Subgroups — #15881175

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#6099	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718672	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718785	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88062	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115611	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115609	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115041	C₂	1	1	yes	maximal, characteristic, complemented
8	#13115041	C₂	1	1	yes	maximal, characteristic, complemented
9	#13115040	C₂	1	1	yes	maximal, characteristic, complemented
10	#13115040	C₂	1	1	yes	maximal, characteristic, complemented
11	#13115010	C₂	1	1	yes	maximal, characteristic, complemented
12	#13114876	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114872	C₂	1	1	yes	maximal, characteristic, complemented
14	#13114743	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×#6099	C₂²	1	1	yes	characteristic
20	C₂²×#6099	C₂²	1	1	yes	characteristic
21	C₂²×#6099	C₂²	1	1	yes	characteristic
22	C₂³×#1055	C₂²	1	1	yes	characteristic
23	C₁₃×#436	—	2	1	no	—
24	C₁₃×#435	—	2	1	no	—
25	C₁₃×#435	—	2	1	no	—
26	C₈×D₄×C₁₃	—	2	1	no	—
27	C₁₃×#423	C₂²	1	1	yes	characteristic
28	C₁₃×#407	C₂²	1	1	yes	characteristic
29	C₁₃×#407	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
31	#11718868	C₂²	1	1	yes	characteristic
32	#11718868	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
35	#11718785	—	2	4	no	—
36	C₂×#88062	—	2	4	no	—
37	C₂×#88062	C₂²	1	1	yes	characteristic
38	C₂×#88062	C₂²	1	1	yes	characteristic
39	C₂×#88062	C₂²	1	1	yes	characteristic
40	C₂×#88062	C₂²	1	1	yes	characteristic
41	C₂×#88062	C₂²	1	1	yes	characteristic
42	C₂×#88062	C₂²	1	1	yes	characteristic
43	C₂×#88062	C₂²	1	1	yes	characteristic
44	C₂×#88062	C₂²	1	1	yes	characteristic
45	C₂×#88062	C₂²	1	1	yes	characteristic
46	C₂×#88062	C₂²	1	1	yes	characteristic
47	#11718673	—	2	1	no	—
48	#11718672	—	2	1	no	—
49	#11718672	—	2	1	no	—
50	#11718672	C₄	1	2	yes	—
51	#11718672	C₄	1	2	yes	—
52	#11718672	C₄	1	2	yes	—
53	#11718672	C₄	1	2	yes	—
54	D₄×#1055	—	2	1	no	—
55	#11718585	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
57	C₄×#6099	C₂²	1	1	yes	characteristic
58	C₂×#88043	C₂²	1	1	yes	characteristic
59	#11718150	C₂²	1	1	yes	characteristic
60	#11718150	C₂²	1	1	yes	characteristic
61	#11718150	C₂²	1	1	yes	characteristic
62	#11718150	C₂²	1	1	yes	characteristic
63	#11718150	C₂²	1	1	yes	characteristic
64	#11718150	C₂²	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×M₁₆	—	2	1	no	—
69	C₂×C₁₃×M₁₆	—	2	1	no	—
70	C₂×C₁₃×M₁₆	—	2	2	no	—
71	C₂×C₁₃×M₁₆	—	2	2	no	—
72	C₂×C₁₃×M₁₆	—	4	1	no	—
73	C₂×C₁₃×M₁₆	—	4	1	no	—
74	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
81	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
84	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
85	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
86	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
87	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	Q₈	1	1	yes	characteristic
89	C₂×C₁₃×C₂²⋊C₄	Q₈	1	1	yes	characteristic
