Subgroups — #13128761

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	D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719511	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719511	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719511	C₂	1	2	yes	maximal, complemented
5	#11719503	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#88189	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719424	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719418	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719319	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719316	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719308	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719307	C₂	1	2	yes	maximal, complemented
14	#11719306	C₂	1	2	yes	maximal, complemented
15	#11719305	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719298	C₂	1	2	yes	maximal, complemented
17	#11719292	C₂	1	2	yes	maximal, complemented
18	#11719292	C₂	1	2	yes	maximal, complemented
19	#11719291	C₂	1	2	yes	maximal, complemented
20	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719246	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂³×Dic₁₃	C₂²	1	2	yes	complemented
28	C₂×#6129	C₂²	1	1	yes	characteristic
29	C₂×#6129	C₂²	1	2	yes	complemented
30	C₁₃×#127	C₂²	1	1	yes	characteristic
31	C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₁₃×#121	C₂²	1	2	yes	—
33	C₁₃×#121	C₂²	1	1	yes	characteristic
34	C₁₃×#120	C₂²	1	2	yes	—
35	C₁₃×#120	C₂²	1	2	yes	—
36	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	#88207	C₂²	1	2	yes	complemented
39	#88207	C₂²	1	2	yes	complemented
40	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
41	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
44	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
45	#88193	C₂²	1	1	yes	characteristic
46	#88193	C₂²	1	2	yes	complemented
47	#88193	C₂²	1	2	yes	complemented
48	#88193	C₂²	1	2	yes	complemented
49	#88193	C₂²	1	2	yes	complemented
50	#88192	C₂²	1	1	yes	characteristic, complemented
51	#88192	C₂²	1	1	yes	characteristic, complemented
52	#88192	C₂²	1	2	yes	complemented
53	#88190	C₂²	1	2	yes	complemented
54	#88190	C₂²	1	1	yes	characteristic, complemented
55	#88190	C₂²	1	1	yes	characteristic, complemented
56	#88190	C₂²	1	2	yes	complemented
57	#88189	C₂²	1	1	yes	characteristic
58	#88189	C₂²	1	2	yes	—
59	#88189	C₂²	1	2	yes	complemented
60	#88189	C₂²	1	2	yes	complemented
61	#88189	C₂²	1	2	yes	complemented
62	#88189	C₂²	1	2	yes	complemented
63	#88189	C₂²	1	2	yes	complemented
64	#88189	C₂²	1	2	yes	complemented
65	#88189	C₂²	1	2	yes	complemented
66	#88189	C₂²	1	2	yes	complemented
67	#88189	C₂²	1	2	yes	complemented
68	#88189	C₂²	1	2	yes	complemented
69	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
70	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
71	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
72	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
73	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
74	D₄×Dic₁₃	C₂²	1	2	yes	complemented
