Subgroups — #13129402

Order 1664.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 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×#88201	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719440	C₂	1	2	yes	maximal, complemented
7	#11719438	C₂	1	2	yes	maximal, complemented
8	#11719437	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719429	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719352	C₂	1	2	yes	maximal, complemented
11	#11719348	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719345	C₂	1	2	yes	maximal, complemented
13	#11719342	C₂	1	2	yes	maximal, complemented
14	#11719339	C₂	1	2	yes	maximal, complemented
15	#11719338	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719335	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719327	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719287	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719265	C₂	1	2	yes	maximal, complemented
21	#11719261	C₂	1	2	yes	maximal, complemented
22	#11719255	C₂	1	1	yes	maximal, characteristic, 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, complemented
26	C₂×#6131	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×D₅₂	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	1	yes	characteristic
33	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
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	1	yes	characteristic
40	#88201	C₂²	1	1	yes	characteristic
41	#88201	C₂²	1	1	yes	characteristic
42	#88201	C₂²	1	2	yes	—
43	#88201	C₂²	1	2	yes	—
44	#88201	C₂²	1	1	yes	characteristic
45	#88201	C₂²	1	1	yes	characteristic
46	#88201	C₂²	1	2	yes	complemented
47	#88200	C₂²	1	2	yes	complemented
48	#88200	C₂²	1	2	yes	complemented
49	#88200	C₂²	1	2	yes	complemented
50	#88200	C₂²	1	2	yes	complemented
51	#88200	C₂²	1	1	yes	characteristic, complemented
52	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
53	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
54	#88198	C₂²	1	1	yes	characteristic, 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	2	yes	—
59	#88189	C₂²	1	1	yes	characteristic
60	#88184	C₂²	1	1	yes	characteristic
61	#88184	C₂²	1	2	yes	complemented
62	#88183	C₂²	1	2	yes	complemented
63	#88183	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
66	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
68	C₂×#6103	C₂²	1	2	yes	—
69	C₂×#6103	C₂²	1	2	yes	—
70	#88180	C₂²	1	1	yes	characteristic, complemented
71	#88178	C₂²	1	1	yes	characteristic
72	#88178	C₂²	1	2	yes	—
73	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
74	#88152	C₂²	1	2	yes	complemented
75	#88152	C₂²	1	2	yes	complemented
76	#88152	C₂²	1	1	yes	characteristic, complemented
77	#88152	C₂²	1	2	yes	complemented
78	#88152	C₂²	1	2	yes	complemented
79	#88151	C₂²	1	2	yes	complemented
80	#88151	C₂²	1	2	yes	complemented
81	#88150	C₂²	1	2	yes	complemented
82	#88150	C₂²	1	2	yes	complemented
83	#88150	C₂²	1	2	yes	complemented
84	#88150	C₂²	1	2	yes	complemented
