Subgroups — #15828691

Order 3328.

720 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123803	C₂	1	1	yes	maximal, characteristic
2	#13123480	C₂	1	1	yes	maximal, characteristic
3	#13113139	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113136	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113136	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113133	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113131	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113131	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113120	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113119	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#6099	C₂	1	1	yes	maximal, characteristic, complemented
13	M₁₆×#1055	C₂	1	1	yes	maximal, characteristic, complemented
14	M₁₆×#1055	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2965	C₂	1	1	yes	maximal, characteristic
16	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₁₃×#446	C₄	1	2	yes	—
18	C₁₃×#436	C₄	1	2	yes	—
19	C₁₃×#435	C₄	1	2	yes	—
20	C₁₃×#435	C₄	1	2	yes	—
21	C₁₃×#431	C₂²	1	1	yes	characteristic
22	C₁₃×#431	C₂²	1	1	yes	characteristic
23	C₁₃×#431	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	#11718895	C₄	1	2	yes	—
28	#11718685	C₄	1	2	yes	—
29	#11718673	C₄	1	2	yes	—
30	#11718672	C₄	1	2	yes	—
31	#11718672	C₄	1	2	yes	—
32	#11718661	C₄	1	2	yes	—
33	#11718661	C₄	1	2	yes	—
34	#11718660	C₄	1	2	yes	—
35	#11718586	C₂²	1	1	yes	characteristic
36	#11718586	C₂²	1	1	yes	characteristic
37	#11718586	C₂²	1	1	yes	characteristic
38	#11718586	C₂²	1	1	yes	characteristic
39	#11718586	C₂²	1	1	yes	characteristic
40	#11718586	C₂²	1	1	yes	characteristic
41	#11718586	C₂²	1	1	yes	characteristic
42	C₄×#6099	C₂²	1	1	yes	characteristic
43	C₄×#6099	C₂²	1	1	yes	characteristic
44	C₄×#6099	C₂²	1	1	yes	characteristic
45	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
46	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
47	#11718047	C₂²	1	1	yes	characteristic
48	#11718047	C₂²	1	1	yes	characteristic
49	#11718047	C₂²	1	1	yes	characteristic
50	#11718047	C₂²	1	1	yes	characteristic
51	#11718046	C₂²	1	1	yes	characteristic
52	#11718046	C₂²	1	1	yes	characteristic
53	#11718046	C₂²	1	1	yes	characteristic
54	#11718046	C₂²	1	1	yes	characteristic
55	#11718046	C₂²	1	1	yes	characteristic
56	#11718046	C₂²	1	1	yes	characteristic
57	C₈×#1055	C₂²	1	1	yes	characteristic
58	C₈×#1055	C₂²	1	1	yes	characteristic
59	C₈×#1055	C₂²	1	1	yes	characteristic
60	C₈×#1055	C₂²	1	1	yes	characteristic
61	C₈×#1055	C₂²	1	1	yes	characteristic
62	C₈×#1055	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
65	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
67	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
70	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
71	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
72	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
76	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
77	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×#6099	C₂×C₄	1	2	yes	—
82	C₂×#6099	C₂×C₄	1	2	yes	—
83	C₂×#6099	C₂×C₄	1	2	yes	—
84	C₂²×#1055	C₂×C₄	1	2	yes	—
85	C₂²×#1055	C₂×C₄	1	2	yes	—
86	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
87	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
89	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
90	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₃×#97	C₂×C₄	1	2	yes	—
93	C₁₃×#97	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²⋊#1055	C₂×C₄	1	2	yes	—
100	C₂²⋊#1055	C₂×C₄	1	2	yes	—
101	C₂²⋊#1055	C₂×C₄	1	2	yes	—
102	C₂²⋊#1055	C₂×C₄	1	2	yes	—
103	C₂²⋊#1055	C₂×C₄	1	2	yes	—
104	C₂²⋊#1055	C₂×C₄	1	2	yes	—
105	C₂²⋊#1055	C₂×C₄	1	2	yes	—
