Subgroups — #15880758

Order 3328.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115560	C₂	1	1	yes	maximal, characteristic, complemented
2	#13115555	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115395	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115395	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115395	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114820	C₂	1	1	yes	maximal, characteristic
8	#13114820	C₂	1	1	yes	maximal, characteristic
9	#13114816	C₂	1	1	yes	maximal, characteristic
10	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
12	#13114602	C₂	1	1	yes	maximal, characteristic
13	#13114602	C₂	1	1	yes	maximal, characteristic
14	C₄×C₂²⋊#1055	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#389	C₄	1	1	yes	characteristic
20	C₁₃×#389	C₄	1	1	yes	characteristic
21	C₁₃×#389	C₄	1	1	yes	characteristic
22	C₁₃×#389	C₄	1	1	yes	characteristic
23	C₁₃×#385	C₄	1	1	yes	characteristic
24	C₁₃×#385	C₄	1	1	yes	characteristic
25	C₁₃×#385	C₄	1	1	yes	characteristic
26	C₁₃×#385	C₄	1	1	yes	characteristic
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊#1055	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×C₄⋊#1055	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊#1055	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	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×#117	—	2	2	no	—
63	C₁₃×#117	—	2	2	no	—
64	C₁₃×#117	—	4	1	no	—
65	C₁₃×#117	—	4	1	no	—
66	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂×C₄	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×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	—	4	1	no	—
83	C₂×C₄²×C₁₃	—	4	1	no	—
84	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×#1055	C₂³	1	1	yes	characteristic
93	C₂²×#1055	C₂³	1	1	yes	characteristic
94	C₂²×#1055	C₂³	1	1	yes	characteristic
95	C₂²×#1055	C₂³	1	1	yes	characteristic
96	C₂²×#1055	C₂³	1	1	yes	characteristic
97	C₂²×#1055	C₂³	1	1	yes	characteristic
98	C₂²×#1055	C₂³	1	1	yes	characteristic
99	C₂²×#1055	C₂³	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	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
107	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
108	C₂²⋊#1055	—	2	2	no	—
109	C₂²⋊#1055	—	2	2	no	—
110	C₂²⋊#1055	—	2	2	no	—
111	C₂²⋊#1055	Q₈	1	4	yes	—
112	C₄⋊#1055	—	2	2	no	—
113	C₄⋊#1055	—	2	2	no	—
114	C₄⋊#1055	—	4	1	no	—
115	C₄⋊#1055	—	4	1	no	—
116	C₄⋊#1055	—	4	1	no	—
117	C₄⋊#1055	—	4	1	no	—
118	#88043	—	2	2	no	—
119	#88043	—	4	1	no	—
120	C₄×#1055	—	2	2	no	—
121	C₄×#1055	—	4	1	no	—
122	C₄×#1055	—	4	1	no	—
123	C₄×#1055	—	4	1	no	—
124	#22630	—	13	1	no	maximal, Sylow
125	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	4	1	no	—
134	C₂²×C₄×C₁₃	—	4	1	no	—
135	C₂²×C₄×C₁₃	—	4	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
150	C₂²×C₄×C₁₃	#41	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	4	1	no	—
161	C₁₃×C₄⋊C₄	—	4	1	no	—
162	C₁₃×C₄⋊C₄	—	4	1	no	—
163	C₁₃×C₄⋊C₄	—	4	1	no	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	4	1	no	—
167	C₁₃×C₂²⋊C₄	—	4	1	no	—
168	C₄²×C₁₃	—	2	1	no	—
169	C₄²×C₁₃	—	2	1	no	—
170	C₄²×C₁₃	—	2	1	no	—
171	C₄²×C₁₃	—	2	1	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₄²×C₁₃	—	2	1	no	—