85	#88150	C₂²	1	2	yes	complemented
86	#88149	C₂²	1	2	yes	—
87	#88149	C₂²	1	1	yes	characteristic
88	#88148	C₂²	1	2	yes	—
89	#88148	C₂²	1	2	yes	—
90	#88148	C₂²	1	2	yes	complemented
91	#88148	C₂²	1	2	yes	complemented
92	#88148	C₂²	1	2	yes	complemented
93	#88147	C₂²	1	1	yes	characteristic
94	#88147	C₂²	1	2	yes	complemented
95	#88146	C₂²	1	2	yes	complemented
96	#88143	C₂²	1	1	yes	characteristic, complemented
97	#88143	C₂²	1	2	yes	complemented
98	#88142	C₂²	1	1	yes	characteristic, complemented
99	#88141	C₂²	1	2	yes	complemented
100	#88141	C₂²	1	1	yes	characteristic, complemented
101	#88140	C₂²	1	1	yes	characteristic
102	#88139	C₂²	1	1	yes	characteristic, complemented
103	#88139	C₂²	1	2	yes	complemented
104	#88139	C₂²	1	2	yes	complemented
105	#88138	C₂²	1	2	yes	—
106	#88138	C₂²	1	2	yes	complemented
107	#88137	C₂²	1	2	yes	complemented
108	#88136	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
111	#88133	C₂²	1	1	yes	characteristic, complemented
112	#88132	C₂²	1	1	yes	characteristic
113	#88132	C₂²	1	2	yes	—
114	#88131	C₂²	1	2	yes	—
115	#88130	C₂²	1	2	yes	complemented
116	#88130	C₂²	1	2	yes	complemented
117	#88129	C₂²	1	1	yes	characteristic
118	#88129	C₂²	1	2	yes	complemented
119	C₄×D₅₂	C₂²	1	1	yes	characteristic
120	#88126	C₂²	1	1	yes	characteristic, complemented
121	#88126	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
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	2	yes	—
138	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
142	#6131	—	4	2	no	—
143	Q₈×D₁₃	—	4	2	no	—
144	#6127	—	4	2	no	—
145	C₂×D₅₂	—	4	2	no	—
146	C₂×D₅₂	C₂³	1	1	yes	characteristic
147	C₂×D₅₂	C₂³	1	1	yes	characteristic
148	C₂×D₅₂	C₂³	1	2	yes	—
149	C₂×D₅₂	C₂³	1	2	yes	—
150	C₂×D₅₂	C₂³	1	2	yes	—
151	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₃	C₂³	1	2	yes	—
157	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
158	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
159	C₂×Dic₂₆	C₂³	1	2	yes	—
160	C₂×Dic₂₆	C₂³	1	2	yes	—
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	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	#6103	C₂³	1	2	yes	—
180	#6103	C₂³	1	1	yes	characteristic
181	#6103	C₂³	1	1	yes	characteristic
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	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	2	yes	—
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	2	yes	—
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	2	yes	—
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	1	yes	characteristic
199	#6103	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₃	C₂³	1	2	yes	—
203	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₃	C₂³	1	2	yes	—
205	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
206	#6101	C₂³	1	1	yes	characteristic
207	#6101	C₂³	1	1	yes	characteristic
208	#6101	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