75	D₄×Dic₁₃	C₂²	1	2	yes	complemented
76	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
77	D₄×Dic₁₃	C₂²	1	2	yes	complemented
78	D₄×Dic₁₃	C₂²	1	2	yes	complemented
79	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
80	D₄×Dic₁₃	C₂²	1	2	yes	complemented
81	D₄×Dic₁₃	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
85	#88180	C₂²	1	1	yes	characteristic, complemented
86	#88180	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
88	#88178	C₂²	1	2	yes	complemented
89	#88178	C₂²	1	1	yes	characteristic, complemented
90	#88178	C₂²	1	1	yes	characteristic, complemented
91	C₂×#6101	C₂²	1	2	yes	complemented
92	C₂×#6101	C₂²	1	2	yes	complemented
93	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
94	#88152	C₂²	1	1	yes	characteristic, complemented
95	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
96	#88144	C₂²	1	1	yes	characteristic, complemented
97	#88143	C₂²	1	1	yes	characteristic, complemented
98	#88143	C₂²	1	2	yes	complemented
99	#88142	C₂²	1	1	yes	characteristic, complemented
100	#88141	C₂²	1	1	yes	characteristic, complemented
101	#88140	C₂²	1	1	yes	characteristic, complemented
102	#88139	C₂²	1	1	yes	characteristic, complemented
103	#88137	C₂²	1	2	yes	complemented
104	#88135	C₂²	1	2	yes	complemented
105	#88135	C₂²	1	2	yes	complemented
106	#88133	C₂²	1	1	yes	characteristic, complemented
107	#88133	C₂²	1	2	yes	complemented
108	#88133	C₂²	1	2	yes	complemented
109	#88133	C₂²	1	2	yes	complemented
110	#88133	C₂²	1	2	yes	complemented
111	#88132	C₂²	1	1	yes	characteristic, complemented
112	#88132	C₂²	1	2	yes	complemented
113	#88132	C₂²	1	2	yes	complemented
114	#88132	C₂²	1	2	yes	complemented
115	#88132	C₂²	1	2	yes	complemented
116	#88131	C₂²	1	2	yes	complemented
117	#88131	C₂²	1	2	yes	complemented
118	#88131	C₂²	1	2	yes	complemented
119	#88126	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	C₂⁴×C₁₃	C₂³	1	2	yes	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	C₂³	1	2	yes	—
129	C₂×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₃	C₂³	1	2	yes	—
133	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₁₃	C₂³	1	2	yes	—
135	C₂×D₄×C₁₃	C₂³	1	2	yes	—
136	C₂×D₄×C₁₃	C₂³	1	2	yes	—
137	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₃	—	4	4	no	—
147	C₂²×Dic₁₃	C₂³	1	2	yes	—
148	C₂²×Dic₁₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
150	C₂²×Dic₁₃	C₂³	1	2	yes	—
151	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
152	C₂²×Dic₁₃	C₂³	1	2	yes	—
153	C₂²×Dic₁₃	C₂³	1	2	yes	—
154	C₂²×Dic₁₃	C₂³	1	2	yes	—
155	C₂²×Dic₁₃	C₂³	1	2	yes	—
156	C₂²×Dic₁₃	C₂³	1	2	yes	—
157	C₂²×Dic₁₃	C₂³	1	2	yes	—
158	#6129	—	2	4	no	—
159	#6129	—	4	4	no	—
160	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
172	C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
183	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	1	yes	characteristic
195	#6103	C₂³	1	1	yes	characteristic
196	#6103	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	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	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	1	yes	characteristic