175	C₄²×C₁₃	—	2	1	no	—
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	4	1	no	—
179	C₄²×C₁₃	—	4	1	no	—
180	C₄²×C₁₃	#41	1	2	yes	—
181	C₄²×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
191	C₂×#1055	—	2	1	no	—
192	C₂×#1055	—	2	1	no	—
193	C₂×#1055	—	2	1	no	—
194	C₂×#1055	—	2	1	no	—
195	C₂×#1055	—	2	1	no	—
196	C₂×#1055	—	2	1	no	—
197	C₂×#1055	—	2	1	no	—
198	C₂×#1055	—	2	1	no	—
199	C₂×#1055	—	2	1	no	—
200	C₂×#1055	—	2	1	no	—
201	C₂×#1055	—	2	1	no	—
202	C₂×#1055	—	2	1	no	—
203	C₂×#1055	—	2	1	no	—
204	C₂×#1055	C₂×Q₈	1	2	yes	—
205	C₂×#1055	C₂×Q₈	1	2	yes	—
206	#2296	D₁₃	1	1	yes	characteristic
207	#1940	—	13	1	no	—
208	#1939	—	13	1	no	—
209	#1917	—	13	1	no	—
210	#1916	—	13	1	no	—
211	#1916	—	13	1	no	—
212	#1916	—	13	1	no	—
213	#1798	—	13	1	no	—
214	#1798	—	13	1	no	—
215	#1797	—	13	1	no	—
216	#1771	—	13	1	no	—
217	C₈×C₄⋊C₄	—	13	1	no	—
218	#1750	—	13	1	no	—
219	#1750	—	13	1	no	—
220	C₄×C₂²⋊C₈	—	13	1	no	—
221	C₂³×C₁₃	—	2	1	no	—
222	C₂³×C₁₃	—	2	1	no	—
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	—	2	1	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
228	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
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	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	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	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	4	4	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	#117	1	2	yes	—
269	C₂×C₄×C₁₃	#117	1	2	yes	—
270	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
271	C₂×C₄×C₁₃	#131	1	2	yes	—
272	C₂×C₄×C₁₃	#131	1	2	yes	—
273	C₂×C₄×C₁₃	#131	1	2	yes	—
274	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
280	#1055	—	2	2	no	—
281	#1055	—	2	2	no	—
282	#1055	—	4	1	no	—
283	#1055	—	4	1	no	—
284	#1055	—	4	1	no	—
285	#1055	—	4	1	no	—
286	#1055	—	4	1	no	—
287	#1055	—	4	1	no	—
288	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
289	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
290	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
291	C₂×C₄⋊C₈	—	13	1	no	—
292	C₂×C₄⋊C₈	—	13	1	no	—
293	C₂×C₄⋊C₈	—	13	1	no	—
294	C₂×C₄⋊C₈	—	13	1	no	—
295	C₂×C₄⋊C₈	—	13	1	no	—
296	C₂×C₄⋊C₈	—	13	1	no	—
297	C₂×C₂²⋊C₈	—	13	1	no	—
298	C₂×C₂²⋊C₈	—	13	1	no	—
299	C₂×C₂²⋊C₈	—	13	1	no	—
300	C₂×C₂²⋊C₈	—	13	1	no	—
301	C₂×#97	—	13	1	no	—
302	C₂×#97	—	13	1	no	—
303	C₂×C₄×C₈	—	13	1	no	—
304	C₂×C₄×C₈	—	13	1	no	—
305	C₂×C₄×C₈	—	13	1	no	—
306	C₂×C₄×C₈	—	13	1	no	—
307	#389	Dic₁₃	1	1	yes	characteristic
308	#389	Dic₁₃	1	1	yes	characteristic
309	#389	Dic₁₃	1	1	yes	characteristic
310	#389	Dic₁₃	1	1	yes	characteristic
311	#385	Dic₁₃	1	1	yes	characteristic
312	#385	Dic₁₃	1	1	yes	characteristic
313	#385	Dic₁₃	1	1	yes	characteristic
314	#385	Dic₁₃	1	1	yes	characteristic
315	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
316	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
317	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
318	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
319	#336	—	13	1	no	—
320	#336	—	13	1	no	—
321	#336	—	13	1	no	—
322	#336	—	13	1	no	—
323	#336	—	13	1	no	—
324	#336	—	13	1	no	—
325	#336	—	13	1	no	—
326	#336	—	13	1	no	—
327	#336	—	13	1	no	—
328	#336	—	13	1	no	—
