Subgroups — #13128776

Order 1664.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719511	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719496	C₂	1	2	yes	maximal, complemented
5	C₂×#88183	C₂	1	2	yes	maximal, complemented
6	#11719269	C₂	1	2	yes	maximal, complemented
7	#11719267	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719266	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719265	C₂	1	2	yes	maximal, complemented
10	#11719264	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719263	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719261	C₂	1	2	yes	maximal, complemented
13	#11719259	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719250	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719245	C₂	1	2	yes	maximal, complemented
17	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719212	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719200	C₂	1	2	yes	maximal, complemented
21	#11719195	C₂	1	2	yes	maximal, complemented
22	#11719184	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719184	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	—
27	C₂×#6129	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
29	C₂×#6127	C₂²	1	2	yes	complemented
30	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
33	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
35	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
38	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	#88207	C₂²	1	2	yes	—
40	#88207	C₂²	1	2	yes	complemented
41	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
42	#88194	C₂²	1	1	yes	characteristic
43	#88193	C₂²	1	2	yes	—
44	#88193	C₂²	1	2	yes	complemented
45	#88192	C₂²	1	1	yes	characteristic
46	#88192	C₂²	1	1	yes	characteristic, complemented
47	#88191	C₂²	1	2	yes	—
48	#88190	C₂²	1	1	yes	characteristic, complemented
49	#88189	C₂²	1	2	yes	complemented
50	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
51	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
52	#88184	C₂²	1	1	yes	characteristic
53	#88184	C₂²	1	1	yes	characteristic
54	#88184	C₂²	1	2	yes	complemented
55	#88184	C₂²	1	2	yes	complemented
56	#88183	C₂²	1	1	yes	characteristic
57	#88183	C₂²	1	2	yes	—
58	#88183	C₂²	1	2	yes	complemented
59	#88183	C₂²	1	1	yes	characteristic, complemented
60	#88183	C₂²	1	2	yes	complemented
61	#88183	C₂²	1	2	yes	complemented
62	#88183	C₂²	1	2	yes	complemented
63	#88183	C₂²	1	2	yes	complemented
64	#88183	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
72	C₂×#6103	C₂²	1	2	yes	complemented
73	C₂×#6103	C₂²	1	2	yes	complemented
74	#88180	C₂²	1	2	yes	complemented
75	#88178	C₂²	1	1	yes	characteristic, complemented
76	#88178	C₂²	1	1	yes	characteristic, complemented
77	#88178	C₂²	1	2	yes	complemented
78	#88178	C₂²	1	2	yes	complemented
79	C₂×#6101	C₂²	1	2	yes	complemented
80	C₂×#6101	C₂²	1	2	yes	complemented
81	#88152	C₂²	1	2	yes	complemented
82	#88151	C₂²	1	1	yes	characteristic, complemented
83	#88150	C₂²	1	2	yes	complemented
84	#88149	C₂²	1	1	yes	characteristic, complemented
85	#88148	C₂²	1	2	yes	complemented
86	#88147	C₂²	1	1	yes	characteristic, complemented
87	#88146	C₂²	1	1	yes	characteristic, complemented
88	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
89	#88144	C₂²	1	1	yes	characteristic, complemented
90	#88143	C₂²	1	2	yes	complemented
91	#88142	C₂²	1	1	yes	characteristic, complemented