219	#6101	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	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3561	—	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	4	no	—
232	C₂²×D₁₃	—	4	2	no	—
233	C₂²×D₁₃	—	4	2	no	—
234	C₂²×D₁₃	C₂⁴	1	2	yes	—
235	C₂²×D₁₃	C₂⁴	1	2	yes	—
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	2	yes	—
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
258	C₂²⋊D₁₃	—	4	2	no	—
259	C₂²⋊D₁₃	—	4	1	no	—
260	C₂×Dic₁₃	—	2	2	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	1	yes	characteristic
265	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
273	D₅₂	—	4	2	no	—
274	D₅₂	—	4	2	no	—
275	D₅₂	—	4	2	no	—
276	C₄×D₁₃	—	2	2	no	—
277	C₄×D₁₃	—	4	2	no	—
278	C₄×D₁₃	—	4	2	no	—
279	C₄×D₁₃	—	4	2	no	—
280	C₄×D₁₃	—	4	2	no	—
281	C₄×D₁₃	—	4	2	no	—
282	Dic₂₆	—	2	2	no	—
283	Dic₂₆	—	4	2	no	—
284	Dic₂₆	—	4	1	no	—
285	Dic₂₆	—	4	2	no	—
286	#563	—	13	2	no	—
287	#562	—	13	2	no	—
288	#556	—	13	1	no	—
289	#556	—	13	1	no	—
290	#551	—	13	2	no	—
291	#551	—	13	2	no	—
292	D₄×Q₈	—	13	1	no	—
293	D₄×Q₈	D₁₃	1	1	yes	characteristic, complemented
294	#548	—	13	1	no	—
295	#548	—	13	1	no	—
296	#546	—	13	1	no	—
297	#546	—	13	1	no	—
298	#543	—	13	2	no	—
299	#542	—	13	2	no	—
300	#542	—	13	2	no	—
301	#542	—	13	1	no	—
302	#542	—	13	1	no	—
303	#538	—	13	2	no	—
304	#536	—	13	1	no	—
305	#536	—	13	1	no	—
306	#533	—	13	1	no	—
307	#529	—	13	1	no	—
308	C₂×#124	—	13	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	no	—
314	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
315	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
316	C₂×D₁₃	—	2	1	no	—
317	C₂×D₁₃	—	2	2	no	—
318	C₂×D₁₃	—	2	2	no	—
319	C₂×D₁₃	—	2	1	no	—
320	C₂×D₁₃	—	2	2	no	—
321	C₂×D₁₃	—	2	2	no	—
322	C₂×D₁₃	—	2	2	no	—
323	C₂×D₁₃	—	2	2	no	—
324	C₂×D₁₃	—	2	1	no	—
325	C₂×D₁₃	—	8	4	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
335	Dic₁₃	—	2	2	no	—
336	Dic₁₃	—	2	1	no	—
337	Dic₁₃	—	2	1	no	—
338	Dic₁₃	—	2	1	no	—
339	Dic₁₃	—	2	1	no	—
340	Dic₁₃	—	2	1	no	—
341	Dic₁₃	—	2	1	no	—
342	Dic₁₃	—	2	2	no	—
343	Dic₁₃	—	2	1	no	—
344	C₂×#41	—	13	1	no	—
345	C₂×#41	—	13	1	no	—
346	C₂²×Q₈	—	13	1	no	—
347	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic
348	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
349	C₂²×D₄	—	13	1	no	—
350	C₄⋊Q₈	—	13	1	no	—
351	C₄⋊Q₈	—	13	1	no	—
352	C₄⋊Q₈	—	13	2	no	—
353	C₄⋊Q₈	—	13	1	no	—
354	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
355	C₄⋊Q₈	C₂×D₁₃	1	2	yes	complemented
356	#126	—	13	1	no	—
357	#126	—	13	2	no	—
358	#126	—	13	2	no	—
359	#126	—	13	2	no	—
360	#126	—	13	2	no	—
361	#126	—	13	1	no	—
362	#126	—	13	2	no	—
363	#126	—	13	2	no	—
364	#125	—	13	1	no	—
365	#125	—	13	2	no	—
366	#124	—	13	1	no	—
367	#124	—	13	1	no	—
368	#124	—	13	2	no	—
369	#124	—	13	1	no	—
370	#124	—	13	1	no	—
371	#124	—	13	2	no	—
372	#124	—	13	1	no	—
373	#124	—	13	2	no	—
374	#124	—	13	1	no	—
375	#124	—	13	2	no	—
376	#124	—	13	2	no	—
377	#124	—	13	1	no	—
378	#124	—	13	2	no	—
379	#123	—	13	1	no	—
380	#123	—	13	2	no	—
381	#123	—	13	2	no	—
382	#123	—	13	2	no	—