90	C₂×C₁₃×C₂²⋊C₄	Q₈	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₂×#6099	—	2	1	no	—
93	C₂×#6099	—	2	1	no	—
94	C₂×#6099	—	2	2	no	—
95	C₂×#6099	—	2	2	no	—
96	C₂×#6099	—	2	2	no	—
97	C₂×#6099	—	2	2	no	—
98	C₂×#6099	—	4	1	no	—
99	C₂×#6099	—	4	1	no	—
100	C₂×#6099	C₂×C₄	1	2	yes	—
101	C₂×#6099	C₂×C₄	1	2	yes	—
102	C₂×#6099	C₂³	1	1	yes	characteristic
103	C₂×#6099	C₂³	1	1	yes	characteristic
104	C₂×#6099	C₂³	1	1	yes	characteristic
105	C₂×#6099	C₂³	1	1	yes	characteristic
106	C₂²×#1055	—	2	2	no	—
107	C₂²×#1055	—	2	2	no	—
108	C₂²×#1055	—	2	1	no	—
109	C₂²×#1055	—	2	1	no	—
110	C₂²×#1055	C₂×C₄	1	2	yes	—
111	C₂²×#1055	C₂×C₄	1	2	yes	—
112	C₂²×#1055	C₂³	1	1	yes	characteristic
113	C₂²×#1055	C₂³	1	1	yes	characteristic
114	C₂²×#1055	C₂³	1	1	yes	characteristic
115	C₂²×#1055	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	—	2	1	no	—
117	C₁₃×C₄⋊C₈	—	2	1	no	—
118	C₁₃×C₂²⋊C₈	—	2	1	no	—
119	C₁₃×C₂²⋊C₈	—	2	1	no	—
120	C₁₃×C₂²⋊C₈	—	2	1	no	—
121	C₁₃×C₂²⋊C₈	—	2	1	no	—
122	C₁₃×#97	—	2	1	no	—
123	C₄×C₈×C₁₃	—	2	1	no	—
124	C₂²⋊#1055	—	2	1	no	—
125	C₂²⋊#1055	—	2	1	no	—
126	C₂²⋊#1055	—	2	1	no	—
127	C₂²⋊#1055	—	2	1	no	—
128	C₂²⋊#1055	C₂×C₄	1	2	yes	—
129	C₂²⋊#1055	C₂×C₄	1	2	yes	—
130	C₂²⋊#1055	C₂×C₄	1	2	yes	—
131	C₂²⋊#1055	C₂×C₄	1	2	yes	—
132	#88062	—	2	2	no	—
133	#88062	—	2	2	no	—
134	#88062	—	2	2	no	—
135	#88062	—	2	2	no	—
136	#88062	—	2	2	no	—
137	#88062	—	2	2	no	—
138	#88062	—	2	2	no	—
139	#88062	—	4	1	no	—
140	#88062	—	4	1	no	—
141	#88062	D₄	1	4	yes	complemented
142	C₄⋊#1055	—	2	1	no	—
143	C₄⋊#1055	—	2	1	no	—
144	C₄⋊#1055	C₂×C₄	1	2	yes	—
145	C₄⋊#1055	C₂×C₄	1	2	yes	—
146	#88043	—	2	1	no	—
147	#88043	C₂×C₄	1	2	yes	—
148	#88043	C₂×C₄	1	2	yes	—
149	C₄×#1055	—	2	1	no	—
150	#22668	—	13	1	no	maximal, Sylow
151	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
152	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
153	C₂×D₄×C₁₃	—	4	2	no	—
154	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
155	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
156	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₁₃×M₁₆	—	2	1	no	—
180	C₁₃×M₁₆	—	2	1	no	—
181	C₁₃×M₁₆	—	2	1	no	—
182	C₁₃×M₁₆	—	2	1	no	—
183	C₁₃×M₁₆	—	2	1	no	—
184	C₁₃×M₁₆	—	2	1	no	—
185	C₁₃×M₁₆	—	2	1	no	—
186	C₁₃×M₁₆	—	4	2	no	—
187	C₁₃×M₁₆	—	4	2	no	—
188	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	4	2	no	—
194	C₂×C₈×C₁₃	—	4	2	no	—
195	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
199	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
200	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
201	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
202	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
203	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
204	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
205	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
206	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
207	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
211	#6099	—	2	1	no	—
212	#6099	—	2	4	no	—
213	#6099	—	2	4	no	—
214	#6099	—	2	1	no	—
215	#6099	—	2	1	no	—
216	#6099	—	2	1	no	—
217	#6099	—	2	1	no	—