92	#88141	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	2	yes	complemented
94	#88139	C₂²	1	2	yes	complemented
95	#88139	C₂²	1	2	yes	complemented
96	#88138	C₂²	1	2	yes	complemented
97	#88138	C₂²	1	2	yes	complemented
98	#88137	C₂²	1	2	yes	complemented
99	#88137	C₂²	1	2	yes	complemented
100	#88136	C₂²	1	2	yes	complemented
101	#88135	C₂²	1	2	yes	complemented
102	#88135	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
104	#88133	C₂²	1	2	yes	complemented
105	#88133	C₂²	1	2	yes	complemented
106	#88132	C₂²	1	2	yes	complemented
107	#88132	C₂²	1	2	yes	complemented
108	#88131	C₂²	1	2	yes	complemented
109	#88130	C₂²	1	1	yes	characteristic, complemented
110	#88130	C₂²	1	1	yes	characteristic, complemented
111	#88130	C₂²	1	2	yes	complemented
112	#88129	C₂²	1	1	yes	characteristic, complemented
113	#88129	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
116	#88126	C₂²	1	2	yes	complemented
117	#88126	C₂²	1	1	yes	characteristic, complemented
118	#88126	C₂²	1	1	yes	characteristic, complemented
119	#88124	C₂²	1	1	yes	characteristic, complemented
120	#88124	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	C₂⁴×C₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₃	C₂³	1	2	yes	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	C₂³	1	2	yes	—
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	—	4	4	no	—
130	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
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	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₃	—	4	4	no	—
139	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
148	C₂²×Dic₁₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₃	C₂³	1	2	yes	—
150	C₂²×Dic₁₃	C₂³	1	2	yes	—
151	#6129	—	2	4	no	—
152	D₄×D₁₃	—	2	4	no	—
153	#6127	—	4	4	no	—
154	C₂×D₅₂	C₂³	1	1	yes	characteristic
155	C₂×D₅₂	C₂³	1	1	yes	characteristic
156	C₂×D₅₂	C₂³	1	2	yes	—
157	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₃	C₂³	1	2	yes	—
160	C₂×C₄×D₁₃	C₂³	1	2	yes	—
161	C₂×C₄×D₁₃	C₂³	1	2	yes	—
162	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
163	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
164	C₂×Dic₂₆	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
185	#6103	C₂³	1	1	yes	characteristic
186	#6103	C₂³	1	2	yes	—
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	1	yes	characteristic
189	#6103	C₂³	1	1	yes	characteristic
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	1	yes	characteristic
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	1	yes	characteristic
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	2	yes	—
199	#6103	C₂³	1	2	yes	—
200	#6103	C₂³	1	2	yes	—
201	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	C₄⋊Dic₁₃	C₂³	1	2	yes	—
207	#6101	C₂³	1	1	yes	characteristic
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	1	yes	characteristic
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	1	yes	characteristic
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	1	yes	characteristic
215	#6101	C₂³	1	1	yes	characteristic
216	#6101	C₂³	1	1	yes	characteristic
217	#6101	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	2	yes	—
221	#6101	C₂³	1	2	yes	—
222	#6101	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3513	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	4	2	no	—
232	C₂³×C₁₃	C₂⁴	1	2	yes	—
233	C₂³×C₁₃	C₂⁴	1	2	yes	—
