Subgroups — #15880268

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123494	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123285	C₂	1	1	yes	maximal, characteristic
3	#13115549	C₂	1	2	yes	maximal, complemented
4	#13115486	C₂	1	2	yes	maximal, complemented
5	#13115113	C₂	1	2	yes	maximal, complemented
6	#13114935	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114874	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114780	C₂	1	1	yes	maximal, characteristic
9	#13114683	C₂	1	2	yes	maximal, complemented
10	#13114612	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂×#88202	C₂²	1	2	yes	—
16	C₁₃×#416	C₄	1	1	yes	characteristic, complemented
17	C₁₃×#416	C₄	1	1	yes	characteristic, complemented
18	C₁₃×#416	C₄	1	1	yes	characteristic, complemented
19	C₁₃×#416	C₄	1	1	yes	characteristic, complemented
20	C₁₃×#416	C₂²	1	1	yes	characteristic
21	C₁₃×#416	C₂²	1	1	yes	characteristic
22	C₁₃×#416	C₂²	1	1	yes	characteristic
23	C₁₃×#416	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₄	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#103	C₄	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#102	C₄	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#102	C₄	1	1	yes	characteristic, complemented
28	C₂×#88077	C₂²	1	2	yes	—
29	C₂×#88077	C₂²	1	2	yes	—
30	#11718895	—	2	2	no	—
31	#11718895	C₂²	1	2	yes	—
32	C₄×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
33	#11718868	—	2	1	no	—
34	#11718868	C₂²	1	1	yes	characteristic
35	#11718868	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊#1055	—	2	1	no	—
37	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
38	C₂×#88059	C₂²	1	2	yes	complemented
39	C₂×#88055	C₂²	1	2	yes	complemented
40	#11718661	—	2	2	no	—
41	#11718660	C₂²	1	2	yes	complemented
42	#11718658	C₂²	1	2	yes	complemented
43	#11718587	—	2	1	no	—
44	#11718586	—	2	1	no	—
45	#11718144	C₂²	1	2	yes	complemented
46	#11718142	C₂²	1	2	yes	complemented
47	#11718124	C₂²	1	2	yes	complemented
48	#11718124	C₂²	1	2	yes	complemented
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	—	2	1	no	—
51	C₂×C₁₃×#41	—	2	4	no	—
52	C₂×C₁₃×#41	—	4	2	no	—
53	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	—	4	2	no	—
63	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#117	—	2	1	no	—
70	C₁₃×#117	—	2	1	no	—
71	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
72	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
73	C₁₃×#117	C₂³	1	1	yes	characteristic
74	C₁₃×#117	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
80	#88202	—	2	4	no	—
81	#88202	—	4	2	no	—
82	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
83	C₂×#6099	—	2	2	no	—
84	C₂×#6099	C₂³	1	2	yes	—
85	C₂×#6099	C₂³	1	2	yes	—
86	C₂²×#1055	—	2	2	no	—
87	C₂²×#1055	C₂³	1	2	yes	—
88	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
89	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
90	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
91	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
92	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
94	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
95	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
96	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
97	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
98	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
99	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
100	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
101	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
102	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
103	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
104	#88077	—	2	4	no	—
105	#88077	—	4	2	no	—
106	#88071	—	2	1	no	—
107	C₂²⋊#1055	—	2	1	no	—
108	C₂²⋊#1055	—	2	1	no	—
109	C₂²⋊#1055	—	2	1	no	—
110	C₂²⋊#1055	—	2	1	no	—
111	C₂²⋊#1055	—	2	2	no	—
112	C₂²⋊#1055	—	2	2	no	—
113	C₂²⋊#1055	D₄	1	2	yes	—
114	C₂²⋊#1055	D₄	1	1	yes	characteristic
115	C₂²⋊#1055	D₄	1	1	yes	characteristic
116	#88059	—	4	2	no	—
117	#88055	—	4	2	no	—
118	C₄⋊#1055	—	2	2	no	—
119	C₄⋊#1055	—	2	2	no	—
120	#88043	—	2	2	no	—
121	C₄×#1055	—	2	2	no	—
122	#22586	—	13	1	no	maximal, Sylow
123	C₂⁴×C₁₃	—	2	1	no	—
124	C₂⁴×C₁₃	#41	1	1	yes	characteristic
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	—	2	2	no	—
127	C₁₃×#41	—	2	2	no	—
128	C₁₃×#41	—	2	2	no	—
129	C₁₃×#41	—	2	2	no	—
130	C₁₃×#41	—	4	4	no	—
131	C₁₃×#41	—	4	1	no	—
132	C₁₃×#41	—	4	1	no	—
133	C₁₃×#41	—	4	4	no	—
134	C₁₃×#41	#41	1	4	yes	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	4	1	no	—
138	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	4	1	no	—
147	C₂×D₄×C₁₃	—	4	4	no	—
148	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	4	4	no	—