207	#6101	C₂³	1	1	yes	characteristic
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	2	yes	—
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	1	yes	characteristic
217	#6101	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	C₄×Dic₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
228	#3513	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	4	2	no	—
233	C₂³×C₁₃	—	4	2	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂³×C₁₃	C₂⁴	1	2	yes	—
237	C₂³×C₁₃	C₂⁴	1	2	yes	—
238	C₂³×C₁₃	C₂⁴	1	2	yes	—
239	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
241	D₄×C₁₃	—	2	4	no	—
242	D₄×C₁₃	—	2	4	no	—
243	D₄×C₁₃	—	2	4	no	—
244	D₄×C₁₃	—	2	2	no	—
245	D₄×C₁₃	—	2	2	no	—
246	D₄×C₁₃	—	2	2	no	—
247	D₄×C₁₃	—	4	2	no	—
248	D₄×C₁₃	—	4	2	no	—
249	D₄×C₁₃	—	4	2	no	—
250	D₄×C₁₃	#41	1	4	yes	complemented
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
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	2	yes	—
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₁₃	—	2	4	no	—
261	C₂²⋊D₁₃	—	2	2	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂²⋊D₁₃	—	4	1	no	—
264	C₂²⋊D₁₃	—	4	2	no	—
265	C₂×Dic₁₃	—	2	4	no	—
266	C₂×Dic₁₃	—	2	4	no	—
267	C₂×Dic₁₃	—	2	2	no	—
268	C₂×Dic₁₃	—	4	2	no	—
269	C₂×Dic₁₃	—	4	2	no	—
270	C₂×Dic₁₃	—	4	2	no	—
271	C₂×Dic₁₃	—	4	2	no	—
272	C₂×Dic₁₃	—	4	2	no	—
273	C₂×Dic₁₃	—	4	2	no	—
274	C₂×Dic₁₃	—	4	1	no	—
275	C₂×Dic₁₃	—	4	2	no	—
276	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
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	C₂×Dic₁₃	C₂⁴	1	2	yes	—
282	C₂×Dic₁₃	C₂⁴	1	2	yes	—
283	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₁₃	C₂⁴	1	2	yes	—
287	C₄×D₁₃	—	2	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	2	no	—
301	#546	—	13	1	no	—
302	#546	—	13	1	no	—
303	D₄²	D₁₃	1	1	yes	characteristic, complemented
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	—	13	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	4	8	no	—
329	C₂²×C₁₃	—	8	4	no	—
330	C₂²×C₁₃	C₂×#41	1	4	yes	—
331	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
332	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
333	C₂×D₁₃	—	2	1	no	—
334	C₂×D₁₃	—	2	1	no	—
335	C₂×D₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	C₂×#41	1	2	yes	—
342	Dic₁₃	—	2	2	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	—	2	1	no	—
345	Dic₁₃	—	2	2	no	—
346	Dic₁₃	—	2	2	no	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	—	2	1	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	C₂×D₁₃	1	1	yes	characteristic
356	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
357	C₂²×D₄	C₂×D₁₃	1	2	yes	—
358	C₂³×C₄	—	13	2	no	—
359	C₄⋊Q₈	—	13	1	no	—
360	#127	C₂×D₁₃	1	1	yes	characteristic
361	#126	—	13	1	no	—
362	#126	—	13	2	no	—
363	#126	—	13	1	no	—
364	#126	—	13	2	no	—
365	#126	—	13	2	no	—
366	#126	—	13	2	no	—
367	#125	—	13	1	no	—
368	#125	—	13	1	no	—
369	#125	—	13	2	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	1	no	—
377	#123	—	13	2	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	2	no	—
386	#123	—	13	2	no	—
387	#123	—	13	2	no	—
388	#123	—	13	1	no	—
389	#123	—	13	2	no	—