218	#6099	—	2	1	no	—
219	#6099	—	2	1	no	—
220	#6099	—	4	2	no	—
221	#6099	—	4	2	no	—
222	#6099	C₂×D₄	1	2	yes	—
223	C₂×#1055	—	2	1	no	—
224	C₂×#1055	—	2	1	no	—
225	C₂×#1055	—	2	1	no	—
226	C₂×#1055	—	2	1	no	—
227	C₂×#1055	—	2	1	no	—
228	C₂×#1055	—	2	1	no	—
229	C₂×#1055	—	2	1	no	—
230	C₂×#1055	—	2	4	no	—
231	C₂×#1055	—	2	4	no	—
232	C₂×#1055	—	2	1	no	—
233	C₂×#1055	—	2	1	no	—
234	C₂×#1055	—	2	1	no	—
235	C₂×#1055	—	4	2	no	—
236	C₂×#1055	—	4	2	no	—
237	C₂×#1055	C₂²×C₄	1	2	yes	—
238	C₂×#1055	C₂²×C₄	1	2	yes	—
239	C₂×#1055	C₂²×C₄	1	2	yes	—
240	C₂×#1055	C₂²×C₄	1	2	yes	—
241	C₂×#1055	C₂×D₄	1	2	yes	—
242	C₂×#1055	#41	1	2	yes	—
243	D₄×M₁₆	—	13	1	no	—
244	D₄×M₁₆	D₁₃	1	1	yes	characteristic
245	C₂×#435	—	13	1	no	—
246	C₂×#430	—	13	1	no	—
247	C₂²×#108	—	13	1	no	—
248	#1950	—	13	1	no	—
249	#1950	—	13	1	no	—
250	#1855	—	13	1	no	—
251	#1855	—	13	1	no	—
252	#1855	—	13	1	no	—
253	#1855	—	13	1	no	—
254	#1849	—	13	1	no	—
255	#1811	—	13	1	no	—
256	#1810	—	13	1	no	—
257	#1778	—	13	1	no	—
258	C₂³×C₁₃	—	2	1	no	—
259	C₂³×C₁₃	—	2	1	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	1	no	—
262	C₂³×C₁₃	—	2	1	no	—
263	C₂³×C₁₃	—	4	1	no	—
264	C₂³×C₁₃	—	4	1	no	—
265	C₂³×C₁₃	—	4	1	no	—
266	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
267	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
268	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
269	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
270	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
271	D₄×C₁₃	—	2	2	no	—
272	D₄×C₁₃	—	2	2	no	—
273	D₄×C₁₃	—	4	1	no	—
274	D₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
302	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
305	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
311	C₈×C₁₃	—	2	2	no	—
312	C₈×C₁₃	—	4	1	no	—
313	C₈×C₁₃	—	4	1	no	—
314	C₈×C₁₃	—	4	1	no	—
315	#1055	—	2	2	no	—
316	#1055	—	2	2	no	—
317	#1055	—	2	2	no	—
318	#1055	—	2	2	no	—
319	#1055	—	4	1	no	—
320	#1055	—	4	1	no	—
321	#1055	—	4	1	no	—
322	#1055	C₄×D₄	1	4	yes	—
323	C₂²×M₁₆	—	13	1	no	—
324	C₂²×M₁₆	—	13	1	no	—
325	C₂²×M₁₆	—	13	1	no	—
326	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
327	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
328	C₂³×C₈	—	13	1	no	—
329	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
330	#436	—	2	1	no	—
331	#436	—	26	1	no	—
332	#435	—	2	1	no	—
333	#435	—	2	1	no	—
334	#435	—	13	2	no	—
335	#435	—	13	2	no	—
336	#435	—	13	2	no	—
337	#435	—	13	2	no	—
338	#435	—	26	1	no	—
339	#435	—	26	1	no	—
340	C₈×D₄	—	2	1	no	—
341	C₈×D₄	—	26	1	no	—
342	#430	—	26	4	no	—
343	C₂×#108	—	13	1	no	—
344	C₂×#108	—	13	1	no	—
345	C₂×#108	—	13	1	no	—
346	C₂×#108	—	13	1	no	—
347	C₂×#108	—	13	1	no	—
348	C₂×#108	—	13	1	no	—
349	C₂×#108	—	13	1	no	—
350	C₂×#108	—	13	1	no	—
351	C₂×#108	—	13	1	no	—
352	C₂×#108	—	13	1	no	—
353	C₂×#108	—	26	4	no	—
354	#423	—	13	1	no	—
355	#423	C₂×D₁₃	1	1	yes	characteristic
356	C₂×C₄⋊C₈	—	13	1	no	—
357	#407	—	13	1	no	—
358	#407	—	13	1	no	—
359	#407	C₂×D₁₃	1	1	yes	characteristic
360	#407	C₂×D₁₃	1	1	yes	characteristic
361	C₂×C₂²⋊C₈	—	13	1	no	—
362	C₂×C₂²⋊C₈	—	13	1	no	—
