Subgroups — #16771460

Order 3328.

11534 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719648	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13128517	C₂	1	8	yes	maximal, complemented
4	#13128506	C₂	1	8	yes	maximal, complemented
5	#13128495	C₂	1	2	yes	maximal, complemented
6	#13128488	C₂	1	2	yes	maximal, complemented
7	#13128481	C₂	1	6	yes	maximal, complemented
8	#13128472	C₂	1	6	yes	maximal, complemented
9	#41×D₅₂	C₂	1	16	yes	maximal, complemented
10	#13128169	C₂	1	6	yes	maximal, complemented
11	C₂×#11719229	C₂	1	6	yes	maximal, complemented
12	C₁₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
14	#11719648	—	2	16	no	—
15	C₂×#88257	C₂²	1	4	yes	complemented
16	C₂×#88256	C₂²	1	4	yes	complemented
17	C₂×#41×D₁₃	—	2	16	no	—
18	C₂×#41×D₁₃	C₂²	1	8	yes	complemented
19	C₂×#41×D₁₃	C₂²	1	8	yes	complemented
20	C₂×#41×D₁₃	C₂²	1	8	yes	complemented
21	C₂×#88254	C₂²	1	2	yes	complemented
22	C₂²×#6131	C₂²	1	1	yes	characteristic, complemented
23	C₂²×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×#88251	C₂²	1	6	yes	complemented
25	C₂²×#6129	C₂²	1	3	yes	complemented
26	C₂²×D₄×D₁₃	C₂²	1	3	yes	complemented
27	C₂²×#6127	C₂²	1	3	yes	complemented
28	C₂²×#6127	C₂²	1	6	yes	complemented
29	C₂³×C₄×D₁₃	C₂²	1	3	yes	complemented
30	C₁₃×#520	C₂²	1	8	yes	complemented
31	C₁₃×#519	C₂²	1	2	yes	complemented
32	C₁₃×#518	C₂²	1	6	yes	complemented
33	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
34	C₂×C₁₃×#117	C₂²	1	6	yes	complemented
35	#11719282	C₂²	1	16	yes	complemented
36	#11719281	C₂²	1	16	yes	complemented
37	#11719281	C₂²	1	16	yes	complemented
38	Q₈×D₅₂	C₂²	1	16	yes	complemented
39	#11719260	C₂²	1	48	yes	complemented
40	#11719259	C₂²	1	48	yes	complemented
41	#11719259	C₂²	1	48	yes	complemented
42	D₄×D₅₂	C₂²	1	48	yes	complemented
43	#11719231	C₂²	1	12	yes	complemented
44	#11719231	C₂²	1	12	yes	complemented
45	#11719230	C₂²	1	12	yes	complemented
46	#11719230	C₂²	1	12	yes	complemented
47	#11719229	C₂²	1	12	yes	complemented
48	#11719229	C₂²	1	4	yes	complemented
49	#11719229	C₂²	1	24	yes	complemented
50	#11719229	C₂²	1	24	yes	complemented
51	#11719229	C₂²	1	12	yes	complemented
52	#11719229	C₂²	1	12	yes	complemented
53	#11719229	C₂²	1	24	yes	complemented
54	#11719215	C₂²	1	24	yes	complemented
55	C₂×#88151	C₂²	1	12	yes	complemented
56	C₂×#88149	C₂²	1	12	yes	complemented
57	#11719198	C₂²	1	24	yes	complemented
58	C₂×#88140	C₂²	1	12	yes	complemented
59	C₂×#88136	C₂²	1	12	yes	complemented
60	#11719182	C₂²	1	24	yes	complemented
61	C₂×C₄×D₅₂	C₂²	1	24	yes	complemented
62	C₂⁴×D₁₃	C₂³	1	3	yes	—
63	C₂×C₁₃×#41	D₄	1	16	yes	complemented
64	C₂×C₁₃×#41	C₂³	1	4	yes	—
65	C₂×C₁₃×#41	C₂³	1	4	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
69	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
70	C₂²×C₂²⋊D₁₃	C₂³	1	6	yes	—
71	C₂³×Dic₁₃	C₂³	1	3	yes	—
72	#88257	—	2	32	no	—
73	#88256	—	2	32	no	—
74	#41×D₁₃	—	2	64	no	—
75	#41×D₁₃	—	2	64	no	—