390	C₂²⋊Q₈	—	13	1	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	#121	—	13	2	no	—
399	#121	—	13	2	no	—
400	#121	—	13	1	no	—
401	#121	—	13	2	no	—
402	#121	—	13	2	no	—
403	#121	—	13	1	no	—
404	#121	—	13	1	no	—
405	#121	—	13	2	no	—
406	#121	C₂×D₁₃	1	1	yes	characteristic
407	#121	C₂×D₁₃	1	2	yes	—
408	#121	C₂×D₁₃	1	1	yes	characteristic
409	#120	—	13	2	no	—
410	#120	—	13	2	no	—
411	#120	C₂×D₁₃	1	2	yes	—
412	#120	C₂×D₁₃	1	2	yes	—
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	2	no	—
418	C₄×D₄	—	13	1	no	—
419	C₄×D₄	—	13	1	no	—
420	C₄×D₄	—	13	2	no	—
421	C₄×D₄	—	13	1	no	—
422	C₄×D₄	—	13	2	no	—
423	C₄×D₄	—	13	1	no	—
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	2	no	—
429	C₄×D₄	—	13	2	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	—	13	1	no	—
432	C₄×D₄	—	13	2	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
435	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
436	#117	—	13	1	no	—
437	#117	—	13	1	no	—
438	#117	—	13	2	no	—
439	#117	—	13	2	no	—
440	#117	—	13	2	no	—
441	#117	—	13	1	no	—
442	C₂×C₄⋊C₄	—	13	1	no	—
443	C₂×C₄⋊C₄	—	13	2	no	—
444	C₂×C₄⋊C₄	—	13	2	no	—
445	C₂×C₄⋊C₄	—	13	1	no	—
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	—	13	2	no	—
451	C₂×C₄²	—	13	1	no	—
452	C₂×C₁₃	—	2	2	no	—
453	C₂×C₁₃	—	2	4	no	—
454	C₂×C₁₃	—	4	2	no	—
455	C₂×C₁₃	—	4	2	no	—
456	C₂×C₁₃	—	4	1	no	—
457	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
458	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₁₃	#585	1	1	yes	characteristic
460	D₁₃	—	4	1	no	—
461	C₂⁴	C₂²×D₁₃	1	2	yes	—
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	—	2	4	no	—
470	C₂×D₄	—	4	4	no	—
471	C₂×D₄	—	13	2	no	—
472	C₂×D₄	—	13	1	no	—
473	C₂×D₄	—	13	1	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	13	2	no	—
476	C₂×D₄	C₂²×D₁₃	1	2	yes	—
477	C₂×D₄	C₂²×D₁₃	1	2	yes	—
478	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
480	C₂×D₄	C₂²×D₁₃	1	2	yes	—
481	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₁₃	1	2	yes	—
483	C₂×D₄	C₂²×D₁₃	1	2	yes	—
484	C₂×D₄	C₂²×D₁₃	1	2	yes	—
485	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₂²×C₄	—	13	1	no	—
487	C₂²×C₄	—	13	2	no	—
488	C₂²×C₄	—	13	2	no	—
489	C₂²×C₄	—	13	1	no	—
490	C₂²×C₄	—	13	2	no	—
491	C₂²×C₄	—	13	2	no	—
492	C₂²×C₄	—	13	2	no	—
493	C₂²×C₄	—	13	2	no	—
494	C₂²×C₄	—	13	2	no	—
495	C₂²×C₄	—	13	2	no	—
496	C₂²×C₄	—	13	2	no	—
497	C₂²×C₄	—	13	1	no	—
498	C₂²×C₄	—	13	2	no	—
499	C₂²×C₄	—	52	4	no	—
500	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
503	C₄⋊C₄	—	13	1	no	—
504	C₄⋊C₄	—	13	2	no	—
505	C₄⋊C₄	—	13	1	no	—
506	C₄⋊C₄	—	13	1	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	—	13	1	no	—
509	C₄⋊C₄	—	13	2	no	—
510	C₄⋊C₄	—	13	2	no	—
511	C₄⋊C₄	—	13	2	no	—
512	C₄⋊C₄	—	13	2	no	—
513	C₄⋊C₄	—	13	2	no	—
514	C₄⋊C₄	—	13	1	no	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	1	no	—
517	C₄⋊C₄	—	13	1	no	—
518	C₄⋊C₄	—	13	2	no	—
519	C₄⋊C₄	—	13	2	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	1	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	—	13	1	no	—
524	C₄⋊C₄	—	13	1	no	—
525	C₄⋊C₄	—	13	1	no	—