329	#336	—	13	1	no	—
330	#336	—	13	1	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
339	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
340	C₂²×C₁₃	#518	1	1	yes	characteristic
341	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
342	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
343	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
344	C₂²×C₁₃	#568	1	1	yes	characteristic
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	—	2	2	no	—
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	—	4	1	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	4	1	no	—
357	C₄×C₁₃	—	4	1	no	—
358	C₄×C₁₃	#553	1	1	yes	characteristic
359	C₄×C₁₃	#553	1	1	yes	characteristic
360	C₄×C₁₃	#554	1	1	yes	characteristic
361	C₄×C₁₃	#554	1	1	yes	characteristic
362	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
363	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
364	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
365	C₂²×C₈	—	13	1	no	—
366	C₂²×C₈	—	13	1	no	—
367	C₂²×C₈	—	13	1	no	—
368	C₂²×C₈	—	13	1	no	—
369	C₂²×C₈	—	13	1	no	—
370	C₂²×C₈	—	13	1	no	—
371	C₂²×C₈	—	13	1	no	—
372	C₂²×C₈	—	13	1	no	—
373	#117	—	2	2	no	—
374	#117	—	2	2	no	—
375	#117	—	4	1	no	—
376	#117	—	4	1	no	—
377	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂×Dic₁₃	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×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
393	C₂×C₄²	—	4	1	no	—
394	C₂×C₄²	—	4	1	no	—
395	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
396	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
397	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
398	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
399	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
400	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
401	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
402	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
403	C₄⋊C₈	—	26	2	no	—
404	C₄⋊C₈	—	26	2	no	—
405	C₄⋊C₈	—	52	1	no	—
406	C₄⋊C₈	—	52	1	no	—
407	C₄⋊C₈	—	52	1	no	—
408	C₄⋊C₈	—	52	1	no	—
409	C₂²⋊C₈	—	13	4	no	—
410	C₂²⋊C₈	—	26	2	no	—
411	C₂²⋊C₈	—	26	2	no	—
412	C₂²⋊C₈	—	26	2	no	—
413	#97	—	26	2	no	—
414	#97	—	52	1	no	—
415	C₄×C₈	—	26	2	no	—
416	C₄×C₈	—	52	1	no	—
417	C₄×C₈	—	52	1	no	—
418	C₄×C₈	—	52	1	no	—
419	#95	C₂×Dic₁₃	1	1	yes	characteristic
420	#95	C₂×Dic₁₃	1	1	yes	characteristic
421	#95	C₂×Dic₁₃	1	1	yes	characteristic
422	#95	C₂×Dic₁₃	1	1	yes	characteristic
423	#95	C₂×Dic₁₃	1	1	yes	characteristic
424	#95	C₂×Dic₁₃	1	1	yes	characteristic
425	#95	C₂×Dic₁₃	1	1	yes	characteristic
426	#95	C₂×Dic₁₃	1	1	yes	characteristic
427	C₂×C₁₃	—	4	2	no	—
428	C₂×C₁₃	#2345	1	1	yes	characteristic
429	C₂×C₁₃	#2922	1	1	yes	characteristic
430	C₂×C₁₃	#2925	1	1	yes	characteristic
431	C₂×C₁₃	#2960	1	1	yes	characteristic
432	C₂×C₁₃	#2962	1	1	yes	characteristic
433	C₂×C₁₃	#2976	1	1	yes	characteristic
434	C₂×C₁₃	#2977	1	1	yes	characteristic
435	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
447	C₂²×C₄	#6131	1	2	yes	—
448	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
456	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
462	C₂×C₈	—	13	2	no	—
463	C₂×C₈	—	13	2	no	—
464	C₂×C₈	—	26	1	no	—