234	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₃	—	2	4	no	—
236	C₂²×D₁₃	—	4	2	no	—
237	C₂²×D₁₃	—	4	2	no	—
238	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₃	C₂⁴	1	2	yes	—
240	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
241	D₄×C₁₃	—	2	4	no	—
242	D₄×C₁₃	—	2	2	no	—
243	D₄×C₁₃	#41	1	4	yes	complemented
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
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	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₁₃	—	2	4	no	—
261	C₂²⋊D₁₃	—	2	4	no	—
262	C₂²⋊D₁₃	—	2	2	no	—
263	C₂²⋊D₁₃	—	2	4	no	—
264	C₂²⋊D₁₃	—	2	2	no	—
265	C₂²⋊D₁₃	—	4	2	no	—
266	C₂²⋊D₁₃	—	4	2	no	—
267	C₂²⋊D₁₃	—	4	2	no	—
268	C₂²⋊D₁₃	—	4	2	no	—
269	C₂×Dic₁₃	—	2	4	no	—
270	C₂×Dic₁₃	—	4	2	no	—
271	C₂×Dic₁₃	—	4	2	no	—
272	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₃	C₂⁴	1	2	yes	—
275	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₃	C₂⁴	1	2	yes	—
277	C₂×Dic₁₃	C₂⁴	1	2	yes	—
278	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
281	D₅₂	—	2	2	no	—
282	D₅₂	—	4	1	no	—
283	D₅₂	—	4	2	no	—
284	C₄×D₁₃	—	2	2	no	—
285	C₄×D₁₃	—	2	2	no	—
286	C₄×D₁₃	—	4	2	no	—
287	C₄×D₁₃	—	4	2	no	—
288	C₄×D₁₃	—	4	2	no	—
289	Dic₂₆	—	2	2	no	—
290	Dic₂₆	—	4	1	no	—
291	Dic₂₆	—	4	2	no	—
292	#559	—	13	1	no	—
293	#554	—	13	1	no	—
294	#553	—	13	2	no	—
295	#553	—	13	1	no	—
296	#552	—	13	1	no	—
297	#551	—	13	2	no	—
298	#551	—	13	2	no	—
299	#547	—	13	1	no	—
300	#546	—	13	1	no	—
301	#546	—	13	1	no	—
302	#546	—	13	2	no	—
303	D₄²	—	13	1	no	—
304	#542	—	13	1	no	—
305	#540	—	13	1	no	—
306	#539	—	13	2	no	—
307	#538	—	13	2	no	—
308	#529	—	13	1	no	—
309	#529	—	13	1	no	—
310	#525	—	13	2	no	—
311	C₂×#123	—	13	2	no	—
312	#520	—	13	1	no	—
313	#518	—	13	1	no	—
314	C₂×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	4	8	no	—
323	C₂²×C₁₃	C₂×#41	1	4	yes	—
324	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
325	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
326	C₂×D₁₃	—	2	1	no	—
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	2	no	—
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	2	no	—
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	2	2	no	—
333	C₂×D₁₃	—	2	1	no	—
334	C₂×D₁₃	—	2	1	no	—
335	C₂×D₁₃	—	8	4	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	C₂×#41	1	2	yes	—
344	Dic₁₃	—	2	2	no	—
345	Dic₁₃	—	2	1	no	—
346	Dic₁₃	—	2	1	no	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	—	2	2	no	—
349	Dic₁₃	—	2	1	no	—
350	Dic₁₃	—	2	1	no	—
351	Dic₁₃	—	2	1	no	—
352	Dic₁₃	—	2	2	no	—
353	C₂×#41	—	13	1	no	—
354	C₂×#41	—	13	2	no	—
355	C₂²×D₄	—	13	2	no	—
356	C₂²×D₄	—	13	1	no	—
357	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
358	C₂³×C₄	C₂×D₁₃	1	2	yes	complemented
359	C₄⋊Q₈	—	13	1	no	—
360	#127	—	13	1	no	—
361	#126	—	13	2	no	—
362	#126	—	13	2	no	—
363	#126	—	13	2	no	—
364	#126	—	13	2	no	—
365	#126	—	13	1	no	—
366	#126	—	13	1	no	—
367	#125	—	13	2	no	—
368	#125	—	13	1	no	—
369	#125	—	13	1	no	—
370	#125	—	13	1	no	—
371	#124	—	13	1	no	—
372	#124	—	13	2	no	—
373	#124	—	13	2	no	—
374	#124	—	13	1	no	—
375	#124	—	13	1	no	—
376	#123	—	13	2	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	2	no	—
385	#123	—	13	1	no	—
386	#123	—	13	2	no	—
387	#123	—	13	2	no	—
388	#123	—	13	2	no	—
389	#123	—	13	2	no	—
390	C₂²⋊Q₈	—	13	2	no	—
391	C₂²⋊Q₈	—	13	2	no	—
392	C₂²⋊Q₈	—	13	1	no	—
393	C₂²⋊Q₈	—	13	1	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	#121	—	13	2	no	—
