Subgroups — #16807325

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131221	C₂	1	2	yes	maximal, complemented
2	#13131218	C₂	1	2	yes	maximal, complemented
3	#13131217	C₂	1	2	yes	maximal, complemented
4	#13131214	C₂	1	2	yes	maximal, complemented
5	#13131198	C₂	1	1	yes	maximal, characteristic, complemented
6	#13131194	C₂	1	1	yes	maximal, characteristic, complemented
7	#13131064	C₂	1	1	yes	maximal, characteristic, complemented
8	#13131063	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₃⋊(C₂²⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂²⋊#6092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11718386	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
13	C₂³×#1055	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
15	C₂×#88106	C₂²	1	2	yes	complemented
16	C₂²×#6092	C₂²	1	2	yes	complemented
17	C₂×#88098	C₂²	1	2	yes	complemented
18	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	complemented
19	C₂×C₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
20	C₂×#88060	C₄	1	1	yes	characteristic
21	C₂×#88054	C₄	1	1	yes	characteristic
22	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
23	#11718386	C₄	1	1	yes	characteristic
24	#11718386	C₄	1	1	yes	characteristic
25	#11718386	C₄	1	1	yes	characteristic
26	#11718386	C₄	1	1	yes	characteristic
27	#11718386	C₂²	1	1	yes	characteristic
28	#11718386	C₂²	1	1	yes	characteristic
29	#11718386	C₂²	1	1	yes	characteristic
30	#11718386	C₂²	1	1	yes	characteristic
31	C₂²⋊#6092	C₂²	1	1	yes	characteristic
32	C₂²⋊#6092	C₂²	1	1	yes	characteristic
33	C₂²⋊#6092	C₂²	1	1	yes	characteristic
34	C₂²⋊#6092	C₂²	1	1	yes	characteristic
35	C₂²⋊#6092	C₂²	1	2	yes	complemented
36	C₂²⋊#6092	C₂²	1	2	yes	complemented
37	#11718260	C₂²	1	2	yes	complemented
38	#11718260	C₂²	1	2	yes	complemented
39	#11718259	C₂²	1	2	yes	complemented
40	#11718259	C₂²	1	2	yes	complemented
41	#11718258	C₂²	1	2	yes	complemented
42	#11718257	C₂²	1	2	yes	complemented
43	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
45	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₂²⋊Dic₁₃	C₈	1	1	yes	characteristic
49	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
51	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
52	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×#6103	C₈	1	1	yes	characteristic
58	C₂×#6101	C₈	1	1	yes	characteristic
59	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×#1055	—	4	2	no	—
61	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
62	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
63	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
64	C₂²×#1055	C₂³	1	1	yes	characteristic
65	C₂²×#1055	C₂³	1	1	yes	characteristic
66	C₂²×#1055	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₁₃	—	4	2	no	—
68	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
72	#88106	—	4	2	no	—
73	C₂×#6092	—	4	2	no	—
74	C₂×#6092	C₂³	1	2	yes	—
75	C₂×#6092	C₂³	1	2	yes	—
76	C₂×#6092	C₂³	1	2	yes	—