383	#123	—	13	2	no	—
384	#123	—	13	2	no	—
385	#123	—	13	2	no	—
386	#123	—	13	2	no	—
387	#123	—	13	1	no	—
388	#123	—	13	2	no	—
389	C₂²⋊Q₈	—	13	2	no	—
390	C₂²⋊Q₈	—	13	2	no	—
391	C₂²⋊Q₈	—	13	1	no	—
392	C₂²⋊Q₈	—	13	2	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	C₂²⋊Q₈	—	13	1	no	—
395	C₂²⋊Q₈	—	13	2	no	—
396	C₂²⋊Q₈	—	13	2	no	—
397	C₂²⋊Q₈	—	13	2	no	—
398	C₂²⋊Q₈	—	13	2	no	—
399	C₂²⋊Q₈	—	13	2	no	—
400	C₂²⋊Q₈	—	13	2	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	—	13	2	no	—
403	C₂²⋊Q₈	—	13	1	no	—
404	C₂²⋊Q₈	—	13	2	no	—
405	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
406	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
407	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
408	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
409	#121	—	13	1	no	—
410	#121	—	13	2	no	—
411	#121	—	13	1	no	—
412	#121	—	13	1	no	—
413	#121	—	13	2	no	—
414	#121	—	13	2	no	—
415	#121	—	13	2	no	—
416	#120	—	13	2	no	—
417	#120	—	13	2	no	—
418	C₄×Q₈	—	13	1	no	—
419	C₄×Q₈	—	13	1	no	—
420	C₄×Q₈	—	13	2	no	—
421	C₄×Q₈	—	13	1	no	—
422	C₄×Q₈	—	13	1	no	—
423	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
424	C₄×D₄	—	13	1	no	—
425	C₄×D₄	—	13	1	no	—
426	C₄×D₄	—	13	2	no	—
427	C₄×D₄	—	13	2	no	—
428	C₄×D₄	—	13	1	no	—
429	C₄×D₄	—	13	2	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
432	C₄×D₄	C₂×D₁₃	1	2	yes	—
433	#117	—	13	1	no	—
434	#117	—	13	2	no	—
435	#117	—	13	2	no	—
436	#117	—	13	1	no	—
437	#117	—	13	2	no	—
438	C₂×C₂²⋊C₄	—	13	2	no	—
439	C₂×C₂²⋊C₄	—	13	2	no	—
440	C₂×C₂²⋊C₄	—	13	2	no	—
441	C₂×C₂²⋊C₄	—	13	2	no	—
442	C₂×C₄²	—	13	1	no	—
443	C₂×C₁₃	—	2	2	no	—
444	C₂×C₁₃	—	4	1	no	—
445	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
447	C₂×C₁₃	#585	1	1	yes	characteristic
448	D₁₃	—	4	1	no	—
449	D₁₃	—	4	2	no	—
450	D₁₃	—	4	2	no	—
451	C₂⁴	—	13	2	no	—
452	#41	—	52	2	no	—
453	#41	—	52	2	no	—
454	C₂×Q₈	—	4	2	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	13	1	no	—
457	C₂×Q₈	—	13	1	no	—
458	C₂×Q₈	—	13	2	no	—
459	C₂×Q₈	—	13	2	no	—
460	C₂×Q₈	—	52	2	no	—
461	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
462	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
464	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
465	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
466	C₂×D₄	—	13	1	no	—
467	C₂×D₄	—	13	2	no	—
468	C₂×D₄	—	13	1	no	—
469	C₂×D₄	—	13	2	no	—
470	C₂×D₄	—	13	1	no	—
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	13	2	no	—
473	C₂×D₄	—	13	2	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	52	2	no	—
476	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
477	C₂²×C₄	—	13	1	no	—
478	C₂²×C₄	—	13	1	no	—
479	C₂²×C₄	—	13	1	no	—
480	C₂²×C₄	—	13	2	no	—
481	C₂²×C₄	—	13	2	no	—
482	C₂²×C₄	—	13	2	no	—
483	C₂²×C₄	—	13	2	no	—
484	C₂²×C₄	—	13	2	no	—
485	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
488	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	1	no	—
491	C₄⋊C₄	—	13	1	no	—
492	C₄⋊C₄	—	13	1	no	—