399	#121	—	13	2	no	—
400	#121	—	13	1	no	—
401	#121	—	13	1	no	—
402	#121	—	13	2	no	—
403	#121	—	13	2	no	—
404	#121	—	13	1	no	—
405	#121	—	13	1	no	—
406	#121	—	13	1	no	—
407	#121	—	13	2	no	—
408	#121	—	13	2	no	—
409	#120	—	13	2	no	—
410	#120	—	13	2	no	—
411	#120	—	13	2	no	—
412	#120	—	13	2	no	—
413	C₄×Q₈	—	13	1	no	—
414	C₄×Q₈	—	13	1	no	—
415	C₄×Q₈	—	13	1	no	—
416	C₄×D₄	—	13	1	no	—
417	C₄×D₄	—	13	1	no	—
418	C₄×D₄	—	13	2	no	—
419	C₄×D₄	—	13	2	no	—
420	C₄×D₄	—	13	2	no	—
421	C₄×D₄	—	13	2	no	—
422	C₄×D₄	—	13	1	no	—
423	C₄×D₄	—	13	1	no	—
424	C₄×D₄	—	13	2	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	1	no	—
430	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
431	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
432	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
433	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
434	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
435	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
436	#117	—	13	2	no	—
437	#117	—	13	1	no	—
438	#117	—	13	2	no	—
439	#117	—	13	1	no	—
440	#117	—	13	1	no	—
441	#117	—	13	2	no	—
442	C₂×C₄⋊C₄	—	13	2	no	—
443	C₂×C₄⋊C₄	—	13	2	no	—
444	C₂×C₄⋊C₄	—	13	1	no	—
445	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
446	C₂×C₂²⋊C₄	—	13	2	no	—
447	C₂×C₂²⋊C₄	—	13	2	no	—
448	C₂×C₂²⋊C₄	—	13	2	no	—
449	C₂×C₂²⋊C₄	—	13	2	no	—
450	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
451	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
452	C₂×C₁₃	—	2	4	no	—
453	C₂×C₁₃	—	2	2	no	—
454	C₂×C₁₃	—	4	2	no	—
455	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
456	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₁₃	#585	1	1	yes	characteristic
458	D₁₃	—	4	1	no	—
459	D₁₃	—	4	2	no	—
460	D₁₃	—	4	1	no	—
461	C₂⁴	—	13	2	no	—
462	C₂⁴	C₂²×D₁₃	1	2	yes	—
463	#41	—	26	4	no	—
464	#41	—	52	4	no	—
465	C₂×Q₈	—	13	1	no	—
466	C₂×Q₈	—	13	1	no	—
467	C₂×Q₈	—	13	2	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	13	2	no	—
470	C₂×D₄	—	13	2	no	—
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	13	2	no	—
473	C₂×D₄	—	13	1	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	13	2	no	—
476	C₂×D₄	—	13	2	no	—
477	C₂×D₄	—	13	2	no	—
478	C₂×D₄	—	13	1	no	—
479	C₂×D₄	—	13	1	no	—
480	C₂×D₄	—	13	2	no	—
481	C₂×D₄	—	26	4	no	—
482	C₂×D₄	—	52	4	no	—
483	C₂×D₄	C₂²×D₁₃	1	2	yes	—
484	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₂²×C₄	—	4	4	no	—
487	C₂²×C₄	—	13	2	no	—
488	C₂²×C₄	—	13	2	no	—
489	C₂²×C₄	—	13	2	no	—
490	C₂²×C₄	—	13	1	no	—
491	C₂²×C₄	—	13	1	no	—
492	C₂²×C₄	—	13	2	no	—
493	C₂²×C₄	—	13	2	no	—
494	C₂²×C₄	—	13	2	no	—
495	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
498	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
500	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
501	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
502	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	—	13	1	no	—
505	C₄⋊C₄	—	13	1	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	1	no	—
508	C₄⋊C₄	—	13	2	no	—
509	C₄⋊C₄	—	13	2	no	—
510	C₄⋊C₄	—	13	2	no	—
511	C₄⋊C₄	—	13	2	no	—
512	C₄⋊C₄	—	13	1	no	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	—	13	1	no	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	2	no	—
517	C₄⋊C₄	—	13	2	no	—
518	C₄⋊C₄	—	13	2	no	—
519	C₄⋊C₄	—	13	1	no	—
520	C₄⋊C₄	—	13	1	no	—
521	C₄⋊C₄	—	13	2	no	—
522	C₄⋊C₄	—	13	1	no	—
523	C₄⋊C₄	—	13	1	no	—