77	C₂×#6092	C₂³	1	2	yes	—
78	#88098	—	4	2	no	—
79	D₁₃⋊C₁₆	—	4	2	no	—
80	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
84	#88060	C₂×C₄	1	1	yes	characteristic
85	#88060	C₂×C₄	1	1	yes	characteristic
86	#88060	C₂×C₄	1	1	yes	characteristic
87	#88060	C₂×C₄	1	1	yes	characteristic
88	#88054	C₂×C₄	1	1	yes	characteristic
89	#88054	C₂×C₄	1	1	yes	characteristic
90	#88054	C₂×C₄	1	1	yes	characteristic
91	#88054	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
95	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
96	#33488	—	13	1	no	maximal, Sylow
97	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
98	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊D₁₃	—	2	4	no	—
108	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
109	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
110	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
111	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
112	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
113	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
114	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
115	C₂×C₄×D₁₃	—	4	1	no	—
116	C₂×C₄×D₁₃	—	4	1	no	—
117	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	—	4	1	no	—
122	C₂×C₈×C₁₃	—	4	1	no	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
128	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
129	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
130	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
131	#6103	C₂×C₈	1	1	yes	characteristic
132	#6103	C₂×C₈	1	1	yes	characteristic
133	#6103	C₂×C₈	1	1	yes	characteristic
134	#6103	C₂×C₈	1	1	yes	characteristic
135	#6101	C₂×C₈	1	1	yes	characteristic
136	#6101	C₂×C₈	1	1	yes	characteristic
137	#6101	C₂×C₈	1	1	yes	characteristic
138	#6101	C₂×C₈	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×#1055	—	2	2	no	—
144	C₂×#1055	—	2	2	no	—
145	C₂×#1055	—	2	2	no	—
146	C₂×#1055	—	4	1	no	—
147	C₂×#1055	—	4	1	no	—
148	C₂×#1055	—	4	1	no	—
149	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
150	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
151	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
152	C₂×#1055	C₂⁴	1	1	yes	characteristic
153	C₈×D₁₃	—	2	2	no	—
154	C₈×D₁₃	—	2	2	no	—
155	C₈×D₁₃	—	4	1	no	—
156	C₈×D₁₃	—	4	1	no	—
157	#6092	—	2	2	no	—
158	#6092	—	2	2	no	—
159	#6092	—	2	2	no	—
160	#6092	—	2	2	no	—
161	C₂×C₈×D₄	—	13	1	no	—
162	#2169	—	13	2	no	—
163	#2168	—	13	2	no	—
164	#2168	—	13	2	no	—
165	D₄×C₁₆	—	13	2	no	—
166	#2163	—	13	1	no	—
167	#2162	—	13	1	no	—
168	#2112	—	13	1	no	—
169	#2112	—	13	1	no	—
170	C₂×C₂²⋊C₁₆	—	13	1	no	—
171	C₂×C₂²⋊C₁₆	—	13	1	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
176	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
177	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
178	C₂²×D₁₃	—	2	2	no	—
179	C₂²×D₁₃	—	2	2	no	—
180	C₂²×D₁₃	—	4	1	no	—
181	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
