋊C₄	—	13	1	no	—
481	C₄⋊C₄	—	13	2	no	—
482	C₄⋊C₄	—	13	1	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	2	no	—
488	C₄⋊C₄	—	13	2	no	—
489	C₄⋊C₄	—	13	2	no	—
490	C₄⋊C₄	—	13	2	no	—
491	C₄⋊C₄	—	13	2	no	—
492	C₄⋊C₄	—	13	1	no	—
493	C₄⋊C₄	—	13	1	no	—
494	C₄⋊C₄	—	13	1	no	—
495	C₄⋊C₄	—	13	1	no	—
496	C₄⋊C₄	—	13	1	no	—
497	C₄⋊C₄	—	13	1	no	—
498	C₄⋊C₄	—	13	1	no	—
499	C₄⋊C₄	—	13	1	no	—
500	C₄⋊C₄	—	13	2	no	—
501	C₄⋊C₄	—	13	1	no	—
502	C₄⋊C₄	—	13	1	no	—
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	—	13	1	no	—
505	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
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	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
516	C₂²⋊C₄	—	13	2	no	—
517	C₂²⋊C₄	—	13	2	no	—
518	C₂²⋊C₄	—	13	2	no	—
519	C₂²⋊C₄	—	13	2	no	—
520	C₂²⋊C₄	—	13	1	no	—
521	C₂²⋊C₄	—	13	1	no	—
522	C₂²⋊C₄	—	13	2	no	—
523	C₂²⋊C₄	—	13	1	no	—
524	C₂²⋊C₄	—	13	1	no	—
525	C₂²⋊C₄	—	13	2	no	—
526	C₂²⋊C₄	—	13	2	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	C₂²×D₁₃	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
534	C₄²	—	13	1	no	—
535	C₄²	—	13	1	no	—
536	C₄²	—	13	1	no	—
537	C₄²	—	13	2	no	—
538	C₄²	—	13	2	no	—
539	C₄²	—	13	1	no	—
540	C₄²	—	13	1	no	—
541	C₄²	C₂²×D₁₃	1	1	yes	characteristic
542	C₄²	C₂²×D₁₃	1	1	yes	characteristic
543	C₄²	C₂²×D₁₃	1	1	yes	characteristic
544	C₁₃	#3501	1	1	yes	characteristic, complemented, Sylow
545	C₂³	—	13	1	no	—
546	C₂³	—	13	2	no	—
547	C₂³	—	13	8	no	—
548	C₂³	—	52	2	no	—
549	C₂³	—	52	2	no	—
550	C₂³	C₂³×D₁₃	1	2	yes	—
551	Q₈	—	4	2	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	26	2	no	—
554	Q₈	—	26	4	no	—
555	Q₈	—	26	2	no	—
556	Q₈	—	52	2	no	—
557	Q₈	—	52	1	no	—
558	Q₈	—	52	2	no	—
559	Q₈	—	52	2	no	—
560	Q₈	—	52	2	no	—
561	D₄	—	13	8	no	—
562	D₄	—	13	4	no	—
563	D₄	Q₈×D₁₃	1	4	yes	complemented
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	13	1	no	—
568	C₂×C₄	—	13	1	no	—
569	C₂×C₄	—	13	4	no	—
570	C₂×C₄	—	13	1	no	—
571	C₂×C₄	—	13	1	no	—
572	C₂×C₄	—	13	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	2	no	—
578	C₂×C₄	—	26	2	no	—
579	C₂×C₄	—	26	4	no	—
580	C₂×C₄	—	26	4	no	—
581	C₂×C₄	—	52	2	no	—
582	C₂×C₄	—	52	2	no	—
583	C₂×C₄	—	52	1	no	—
584	C₂×C₄	—	52	2	no	—
585	C₂×C₄	—	52	2	no	—
586	C₂×C₄	—	52	2	no	—
587	C₂×C₄	—	52	2	no	—
588	C₂×C₄	—	52	2	no	—
589	C₂×C₄	—	52	2	no	—
590	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₃	1	2	yes	—
593	C₂×C₄	C₂³×D₁₃	1	2	yes	—
594	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₃	1	2	yes	—
599	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	13	2	no	—
603	C₂²	—	13	4	no	—
604	C₂²	—	26	2	no	—
605	C₂²	—	26	1	no	—
606	C₂²	—	26	2	no	—
607	C₂²	—	26	1	no	—
608	C₂²	—	52	8	no	—
609	C₂²	C₂×Q₈×D₁₃	1	4	yes	—
610	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	13	2	no	—
621	C₄	—	13	2	no	—
622	C₄	—	26	1	no	—
623	C₄	—	26	2	no	—
624	C₄	—	26	1	no	—
625	C₄	—	26	1	no	—
626	C₄	—	26	2	no	—
627	C₄	—	26	1	no	—
628	C₄	—	26	2	no	—
629	C₄	—	26	1	no	—
630	C₄	C₂×Q₈×D₁₃	1	2	yes	—
631	C₂	—	2	4	no	—
632	C₂	—	26	2	no	—
633	C₂	—	26	4	no	—
634	C₂	C₂²×Q₈×D₁₃	1	1	yes	characteristic
635	C₂	#11719648	1	1	yes	characteristic
