Subgroups — #15871166

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115451	C₂	1	1	yes	maximal, characteristic
2	#13115451	C₂	1	1	yes	maximal, characteristic
3	#13115444	C₂	1	1	yes	maximal, characteristic
4	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115395	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114979	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114705	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114620	C₂	1	1	yes	maximal, characteristic
12	#13114620	C₂	1	1	yes	maximal, characteristic
13	#13114620	C₂	1	1	yes	maximal, characteristic
14	C₄×#88043	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#126	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#126	C₄	1	1	yes	characteristic
17	C₂²×#6099	C₂²	1	1	yes	characteristic
18	C₁₃×#388	C₄	1	1	yes	characteristic
19	C₁₃×#388	C₄	1	1	yes	characteristic
20	C₁₃×#388	C₄	1	1	yes	characteristic
21	C₁₃×#387	C₄	1	1	yes	characteristic
22	C₁₃×#387	C₄	1	1	yes	characteristic
23	C₁₃×#387	C₄	1	1	yes	characteristic
24	C₁₃×#383	C₄	1	1	yes	characteristic
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₄³×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
38	C₂×#88043	C₂²	1	1	yes	characteristic
39	C₂×#88043	C₂²	1	1	yes	characteristic
40	C₂×#88043	C₂²	1	1	yes	characteristic
41	C₂×#88043	C₂²	1	1	yes	characteristic
42	C₂×#88043	C₂²	1	1	yes	characteristic
43	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
44	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
45	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
46	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
47	#11718116	C₂²	1	1	yes	characteristic
48	#11718116	C₂²	1	1	yes	characteristic
49	#11718116	C₂²	1	1	yes	characteristic
50	#11718116	C₂²	1	1	yes	characteristic
51	#11718116	C₂²	1	1	yes	characteristic
52	#11718116	C₂²	1	1	yes	characteristic
53	#11718116	C₂²	1	1	yes	characteristic
54	#11718116	C₂²	1	1	yes	characteristic
55	#11718116	C₂²	1	1	yes	characteristic
56	#11718116	C₂²	1	1	yes	characteristic
57	#11718116	C₂²	1	1	yes	characteristic
58	#11718116	C₂²	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#126	—	2	4	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	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×C₄²×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×#6099	—	2	2	no	—
84	C₂×#6099	—	2	2	no	—
85	C₂×#6099	—	2	2	no	—
86	C₂²×#1055	C₂³	1	1	yes	characteristic
87	C₂²×#1055	C₂³	1	1	yes	characteristic
88	C₂²×#1055	C₂³	1	1	yes	characteristic
89	C₂²×#1055	C₂³	1	1	yes	characteristic
90	C₂²×#1055	C₂³	1	1	yes	characteristic
91	C₂²×#1055	C₂³	1	1	yes	characteristic
92	C₂²×#1055	C₂³	1	1	yes	characteristic
93	C₂²×#1055	C₂³	1	1	yes	characteristic
94	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
95	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
96	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
97	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
98	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
99	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
100	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
101	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
102	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
103	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
104	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
105	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊#1055	—	2	2	no	—