106	C₄⋊#1055	C₂×C₄	1	2	yes	—
107	C₄⋊#1055	C₂×C₄	1	2	yes	—
108	C₄⋊#1055	C₂×C₄	1	2	yes	—
109	C₄⋊#1055	C₂×C₄	1	2	yes	—
110	C₄⋊#1055	C₂×C₄	1	2	yes	—
111	C₄⋊#1055	C₂×C₄	1	2	yes	—
112	C₄⋊#1055	C₂×C₄	1	2	yes	—
113	#88043	C₂×C₄	1	2	yes	—
114	#88043	C₂×C₄	1	2	yes	—
115	#88043	C₂×C₄	1	2	yes	—
116	C₄×#1055	C₂×C₄	1	2	yes	—
117	C₄×#1055	C₂×C₄	1	2	yes	—
118	C₄×#1055	C₂³	1	1	yes	characteristic
119	C₄×#1055	C₂³	1	1	yes	characteristic
120	C₄×#1055	C₂³	1	1	yes	characteristic
121	C₄×#1055	C₂³	1	1	yes	characteristic
122	C₄×#1055	C₂³	1	1	yes	characteristic
123	C₄×#1055	C₂³	1	1	yes	characteristic
124	C₄×#1055	C₂³	1	1	yes	characteristic
125	C₄×#1055	C₂³	1	1	yes	characteristic
126	#17341	—	13	1	no	maximal, Sylow
127	C₁₃×#41	—	4	2	no	—
128	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
131	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₁₃×M₁₆	—	2	4	no	—
142	C₁₃×M₁₆	—	2	4	no	—
143	C₂×C₈×C₁₃	—	2	4	no	—
144	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
148	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
150	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
153	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
154	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
155	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
156	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
157	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
158	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
159	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
160	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
170	#6099	—	2	4	no	—
171	#6099	—	2	4	no	—
172	#6099	—	4	2	no	—
173	C₂×#1055	—	2	4	no	—
174	C₂×#1055	—	4	2	no	—
175	C₂×#1055	C₂²×C₄	1	2	yes	—
176	C₂×#1055	C₂²×C₄	1	2	yes	—
177	C₂×#1055	C₂²×C₄	1	2	yes	—
178	C₂×#1055	C₂²×C₄	1	2	yes	—
179	C₂×#1055	C₂²×C₄	1	2	yes	—
180	C₂×#1055	C₂²×C₄	1	2	yes	—
181	C₂×#1055	C₂²×C₄	1	2	yes	—
182	C₂×#1055	C₂²×C₄	1	2	yes	—
183	#2965	—	13	1	no	—
184	#2965	D₁₃	1	1	yes	characteristic
185	#2922	—	13	1	no	—
186	#1455	—	13	1	no	—
187	#1454	—	13	1	no	—
188	#1454	—	13	1	no	—
189	#1453	—	13	1	no	—
190	#1453	—	13	1	no	—
191	#1453	—	13	1	no	—
192	#1450	—	13	1	no	—
193	#1450	—	13	1	no	—
194	C₈×M₁₆	—	13	1	no	—
195	C₈×M₁₆	—	13	1	no	—
196	C₈×M₁₆	—	13	1	no	—
197	C₈×M₁₆	—	13	1	no	—
198	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
199	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
200	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
201	Q₈×C₁₃	—	4	1	no	—
202	D₄×C₁₃	—	4	1	no	—
203	D₄×C₁₃	—	4	1	no	—
204	D₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
226	C₈×C₁₃	—	2	2	no	—
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	2	2	no	—
229	C₈×C₁₃	#131	1	4	yes	—
230	#1055	—	2	2	no	—
231	#1055	—	2	2	no	—
232	#1055	—	2	2	no	—
233	#1055	—	2	2	no	—
234	#1055	—	2	2	no	—
235	#1055	—	2	2	no	—
236	#1055	—	2	2	no	—
237	#1055	#131	1	4	yes	—
238	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
239	#446	—	13	2	no	—
240	#446	Dic₁₃	1	2	yes	—
241	#436	—	13	2	no	—
242	#436	Dic₁₃	1	2	yes	—
243	#435	—	13	2	no	—
244	#435	—	13	2	no	—
245	#435	Dic₁₃	1	2	yes	—
246	#435	Dic₁₃	1	2	yes	—
247	#433	—	13	2	no	—
248	#433	—	13	2	no	—
249	#431	—	13	1	no	—
250	#431	—	13	1	no	—
251	#431	—	13	1	no	—
252	#431	—	13	1	no	—
253	#431	—	13	1	no	—
254	#431	—	13	1	no	—
255	#431	—	13	1	no	—
256	#431	C₂×D₁₃	1	1	yes	characteristic
257	#431	C₂×D₁₃	1	1	yes	characteristic
258	#431	C₂×D₁₃	1	1	yes	characteristic
259	#424	—	13	2	no	—
260	#408	—	13	2	no	—
261	C₄×M₁₆	—	13	1	no	—
262	C₄×M₁₆	—	13	1	no	—
263	C₄×M₁₆	—	13	1	no	—
264	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
265	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
266	C₂×C₄×C₈	—	13	1	no	—