363	C₄×M₁₆	—	13	1	no	—
364	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
365	C₂×#97	—	13	1	no	—
366	#341	—	13	1	no	—
367	#341	—	13	1	no	—
368	#341	—	13	1	no	—
369	#341	—	13	1	no	—
370	#341	—	13	1	no	—
371	#341	—	13	1	no	—
372	C₂²×C₁₃	—	2	1	no	—
373	C₂²×C₁₃	—	2	1	no	—
374	C₂²×C₁₃	—	2	1	no	—
375	C₂²×C₁₃	—	2	1	no	—
376	C₂²×C₁₃	—	2	1	no	—
377	C₂²×C₁₃	—	2	1	no	—
378	C₂²×C₁₃	—	2	1	no	—
379	C₂²×C₁₃	—	2	1	no	—
380	C₂²×C₁₃	—	2	1	no	—
381	C₂²×C₁₃	—	2	1	no	—
382	C₂²×C₁₃	—	2	1	no	—
383	C₂²×C₁₃	—	2	1	no	—
384	C₂²×C₁₃	—	2	1	no	—
385	C₂²×C₁₃	—	4	2	no	—
386	C₂²×C₁₃	—	4	2	no	—
387	C₂²×C₁₃	—	8	1	no	—
388	C₂²×C₁₃	—	8	1	no	—
389	C₂²×C₁₃	#430	1	2	yes	complemented
390	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
391	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
392	C₂²×C₁₃	#554	1	1	yes	characteristic
393	C₄×C₁₃	—	2	1	no	—
394	C₄×C₁₃	—	2	1	no	—
395	C₄×C₁₃	—	2	1	no	—
396	C₄×C₁₃	—	2	1	no	—
397	C₄×C₁₃	—	2	1	no	—
398	C₄×C₁₃	—	2	1	no	—
399	C₄×C₁₃	—	2	1	no	—
400	C₄×C₁₃	—	2	1	no	—
401	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
402	C₄×C₁₃	#520	1	1	yes	characteristic
403	C₄×C₁₃	D₄²	1	1	yes	characteristic
404	C₄×C₁₃	#547	1	1	yes	characteristic
405	C₂²×D₄	Dic₂₆	1	1	yes	characteristic
406	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
407	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
408	C₂×M₁₆	—	2	1	no	—
409	C₂×M₁₆	—	2	1	no	—
410	C₂×M₁₆	—	2	2	no	—
411	C₂×M₁₆	—	2	2	no	—
412	C₂×M₁₆	—	4	1	no	—
413	C₂×M₁₆	—	4	1	no	—
414	C₂×M₁₆	—	13	2	no	—
415	C₂×M₁₆	—	13	2	no	—
416	C₂×M₁₆	—	13	1	no	—
417	C₂×M₁₆	—	13	1	no	—
418	C₂×M₁₆	—	13	1	no	—
419	C₂×M₁₆	—	13	1	no	—
420	C₂×M₁₆	—	26	2	no	—
421	C₂×M₁₆	—	26	2	no	—
422	C₂×M₁₆	—	26	1	no	—
423	C₂×M₁₆	—	26	1	no	—
424	C₂×M₁₆	—	26	2	no	—
425	C₂×M₁₆	—	26	2	no	—
426	C₂×M₁₆	—	52	1	no	—
427	C₂×M₁₆	—	52	1	no	—
428	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
429	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
430	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
431	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
432	C₂²×C₈	—	2	1	no	—
433	C₂²×C₈	—	2	1	no	—
434	C₂²×C₈	—	13	1	no	—
435	C₂²×C₈	—	13	2	no	—
436	C₂²×C₈	—	13	2	no	—
437	C₂²×C₈	—	13	1	no	—
438	C₂²×C₈	—	13	1	no	—
439	C₂²×C₈	—	13	1	no	—
440	C₂²×C₈	—	26	2	no	—
441	C₂²×C₈	—	26	2	no	—
442	C₂²×C₈	—	26	1	no	—
443	C₂²×C₈	—	26	1	no	—
444	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
445	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
446	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
447	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
448	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
449	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
450	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
451	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	Dic₂₆	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	Dic₂₆	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	Dic₂₆	1	1	yes	characteristic
455	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
456	#108	—	13	4	no	—
457	#108	—	26	2	no	—
458	#108	—	26	2	no	—
459	#108	—	26	2	no	—