107	C₂²⋊#1055	—	2	2	no	—
108	C₂²⋊#1055	—	2	2	no	—
109	C₄⋊#1055	—	2	2	no	—
110	C₄⋊#1055	—	2	2	no	—
111	C₄⋊#1055	—	2	2	no	—
112	#88043	—	2	2	no	—
113	#88043	—	2	2	no	—
114	#88043	—	2	2	no	—
115	#88043	—	2	2	no	—
116	#88043	—	2	2	no	—
117	C₄×#1055	—	2	2	no	—
118	C₄×#1055	—	2	2	no	—
119	C₄×#1055	—	2	2	no	—
120	C₄×#1055	—	2	2	no	—
121	#21667	—	13	1	no	maximal, Sylow
122	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	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	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	4	1	no	—
147	C₁₃×C₄⋊C₄	—	4	1	no	—
148	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	complemented
149	C₁₃×C₂²⋊C₄	—	2	2	no	—
150	C₁₃×C₂²⋊C₄	—	2	2	no	—
151	C₁₃×C₂²⋊C₄	—	2	2	no	—
152	C₁₃×C₂²⋊C₄	—	2	2	no	—
153	C₁₃×C₂²⋊C₄	—	4	1	no	—
154	C₁₃×C₂²⋊C₄	—	4	1	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	C₄²×C₁₃	—	2	1	no	—
165	C₄²×C₁₃	—	2	1	no	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₄²×C₁₃	—	2	1	no	—
168	C₄²×C₁₃	—	2	1	no	—
169	C₄²×C₁₃	—	4	1	no	—
170	C₄²×C₁₃	—	4	1	no	—
171	#6099	—	4	4	no	—
172	C₂×#1055	—	2	1	no	—
173	C₂×#1055	—	2	1	no	—
174	C₂×#1055	—	2	1	no	—
175	C₂×#1055	—	2	1	no	—
176	C₂×#1055	—	2	1	no	—
177	C₂×#1055	—	2	1	no	—
178	C₂×#1055	—	2	1	no	—
179	C₂×#1055	—	2	1	no	—
180	C₂×#1055	—	2	1	no	—
181	C₂×#1055	—	2	1	no	—
182	C₂×#1055	—	2	1	no	—
183	C₂×#1055	—	2	1	no	—
184	C₂×#1055	—	2	1	no	—
185	C₂×#1055	—	2	1	no	—
186	C₂×#1055	—	2	1	no	—
187	C₂×#1055	—	2	1	no	—
188	C₂×#1055	—	2	1	no	—
189	C₂×#1055	—	2	1	no	—
190	C₂×#1055	#41	1	2	yes	—
191	C₂×#1055	#41	1	2	yes	—
192	C₂×#1055	#41	1	2	yes	—
193	C₂×#1055	#41	1	2	yes	—
194	C₂×#1055	#41	1	2	yes	—
195	C₂×#1055	#41	1	2	yes	—
196	C₄×#126	D₁₃	1	1	yes	characteristic
197	#1924	—	13	1	no	—
198	#1924	—	13	1	no	—
199	#1923	—	13	1	no	—
200	#1917	—	13	1	no	—
201	#1917	—	13	1	no	—
202	#1916	—	13	1	no	—
203	#1839	—	13	1	no	—
204	#1771	—	13	1	no	—
205	#1770	—	13	1	no	—
206	C₈×C₄⋊C₄	—	13	1	no	—
207	#1753	—	13	1	no	—
208	#1753	—	13	1	no	—
209	#1753	—	13	1	no	—
210	C₄×#97	—	13	1	no	—
211	C₂³×C₁₃	—	2	1	no	—
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	2	1	no	—
214	C₂³×C₁₃	—	2	1	no	—
215	C₂³×C₁₃	—	2	1	no	—
216	C₂³×C₁₃	—	2	1	no	—
217	C₂³×C₁₃	—	2	1	no	—
218	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	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	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
259	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
260	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
261	C₂×C₄×C₁₃	#131	1	2	yes	—
262	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
268	#1055	—	2	2	no	—
269	#1055	—	2	2	no	—
270	#1055	—	2	2	no	—
271	#1055	—	4	1	no	—
272	#1055	—	4	1	no	—
273	#1055	—	4	1	no	—
274	#1055	—	4	1	no	—
275	#1055	#126	1	4	yes	complemented
276	C₂²×M₁₆	—	13	1	no	—
277	C₂×#126	Dic₁₃	1	1	yes	characteristic
278	C₂×C₄⋊C₈	—	13	1	no	—
279	C₂×C₄⋊C₈	—	13	1	no	—
280	C₂×C₄⋊C₈	—	13	1	no	—
281	C₂×C₂²⋊C₈	—	13	1	no	—
282	C₂×C₂²⋊C₈	—	13	1	no	—
283	C₂×C₂²⋊C₈	—	13	1	no	—
284	C₂×#97	—	13	1	no	—
285	C₂×#97	—	13	1	no	—
286	C₂×#97	—	13	1	no	—
287	C₂×#97	—	13	1	no	—
288	C₂×#97	—	13	1	no	—
289	C₂×C₄×C₈	—	13	1	no	—
290	C₂×C₄×C₈	—	13	1	no	—
291	C₂×C₄×C₈	—	13	1	no	—
292	C₂×C₄×C₈	—	13	1	no	—
293	#388	Dic₁₃	1	1	yes	characteristic
294	#388	Dic₁₃	1	1	yes	characteristic
295	#388	Dic₁₃	1	1	yes	characteristic
296	#387	Dic₁₃	1	1	yes	characteristic
297	#387	Dic₁₃	1	1	yes	characteristic