465	C₂×C₈	—	26	1	no	—
466	C₂×C₈	—	26	1	no	—
467	C₂×C₈	—	26	1	no	—
468	C₂×C₈	—	26	1	no	—
469	C₂×C₈	—	26	1	no	—
470	C₂×C₈	—	26	1	no	—
471	C₂×C₈	—	26	1	no	—
472	C₂×C₈	—	26	1	no	—
473	C₂×C₈	—	26	1	no	—
474	C₂×C₈	—	26	1	no	—
475	C₂×C₈	—	26	1	no	—
476	C₂×C₈	—	26	1	no	—
477	C₂×C₈	—	26	1	no	—
478	C₂×C₈	—	26	1	no	—
479	C₂×C₈	—	26	1	no	—
480	C₂×C₈	—	26	1	no	—
481	C₂×C₈	—	26	1	no	—
482	C₂×C₈	—	26	1	no	—
483	C₂×C₈	—	26	1	no	—
484	C₂×C₈	—	26	1	no	—
485	C₂×C₈	—	26	1	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	4	1	no	—
513	C₄²	—	4	1	no	—
514	C₄²	#6127	1	2	yes	—
515	C₄²	#6127	1	2	yes	—
516	C₁₃	#22630	1	1	yes	characteristic, complemented, Sylow
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	Q₈×Dic₁₃	1	2	yes	—
524	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
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	2	no	—
538	C₂×C₄	—	2	2	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	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	#88180	1	2	yes	—
565	C₂×C₄	#88180	1	2	yes	—
566	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
567	C₂×C₄	#88202	1	2	yes	—
568	C₂×C₄	#88202	1	2	yes	—
569	C₂×C₄	#88202	1	2	yes	—
570	C₂×C₄	C₂×#6127	1	1	yes	characteristic
571	C₂×C₄	C₂×#6127	1	1	yes	characteristic
572	C₂×C₄	#88251	1	1	yes	characteristic
573	C₂×C₄	#88251	1	1	yes	characteristic
574	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
575	C₂×C₄	C₂×#6131	1	1	yes	characteristic
576	C₈	—	26	2	no	—
577	C₈	—	26	2	no	—
578	C₈	—	52	1	no	—
579	C₈	—	52	1	no	—
580	C₈	—	52	1	no	—
581	C₈	—	52	1	no	—
582	C₈	—	52	1	no	—
583	C₈	—	52	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	C₂×#88180	1	1	yes	characteristic
592	C₂²	#11719503	1	1	yes	characteristic
593	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
594	C₂²	C₂×#88202	1	1	yes	characteristic
595	C₂²	C₂×#88202	1	1	yes	characteristic
596	C₂²	C₂×#88202	1	1	yes	characteristic
597	C₂²	#11719524	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	#11719216	1	1	yes	characteristic
612	C₄	#11719216	1	1	yes	characteristic
613	C₄	#11719219	1	1	yes	characteristic
614	C₄	#11719219	1	1	yes	characteristic
615	C₂	—	4	2	no	—
616	C₂	#13117713	1	1	yes	characteristic
617	C₂	#13123480	1	1	yes	characteristic
618	C₂	#13123502	1	1	yes	characteristic
619	C₂	#13123771	1	1	yes	characteristic
620	C₂	#13123785	1	1	yes	characteristic
621	C₂	#13123884	1	1	yes	characteristic
622	C₂	#13123892	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2296	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2296	D₁₃
hypocenter	C₁₃	#22630
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2296

Complements

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

N	H ≅ G/N	type
1. #13115560	C₂	semidirect
2. #13115555	C₂	semidirect
3. #13115402	C₂	semidirect
4. #13115395	C₂	semidirect
5. #13115395	C₂	semidirect
6. #13115395	C₂	semidirect
10. #13114711	C₂	semidirect
11. C₄⋊C₄×#1055	C₂	semidirect
516. C₁₃	#22630	semidirect

Maximal subgroups

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

subgroup	index
#13115560	2
#13115555	2
#13115402	2
#13115395	2
#13114820	2
#13114816	2
#13114711	2
C₄⋊C₄×#1055	2
#13114602	2
C₄×C₂²⋊#1055	2
C₁₃×#2296	2
#22630	13