526	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
528	C₂²⋊C₄	—	13	2	no	—
529	C₂²⋊C₄	—	13	2	no	—
530	C₂²⋊C₄	—	13	1	no	—
531	C₂²⋊C₄	—	13	1	no	—
532	C₂²⋊C₄	—	13	1	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	2	no	—
539	C₂²⋊C₄	—	13	2	no	—
540	C₂²⋊C₄	—	13	2	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	2	no	—
547	C₂²⋊C₄	—	13	2	no	—
548	C₂²⋊C₄	—	13	1	no	—
549	C₂²⋊C₄	—	13	1	no	—
550	C₂²⋊C₄	—	13	1	no	—
551	C₂²⋊C₄	—	13	1	no	—
552	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	yes	characteristic
557	C₄²	—	13	1	no	—
558	C₄²	—	13	1	no	—
559	C₄²	—	13	1	no	—
560	C₄²	—	13	1	no	—
561	C₄²	—	13	2	no	—
562	C₄²	—	13	2	no	—
563	C₄²	—	13	2	no	—
564	C₄²	—	13	1	no	—
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	—	2	4	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	13	1	no	—
574	C₂³	C₂³×D₁₃	1	1	yes	characteristic
575	C₂³	C₂³×D₁₃	1	2	yes	—
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	4	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	4	no	—
586	D₄	—	2	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	26	4	no	—
592	D₄	—	26	2	no	—
593	D₄	—	52	2	no	—
594	D₄	—	52	1	no	—
595	D₄	—	52	2	no	—
596	D₄	#6129	1	4	yes	complemented
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	13	1	no	—
601	C₂×C₄	—	13	2	no	—
602	C₂×C₄	—	13	1	no	—
603	C₂×C₄	—	13	1	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	13	2	no	—
606	C₂×C₄	—	13	1	no	—
607	C₂×C₄	—	13	2	no	—
608	C₂×C₄	—	13	1	no	—
609	C₂×C₄	—	13	1	no	—
610	C₂×C₄	—	13	2	no	—
611	C₂×C₄	—	26	4	no	—
612	C₂×C₄	—	26	2	no	—
613	C₂×C₄	—	26	4	no	—
614	C₂×C₄	—	26	2	no	—
615	C₂×C₄	—	52	2	no	—
616	C₂×C₄	—	52	2	no	—
617	C₂×C₄	—	52	1	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	—	52	2	no	—
623	C₂×C₄	—	52	2	no	—
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	2	yes	—
628	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
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	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	4	8	no	—
644	C₂²	—	8	4	no	—
645	C₂²	—	26	1	no	—
646	C₂²	—	26	1	no	—
647	C₂²	—	26	1	no	—
648	C₂²	C₂×#6129	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	1	no	—
656	C₄	—	26	1	no	—
657	C₄	—	26	2	no	—
658	C₄	—	26	2	no	—
659	C₄	—	26	1	no	—
660	C₄	—	26	1	no	—
661	C₄	—	26	2	no	—
662	C₄	—	26	1	no	—
663	C₄	—	26	1	no	—
664	C₄	—	26	2	no	—
665	C₄	—	26	1	no	—
666	C₄	—	26	1	no	—
667	C₄	C₂×#6129	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	52	1	no	—
674	C₂	C₂²×#6129	1	1	yes	characteristic
675	C₂	C₂×#88251	1	1	yes	characteristic
676	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	D₄²×C₁₃	C₂
hypercenter	D₄²	D₁₃
hypocenter	C₁₃	#3513
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. D₄²×C₁₃	C₂	semidirect
2. #11719511	C₂	semidirect
3. #11719511	C₂	semidirect
4. #11719511	C₂	semidirect
5. #11719503	C₂	semidirect
6. C₂×#88189	C₂	semidirect
7. C₂×D₄×Dic₁₃	C₂	semidirect
8. #11719424	C₂	semidirect
9. #11719418	C₂	semidirect
10. #11719319	C₂	semidirect
11. #11719316	C₂	semidirect
12. #11719308	C₂	semidirect
13. #11719307	C₂	semidirect
14. #11719306	C₂	semidirect