460	#108	—	26	2	no	—
461	#108	—	26	2	no	—
462	#108	—	26	2	no	—
463	#108	—	26	2	no	—
464	#108	—	52	1	no	—
465	#108	—	52	1	no	—
466	C₄⋊C₈	—	2	1	no	—
467	C₄⋊C₈	—	2	1	no	—
468	C₄⋊C₈	—	13	2	no	—
469	C₄⋊C₈	—	13	2	no	—
470	C₄⋊C₈	—	26	1	no	—
471	C₄⋊C₈	—	26	1	no	—
472	C₂²⋊C₈	—	2	1	no	—
473	C₂²⋊C₈	—	2	1	no	—
474	C₂²⋊C₈	—	2	1	no	—
475	C₂²⋊C₈	—	2	1	no	—
476	C₂²⋊C₈	—	13	2	no	—
477	C₂²⋊C₈	—	13	2	no	—
478	C₂²⋊C₈	—	13	2	no	—
479	C₂²⋊C₈	—	13	2	no	—
480	C₂²⋊C₈	—	26	1	no	—
481	C₂²⋊C₈	—	26	1	no	—
482	C₂²⋊C₈	—	26	1	no	—
483	C₂²⋊C₈	—	26	1	no	—
484	#97	—	2	1	no	—
485	#97	—	13	2	no	—
486	#97	—	13	2	no	—
487	#97	—	26	1	no	—
488	C₄×C₈	—	2	1	no	—
489	C₄×C₈	—	26	1	no	—
490	C₂×C₁₃	—	2	1	no	—
491	C₂×C₁₃	—	2	1	no	—
492	C₂×C₁₃	—	2	2	no	—
493	C₂×C₁₃	—	4	1	no	—
494	C₂×C₁₃	—	4	1	no	—
495	C₂×C₁₃	—	4	1	no	—
496	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
497	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
498	C₂×C₁₃	#2916	1	1	yes	characteristic
499	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
500	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	#6101	1	1	yes	characteristic
503	C₂×D₄	#6101	1	1	yes	characteristic
504	C₂×D₄	#6101	1	1	yes	characteristic
505	C₂×D₄	#6101	1	1	yes	characteristic
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
515	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
516	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
517	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
518	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
519	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
520	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
527	M₁₆	—	2	1	no	—
528	M₁₆	—	2	1	no	—
529	M₁₆	—	2	1	no	—
530	M₁₆	—	2	1	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	4	2	no	—
535	M₁₆	—	4	2	no	—
536	M₁₆	—	13	2	no	—
537	M₁₆	—	26	4	no	—
538	M₁₆	—	26	4	no	—
539	M₁₆	—	26	1	no	—
540	M₁₆	—	26	1	no	—
541	M₁₆	—	26	1	no	—
542	M₁₆	—	26	1	no	—
543	M₁₆	—	26	1	no	—
544	M₁₆	—	26	1	no	—
545	M₁₆	—	26	1	no	—
546	M₁₆	—	52	2	no	—
547	M₁₆	—	52	2	no	—
548	M₁₆	D₄×D₁₃	1	2	yes	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	4	2	no	—
554	C₂×C₈	—	4	2	no	—
555	C₂×C₈	—	13	2	no	—
556	C₂×C₈	—	13	2	no	—
557	C₂×C₈	—	13	2	no	—
558	C₂×C₈	—	13	2	no	—
559	C₂×C₈	—	13	2	no	—
560	C₂×C₈	—	13	2	no	—
561	C₂×C₈	—	26	4	no	—
562	C₂×C₈	—	26	4	no	—
563	C₂×C₈	—	26	1	no	—
564	C₂×C₈	—	26	1	no	—
565	C₂×C₈	—	26	1	no	—
566	C₂×C₈	—	26	1	no	—
567	C₂×C₈	—	26	1	no	—
568	C₂×C₈	—	26	1	no	—
569	C₂×C₈	—	26	1	no	—
570	C₂×C₈	—	26	1	no	—
571	C₂×C₈	—	26	1	no	—
572	C₂×C₈	—	26	1	no	—
573	C₂×C₈	—	52	2	no	—
574	C₂×C₈	—	52	2	no	—
575	C₄⋊C₄	#6101	1	1	yes	characteristic
576	C₄⋊C₄	#6101	1	1	yes	characteristic
577	C₄⋊C₄	#6101	1	1	yes	characteristic
578	C₄⋊C₄	#6101	1	1	yes	characteristic
579	C₂²⋊C₄	#6101	1	1	yes	characteristic
580	C₂²⋊C₄	#6101	1	1	yes	characteristic
581	C₂²⋊C₄	#6101	1	1	yes	characteristic
582	C₂²⋊C₄	#6101	1	1	yes	characteristic
583	C₂²⋊C₄	#6101	1	1	yes	characteristic
584	C₂²⋊C₄	#6101	1	1	yes	characteristic
585	C₂²⋊C₄	#6101	1	1	yes	characteristic
586	C₂²⋊C₄	#6101	1	1	yes	characteristic