298	#387	Dic₁₃	1	1	yes	characteristic
299	#383	Dic₁₃	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
301	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
302	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
303	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
304	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
305	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
306	C₄³	C₂×D₁₃	1	1	yes	characteristic
307	#336	—	13	1	no	—
308	#336	—	13	1	no	—
309	#336	—	13	1	no	—
310	#336	—	13	1	no	—
311	#336	—	13	1	no	—
312	#336	—	13	1	no	—
313	#336	—	13	1	no	—
314	#336	—	13	1	no	—
315	#336	—	13	1	no	—
316	#336	—	13	1	no	—
317	#336	—	13	1	no	—
318	#336	—	13	1	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	—	4	1	no	—
321	C₂²×C₁₃	—	4	1	no	—
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
327	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
328	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
329	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
330	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
331	C₂²×C₁₃	#568	1	1	yes	characteristic
332	C₂²×C₁₃	#568	1	1	yes	characteristic
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	2	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	—	4	1	no	—
343	C₄×C₁₃	—	4	1	no	—
344	C₄×C₁₃	—	4	1	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
347	C₄×C₁₃	#529	1	1	yes	characteristic
348	C₄×C₁₃	#529	1	1	yes	characteristic
349	C₄×C₁₃	#529	1	1	yes	characteristic
350	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
351	C₂×M₁₆	—	26	2	no	—
352	C₂×M₁₆	—	26	2	no	—
353	C₂×M₁₆	—	26	2	no	—
354	C₂²×C₈	—	13	1	no	—
355	C₂²×C₈	—	13	1	no	—
356	C₂²×C₈	—	13	1	no	—
357	C₂²×C₈	—	13	1	no	—
358	C₂²×C₈	—	13	1	no	—
359	C₂²×C₈	—	13	1	no	—
360	C₂²×C₈	—	13	1	no	—
361	C₂²×C₈	—	13	1	no	—
362	#126	—	2	4	no	—
363	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
375	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
376	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
377	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
378	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
379	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
380	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
381	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
382	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
383	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
384	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
385	C₄⋊C₈	—	26	2	no	—
386	C₄⋊C₈	—	26	2	no	—
387	C₄⋊C₈	—	26	2	no	—
388	C₂²⋊C₈	—	26	2	no	—
389	C₂²⋊C₈	—	26	2	no	—
390	C₂²⋊C₈	—	26	2	no	—
391	#97	—	26	2	no	—
392	#97	—	26	2	no	—
393	#97	—	26	2	no	—
394	#97	—	26	2	no	—
395	#97	—	26	2	no	—
396	C₄×C₈	—	26	2	no	—
397	C₄×C₈	—	26	2	no	—
398	C₄×C₈	—	26	2	no	—
399	C₄×C₈	—	26	2	no	—
400	#95	C₂×Dic₁₃	1	1	yes	characteristic
401	#95	C₂×Dic₁₃	1	1	yes	characteristic
402	#95	C₂×Dic₁₃	1	1	yes	characteristic
403	#95	C₂×Dic₁₃	1	1	yes	characteristic
404	#95	C₂×Dic₁₃	1	1	yes	characteristic
405	#95	C₂×Dic₁₃	1	1	yes	characteristic
406	#95	C₂×Dic₁₃	1	1	yes	characteristic
407	#95	C₂×Dic₁₃	1	1	yes	characteristic
408	#95	C₂×Dic₁₃	1	1	yes	characteristic
409	#95	C₂×Dic₁₃	1	1	yes	characteristic
410	#95	C₂×Dic₁₃	1	1	yes	characteristic
411	#95	C₂×Dic₁₃	1	1	yes	characteristic
412	C₂×C₁₃	—	8	1	no	—
413	C₂×C₁₃	C₄×#126	1	1	yes	characteristic