76	#41×D₁₃	—	2	64	no	—
77	#88254	—	2	16	no	—
78	C₂×#6131	—	2	8	no	—
79	C₂×#6131	C₂³	1	8	yes	—
80	C₂×#6131	C₂³	1	8	yes	complemented
81	C₂×Q₈×D₁₃	—	2	8	no	—
82	C₂×Q₈×D₁₃	C₂³	1	8	yes	—
83	C₂×Q₈×D₁₃	C₂³	1	8	yes	complemented
84	#88251	—	2	48	no	—
85	C₂×#6129	—	2	24	no	—
86	C₂×#6129	C₂³	1	24	yes	—
87	C₂×#6129	C₂³	1	24	yes	complemented
88	C₂×D₄×D₁₃	—	2	24	no	—
89	C₂×D₄×D₁₃	C₂³	1	24	yes	—
90	C₂×D₄×D₁₃	C₂³	1	24	yes	complemented
91	C₂×#6127	—	2	24	no	—
92	C₂×#6127	—	2	48	no	—
93	C₂×#6127	C₂³	1	12	yes	—
94	C₂×#6127	C₂³	1	12	yes	—
95	C₂×#6127	C₂³	1	4	yes	—
96	C₂×#6127	C₂³	1	12	yes	—
97	C₂×#6127	C₂³	1	12	yes	complemented
98	C₂×#6127	C₂³	1	12	yes	complemented
99	C₂²×D₅₂	C₂³	1	3	yes	—
100	C₂²×D₅₂	C₂³	1	24	yes	—
101	C₂²×D₅₂	C₂³	1	6	yes	complemented
102	C₂²×C₄×D₁₃	—	2	24	no	—
103	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
104	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
105	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
106	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
107	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
108	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
109	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
110	C₂²×Dic₂₆	C₂³	1	3	yes	—
111	C₂²×Dic₂₆	C₂³	1	6	yes	complemented
112	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
113	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
114	C₁₃×#117	C₂³	1	4	yes	—
115	C₁₃×#117	C₂³	1	12	yes	—
116	C₁₃×#117	C₂³	1	12	yes	complemented
117	C₁₃×#117	C₂³	1	12	yes	complemented
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
121	#88184	C₂³	1	96	yes	complemented
122	C₂×#6103	C₂³	1	24	yes	—
123	C₂×#6103	C₂³	1	24	yes	complemented
124	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	complemented
125	#88151	C₂³	1	8	yes	—
126	#88151	C₂³	1	24	yes	—
127	#88151	C₂³	1	24	yes	complemented
128	#88151	C₂³	1	24	yes	complemented
129	#88151	C₂³	1	48	yes	complemented
130	#88149	C₂³	1	8	yes	—
131	#88149	C₂³	1	24	yes	—
132	#88149	C₂³	1	24	yes	complemented
133	#88149	C₂³	1	24	yes	complemented
134	#88149	C₂³	1	48	yes	complemented
135	#88140	C₂³	1	8	yes	—
136	#88140	C₂³	1	24	yes	—
137	#88140	C₂³	1	48	yes	complemented
138	#88140	C₂³	1	48	yes	complemented
139	#88136	C₂³	1	8	yes	—
140	#88136	C₂³	1	24	yes	—
141	#88136	C₂³	1	48	yes	—
142	#88136	C₂³	1	48	yes	complemented
143	#88129	C₂³	1	24	yes	complemented
144	#88129	C₂³	1	24	yes	complemented
145	#88128	C₂³	1	24	yes	complemented
146	C₄×D₅₂	C₂³	1	16	yes	—
147	C₄×D₅₂	C₂³	1	48	yes	—
148	C₄×D₅₂	C₂³	1	48	yes	complemented
149	C₄×D₅₂	C₂³	1	48	yes	complemented
150	#88123	C₂³	1	24	yes	complemented
151	#62811	—	13	1	no	maximal, Sylow
152	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
153	C₂³×D₁₃	—	2	12	no	—
154	C₂³×D₁₃	—	4	12	no	—
155	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
156	C₂³×D₁₃	C₂⁴	1	12	yes	—
157	C₂³×D₁₃	C₂⁴	1	3	yes	—
158	C₂³×D₁₃	C₂⁴	1	12	yes	—