15. #11719305	C₂	semidirect
16. #11719298	C₂	semidirect
17. #11719292	C₂	semidirect
18. #11719292	C₂	semidirect
19. #11719291	C₂	semidirect
20. #11719251	C₂	semidirect
21. #11719246	C₂	semidirect
22. #11719244	C₂	semidirect
23. #11719243	C₂	semidirect
27. C₂³×Dic₁₃	C₂²	semidirect
29. C₂×#6129	C₂²	semidirect
38. #88207	C₂²	semidirect
39. #88207	C₂²	semidirect
40. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
41. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
42. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
43. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
44. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
46. #88193	C₂²	semidirect
47. #88193	C₂²	semidirect
48. #88193	C₂²	semidirect
49. #88193	C₂²	semidirect
50. #88192	C₂²	semidirect
51. #88192	C₂²	semidirect
52. #88192	C₂²	semidirect
53. #88190	C₂²	semidirect
54. #88190	C₂²	semidirect
55. #88190	C₂²	semidirect
56. #88190	C₂²	semidirect
59. #88189	C₂²	semidirect
60. #88189	C₂²	semidirect
61. #88189	C₂²	semidirect
62. #88189	C₂²	semidirect
63. #88189	C₂²	semidirect
64. #88189	C₂²	semidirect
65. #88189	C₂²	semidirect
66. #88189	C₂²	semidirect
67. #88189	C₂²	semidirect
68. #88189	C₂²	semidirect
72. D₄×Dic₁₃	C₂²	semidirect
73. D₄×Dic₁₃	C₂²	semidirect
74. D₄×Dic₁₃	C₂²	semidirect
75. D₄×Dic₁₃	C₂²	semidirect
76. D₄×Dic₁₃	C₂²	semidirect
77. D₄×Dic₁₃	C₂²	semidirect
78. D₄×Dic₁₃	C₂²	semidirect
79. D₄×Dic₁₃	C₂²	semidirect
80. D₄×Dic₁₃	C₂²	semidirect
81. D₄×Dic₁₃	C₂²	semidirect
82. C₄×C₂²⋊D₁₃	C₂²	semidirect
83. C₄×C₂²⋊D₁₃	C₂²	semidirect
84. C₄×C₂²⋊D₁₃	C₂²	semidirect
85. #88180	C₂²	semidirect
86. #88180	C₂²	semidirect
87. C₂×C₄⋊Dic₁₃	C₂²	semidirect
88. #88178	C₂²	semidirect
89. #88178	C₂²	semidirect
90. #88178	C₂²	semidirect
91. C₂×#6101	C₂²	semidirect
92. C₂×#6101	C₂²	semidirect
93. C₂×C₄×Dic₁₃	C₂²	semidirect
94. #88152	C₂²	semidirect
95. C₄⋊C₄×D₁₃	C₂²	semidirect
96. #88144	C₂²	semidirect
97. #88143	C₂²	semidirect
98. #88143	C₂²	semidirect
99. #88142	C₂²	semidirect
100. #88141	C₂²	semidirect
101. #88140	C₂²	semidirect
102. #88139	C₂²	semidirect
103. #88137	C₂²	semidirect
104. #88135	C₂²	semidirect
105. #88135	C₂²	semidirect
106. #88133	C₂²	semidirect
107. #88133	C₂²	semidirect
108. #88133	C₂²	semidirect
109. #88133	C₂²	semidirect
110. #88133	C₂²	semidirect
111. #88132	C₂²	semidirect
112. #88132	C₂²	semidirect
113. #88132	C₂²	semidirect
114. #88132	C₂²	semidirect
115. #88132	C₂²	semidirect
116. #88131	C₂²	semidirect
117. #88131	C₂²	semidirect
118. #88131	C₂²	semidirect
119. #88126	C₂²	semidirect
120. #88124	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
250. D₄×C₁₃	#41	semidirect
303. D₄²	D₁₃	semidirect
566. C₁₃	#3513	semidirect
596. D₄	#6129	semidirect

Maximal subgroups

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

subgroup	index
D₄²×C₁₃	2
#11719511	2
#11719503	2
C₂×#88189	2
C₂×D₄×Dic₁₃	2
#11719424	2
#11719418	2
#11719319	2
#11719316	2
#11719308	2
#11719307	2
#11719306	2
#11719305	2
#11719298	2
#11719292	2
#11719291	2
#11719251	2
#11719246	2
#11719244	2
#11719243	2
#3513	13