414	C₂×C₁₃	#2965	1	1	yes	characteristic
415	C₂×C₁₃	#2967	1	1	yes	characteristic
416	C₂×C₁₃	#2968	1	1	yes	characteristic
417	C₂×C₁₃	#2969	1	1	yes	characteristic
418	C₂×C₁₃	#2970	1	1	yes	characteristic
419	C₂×C₁₃	#2971	1	1	yes	characteristic
420	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
441	M₁₆	—	52	4	no	—
442	C₂×C₈	—	13	2	no	—
443	C₂×C₈	—	13	2	no	—
444	C₂×C₈	—	13	2	no	—
445	C₂×C₈	—	13	2	no	—
446	C₂×C₈	—	13	2	no	—
447	C₂×C₈	—	13	2	no	—
448	C₂×C₈	—	26	1	no	—
449	C₂×C₈	—	26	1	no	—
450	C₂×C₈	—	26	1	no	—
451	C₂×C₈	—	26	1	no	—
452	C₂×C₈	—	26	1	no	—
453	C₂×C₈	—	26	1	no	—
454	C₂×C₈	—	26	1	no	—
455	C₂×C₈	—	26	1	no	—
456	C₂×C₈	—	26	1	no	—
457	C₂×C₈	—	26	1	no	—
458	C₂×C₈	—	26	1	no	—
459	C₂×C₈	—	26	1	no	—
460	C₂×C₈	—	26	1	no	—
461	C₂×C₈	—	26	1	no	—
462	C₂×C₈	—	26	1	no	—
463	C₂×C₈	—	26	1	no	—
464	C₂×C₈	—	26	1	no	—
465	C₂×C₈	—	26	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	#6099	1	4	yes	complemented
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	4	1	no	—
493	C₄²	—	4	1	no	—
494	C₁₃	#21667	1	1	yes	characteristic, complemented, Sylow
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	C₂×#6099	1	2	yes	—
543	C₂×C₄	C₂×#6099	1	2	yes	—
544	C₂×C₄	C₂×#6099	1	2	yes	—
545	C₂×C₄	#88202	1	2	yes	—
546	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
547	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
548	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
549	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
550	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
551	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
552	C₈	—	13	4	no	—
553	C₈	—	26	2	no	—
554	C₈	—	26	2	no	—
555	C₈	—	26	2	no	—
556	C₈	—	52	1	no	—
557	C₈	—	52	1	no	—
558	C₈	—	52	1	no	—
559	C₈	—	52	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	C₂²×#6099	1	1	yes	characteristic
568	C₂²	C₂×#88202	1	1	yes	characteristic
569	C₂²	#11719524	1	1	yes	characteristic
570	C₂²	#11719524	1	1	yes	characteristic
571	C₂²	#41×Dic₁₃	1	1	yes	characteristic
572	C₂²	#41×Dic₁₃	1	1	yes	characteristic
573	C₂²	#41×Dic₁₃	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	D₁₃×#126	1	1	yes	characteristic
588	C₄	#11719411	1	1	yes	characteristic
589	C₄	#11719411	1	1	yes	characteristic
590	C₄	#11719411	1	1	yes	characteristic
591	C₂	—	8	1	no	—
592	C₂	#126×Dic₁₃	1	1	yes	characteristic
593	C₂	#13123803	1	1	yes	characteristic
594	C₂	#13123823	1	1	yes	characteristic
595	C₂	#13123832	1	1	yes	characteristic
596	C₂	#13123841	1	1	yes	characteristic
597	C₂	#13123850	1	1	yes	characteristic
598	C₂	#13123856	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₄×C₁₃×#126	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#126	D₁₃
hypocenter	C₁₃	#21667
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#126

Complements

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

N	H ≅ G/N	type
4. #13115402	C₂	semidirect
5. #13115402	C₂	semidirect
6. #13115395	C₂	semidirect
7. #13114979	C₂	semidirect
8. #13114711	C₂	semidirect
9. #13114705	C₂	semidirect
10. C₄⋊C₄×#1055	C₂	semidirect
14. C₄×#88043	C₂	semidirect
148. C₁₃×C₄⋊C₄	M₁₆	semidirect
275. #1055	#126	semidirect
471. C₄⋊C₄	#6099	semidirect
494. C₁₃	#21667	semidirect

Maximal subgroups

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

subgroup	index
#13115451	2
#13115444	2
#13115402	2
#13115395	2
#13114979	2
#13114711	2
#13114705	2
C₄⋊C₄×#1055	2
#13114620	2
C₄×#88043	2
C₄×C₁₃×#126	2
#21667	13