159	C₁₃×#41	C₂×D₄	1	32	yes	complemented
160	C₁₃×#41	C₂×D₄	1	32	yes	complemented
161	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
162	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
163	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	complemented
164	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	complemented
166	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₂²⋊D₁₃	—	2	24	no	—
172	C₂×C₂²⋊D₁₃	—	2	48	no	—
173	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
174	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
175	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
176	C₂²×Dic₁₃	—	2	12	no	—
177	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
178	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
179	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
180	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
181	#6131	—	2	32	no	—
182	#6131	—	2	32	no	—
183	Q₈×D₁₃	—	2	32	no	—
184	Q₈×D₁₃	—	2	32	no	—
185	#6129	—	2	96	no	—
186	#6129	—	2	96	no	—
187	D₄×D₁₃	—	2	96	no	—
188	D₄×D₁₃	—	2	96	no	—
189	#6127	—	2	16	no	—
190	#6127	—	2	48	no	—
191	#6127	—	2	48	no	—
192	#6127	—	2	48	no	—
193	#6127	—	2	48	no	—
194	#6127	—	2	48	no	—
195	C₂×D₅₂	—	2	12	no	—
196	C₂×D₅₂	—	2	24	no	—
197	C₂×D₅₂	—	4	48	no	—
198	C₂×D₅₂	C₂⁴	1	16	yes	—
199	C₂×D₅₂	C₂⁴	1	12	yes	—
200	C₂×D₅₂	C₂⁴	1	12	yes	—
201	C₂×D₅₂	C₂⁴	1	4	yes	—
202	C₂×D₅₂	C₂⁴	1	48	yes	—
203	C₂×C₄×D₁₃	—	2	4	no	—
204	C₂×C₄×D₁₃	—	2	12	no	—
205	C₂×C₄×D₁₃	—	2	12	no	—
206	C₂×C₄×D₁₃	—	2	12	no	—
207	C₂×C₄×D₁₃	—	2	48	no	—
208	C₂×C₄×D₁₃	—	2	48	no	—
209	C₂×C₄×D₁₃	—	2	48	no	—
210	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
211	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
212	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
213	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
214	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
215	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
216	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
217	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
218	C₂×Dic₂₆	—	2	12	no	—
219	C₂×Dic₂₆	—	2	24	no	—
220	C₂×Dic₂₆	C₂⁴	1	12	yes	—
221	C₂×Dic₂₆	C₂⁴	1	12	yes	—
222	C₂×Dic₂₆	C₂⁴	1	4	yes	—
223	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
224	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
225	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
226	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
227	C₄²×C₁₃	C₂⁴	1	24	yes	—
228	C₄²×C₁₃	C₂⁴	1	8	yes	—
229	#6103	C₂⁴	1	16	yes	—
230	#6103	C₂⁴	1	16	yes	—
231	#6103	C₂⁴	1	48	yes	—
232	#6103	C₂⁴	1	48	yes	—
233	C₄⋊Dic₁₃	C₂⁴	1	48	yes	—
234	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
235	C₂×#585	—	13	1	no	—
236	C₂³×#41	—	13	1	no	—
237	#3489	—	13	8	no	—
238	#3488	—	13	8	no	—
239	#3487	—	13	2	no	—
240	#3486	—	13	2	no	—
241	#3485	—	13	6	no	—
242	#3484	—	13	6	no	—
243	D₄×#41	—	13	16	no	—
244	#3449	—	13	6	no	—