493	C₄⋊C₄	—	13	2	no	—
494	C₄⋊C₄	—	13	2	no	—
495	C₄⋊C₄	—	13	1	no	—
496	C₄⋊C₄	—	13	1	no	—
497	C₄⋊C₄	—	13	2	no	—
498	C₄⋊C₄	—	13	1	no	—
499	C₄⋊C₄	—	13	1	no	—
500	C₄⋊C₄	—	13	2	no	—
501	C₄⋊C₄	—	13	2	no	—
502	C₄⋊C₄	—	13	1	no	—
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	—	13	2	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	1	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	—	13	2	no	—
509	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
510	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
512	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
513	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
516	C₂²⋊C₄	—	13	1	no	—
517	C₂²⋊C₄	—	13	2	no	—
518	C₂²⋊C₄	—	13	1	no	—
519	C₂²⋊C₄	—	13	1	no	—
520	C₂²⋊C₄	—	13	1	no	—
521	C₂²⋊C₄	—	13	2	no	—
522	C₂²⋊C₄	—	13	2	no	—
523	C₂²⋊C₄	—	13	2	no	—
524	C₂²⋊C₄	—	13	2	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	—	13	2	no	—
532	C₂²⋊C₄	—	13	2	no	—
533	C₂²⋊C₄	—	13	2	no	—
534	C₂²⋊C₄	—	13	2	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	2	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
546	C₄²	—	13	1	no	—
547	C₄²	—	13	1	no	—
548	C₄²	—	13	1	no	—
549	C₄²	—	13	1	no	—
550	C₄²	—	13	2	no	—
551	C₄²	—	13	2	no	—
552	C₄²	—	13	1	no	—
553	C₄²	—	13	2	no	—
554	C₄²	C₂²×D₁₃	1	1	yes	characteristic
555	C₄²	C₂²×D₁₃	1	2	yes	—
556	C₁₃	#3561	1	1	yes	characteristic, complemented, Sylow
557	C₂³	—	13	2	no	—
558	C₂³	—	13	2	no	—
559	C₂³	—	13	1	no	—
560	C₂³	—	26	4	no	—
561	C₂³	—	52	2	no	—
562	C₂³	—	52	2	no	—
563	C₂³	C₂³×D₁₃	1	1	yes	characteristic
564	C₂³	C₂³×D₁₃	1	1	yes	characteristic
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	4	2	no	—
570	Q₈	—	26	2	no	—
571	Q₈	—	52	1	no	—
572	Q₈	—	52	2	no	—
573	Q₈	—	52	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	26	2	no	—
576	D₄	—	26	2	no	—
577	D₄	—	26	2	no	—
578	D₄	—	52	2	no	—
579	D₄	—	52	2	no	—
580	D₄	—	52	2	no	—
581	D₄	—	52	2	no	—
582	D₄	—	52	1	no	—
583	D₄	—	52	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	13	1	no	—
589	C₂×C₄	—	13	1	no	—
590	C₂×C₄	—	13	1	no	—
591	C₂×C₄	—	13	1	no	—
592	C₂×C₄	—	13	1	no	—
593	C₂×C₄	—	13	2	no	—
594	C₂×C₄	—	13	1	no	—
595	C₂×C₄	—	13	2	no	—
596	C₂×C₄	—	13	1	no	—
597	C₂×C₄	—	26	2	no	—
598	C₂×C₄	—	26	2	no	—
599	C₂×C₄	—	52	2	no	—
600	C₂×C₄	—	52	2	no	—
601	C₂×C₄	—	52	2	no	—
602	C₂×C₄	—	52	2	no	—
603	C₂×C₄	—	52	2	no	—
604	C₂×C₄	—	52	1	no	—
605	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₁₃	1	2	yes	—
607	C₂×C₄	C₂³×D₁₃	1	2	yes	—
608	C₂×C₄	C₂³×D₁₃	1	2	yes	—
609	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₁₃	1	2	yes	—
611	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	26	1	no	—
620	C₂²	—	26	2	no	—
621	C₂²	—	26	2	no	—
622	C₂²	—	26	1	no	—
623	C₂²	—	26	2	no	—
624	C₂²	—	26	2	no	—
625	C₂²	—	26	2	no	—
626	C₂²	—	26	2	no	—
627	C₂²	—	26	1	no	—
628	C₂²	—	104	4	no	—
629	C₂²	#88254	1	2	yes	—
630	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	26	1	no	—
640	C₄	—	26	2	no	—
641	C₄	—	26	1	no	—