587	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
588	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
589	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
590	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
591	C₁₃	#22668	1	1	yes	characteristic, complemented, Sylow
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	C₂×#6101	1	1	yes	characteristic
601	C₂³	C₂×#6101	1	1	yes	characteristic
602	C₂³	C₂×#6101	1	1	yes	characteristic
603	C₂³	C₂×#6101	1	1	yes	characteristic
604	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
605	D₄	—	2	2	no	—
606	D₄	—	2	2	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	C₂×#6101	1	1	yes	characteristic
632	C₂×C₄	C₂×#6101	1	1	yes	characteristic
633	C₂×C₄	C₂×#6101	1	1	yes	characteristic
634	C₂×C₄	C₂×#6101	1	1	yes	characteristic
635	C₂×C₄	C₂×#6101	1	1	yes	characteristic
636	C₂×C₄	C₂×#6101	1	1	yes	characteristic
637	C₂×C₄	C₂×#6101	1	1	yes	characteristic
638	C₂×C₄	C₂×#6101	1	1	yes	characteristic
639	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
640	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
641	C₂×C₄	#88251	1	1	yes	characteristic
642	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
643	C₂×C₄	#88257	1	1	yes	characteristic
644	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
645	C₈	—	2	2	no	—
646	C₈	—	4	1	no	—
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₈	—	13	4	no	—
650	C₈	—	26	2	no	—
651	C₈	—	26	2	no	—
652	C₈	—	26	2	no	—
653	C₈	—	26	2	no	—
654	C₈	—	52	1	no	—
655	C₈	—	52	1	no	—
656	C₈	—	52	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	#11718785	1	2	yes	complemented
675	C₂²	D₄×Dic₂₆	1	1	yes	characteristic
676	C₂²	#11719244	1	1	yes	characteristic
677	C₂²	C₂²×#6101	1	1	yes	characteristic
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
687	C₄	#11719251	1	1	yes	characteristic
688	C₄	D₄×C₂²⋊D₁₃	1	1	yes	characteristic
689	C₄	#11719529	1	1	yes	characteristic
690	C₂	—	2	1	no	—
691	C₂	—	2	1	no	—
692	C₂	—	2	2	no	—
693	C₂	—	4	1	no	—
694	C₂	—	4	1	no	—
695	C₂	—	4	1	no	—
696	C₂	D₄×#6101	1	1	yes	characteristic
697	C₂	C₂×#11718785	1	1	yes	characteristic
698	C₂	#13123445	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	D₄×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₁₃	Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	D₄×M₁₆	D₁₃
hypocenter	C₁₃	#22668
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×#11718785	C₂	semidirect
4. C₂²×#88062	C₂	semidirect
5. #13115611	C₂	semidirect
6. #13115609	C₂	semidirect
7. #13115041	C₂	semidirect
8. #13115041	C₂	semidirect
9. #13115040	C₂	semidirect
10. #13115040	C₂	semidirect
11. #13115010	C₂	semidirect
12. #13114876	C₂	semidirect
13. #13114872	C₂	semidirect
14. #13114743	C₂	semidirect
141. #88062	D₄	semidirect
389. C₂²×C₁₃	#430	semidirect
591. C₁₃	#22668	semidirect
674. C₂²	#11718785	semidirect

Maximal subgroups

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

subgroup	index
D₄×#6099	2
C₂×#11718672	2
C₂×#11718785	2
C₂²×#88062	2
#13115611	2
#13115609	2
#13115041	2
#13115040	2
#13115010	2
#13114876	2
#13114872	2
#13114743	2
D₄×C₁₃×M₁₆	2
#22668	13