245	C₂×#525	—	13	6	no	—
246	#3428	D₁₃	1	1	yes	characteristic, complemented
247	C₂³×C₁₃	—	4	6	no	—
248	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
249	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
250	C₂³×C₁₃	C₂⁵	1	6	yes	—
251	C₂²×D₁₃	—	2	2	no	—
252	C₂²×D₁₃	—	2	4	no	—
253	C₂²×D₁₃	—	2	6	no	—
254	C₂²×D₁₃	—	2	24	no	—
255	C₂²×D₁₃	—	2	24	no	—
256	C₂²×D₁₃	—	2	24	no	—
257	C₂²×D₁₃	—	4	12	no	—
258	C₂²×D₁₃	—	4	6	no	—
259	C₂²×D₁₃	—	4	24	no	—
260	C₂²×D₁₃	—	4	48	no	—
261	C₂²×D₁₃	C₂⁵	1	8	yes	—
262	C₂²×D₁₃	C₂⁵	1	6	yes	—
263	C₂²×D₁₃	C₂⁵	1	2	yes	—
264	Q₈×C₁₃	C₂²×D₄	1	16	yes	—
265	D₄×C₁₃	C₂²×D₄	1	48	yes	—
266	C₂×C₄×C₁₃	—	4	24	no	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
270	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
271	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
272	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
273	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
275	C₂²⋊D₁₃	—	2	16	no	—
276	C₂²⋊D₁₃	—	2	48	no	—
277	C₂²⋊D₁₃	—	2	48	no	—
278	C₂×Dic₁₃	—	2	6	no	—
279	C₂×Dic₁₃	—	2	24	no	—
280	C₂×Dic₁₃	—	2	2	no	—
281	C₂×Dic₁₃	—	2	24	no	—
282	C₂×Dic₁₃	C₂⁵	1	6	yes	—
283	C₂×Dic₁₃	C₂⁵	1	8	yes	—
284	C₂×Dic₁₃	C₂⁵	1	2	yes	—
285	D₅₂	—	2	32	no	—
286	D₅₂	—	2	8	no	—
287	D₅₂	—	2	24	no	—
288	D₅₂	—	2	24	no	—
289	D₅₂	—	4	48	no	—
290	C₄×D₁₃	—	2	4	no	—
291	C₄×D₁₃	—	2	4	no	—
292	C₄×D₁₃	—	2	12	no	—
293	C₄×D₁₃	—	2	12	no	—
294	C₄×D₁₃	—	2	16	no	—
295	C₄×D₁₃	—	2	24	no	—
296	C₄×D₁₃	—	2	24	no	—
297	C₄×D₁₃	—	2	48	no	—
298	Dic₂₆	—	2	8	no	—
299	Dic₂₆	—	2	24	no	—
300	Dic₂₆	—	2	24	no	—
301	#585	—	26	16	no	—
302	C₂×2₋¹⁺⁴	—	13	4	no	—
303	C₂×2₋¹⁺⁴	—	13	2	no	—
304	C₂×H(5,𝔽₂)	—	13	4	no	—
305	C₂×H(5,𝔽₂)	—	13	6	no	—
306	C₂²×#41	—	13	8	no	—
307	C₂²×#41	—	13	8	no	—
308	C₂²×#41	—	13	8	no	—
309	C₂²×#41	—	13	1	no	—
310	C₂²×#41	—	13	3	no	—
311	C₂²×#41	—	13	3	no	—
312	C₂²×#41	—	13	6	no	—
313	C₂²×#41	—	26	16	no	—
314	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
315	C₂³×Q₈	—	13	1	no	—
316	C₂³×D₄	—	13	3	no	—
317	C₂⁴×C₄	—	13	3	no	—
318	#550	—	13	16	no	—
319	D₄×Q₈	—	13	16	no	—
320	#548	—	13	16	no	—
321	#548	—	13	16	no	—
322	#547	—	13	48	no	—
323	#546	—	13	48	no	—
324	#546	—	13	48	no	—
325	D₄²	—	13	48	no	—
326	#537	—	13	24	no	—
327	#536	—	13	12	no	—
328	#536	—	13	12	no	—
329	#535	—	13	12	no	—
330	#535	—	13	12	no	—
331	#534	—	13	24	no	—
332	#532	—	13	24	no	—
333	#525	—	13	4	no	—
334	#525	—	13	12	no	—
335	#525	—	13	12	no	—
336	#525	—	13	12	no	—
337	#525	—	13	24	no	—
338	#525	—	13	24	no	—
339	#525	—	13	24	no	—
340	C₂×#123	—	13	12	no	—
341	C₂×C₂²⋊Q₈	—	13	12	no	—
342	C₂×#121	—	13	12	no	—
343	C₂×#120	—	13	12	no	—
344	#520	C₂×D₁₃	1	8	yes	complemented
345	#519	C₂×D₁₃	1	2	yes	complemented
346	#518	C₂×D₁₃	1	6	yes	complemented
347	C₄×#41	C₂×D₁₃	1	8	yes	complemented
348	C₂×C₄×D₄	—	13	24	no	—
349	C₂×#117	C₂×D₁₃	1	6	yes	complemented
350	C₂²×C₁₃	—	2	12	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	4	12	no	—