182	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
196	C₂²⋊D₁₃	—	2	2	no	—
197	C₂²⋊D₁₃	—	2	2	no	—
198	C₂²⋊D₁₃	—	2	2	no	—
199	C₂²⋊D₁₃	M₃₂	1	4	yes	complemented
200	C₂×Dic₁₃	—	2	2	no	—
201	C₂×Dic₁₃	—	2	2	no	—
202	C₂×Dic₁₃	—	4	1	no	—
203	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
204	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
205	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
206	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
207	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
208	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
209	C₄×D₁₃	—	2	1	no	—
210	C₄×D₁₃	—	2	1	no	—
211	C₄×D₁₃	—	2	1	no	—
212	C₄×D₁₃	—	2	1	no	—
213	C₄×D₁₃	—	4	1	no	—
214	C₄×D₁₃	—	4	1	no	—
215	C₈×C₁₃	—	2	1	no	—
216	C₈×C₁₃	—	2	1	no	—
217	C₈×C₁₃	—	2	1	no	—
218	C₈×C₁₃	—	2	1	no	—
219	#1055	—	2	1	no	—
220	#1055	—	2	1	no	—
221	#1055	—	2	1	no	—
222	#1055	H(5,𝔽₂)	1	2	yes	—
223	C₂³×C₈	—	13	1	no	—
224	C₂³×C₈	—	13	1	no	—
225	C₂×C₄×D₄	—	13	1	no	—
226	C₂×M₃₂	—	13	2	no	—
227	C₂×M₃₂	—	13	2	no	—
228	C₂²×C₁₆	—	13	2	no	—
229	C₂²×C₁₆	—	13	2	no	—
230	C₈×D₄	—	13	1	no	—
231	C₈×D₄	—	13	1	no	—
232	C₈×D₄	—	13	1	no	—
233	C₈×D₄	—	13	1	no	—
234	C₈×D₄	—	13	1	no	—
235	C₈×D₄	—	13	1	no	—
236	C₈×D₄	—	13	1	no	—
237	C₈×D₄	—	13	1	no	—
238	C₂×C₄⋊C₈	—	13	1	no	—
239	C₂×C₂²⋊C₈	—	13	1	no	—
240	C₂×C₂²⋊C₈	#261	1	1	yes	characteristic
241	C₂×C₄×C₈	—	13	1	no	—
242	C₄⋊C₁₆	—	13	2	no	—
243	C₄⋊C₁₆	—	13	2	no	—
244	C₂²⋊C₁₆	—	13	1	no	—
245	C₂²⋊C₁₆	—	13	1	no	—
246	C₂²⋊C₁₆	—	13	1	no	—
247	C₂²⋊C₁₆	—	13	2	no	—
248	C₂²⋊C₁₆	—	13	2	no	—
249	C₂²⋊C₁₆	—	13	1	no	—
250	C₂²⋊C₁₆	—	13	2	no	—
251	C₂²⋊C₁₆	—	13	2	no	—
252	#346	—	13	2	no	—
253	C₄×C₁₆	—	13	2	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	—	2	1	no	—
260	C₂²×C₁₃	—	2	1	no	—
261	C₂²×C₁₃	—	4	4	no	—
262	C₂²×C₁₃	C₂×M₃₂	1	2	yes	—
263	C₂²×C₁₃	#504	1	2	yes	—
264	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
265	C₂×D₁₃	—	2	1	no	—
266	C₂×D₁₃	—	2	1	no	—
267	C₂×D₁₃	—	2	1	no	—
268	C₂×D₁₃	—	2	1	no	—
269	C₂×D₁₃	—	2	1	no	—
270	C₂×D₁₃	—	4	4	no	—
271	C₂×D₁₃	C₂×M₃₂	1	2	yes	—
272	C₄×C₁₃	—	2	1	no	—
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	2	1	no	—
275	C₄×C₁₃	#518	1	1	yes	characteristic
276	C₄×C₁₃	#568	1	1	yes	characteristic
277	Dic₁₃	—	2	1	no	—
278	Dic₁₃	—	2	1	no	—
279	Dic₁₃	—	2	1	no	—
280	Dic₁₃	—	2	1	no	—
281	Dic₁₃	—	2	1	no	—
282	Dic₁₃	C₂×M₃₂	1	2	yes	—
283	C₂²×D₄	—	13	1	no	—
284	C₂³×C₄	—	13	1	no	—
285	C₂³×C₄	C₂×#261	1	1	yes	characteristic
286	C₂²×C₈	—	13	1	no	—
287	C₂²×C₈	—	13	1	no	—
288	C₂²×C₈	—	13	1	no	—
289	C₂²×C₈	—	13	1	no	—
290	C₂²×C₈	—	13	1	no	—
291	C₂²×C₈	—	13	1	no	—
292	C₂²×C₈	—	13	1	no	—
293	C₂²×C₈	—	13	1	no	—
294	C₂²×C₈	—	13	1	no	—
295	C₂²×C₈	—	13	1	no	—
296	C₂²×C₈	—	52	2	no	—
297	C₂²×C₈	—	52	2	no	—
298	C₂²×C₈	C₂×#261	1	1	yes	characteristic
299	C₂²×C₈	C₂×#261	1	1	yes	characteristic
300	C₄×D₄	—	13	1	no	—
301	C₄×D₄	—	13	1	no	—
302	C₄×D₄	—	13	1	no	—
303	C₄×D₄	—	13	1	no	—
304	C₄×D₄	—	13	1	no	—