642	C₄	—	26	1	no	—
643	C₄	—	26	1	no	—
644	C₄	—	26	1	no	—
645	C₄	—	26	2	no	—
646	C₄	—	26	1	no	—
647	C₄	—	26	1	no	—
648	C₄	#88251	1	2	yes	—
649	C₂	—	2	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	52	2	no	—
652	C₂	—	52	2	no	—
653	C₂	—	52	1	no	—
654	C₂	C₂×#88251	1	1	yes	characteristic
655	C₂	C₂×#88254	1	1	yes	characteristic
656	C₂	#11719652	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	#3561
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×#88201	C₂	semidirect
6. #11719440	C₂	semidirect
7. #11719438	C₂	semidirect
8. #11719437	C₂	semidirect
9. #11719429	C₂	semidirect
10. #11719352	C₂	semidirect
11. #11719348	C₂	semidirect
12. #11719345	C₂	semidirect
13. #11719342	C₂	semidirect
14. #11719339	C₂	semidirect
15. #11719338	C₂	semidirect
16. #11719335	C₂	semidirect
17. #11719327	C₂	semidirect
18. #11719287	C₂	semidirect
19. #11719273	C₂	semidirect
20. #11719265	C₂	semidirect
21. #11719261	C₂	semidirect
22. #11719255	C₂	semidirect
23. #11719243	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
46. #88201	C₂²	semidirect
47. #88200	C₂²	semidirect
48. #88200	C₂²	semidirect
49. #88200	C₂²	semidirect
50. #88200	C₂²	semidirect
51. #88200	C₂²	semidirect
52. Q₈×Dic₁₃	C₂²	semidirect
53. Q₈×Dic₁₃	C₂²	semidirect
54. #88198	C₂²	semidirect
55. #88198	C₂²	semidirect
56. #88198	C₂²	semidirect
61. #88184	C₂²	semidirect
62. #88183	C₂²	semidirect
63. #88183	C₂²	semidirect
66. C₄×C₂²⋊D₁₃	C₂²	semidirect
67. C₄×C₂²⋊D₁₃	C₂²	semidirect
70. #88180	C₂²	semidirect
74. #88152	C₂²	semidirect
75. #88152	C₂²	semidirect
76. #88152	C₂²	semidirect
77. #88152	C₂²	semidirect
78. #88152	C₂²	semidirect
79. #88151	C₂²	semidirect
80. #88151	C₂²	semidirect
81. #88150	C₂²	semidirect
82. #88150	C₂²	semidirect
83. #88150	C₂²	semidirect
84. #88150	C₂²	semidirect
85. #88150	C₂²	semidirect
90. #88148	C₂²	semidirect
91. #88148	C₂²	semidirect
92. #88148	C₂²	semidirect
94. #88147	C₂²	semidirect
95. #88146	C₂²	semidirect
96. #88143	C₂²	semidirect
97. #88143	C₂²	semidirect
98. #88142	C₂²	semidirect
99. #88141	C₂²	semidirect
100. #88141	C₂²	semidirect
102. #88139	C₂²	semidirect
103. #88139	C₂²	semidirect
104. #88139	C₂²	semidirect
106. #88138	C₂²	semidirect
107. #88137	C₂²	semidirect
111. #88133	C₂²	semidirect
115. #88130	C₂²	semidirect
116. #88130	C₂²	semidirect
118. #88129	C₂²	semidirect
120. #88126	C₂²	semidirect
121. #88126	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
293. D₄×Q₈	D₁₃	semidirect
348. C₂²×Q₈	C₂×D₁₃	semidirect
354. C₄⋊Q₈	C₂×D₁₃	semidirect
355. C₄⋊Q₈	C₂×D₁₃	semidirect
407. C₂²⋊Q₈	C₂×D₁₃	semidirect
408. C₂²⋊Q₈	C₂×D₁₃	semidirect
423. C₄×Q₈	C₂×D₁₃	semidirect
556. C₁₃	#3561	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×#88201	2
#11719440	2
#11719438	2
#11719437	2
#11719429	2
#11719352	2
#11719348	2
#11719345	2
#11719342	2
#11719339	2
#11719338	2
#11719335	2
#11719327	2
#11719287	2
#11719273	2
#11719265	2
#11719261	2
#11719255	2
#11719243	2
#3561	13