353	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
354	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
355	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
356	C₂×D₁₃	—	2	8	no	—
357	C₂×D₁₃	—	2	2	no	—
358	C₂×D₁₃	—	2	2	no	—
359	C₂×D₁₃	—	2	6	no	—
360	C₂×D₁₃	—	2	8	no	—
361	C₂×D₁₃	—	2	16	no	—
362	C₂×D₁₃	—	2	12	no	—
363	C₂×D₁₃	—	4	48	no	—
364	C₂×D₁₃	—	4	12	no	—
365	C₂×D₁₃	—	8	24	no	—
366	C₂×D₁₃	#585	1	4	yes	complemented
367	C₄×C₁₃	—	2	16	no	—
368	C₄×C₁₃	C₂³×D₄	1	2	yes	—
369	C₄×C₁₃	C₂³×D₄	1	12	yes	—
370	C₄×C₁₃	C₂³×D₄	1	2	yes	—
371	Dic₁₃	—	2	8	no	—
372	Dic₁₃	—	2	6	no	—
373	Dic₁₃	—	2	2	no	—
374	C₂⁵	—	13	3	no	—
375	2₋¹⁺⁴	—	26	32	no	—
376	2₋¹⁺⁴	—	26	16	no	—
377	H(5,𝔽₂)	—	26	32	no	—
378	H(5,𝔽₂)	—	26	48	no	—
379	C₂×#41	—	13	8	no	—
380	C₂×#41	—	13	8	no	—
381	C₂×#41	—	13	24	no	—
382	C₂×#41	—	13	24	no	—
383	C₂×#41	—	13	4	no	—
384	C₂×#41	—	13	12	no	—
385	C₂×#41	—	13	12	no	—
386	C₂×#41	—	13	12	no	—
387	C₂×#41	—	13	12	no	—
388	C₂×#41	—	13	12	no	—
389	C₂×#41	—	26	64	no	—
390	C₂×#41	—	26	64	no	—
391	C₂×#41	—	26	64	no	—
392	C₂×#41	—	26	8	no	—
393	C₂×#41	—	26	24	no	—
394	C₂×#41	—	26	24	no	—
395	C₂×#41	—	26	48	no	—
396	C₂×#41	D₅₂	1	16	yes	complemented
397	C₂×#41	C₂²×D₁₃	1	4	yes	—
398	C₂×#41	C₂²×D₁₃	1	4	yes	—
399	C₂²×Q₈	—	13	8	no	—
400	C₂²×Q₈	—	13	8	no	—
401	C₂²×Q₈	—	13	6	no	—
402	C₂²×Q₈	—	13	3	no	—
403	C₂²×Q₈	—	26	8	no	—
404	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
405	C₂²×D₄	—	13	12	no	—
406	C₂²×D₄	—	13	6	no	—
407	C₂²×D₄	—	13	24	no	—
408	C₂²×D₄	—	13	24	no	—
409	C₂²×D₄	—	13	6	no	—
410	C₂²×D₄	—	13	3	no	—
411	C₂²×D₄	—	13	24	no	—
412	C₂²×D₄	—	26	24	no	—
413	C₂²×D₄	C₂²×D₁₃	1	3	yes	—
414	C₂³×C₄	—	13	3	no	—
415	C₂³×C₄	—	13	12	no	—
416	C₂³×C₄	—	13	12	no	—
417	C₂³×C₄	—	13	12	no	—
418	C₂³×C₄	—	13	1	no	—
419	C₂³×C₄	—	13	3	no	—
420	C₂³×C₄	—	13	3	no	—
421	C₂³×C₄	—	13	3	no	—
422	C₂³×C₄	—	26	24	no	—
423	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
424	C₄⋊Q₈	—	13	24	no	—
425	#127	—	13	24	no	—
426	#124	—	13	24	no	—
427	#124	—	13	24	no	—
428	#123	—	13	8	no	—
429	#123	—	13	24	no	—
430	#123	—	13	48	no	—
431	#123	—	13	48	no	—
432	C₂²⋊Q₈	—	13	8	no	—
433	C₂²⋊Q₈	—	13	24	no	—
434	C₂²⋊Q₈	—	13	24	no	—
435	C₂²⋊Q₈	—	13	24	no	—
436	C₂²⋊Q₈	—	13	48	no	—
437	#121	—	13	96	no	—
438	#121	—	13	8	no	—
439	#121	—	13	24	no	—
440	#121	—	13	24	no	—
441	#121	—	13	24	no	—
442	#121	—	13	48	no	—
443	#120	—	13	8	no	—
444	#120	—	13	24	no	—
445	#120	—	13	48	no	—
446	#120	—	13	48	no	—
447	C₄×Q₈	C₂²×D₁₃	1	16	yes	complemented
448	C₄×D₄	—	13	16	no	—
449	C₄×D₄	—	13	48	no	—
450	C₄×D₄	—	13	48	no	—
451	C₄×D₄	—	13	48	no	—
452	C₄×D₄	C₂²×D₁₃	1	48	yes	complemented
453	#117	C₂²×D₁₃	1	4	yes	—
454	#117	C₂²×D₁₃	1	12	yes	—
455	#117	C₂²×D₁₃	1	12	yes	complemented
456	#117	C₂²×D₁₃	1	12	yes	complemented
457	C₂×C₄⋊C₄	—	13	24	no	—
458	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
459	C₂×C₂²⋊C₄	—	13	24	no	—
460	C₂×C₂²⋊C₄	—	13	24	no	—
461	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	—