524	C₄⋊C₄	—	13	1	no	—
525	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
528	C₂²⋊C₄	—	13	1	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	1	no	—
534	C₂²⋊C₄	—	13	2	no	—
535	C₂²⋊C₄	—	13	2	no	—
536	C₂²⋊C₄	—	13	2	no	—
537	C₂²⋊C₄	—	13	2	no	—
538	C₂²⋊C₄	—	13	1	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	—	13	2	no	—
544	C₂²⋊C₄	—	13	2	no	—
545	C₂²⋊C₄	—	13	2	no	—
546	C₂²⋊C₄	—	13	1	no	—
547	C₂²⋊C₄	—	13	1	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	1	no	—
550	C₂²⋊C₄	—	13	1	no	—
551	C₂²⋊C₄	—	13	2	no	—
552	C₂²⋊C₄	—	13	1	no	—
553	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
557	C₄²	—	13	2	no	—
558	C₄²	—	13	2	no	—
559	C₄²	—	13	2	no	—
560	C₄²	—	13	1	no	—
561	C₄²	—	13	1	no	—
562	C₄²	C₂²×D₁₃	1	1	yes	characteristic
563	C₄²	C₂²×D₁₃	1	1	yes	characteristic
564	C₄²	C₂²×D₁₃	1	1	yes	characteristic
565	C₄²	C₂²×D₁₃	1	1	yes	characteristic
566	C₁₃	#3513	1	1	yes	characteristic, complemented, Sylow
567	C₂³	—	2	4	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	13	1	no	—
571	C₂³	—	13	2	no	—
572	C₂³	—	13	1	no	—
573	C₂³	—	26	4	no	—
574	C₂³	—	52	2	no	—
575	C₂³	—	52	2	no	—
576	C₂³	C₂³×D₁₃	1	2	yes	—
577	C₂³	C₂³×D₁₃	1	2	yes	—
578	C₂³	C₂³×D₁₃	1	1	yes	characteristic
579	Q₈	—	26	2	no	—
580	Q₈	—	52	1	no	—
581	Q₈	—	52	2	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	26	4	no	—
585	D₄	—	26	4	no	—
586	D₄	—	26	2	no	—
587	D₄	—	26	4	no	—
588	D₄	—	26	2	no	—
589	D₄	—	26	2	no	—
590	D₄	—	52	1	no	—
591	D₄	—	52	2	no	—
592	D₄	—	52	2	no	—
593	D₄	—	52	2	no	—
594	D₄	—	52	2	no	—
595	D₄	—	52	2	no	—
596	D₄	#6127	1	4	yes	complemented
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	13	1	no	—
606	C₂×C₄	—	13	2	no	—
607	C₂×C₄	—	13	1	no	—
608	C₂×C₄	—	13	1	no	—
609	C₂×C₄	—	13	2	no	—
610	C₂×C₄	—	13	1	no	—
611	C₂×C₄	—	13	2	no	—
612	C₂×C₄	—	13	1	no	—
613	C₂×C₄	—	13	1	no	—
614	C₂×C₄	—	26	4	no	—
615	C₂×C₄	—	26	2	no	—
616	C₂×C₄	—	26	2	no	—
617	C₂×C₄	—	52	2	no	—
618	C₂×C₄	—	52	2	no	—
619	C₂×C₄	—	52	2	no	—
620	C₂×C₄	—	52	2	no	—
621	C₂×C₄	—	52	2	no	—
622	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₃	1	2	yes	—
624	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₃	1	2	yes	—
629	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	4	8	no	—
638	C₂²	—	26	1	no	—
639	C₂²	—	26	1	no	—
640	C₂²	—	26	2	no	—
641	C₂²	—	26	1	no	—
642	C₂²	—	26	2	no	—
643	C₂²	—	26	1	no	—
644	C₂²	—	26	2	no	—
645	C₂²	—	26	1	no	—
646	C₂²	—	26	1	no	—
647	C₂²	—	104	4	no	—
648	C₂²	C₂×#6127	1	4	yes	—
649	C₂²	#88251	1	2	yes	—
650	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	26	1	no	—
659	C₄	—	26	1	no	—
660	C₄	—	26	2	no	—
661	C₄	—	26	1	no	—
662	C₄	—	26	2	no	—
663	C₄	—	26	1	no	—
664	C₄	—	26	2	no	—
665	C₄	—	26	1	no	—
666	C₄	—	26	1	no	—
667	C₄	C₂×#6127	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	52	1	no	—
672	C₂	—	52	2	no	—
673	C₂	—	52	1	no	—
674	C₂	C₂²×#6127	1	1	yes	characteristic
675	C₂	C₂×#88251	1	1	yes	characteristic
676	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₂×C₄×D₄×C₁₃	C₂
hypercenter	C₂×C₄×D₄	D₁₃
hypocenter	C₁₃	#3513
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×D₄×C₁₃	C₂	semidirect
2. #11719511	C₂	semidirect
3. D₄×C₂²⋊D₁₃	C₂	semidirect
4. #11719496	C₂	semidirect
5. C₂×#88183	C₂	semidirect
6. #11719269	C₂	semidirect
7. #11719267	C₂	semidirect
8. #11719266	C₂	semidirect
9. #11719265	C₂	semidirect
10. #11719264	C₂	semidirect
11. #11719263	C₂	semidirect