160	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂²×Dic₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	4	1	no	—
170	C₂×C₈×C₁₃	—	4	1	no	—
171	C₂×C₈×C₁₃	—	4	1	no	—
172	C₂×C₈×C₁₃	—	4	1	no	—
173	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
183	C₁₃×C₂²⋊C₄	—	2	1	no	—
184	C₁₃×C₂²⋊C₄	—	2	1	no	—
185	C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	1	no	—
189	C₄²×C₁₃	—	2	1	no	—
190	C₄²×C₁₃	—	2	1	no	—
191	C₂²⋊Dic₁₃	—	4	2	no	—
192	C₄×Dic₁₃	—	2	2	no	—
193	C₄×Dic₁₃	—	2	2	no	—
194	#6099	—	2	2	no	—
195	#6099	—	2	2	no	—
196	#6099	—	2	2	no	—
197	#6099	—	2	2	no	—
198	#6099	—	4	4	no	—
199	C₂×#1055	—	2	2	no	—
200	C₂×#1055	—	2	2	no	—
201	C₂×#1055	—	2	2	no	—
202	C₂×#1055	—	2	2	no	—
203	C₂×#1055	—	4	4	no	—
204	C₂×#1055	C₂×D₄	1	2	yes	—
205	C₂×#1055	C₂×D₄	1	2	yes	—
206	#2924	—	13	1	no	—
207	C₂×#416	D₁₃	1	1	yes	characteristic
208	#2880	—	13	1	no	—
209	#1938	—	13	2	no	—
210	#1929	—	13	2	no	—
211	#1866	—	13	2	no	—
212	#1826	—	13	1	no	—
213	#1810	—	13	1	no	—
214	#1789	—	13	1	no	—
215	#1765	—	13	2	no	—
216	#1752	—	13	1	no	—
217	C₂³×C₁₃	—	2	1	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	1	no	—
221	C₂³×C₁₃	—	4	1	no	—
222	C₂³×C₁₃	—	4	2	no	—
223	C₂³×C₁₃	—	4	2	no	—
224	C₂³×C₁₃	—	8	1	no	—
225	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
226	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
227	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
228	Q₈×C₁₃	—	2	1	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	4	2	no	—
232	Q₈×C₁₃	#117	1	2	yes	—
233	D₄×C₁₃	—	2	4	no	—
234	D₄×C₁₃	—	2	1	no	—
235	D₄×C₁₃	—	2	1	no	—
236	D₄×C₁₃	—	2	1	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	4	2	no	—
239	D₄×C₁₃	—	4	2	no	—
240	D₄×C₁₃	—	4	2	no	—
241	D₄×C₁₃	#117	1	2	yes	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	8	1	no	—
262	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
267	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
268	C₂×Dic₁₃	—	4	2	no	—
269	C₂×Dic₁₃	—	4	2	no	—
270	C₂×Dic₁₃	—	4	2	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	2	1	no	—
274	C₈×C₁₃	—	2	1	no	—
275	#1055	—	2	2	no	—
276	#1055	—	2	2	no	—
277	#1055	—	4	2	no	—
278	#1055	—	4	2	no	—
279	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
280	C₂×#131	—	13	2	no	—
281	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
282	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
283	#433	—	26	2	no	—
284	#432	—	26	1	no	—
285	#431	—	26	1	no	—
286	C₂×#108	—	13	2	no	—
287	#424	—	13	2	no	—
288	C₂×#104	—	13	2	no	—
289	C₂×#104	—	13	2	no	—
290	#416	Dic₁₃	1	1	yes	characteristic, complemented
291	#416	Dic₁₃	1	1	yes	characteristic, complemented
292	#416	Dic₁₃	1	1	yes	characteristic, complemented
293	#416	Dic₁₃	1	1	yes	characteristic, complemented
294	#416	C₂×D₁₃	1	1	yes	characteristic
295	#416	C₂×D₁₃	1	1	yes	characteristic
296	#416	C₂×D₁₃	1	1	yes	characteristic
297	#416	C₂×D₁₃	1	1	yes	characteristic
298	C₂×#103	Dic₁₃	1	1	yes	characteristic, complemented
299	C₂×#103	Dic₁₃	1	1	yes	characteristic, complemented
300	C₂×#102	Dic₁₃	1	1	yes	characteristic, complemented
301	C₂×#102	Dic₁₃	1	1	yes	characteristic, complemented
302	#408	—	13	2	no	—
303	#408	—	26	2	no	—
304	#407	—	13	1	no	—
305	#407	—	13	1	no	—
306	#407	—	26	1	no	—
307	C₂×C₂²⋊C₈	—	13	1	no	—
308	C₂×C₂²⋊C₈	—	26	1	no	—
309	#405	—	13	2	no	—
310	C₂×#97	—	13	2	no	—
311	C₄×C₂²⋊C₄	—	13	1	no	—
312	#341	—	13	2	no	—
313	#339	—	13	2	no	—
314	#339	—	13	2	no	—
315	#336	—	13	2	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	4	4	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	—	4	1	no	—
327	C₂²×C₁₃	—	4	1	no	—
328	C₂²×C₁₃	—	4	1	no	—
329	C₂²×C₁₃	—	4	1	no	—
330	C₂²×C₁₃	—	8	4	no	—
331	C₂²×C₁₃	#444	1	2	yes	—
332	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
333	C₂²×C₁₃	#551	1	2	yes	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	4	1	no	—
338	C₄×C₁₃	—	4	1	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
343	C₄×C₁₃	#518	1	1	yes	characteristic
344	C₄×C₁₃	#546	1	2	yes	—
345	Dic₁₃	—	8	2	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	4	no	—
349	C₂×#41	—	4	2	no	—
350	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
351	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
352	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
353	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
354	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
359	#131	—	26	4	no	—
360	#131	—	52	2	no	—
361	C₂×M₁₆	—	13	2	no	—
362	C₂×M₁₆	—	13	2	no	—
363	C₂×M₁₆	—	26	2	no	—
364	C₂²×C₈	—	4	2	no	—
365	C₂²×C₈	—	13	2	no	—
366	C₂²×C₈	—	26	2	no	—
367	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
368	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
369	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
370	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