462	C₂×C₄²	C₂²×D₁₃	1	12	yes	complemented
463	C₂×C₁₃	—	2	2	no	—
464	C₂×C₁₃	—	2	12	no	—
465	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
466	C₂×C₁₃	C₂×#585	1	2	yes	—
467	D₁₃	—	2	4	no	—
468	D₁₃	—	4	6	no	—
469	D₁₃	—	4	8	no	—
470	C₂⁴	—	13	1	no	—
471	C₂⁴	—	13	12	no	—
472	C₂⁴	—	13	12	no	—
473	C₂⁴	—	13	3	no	—
474	C₂⁴	—	26	12	no	—
475	C₂⁴	—	52	12	no	—
476	C₂⁴	C₂³×D₁₃	1	3	yes	—
477	#41	—	26	32	no	—
478	#41	—	26	32	no	—
479	#41	—	26	96	no	—
480	#41	—	26	96	no	—
481	#41	—	26	16	no	—
482	#41	—	26	48	no	—
483	#41	—	26	48	no	—
484	#41	—	26	48	no	—
485	#41	—	26	48	no	—
486	#41	—	26	48	no	—
487	#41	C₂×D₅₂	1	32	yes	complemented
488	#41	C₂×D₅₂	1	32	yes	complemented
489	C₂×Q₈	—	13	4	no	—
490	C₂×Q₈	—	13	12	no	—
491	C₂×Q₈	—	13	12	no	—
492	C₂×Q₈	—	26	32	no	—
493	C₂×Q₈	—	26	32	no	—
494	C₂×Q₈	—	26	12	no	—
495	C₂×Q₈	—	26	24	no	—
496	C₂×Q₈	C₂×D₅₂	1	8	yes	complemented
497	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
498	C₂×D₄	—	13	8	no	—
499	C₂×D₄	—	13	24	no	—
500	C₂×D₄	—	13	24	no	—
501	C₂×D₄	—	13	16	no	—
502	C₂×D₄	—	13	4	no	—
503	C₂×D₄	—	13	12	no	—
504	C₂×D₄	—	13	12	no	—
505	C₂×D₄	—	13	48	no	—
506	C₂×D₄	—	26	24	no	—
507	C₂×D₄	—	26	48	no	—
508	C₂×D₄	—	26	96	no	—
509	C₂×D₄	—	26	96	no	—
510	C₂×D₄	—	26	12	no	—
511	C₂×D₄	—	26	24	no	—
512	C₂×D₄	—	52	48	no	—
513	C₂×D₄	C₂×D₅₂	1	24	yes	complemented
514	C₂×D₄	C₂³×D₁₃	1	12	yes	—
515	C₂²×C₄	—	13	12	no	—
516	C₂²×C₄	—	13	12	no	—
517	C₂²×C₄	—	13	1	no	—
518	C₂²×C₄	—	13	3	no	—
519	C₂²×C₄	—	13	12	no	—
520	C₂²×C₄	—	13	12	no	—
521	C₂²×C₄	—	13	24	no	—
522	C₂²×C₄	—	13	2	no	—
523	C₂²×C₄	—	13	6	no	—
524	C₂²×C₄	—	13	2	no	—
525	C₂²×C₄	—	13	8	no	—
526	C₂²×C₄	—	13	6	no	—
527	C₂²×C₄	—	26	12	no	—
528	C₂²×C₄	—	26	4	no	—
529	C₂²×C₄	—	26	12	no	—
530	C₂²×C₄	—	26	12	no	—
531	C₂²×C₄	—	26	12	no	—
532	C₂²×C₄	—	26	48	no	—
533	C₂²×C₄	—	26	48	no	—
534	C₂²×C₄	—	26	48	no	—
535	C₂²×C₄	C₂×D₅₂	1	24	yes	complemented
536	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
537	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
538	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
539	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
540	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
541	C₄⋊C₄	—	13	16	no	—
542	C₄⋊C₄	—	13	48	no	—
543	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
544	C₄⋊C₄	C₂³×D₁₃	1	24	yes	—
545	C₂²⋊C₄	—	13	16	no	—
546	C₂²⋊C₄	—	13	16	no	—
547	C₂²⋊C₄	—	13	48	no	—
548	C₂²⋊C₄	—	13	48	no	—
549	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
550	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
551	C₄²	C₂³×D₁₃	1	24	yes	—
552	C₄²	C₂³×D₁₃	1	8	yes	—
553	C₁₃	#62811	1	1	yes	characteristic, complemented, Sylow
554	C₂³	—	4	6	no	—
555	C₂³	—	13	2	no	—
556	C₂³	—	13	8	no	—
557	C₂³	—	13	6	no	—
558	C₂³	—	26	4	no	—
559	C₂³	—	26	24	no	—
560	C₂³	—	26	2	no	—
561	C₂³	—	26	24	no	—
562	C₂³	—	26	6	no	—
563	C₂³	—	26	24	no	—
564	C₂³	—	52	12	no	—
565	C₂³	—	52	6	no	—