267	C₂×C₄×C₈	—	13	1	no	—
268	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
269	#322	—	13	1	no	—
270	#322	—	13	1	no	—
271	#322	—	13	1	no	—
272	#322	—	13	1	no	—
273	#322	—	13	1	no	—
274	#322	—	13	1	no	—
275	#322	—	13	1	no	—
276	#322	—	13	1	no	—
277	#322	—	13	1	no	—
278	#322	—	13	1	no	—
279	C₈²	—	13	1	no	—
280	C₈²	—	13	1	no	—
281	C₈²	—	13	1	no	—
282	C₈²	—	13	1	no	—
283	C₈²	—	13	1	no	—
284	C₈²	—	13	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	—	2	1	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	2	1	no	—
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	—	2	1	no	—
294	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	1	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	C₂×#131	1	2	yes	—
305	C₄×C₁₃	C₂×#131	1	2	yes	—
306	C₄×C₁₃	#568	1	2	yes	—
307	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
308	C₂×M₁₆	—	13	2	no	—
309	C₂×M₁₆	—	13	2	no	—
310	C₂×M₁₆	—	13	2	no	—
311	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
312	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
313	C₂²×C₈	—	13	2	no	—
314	C₂²×C₈	—	13	2	no	—
315	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
316	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
317	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
318	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
319	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
320	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
321	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
322	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
323	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
324	#117	C₄×D₁₃	1	1	yes	characteristic
325	#117	C₄×D₁₃	1	1	yes	characteristic
326	#117	C₄×D₁₃	1	1	yes	characteristic
327	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
328	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
329	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
330	C₄⋊C₈	—	13	2	no	—
331	C₄⋊C₈	—	13	2	no	—
332	C₄⋊C₈	—	13	2	no	—
333	C₄⋊C₈	—	13	2	no	—
334	C₄⋊C₈	—	13	2	no	—
335	C₄⋊C₈	—	13	2	no	—
336	C₄⋊C₈	—	13	2	no	—
337	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
338	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
339	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
340	C₂²⋊C₈	—	13	2	no	—
341	C₂²⋊C₈	—	13	2	no	—
342	C₂²⋊C₈	—	13	2	no	—
343	C₂²⋊C₈	—	13	2	no	—
344	C₂²⋊C₈	—	13	2	no	—
345	C₂²⋊C₈	—	13	2	no	—
346	C₂²⋊C₈	—	13	2	no	—
347	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
348	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
349	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
350	#97	—	13	2	no	—
351	#97	—	13	2	no	—
352	#97	—	13	2	no	—
353	#97	C₂×Dic₁₃	1	2	yes	—
354	#97	C₂×Dic₁₃	1	2	yes	—
355	C₄×C₈	—	13	2	no	—
356	C₄×C₈	—	13	2	no	—
357	C₄×C₈	—	13	1	no	—
358	C₄×C₈	—	13	1	no	—
359	C₄×C₈	—	13	1	no	—
360	C₄×C₈	—	13	1	no	—
361	C₄×C₈	—	13	1	no	—
362	C₄×C₈	—	13	1	no	—
363	C₄×C₈	—	13	1	no	—
364	C₄×C₈	—	13	1	no	—
365	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
366	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
367	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
368	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
369	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
370	C₂×C₁₃	—	4	1	no	—
371	C₂×C₁₃	—	4	1	no	—
372	C₂×C₁₃	—	4	1	no	—
373	C₂×C₁₃	#2873	1	1	yes	characteristic
374	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
375	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
376	#41	—	4	2	no	—
377	C₂×Q₈	C₄×Dic₁₃	1	1	yes	characteristic
378	C₂×D₄	C₄×Dic₁₃	1	1	yes	characteristic
379	C₂×D₄	C₄×Dic₁₃	1	1	yes	characteristic
380	C₂×D₄	C₄×Dic₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
390	M₁₆	—	2	4	no	—