305	C₄×D₄	—	13	1	no	—
306	C₄×D₄	—	13	1	no	—
307	C₄×D₄	—	13	1	no	—
308	C₂×C₄⋊C₄	—	13	1	no	—
309	C₂×C₂²⋊C₄	—	13	1	no	—
310	C₂×C₂²⋊C₄	—	13	1	no	—
311	C₂×C₄²	—	13	1	no	—
312	M₃₂	—	52	2	no	—
313	M₃₂	—	52	2	no	—
314	C₂×C₁₆	—	13	2	no	—
315	C₂×C₁₆	—	13	2	no	—
316	C₂×C₁₆	—	13	2	no	—
317	C₂×C₁₆	—	13	2	no	—
318	C₂×C₁₆	—	52	2	no	—
319	C₂×C₁₆	—	52	2	no	—
320	C₄⋊C₈	—	13	1	no	—
321	C₄⋊C₈	—	13	1	no	—
322	C₄⋊C₈	—	13	1	no	—
323	C₄⋊C₈	—	13	1	no	—
324	C₂²⋊C₈	—	13	1	no	—
325	C₂²⋊C₈	—	13	1	no	—
326	C₂²⋊C₈	—	13	1	no	—
327	C₂²⋊C₈	—	13	1	no	—
328	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
329	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
330	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
331	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
332	C₄×C₈	—	13	1	no	—
333	C₄×C₈	—	13	1	no	—
334	C₄×C₈	—	13	1	no	—
335	C₄×C₈	—	13	1	no	—
336	C₂×C₁₃	—	2	2	no	—
337	C₂×C₁₃	—	2	2	no	—
338	C₂×C₁₃	—	4	1	no	—
339	C₂×C₁₃	#2972	1	1	yes	characteristic
340	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
341	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
342	D₁₃	—	2	2	no	—
343	D₁₃	—	4	1	no	—
344	C₂⁴	—	13	1	no	—
345	C₂⁴	D₁₃⋊C₈	1	1	yes	characteristic
346	C₂×D₄	—	13	1	no	—
347	C₂×D₄	—	13	1	no	—
348	C₂×D₄	—	13	1	no	—
349	C₂×D₄	—	13	1	no	—
350	C₂×D₄	—	26	4	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	13	1	no	—
354	C₂²×C₄	—	13	1	no	—
355	C₂²×C₄	—	13	1	no	—
356	C₂²×C₄	—	13	1	no	—
357	C₂²×C₄	—	13	1	no	—
358	C₂²×C₄	—	13	1	no	—
359	C₂²×C₄	—	13	1	no	—
360	C₂²×C₄	—	52	1	no	—
361	C₂²×C₄	—	52	1	no	—
362	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
363	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
364	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
365	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
366	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
367	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	13	1	no	—
371	C₂×C₈	—	13	1	no	—
372	C₂×C₈	—	13	1	no	—
373	C₂×C₈	—	13	1	no	—
374	C₂×C₈	—	26	2	no	—
375	C₂×C₈	—	26	2	no	—
376	C₂×C₈	—	26	2	no	—
377	C₂×C₈	—	26	2	no	—
378	C₂×C₈	—	26	2	no	—
379	C₂×C₈	—	52	1	no	—
380	C₂×C₈	—	52	1	no	—
381	C₂×C₈	—	52	1	no	—
382	C₂×C₈	—	52	1	no	—
383	C₂×C₈	—	52	1	no	—
384	C₂×C₈	C₂²×#261	1	1	yes	characteristic
385	C₂×C₈	C₂²×#261	1	1	yes	characteristic
386	C₂×C₈	C₂²×#261	1	1	yes	characteristic
387	C₂×C₈	C₂²×#261	1	1	yes	characteristic
388	C₄⋊C₄	—	13	1	no	—
389	C₄⋊C₄	—	13	1	no	—
390	C₄⋊C₄	—	13	1	no	—
391	C₄⋊C₄	—	13	1	no	—
392	C₂²⋊C₄	—	13	1	no	—
393	C₂²⋊C₄	—	13	1	no	—
394	C₂²⋊C₄	—	13	1	no	—
395	C₂²⋊C₄	—	13	1	no	—
396	C₂²⋊C₄	—	13	1	no	—
397	C₂²⋊C₄	—	13	1	no	—
398	C₂²⋊C₄	—	13	1	no	—
399	C₂²⋊C₄	—	13	1	no	—
400	C₄²	—	13	1	no	—
401	C₄²	—	13	1	no	—
402	C₄²	—	13	1	no	—
403	C₄²	—	13	1	no	—
404	C₁₆	—	26	2	no	—
405	C₁₆	—	26	2	no	—
406	C₁₆	—	26	2	no	—
407	C₁₆	—	26	2	no	—
408	C₁₃	#33488	1	1	yes	characteristic, complemented, Sylow
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	13	1	no	—