566	C₂³	—	52	24	no	—
567	C₂³	—	52	48	no	—
568	C₂³	C₂²×D₅₂	1	12	yes	—
569	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
570	C₂³	C₂⁴×D₁₃	1	6	yes	—
571	Q₈	—	26	8	no	—
572	Q₈	—	26	24	no	—
573	Q₈	—	26	24	no	—
574	Q₈	C₂²×D₅₂	1	16	yes	—
575	D₄	—	26	32	no	—
576	D₄	—	26	16	no	—
577	D₄	—	26	48	no	—
578	D₄	—	26	48	no	—
579	D₄	—	26	8	no	—
580	D₄	—	26	24	no	—
581	D₄	—	26	24	no	—
582	D₄	—	52	48	no	—
583	D₄	C₂²×D₅₂	1	48	yes	—
584	C₂×C₄	—	4	24	no	—
585	C₂×C₄	—	13	2	no	—
586	C₂×C₄	—	13	8	no	—
587	C₂×C₄	—	13	6	no	—
588	C₂×C₄	—	26	2	no	—
589	C₂×C₄	—	26	6	no	—
590	C₂×C₄	—	26	24	no	—
591	C₂×C₄	—	26	24	no	—
592	C₂×C₄	—	26	4	no	—
593	C₂×C₄	—	26	4	no	—
594	C₂×C₄	—	26	24	no	—
595	C₂×C₄	—	26	24	no	—
596	C₂×C₄	—	26	12	no	—
597	C₂×C₄	—	26	16	no	—
598	C₂×C₄	—	26	12	no	—
599	C₂×C₄	—	26	48	no	—
600	C₂×C₄	C₂²×D₅₂	1	4	yes	—
601	C₂×C₄	C₂²×D₅₂	1	24	yes	—
602	C₂×C₄	C₂²×D₅₂	1	12	yes	—
603	C₂×C₄	C₂²×D₅₂	1	24	yes	—
604	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
605	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
606	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
607	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
608	C₂²	—	2	12	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	4	12	no	—
611	C₂²	—	13	4	no	—
612	C₂²	—	26	8	no	—
613	C₂²	—	26	2	no	—
614	C₂²	—	26	2	no	—
615	C₂²	—	26	6	no	—
616	C₂²	—	26	8	no	—
617	C₂²	—	26	16	no	—
618	C₂²	—	26	12	no	—
619	C₂²	—	52	48	no	—
620	C₂²	—	52	12	no	—
621	C₂²	—	104	24	no	—
622	C₂²	C₂³×D₅₂	1	2	yes	—
623	C₂²	C₂³×D₅₂	1	12	yes	—
624	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
625	C₄	—	2	16	no	—
626	C₄	—	26	2	no	—
627	C₄	—	26	6	no	—
628	C₄	—	26	8	no	—
629	C₄	C₂³×D₅₂	1	2	yes	—
630	C₄	C₂³×D₅₂	1	2	yes	—
631	C₄	C₂³×D₅₂	1	12	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	2	12	no	—
634	C₂	—	26	4	no	—
635	C₂	—	52	6	no	—
636	C₂	—	52	8	no	—
637	C₂	C₂⁴×D₅₂	1	1	yes	characteristic
638	C₂	D₁₃×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₁₃×#3428	C₂
hypercenter	#3428	D₁₃
hypocenter	C₁₃	#62811
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #3428

Complements

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

N	H ≅ G/N	type
1. C₂×#11719648	C₂	semidirect
2. C₂²×#41×D₁₃	C₂	semidirect
3. #13128517	C₂	semidirect
4. #13128506	C₂	semidirect
5. #13128495	C₂	semidirect
6. #13128488	C₂	semidirect
7. #13128481	C₂	semidirect
8. #13128472	C₂	semidirect
9. #41×D₅₂	C₂	semidirect
10. #13128169	C₂	semidirect
11. C₂×#11719229	C₂	semidirect
12. C₁₃×#3428	C₂	semidirect
15. C₂×#88257	C₂²	semidirect
16. C₂×#88256	C₂²	semidirect
18. C₂×#41×D₁₃	C₂²	semidirect
19. C₂×#41×D₁₃	C₂²	semidirect
20. C₂×#41×D₁₃	C₂²	semidirect
21. C₂×#88254	C₂²	semidirect
22. C₂²×#6131	C₂²	semidirect
23. C₂²×Q₈×D₁₃	C₂²	semidirect
24. C₂×#88251	C₂²	semidirect
25. C₂²×#6129	C₂²	semidirect
26. C₂²×D₄×D₁₃	C₂²	semidirect
27. C₂²×#6127	C₂²	semidirect
28. C₂²×#6127	C₂²	semidirect
29. C₂³×C₄×D₁₃	C₂²	semidirect