391	M₁₆	—	2	4	no	—
392	M₁₆	—	26	4	no	—
393	M₁₆	—	26	4	no	—
394	M₁₆	—	52	2	no	—
395	C₂×C₈	—	2	4	no	—
396	C₂×C₈	—	13	2	no	—
397	C₂×C₈	—	13	2	no	—
398	C₂×C₈	—	13	2	no	—
399	C₂×C₈	—	13	2	no	—
400	C₂×C₈	—	13	2	no	—
401	C₂×C₈	—	13	2	no	—
402	C₂×C₈	—	13	2	no	—
403	C₂×C₈	—	13	2	no	—
404	C₂×C₈	—	26	4	no	—
405	C₂×C₈	—	52	2	no	—
406	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
407	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
408	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
409	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
410	C₄⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
411	C₄⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
412	C₄⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
413	C₄⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
414	C₄⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
415	C₄⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
416	C₂²⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
417	C₂²⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
418	C₂²⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
419	C₂²⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
420	C₂²⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
421	C₂²⋊C₄	C₄×Dic₁₃	1	1	yes	characteristic
422	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
423	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
424	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
425	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
426	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
427	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
428	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
429	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
430	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
431	C₄²	C₂³×D₁₃	1	1	yes	characteristic
432	C₁₃	#17341	1	1	yes	characteristic, complemented, Sylow
433	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
434	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
435	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
436	Q₈	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
455	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
457	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	13	4	no	—
465	C₈	—	26	2	no	—
466	C₈	—	26	2	no	—
467	C₈	—	26	2	no	—
468	C₈	—	26	2	no	—
469	C₈	—	26	2	no	—
470	C₈	—	26	2	no	—
471	C₈	—	26	2	no	—
472	C₈	#88202	1	4	yes	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	#11719450	1	2	yes	—
493	C₄	D₁₃×#131	1	2	yes	—
494	C₄	C₂×#88202	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	4	1	no	—
497	C₂	—	4	1	no	—
498	C₂	#13123254	1	1	yes	characteristic
499	C₂	#131×Dic₁₃	1	1	yes	characteristic
500	C₂	C₄×#88202	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#2965	C₂
prime radical	C₂×C₁₃×#41	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2965	D₁₃
hypocenter	C₁₃	#17341
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #2965

Complements

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

N	H ≅ G/N	type
3. #13113139	C₂	semidirect
4. #13113136	C₂	semidirect
5. #13113136	C₂	semidirect
6. #13113133	C₂	semidirect
7. #13113131	C₂	semidirect
8. #13113131	C₂	semidirect
9. #13113120	C₂	semidirect
10. #13113119	C₂	semidirect
11. #13113117	C₂	semidirect
12. C₈×#6099	C₂	semidirect
13. M₁₆×#1055	C₂	semidirect
14. M₁₆×#1055	C₂	semidirect
432. C₁₃	#17341	semidirect

Maximal subgroups

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

subgroup	index
#13123803	2
#13123480	2
#13113139	2
#13113136	2
#13113133	2
#13113131	2
#13113120	2
#13113119	2
#13113117	2
C₈×#6099	2
M₁₆×#1055	2
C₁₃×#2965	2
#17341	13