413	C₂³	—	13	1	no	—
414	C₂³	—	26	2	no	—
415	C₂³	—	26	2	no	—
416	C₂³	—	52	1	no	—
417	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
418	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
419	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
420	D₄	—	13	4	no	—
421	D₄	—	26	2	no	—
422	D₄	—	26	2	no	—
423	D₄	—	26	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	13	1	no	—
434	C₂×C₄	—	13	1	no	—
435	C₂×C₄	—	13	1	no	—
436	C₂×C₄	—	13	1	no	—
437	C₂×C₄	—	13	1	no	—
438	C₂×C₄	—	13	1	no	—
439	C₂×C₄	—	26	2	no	—
440	C₂×C₄	—	26	2	no	—
441	C₂×C₄	—	26	1	no	—
442	C₂×C₄	—	26	1	no	—
443	C₂×C₄	—	26	1	no	—
444	C₂×C₄	—	26	1	no	—
445	C₂×C₄	—	52	1	no	—
446	C₂×C₄	—	52	1	no	—
447	C₂×C₄	—	52	1	no	—
448	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
449	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
450	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
451	C₂×C₄	C₂³×#261	1	1	yes	characteristic
452	C₈	—	2	1	no	—
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	13	2	no	—
457	C₈	—	26	1	no	—
458	C₈	—	26	1	no	—
459	C₈	—	26	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	13	2	no	—
469	C₂²	—	26	1	no	—
470	C₂²	—	26	1	no	—
471	C₂²	—	26	1	no	—
472	C₂²	—	26	1	no	—
473	C₂²	—	26	1	no	—
474	C₂²	—	52	4	no	—
475	C₂²	D₁₃⋊M₃₂	1	2	yes	—
476	C₂²	#11719096	1	2	yes	—
477	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	13	2	no	—
482	C₄	—	26	1	no	—
483	C₄	—	26	1	no	—
484	C₄	—	26	1	no	—
485	C₄	—	26	1	no	—
486	C₄	—	26	1	no	—
487	C₄	#11719621	1	1	yes	characteristic
488	C₄	#11719623	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	2	2	no	—
491	C₂	—	4	1	no	—
492	C₂	—	26	2	no	—
493	C₂	—	52	1	no	—
494	C₂	#13131685	1	1	yes	characteristic
495	C₂	C₂×D₁₃⋊M₃₂	1	1	yes	characteristic
496	C₂	C₂×#11719096	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₂×C₁₃×C₂²⋊C₈	C₄
prime radical	C₂²×C₂²⋊D₁₃	C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	C₂×C₂²⋊C₈	#261
hypocenter	C₁₃	#33488
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
1. #13131221	C₂	semidirect
2. #13131218	C₂	semidirect
3. #13131217	C₂	semidirect
4. #13131214	C₂	semidirect
5. #13131198	C₂	semidirect
6. #13131194	C₂	semidirect
7. #13131064	C₂	semidirect
8. #13131063	C₂	semidirect
9. D₁₃⋊(C₂²⋊C₁₆)	C₂	semidirect
10. C₂×C₂²⋊#6092	C₂	semidirect
15. C₂×#88106	C₂²	semidirect
16. C₂²×#6092	C₂²	semidirect
17. C₂×#88098	C₂²	semidirect
18. C₂×D₁₃⋊C₁₆	C₂²	semidirect
35. C₂²⋊#6092	C₂²	semidirect
36. C₂²⋊#6092	C₂²	semidirect
37. #11718260	C₂²	semidirect
38. #11718260	C₂²	semidirect
39. #11718259	C₂²	semidirect
40. #11718259	C₂²	semidirect
41. #11718258	C₂²	semidirect
42. #11718257	C₂²	semidirect
199. C₂²⋊D₁₃	M₃₂	semidirect
408. C₁₃	#33488	semidirect

Maximal subgroups

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

subgroup	index
#13131221	2
#13131218	2
#13131217	2
#13131214	2
#13131198	2
#13131194	2
#13131064	2
#13131063	2
D₁₃⋊(C₂²⋊C₁₆)	2
C₂×C₂²⋊#6092	2
C₂×#11718386	2
#33488	13