30. C₁₃×#520	C₂²	semidirect
31. C₁₃×#519	C₂²	semidirect
32. C₁₃×#518	C₂²	semidirect
33. C₄×C₁₃×#41	C₂²	semidirect
34. C₂×C₁₃×#117	C₂²	semidirect
35. #11719282	C₂²	semidirect
36. #11719281	C₂²	semidirect
37. #11719281	C₂²	semidirect
38. Q₈×D₅₂	C₂²	semidirect
39. #11719260	C₂²	semidirect
40. #11719259	C₂²	semidirect
41. #11719259	C₂²	semidirect
42. D₄×D₅₂	C₂²	semidirect
43. #11719231	C₂²	semidirect
44. #11719231	C₂²	semidirect
45. #11719230	C₂²	semidirect
46. #11719230	C₂²	semidirect
47. #11719229	C₂²	semidirect
48. #11719229	C₂²	semidirect
49. #11719229	C₂²	semidirect
50. #11719229	C₂²	semidirect
51. #11719229	C₂²	semidirect
52. #11719229	C₂²	semidirect
53. #11719229	C₂²	semidirect
54. #11719215	C₂²	semidirect
55. C₂×#88151	C₂²	semidirect
56. C₂×#88149	C₂²	semidirect
57. #11719198	C₂²	semidirect
58. C₂×#88140	C₂²	semidirect
59. C₂×#88136	C₂²	semidirect
60. #11719182	C₂²	semidirect
61. C₂×C₄×D₅₂	C₂²	semidirect
63. C₂×C₁₃×#41	D₄	semidirect
80. C₂×#6131	C₂³	semidirect
83. C₂×Q₈×D₁₃	C₂³	semidirect
87. C₂×#6129	C₂³	semidirect
90. C₂×D₄×D₁₃	C₂³	semidirect
97. C₂×#6127	C₂³	semidirect
98. C₂×#6127	C₂³	semidirect
101. C₂²×D₅₂	C₂³	semidirect
109. C₂²×C₄×D₁₃	C₂³	semidirect
111. C₂²×Dic₂₆	C₂³	semidirect
112. C₄×Q₈×C₁₃	C₂³	semidirect
113. C₄×D₄×C₁₃	C₂³	semidirect
116. C₁₃×#117	C₂³	semidirect
117. C₁₃×#117	C₂³	semidirect
118. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
120. C₂×C₄²×C₁₃	C₂³	semidirect
121. #88184	C₂³	semidirect
123. C₂×#6103	C₂³	semidirect
124. C₂×C₄⋊Dic₁₃	C₂³	semidirect
127. #88151	C₂³	semidirect
128. #88151	C₂³	semidirect
129. #88151	C₂³	semidirect
132. #88149	C₂³	semidirect
133. #88149	C₂³	semidirect
134. #88149	C₂³	semidirect
137. #88140	C₂³	semidirect
138. #88140	C₂³	semidirect
142. #88136	C₂³	semidirect
143. #88129	C₂³	semidirect
144. #88129	C₂³	semidirect
145. #88128	C₂³	semidirect
148. C₄×D₅₂	C₂³	semidirect
149. C₄×D₅₂	C₂³	semidirect
150. #88123	C₂³	semidirect
159. C₁₃×#41	C₂×D₄	semidirect
160. C₁₃×#41	C₂×D₄	semidirect
161. C₂×Q₈×C₁₃	C₂×D₄	semidirect
163. C₂×D₄×C₁₃	C₂×D₄	semidirect
165. C₂²×C₄×C₁₃	C₂×D₄	semidirect
246. #3428	D₁₃	semidirect
344. #520	C₂×D₁₃	semidirect
345. #519	C₂×D₁₃	semidirect
346. #518	C₂×D₁₃	semidirect
347. C₄×#41	C₂×D₁₃	semidirect
349. C₂×#117	C₂×D₁₃	semidirect
366. C₂×D₁₃	#585	semidirect
396. C₂×#41	D₅₂	semidirect
447. C₄×Q₈	C₂²×D₁₃	semidirect
452. C₄×D₄	C₂²×D₁₃	semidirect
455. #117	C₂²×D₁₃	semidirect
456. #117	C₂²×D₁₃	semidirect
458. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
462. C₂×C₄²	C₂²×D₁₃	semidirect
487. #41	C₂×D₅₂	semidirect
488. #41	C₂×D₅₂	semidirect
496. C₂×Q₈	C₂×D₅₂	semidirect
513. C₂×D₄	C₂×D₅₂	semidirect
535. C₂²×C₄	C₂×D₅₂	semidirect
553. C₁₃	#62811	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719648	2
C₂²×#41×D₁₃	2
#13128517	2
#13128506	2
#13128495	2
#13128488	2
#13128481	2
#13128472	2
#41×D₅₂	2
#13128169	2
C₂×#11719229	2
C₁₃×#3428	2
#62811	13