371	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
372	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	C₂×Dic₁₃	1	1	yes	characteristic
376	#117	C₂×Dic₁₃	1	1	yes	characteristic
377	#117	C₂²×D₁₃	1	1	yes	characteristic
378	#117	C₂²×D₁₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	26	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	13	2	no	—
385	#108	—	52	2	no	—
386	C₄⋊C₈	—	26	2	no	—
387	C₄⋊C₈	—	26	2	no	—
388	#104	—	26	4	no	—
389	#104	—	52	2	no	—
390	#103	C₂×Dic₁₃	1	1	yes	characteristic
391	#103	C₂×Dic₁₃	1	1	yes	characteristic
392	#103	C₂×Dic₁₃	1	1	yes	characteristic
393	#103	C₂×Dic₁₃	1	1	yes	characteristic
394	#103	C₂×Dic₁₃	1	1	yes	characteristic
395	#103	C₂×Dic₁₃	1	1	yes	characteristic
396	#103	C₂×Dic₁₃	1	1	yes	characteristic
397	#103	C₂×Dic₁₃	1	1	yes	characteristic
398	#102	C₂×Dic₁₃	1	1	yes	characteristic
399	#102	C₂×Dic₁₃	1	1	yes	characteristic
400	#102	C₂×Dic₁₃	1	1	yes	characteristic
401	#102	C₂×Dic₁₃	1	1	yes	characteristic
402	#102	C₂×Dic₁₃	1	1	yes	characteristic
403	#102	C₂×Dic₁₃	1	1	yes	characteristic
404	#102	C₂×Dic₁₃	1	1	yes	characteristic
405	#102	C₂×Dic₁₃	1	1	yes	characteristic
406	C₂²⋊C₈	—	13	1	no	—
407	C₂²⋊C₈	—	13	1	no	—
408	C₂²⋊C₈	—	13	2	no	—
409	C₂²⋊C₈	—	26	2	no	—
410	C₂²⋊C₈	—	26	2	no	—
411	C₂²⋊C₈	—	26	1	no	—
412	C₂²⋊C₈	—	26	1	no	—
413	C₂²⋊C₈	—	26	1	no	—
414	C₂²⋊C₈	—	26	1	no	—
415	#97	—	26	2	no	—
416	#97	—	52	2	no	—
417	C₄×C₈	—	26	2	no	—
418	#95	—	26	1	no	—
419	C₂×C₁₃	—	2	2	no	—
420	C₂×C₁₃	—	2	2	no	—
421	C₂×C₁₃	—	4	1	no	—
422	C₂×C₁₃	—	4	2	no	—
423	C₂×C₁₃	—	8	1	no	—
424	C₂×C₁₃	#2342	1	1	yes	characteristic
425	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
426	C₂×C₁₃	#2957	1	1	yes	characteristic
427	C₂⁴	—	2	1	no	—
428	C₂⁴	#6129	1	1	yes	characteristic
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	4	4	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	4	no	—
438	#41	#6127	1	4	yes	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	4	1	no	—
442	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
443	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
453	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	4	4	no	—
464	C₂²×C₄	—	26	2	no	—
465	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
466	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
467	C₂²×C₄	#6129	1	1	yes	characteristic
468	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
471	M₁₆	—	26	2	no	—
472	M₁₆	—	26	2	no	—
473	M₁₆	—	26	2	no	—
474	M₁₆	—	26	2	no	—
475	M₁₆	—	52	4	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	13	2	no	—
483	C₂×C₈	—	13	2	no	—
484	C₂×C₈	—	26	2	no	—
485	C₂×C₈	—	26	2	no	—
486	C₂×C₈	—	26	2	no	—
487	C₂×C₈	—	26	2	no	—
488	C₂×C₈	—	52	4	no	—
489	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
490	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
491	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
492	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	52	2	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	26	2	no	—
509	C₄²	—	26	2	no	—
510	C₁₃	#22586	1	1	yes	characteristic, complemented, Sylow
511	C₂³	—	2	2	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	8	1	no	—
519	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
520	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
521	C₂³	C₂×#6129	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	2	1	no	—
525	Q₈	—	4	2	no	—
526	Q₈	#88180	1	2	yes	—
527	D₄	—	2	4	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	#88180	1	2	yes	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	8	1	no	—
556	C₂×C₄	—	52	2	no	—
557	C₂×C₄	—	52	2	no	—
558	C₂×C₄	—	52	2	no	—
559	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
560	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
561	C₂×C₄	C₂×#6127	1	2	yes	—
562	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
563	C₂×C₄	#88251	1	2	yes	—
564	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	26	2	no	—
570	C₈	—	26	2	no	—
571	C₈	—	52	2	no	—
572	C₈	—	52	2	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	8	4	no	—
588	C₂²	#11718858	1	2	yes	—
589	C₂²	#11719200	1	2	yes	—
590	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	104	2	no	—
600	C₄	#11719195	1	2	yes	—
601	C₄	C₂×#88180	1	1	yes	characteristic
602	C₄	#11719503	1	1	yes	characteristic
603	C₂	—	2	2	no	—
604	C₂	—	2	2	no	—
605	C₂	—	4	1	no	—
606	C₂	—	4	2	no	—
607	C₂	—	8	1	no	—
608	C₂	#13117685	1	1	yes	characteristic
609	C₂	C₂×#11718858	1	1	yes	characteristic
610	C₂	#13123753	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#416	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×C₁₃×#41	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#416	D₁₃
hypocenter	C₁₃	#22586
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#416