12. #11719261	C₂	semidirect
13. #11719259	C₂	semidirect
14. #11719251	C₂	semidirect
15. #11719250	C₂	semidirect
16. #11719245	C₂	semidirect
17. #11719244	C₂	semidirect
18. #11719218	C₂	semidirect
19. #11719212	C₂	semidirect
20. #11719200	C₂	semidirect
21. #11719195	C₂	semidirect
22. #11719184	C₂	semidirect
23. #11719184	C₂	semidirect
25. C₂³×C₄×C₁₃	C₂²	semidirect
29. C₂×#6127	C₂²	semidirect
32. C₄×D₄×C₁₃	C₂²	semidirect
33. C₄×D₄×C₁₃	C₂²	semidirect
34. C₄×D₄×C₁₃	C₂²	semidirect
35. C₄×D₄×C₁₃	C₂²	semidirect
36. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
37. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
38. C₂×C₄²×C₁₃	C₂²	semidirect
40. #88207	C₂²	semidirect
41. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
44. #88193	C₂²	semidirect
46. #88192	C₂²	semidirect
48. #88190	C₂²	semidirect
49. #88189	C₂²	semidirect
54. #88184	C₂²	semidirect
55. #88184	C₂²	semidirect
58. #88183	C₂²	semidirect
59. #88183	C₂²	semidirect
60. #88183	C₂²	semidirect
61. #88183	C₂²	semidirect
62. #88183	C₂²	semidirect
63. #88183	C₂²	semidirect
64. #88183	C₂²	semidirect
66. C₄×C₂²⋊D₁₃	C₂²	semidirect
67. C₄×C₂²⋊D₁₃	C₂²	semidirect
68. C₄×C₂²⋊D₁₃	C₂²	semidirect
69. C₄×C₂²⋊D₁₃	C₂²	semidirect
70. C₄×C₂²⋊D₁₃	C₂²	semidirect
71. C₄×C₂²⋊D₁₃	C₂²	semidirect
72. C₂×#6103	C₂²	semidirect
73. C₂×#6103	C₂²	semidirect
74. #88180	C₂²	semidirect
75. #88178	C₂²	semidirect
76. #88178	C₂²	semidirect
77. #88178	C₂²	semidirect
78. #88178	C₂²	semidirect
79. C₂×#6101	C₂²	semidirect
80. C₂×#6101	C₂²	semidirect
81. #88152	C₂²	semidirect
82. #88151	C₂²	semidirect
83. #88150	C₂²	semidirect
84. #88149	C₂²	semidirect
85. #88148	C₂²	semidirect
86. #88147	C₂²	semidirect
87. #88146	C₂²	semidirect
88. C₄⋊C₄×D₁₃	C₂²	semidirect
89. #88144	C₂²	semidirect
90. #88143	C₂²	semidirect
91. #88142	C₂²	semidirect
92. #88141	C₂²	semidirect
93. #88140	C₂²	semidirect
94. #88139	C₂²	semidirect
95. #88139	C₂²	semidirect
96. #88138	C₂²	semidirect
97. #88138	C₂²	semidirect
98. #88137	C₂²	semidirect
99. #88137	C₂²	semidirect
100. #88136	C₂²	semidirect
101. #88135	C₂²	semidirect
102. #88135	C₂²	semidirect
103. C₂²⋊C₄×D₁₃	C₂²	semidirect
104. #88133	C₂²	semidirect
105. #88133	C₂²	semidirect
106. #88132	C₂²	semidirect
107. #88132	C₂²	semidirect
108. #88131	C₂²	semidirect
109. #88130	C₂²	semidirect
110. #88130	C₂²	semidirect
111. #88130	C₂²	semidirect
112. #88129	C₂²	semidirect
113. #88129	C₂²	semidirect
114. C₄×D₅₂	C₂²	semidirect
115. C₄×D₅₂	C₂²	semidirect
116. #88126	C₂²	semidirect
117. #88126	C₂²	semidirect
118. #88126	C₂²	semidirect
119. #88124	C₂²	semidirect
120. #88124	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
243. D₄×C₁₃	#41	semidirect
314. C₂×C₄×D₄	D₁₃	semidirect
358. C₂³×C₄	C₂×D₁₃	semidirect
432. C₄×D₄	C₂×D₁₃	semidirect
433. C₄×D₄	C₂×D₁₃	semidirect
434. C₄×D₄	C₂×D₁₃	semidirect
435. C₄×D₄	C₂×D₁₃	semidirect
445. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
450. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
451. C₂×C₄²	C₂×D₁₃	semidirect
566. C₁₃	#3513	semidirect
596. D₄	#6127	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₄×C₁₃	2
#11719511	2
D₄×C₂²⋊D₁₃	2
#11719496	2
C₂×#88183	2
#11719269	2
#11719267	2
#11719266	2
#11719265	2
#11719264	2
#11719263	2
#11719261	2
#11719259	2
#11719251	2
#11719250	2
#11719245	2
#11719244	2
#11719218	2
#11719212	2
#11719200	2
#11719195	2
#11719184	2
#3513	13