636	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#554	C₂
prime radical	C₂×D₄×D₁₃	C₂²
hypercenter	#554	D₁₃
hypocenter	C₁₃	#3501
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₁₃×#554	C₂	semidirect
2. #11719434	C₂	semidirect
3. #11719432	C₂	semidirect
4. #11719395	C₂	semidirect
5. #11719395	C₂	semidirect
6. #11719394	C₂	semidirect
7. #11719393	C₂	semidirect
8. #11719341	C₂	semidirect
9. #11719341	C₂	semidirect
10. #11719339	C₂	semidirect
11. #11719339	C₂	semidirect
12. #11719337	C₂	semidirect
13. D₁₃×C₂²⋊Q₈	C₂	semidirect
14. #11719284	C₂	semidirect
15. #11719283	C₂	semidirect
19. #11719244	C₂	semidirect
20. #11719244	C₂	semidirect
21. D₄×Dic₂₆	C₂	semidirect
22. #11719216	C₂	semidirect
23. C₂×#88150	C₂	semidirect
24. C₂×Q₈×D₁₃	C₂²	semidirect
27. C₂²×Dic₂₆	C₂²	semidirect
28. C₁₃×C₄⋊Q₈	C₂²	semidirect
29. C₁₃×#125	C₂²	semidirect
30. C₁₃×#125	C₂²	semidirect
31. C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₁₃×C₂²⋊Q₈	C₂²	semidirect
33. C₁₃×C₂²⋊Q₈	C₂²	semidirect
34. C₄×Q₈×C₁₃	C₂²	semidirect
38. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
41. #88200	C₂²	semidirect
42. #88200	C₂²	semidirect
43. #88198	C₂²	semidirect
44. #88198	C₂²	semidirect
53. #88178	C₂²	semidirect
54. #88178	C₂²	semidirect
55. #88178	C₂²	semidirect
56. C₂×#6101	C₂²	semidirect
57. C₂×#6101	C₂²	semidirect
60. #88151	C₂²	semidirect
61. #88151	C₂²	semidirect
68. #88150	C₂²	semidirect
69. #88150	C₂²	semidirect
70. #88150	C₂²	semidirect
71. #88150	C₂²	semidirect
72. #88150	C₂²	semidirect
73. #88150	C₂²	semidirect
74. #88150	C₂²	semidirect
75. #88150	C₂²	semidirect
82. C₄⋊C₄×D₁₃	C₂²	semidirect
83. C₄⋊C₄×D₁₃	C₂²	semidirect
84. C₄⋊C₄×D₁₃	C₂²	semidirect
85. #88144	C₂²	semidirect
86. #88144	C₂²	semidirect
87. #88143	C₂²	semidirect
88. #88143	C₂²	semidirect
89. #88143	C₂²	semidirect
90. #88143	C₂²	semidirect
91. #88142	C₂²	semidirect
92. #88142	C₂²	semidirect
93. #88142	C₂²	semidirect
94. #88142	C₂²	semidirect
95. #88142	C₂²	semidirect
96. #88142	C₂²	semidirect
97. #88141	C₂²	semidirect
98. #88141	C₂²	semidirect
105. #88132	C₂²	semidirect
106. #88132	C₂²	semidirect
107. #88132	C₂²	semidirect
108. #88132	C₂²	semidirect
109. #88132	C₂²	semidirect
110. #88132	C₂²	semidirect
117. #88124	C₂²	semidirect
118. #88124	C₂²	semidirect
119. #88123	C₂²	semidirect
120. C₄×Dic₂₆	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
135. D₄×D₁₃	Q₈	semidirect
230. C₂²×D₁₃	C₂×Q₈	semidirect
235. D₄×C₁₃	C₂×Q₈	semidirect
249. C₂²⋊D₁₃	C₂×Q₈	semidirect
263. D₅₂	C₂×Q₈	semidirect
273. C₄×D₁₃	C₂×Q₈	semidirect
290. #554	D₁₃	semidirect
349. C₄⋊Q₈	C₂×D₁₃	semidirect
358. #125	C₂×D₁₃	semidirect
359. #125	C₂×D₁₃	semidirect
391. C₂²⋊Q₈	C₂×D₁₃	semidirect
392. C₂²⋊Q₈	C₂×D₁₃	semidirect
393. C₂²⋊Q₈	C₂×D₁₃	semidirect
399. C₄×Q₈	C₂×D₁₃	semidirect
428. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
544. C₁₃	#3501	semidirect
563. D₄	Q₈×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#554	2
#11719434	2
#11719432	2
#11719395	2
#11719394	2
#11719393	2
#11719341	2
#11719339	2
#11719337	2
D₁₃×C₂²⋊Q₈	2
#11719284	2
#11719283	2
#11719250	2
C₄×D₄×D₁₃	2
#11719244	2
D₄×Dic₂₆	2
#11719216	2
C₂×#88150	2
#3501	13