Complements

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

N	H ≅ G/N	type
1. #13123494	C₂	semidirect
3. #13115549	C₂	semidirect
4. #13115486	C₂	semidirect
5. #13115113	C₂	semidirect
6. #13114935	C₂	semidirect
7. #13114874	C₂	semidirect
9. #13114683	C₂	semidirect
10. #13114612	C₂	semidirect
16. C₁₃×#416	C₄	semidirect
17. C₁₃×#416	C₄	semidirect
18. C₁₃×#416	C₄	semidirect
19. C₁₃×#416	C₄	semidirect
24. C₂×C₁₃×#103	C₄	semidirect
25. C₂×C₁₃×#103	C₄	semidirect
26. C₂×C₁₃×#102	C₄	semidirect
27. C₂×C₁₃×#102	C₄	semidirect
38. C₂×#88059	C₂²	semidirect
39. C₂×#88055	C₂²	semidirect
41. #11718660	C₂²	semidirect
42. #11718658	C₂²	semidirect
45. #11718144	C₂²	semidirect
46. #11718142	C₂²	semidirect
47. #11718124	C₂²	semidirect
48. #11718124	C₂²	semidirect
290. #416	Dic₁₃	semidirect
291. #416	Dic₁₃	semidirect
292. #416	Dic₁₃	semidirect
293. #416	Dic₁₃	semidirect
298. C₂×#103	Dic₁₃	semidirect
299. C₂×#103	Dic₁₃	semidirect
300. C₂×#102	Dic₁₃	semidirect
301. C₂×#102	Dic₁₃	semidirect
510. C₁₃	#22586	semidirect

Maximal subgroups

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

subgroup	index
#13123494	2
#13123285	2
#13115549	2
#13115486	2
#13115113	2
#13114935	2
#13114874	2
#13114780	2
#13114683	2
#13114612	2
C₂×C₁₃×#416	2
#22586	13