Subgroups — #16807276

Order 3328.

558 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131253	C₂	1	2	yes	maximal, complemented
2	#13131221	C₂	1	2	yes	maximal, complemented
3	#13131218	C₂	1	2	yes	maximal, complemented
4	#13131216	C₂	1	2	yes	maximal, complemented
5	#13131196	C₂	1	1	yes	maximal, characteristic, complemented
6	#13131194	C₂	1	1	yes	maximal, characteristic, complemented
7	#13131194	C₂	1	1	yes	maximal, characteristic, complemented
8	#13131043	C₂	1	1	yes	maximal, characteristic, complemented
9	#13131042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11718257	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#6129	C₂	1	1	yes	maximal, characteristic
12	C₄×#6129	C₄	1	1	yes	characteristic
13	C₂×#88106	C₂²	1	2	yes	—
14	C₂²×#6092	C₂²	1	2	yes	—
15	C₂×#88098	C₂²	1	2	yes	—
16	C₈×D₄×C₁₃	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
19	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
21	D₄×#1055	C₂²	1	1	yes	characteristic
22	#11718494	C₄	1	1	yes	characteristic
23	#11718491	C₂²	1	1	yes	characteristic
24	#11718386	C₂²	1	1	yes	characteristic
25	#11718386	C₂²	1	1	yes	characteristic
26	#11718379	C₄	1	1	yes	characteristic
27	#11718379	C₄	1	1	yes	characteristic
28	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
29	C₈×Dic₂₆	C₄	1	1	yes	characteristic
30	C₂²⋊#6092	C₂²	1	2	yes	—
31	C₂²⋊#6092	C₂²	1	2	yes	—
32	#11718260	C₂²	1	2	yes	—
33	#11718260	C₂²	1	2	yes	—
34	#11718259	C₂²	1	2	yes	—
35	#11718258	C₂²	1	2	yes	—
36	#11718257	C₂²	1	1	yes	characteristic
37	#11718257	C₂²	1	1	yes	characteristic
38	#11718257	C₂²	1	2	yes	—
39	#11718257	C₂²	1	1	yes	characteristic
40	#11718257	C₂²	1	1	yes	characteristic
41	#11718231	C₂²	1	2	yes	—
42	C₄⋊#6092	C₂²	1	2	yes	—
43	C₂×#6129	C₈	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	D₄×Dic₁₃	C₈	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×#1055	C₂³	1	1	yes	characteristic
53	C₂²×#1055	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
56	#88146	C₈	1	1	yes	characteristic
57	#88141	C₈	1	1	yes	characteristic
58	#88135	C₈	1	1	yes	characteristic
59	#88135	C₈	1	1	yes	characteristic
60	#88131	C₈	1	1	yes	characteristic
61	#88131	C₈	1	1	yes	characteristic
62	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
64	#88106	—	2	4	no	—
65	C₂×#6092	—	2	4	no	—
66	C₂×#6092	C₂³	1	2	yes	—
67	C₂×#6092	C₂³	1	2	yes	—
68	C₂×#6092	C₂³	1	2	yes	—
69	C₂×#6092	C₂³	1	2	yes	—
70	#88098	—	2	4	no	—
71	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
76	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
77	#88060	C₂×C₄	1	1	yes	characteristic
78	#88060	C₂×C₄	1	1	yes	characteristic
79	#88054	C₂×C₄	1	1	yes	characteristic
80	#88054	C₂×C₄	1	1	yes	characteristic
81	#88054	C₂×C₄	1	1	yes	characteristic
82	#88054	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
89	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
90	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
91	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
92	C₄×#1055	C₂³	1	1	yes	characteristic
93	#33479	—	13	1	no	maximal, Sylow
94	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
98	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
99	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
100	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
101	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
102	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
103	#6129	—	2	4	no	—
104	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
115	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
116	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
117	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
119	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
120	#6103	C₂×C₈	1	1	yes	characteristic
121	#6103	C₂×C₈	1	1	yes	characteristic
122	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
123	#6101	C₂×C₈	1	1	yes	characteristic
124	#6101	C₂×C₈	1	1	yes	characteristic
125	#6101	C₂×C₈	1	1	yes	characteristic
126	#6101	C₂×C₈	1	1	yes	characteristic
127	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×#1055	—	2	2	no	—
137	C₂×#1055	—	2	2	no	—
138	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
139	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
140	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
141	C₂×#1055	C₂⁴	1	1	yes	characteristic
142	C₈×D₁₃	—	2	2	no	—
143	C₈×D₁₃	—	2	2	no	—
144	#6092	—	2	2	no	—
145	#6092	—	2	2	no	—
146	#6092	—	2	2	no	—
147	#6092	#41	1	4	yes	complemented
148	C₈×#41	—	13	1	no	—
149	#2183	—	13	2	no	—
150	#2169	—	13	2	no	—
151	#2168	—	13	2	no	—
152	#2168	—	13	2	no	—
153	#2162	—	13	1	no	—
154	#2162	—	13	1	no	—
155	#2162	—	13	1	no	—
156	C₄×M₃₂	—	13	1	no	—
157	C₄×M₃₂	—	13	1	no	—
158	C₂×C₄×C₁₆	—	13	1	no	—
159	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
160	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
162	D₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂²⋊D₁₃	—	2	2	no	—
173	C₂²⋊D₁₃	—	2	2	no	—
174	C₂×Dic₁₃	—	2	2	no	—
175	C₂×Dic₁₃	—	2	2	no	—
176	C₂×Dic₁₃	—	2	2	no	—
177	C₂×Dic₁₃	M₃₂	1	4	yes	complemented
178	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
182	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
184	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
185	C₄×D₁₃	—	2	1	no	—
186	C₄×D₁₃	—	2	1	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	2	2	no	—
189	Dic₂₆	—	2	2	no	—
190	C₈×C₁₃	—	2	1	no	—
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	—	2	1	no	—
193	C₈×C₁₃	#131	1	2	yes	—
194	#1055	—	2	1	no	—
195	#1055	—	2	1	no	—
196	#1055	—	2	1	no	—
197	#1055	C₂×#41	1	2	yes	—
198	C₄×#41	—	13	1	no	—
199	C₂×M₃₂	—	13	2	no	—
200	C₂×M₃₂	—	13	2	no	—
201	C₂²×C₁₆	—	13	2	no	—
202	C₈×Q₈	—	13	1	no	—
203	C₈×Q₈	—	13	1	no	—
204	C₈×D₄	—	13	1	no	—
205	C₈×D₄	—	13	1	no	—
206	C₈×D₄	—	13	1	no	—
207	C₈×D₄	—	13	1	no	—
208	C₈×D₄	—	13	1	no	—
209	C₈×D₄	#261	1	1	yes	characteristic
210	#431	—	13	1	no	—
211	#431	—	13	1	no	—
212	#431	—	13	1	no	—
213	C₂×C₄×C₈	—	13	1	no	—
214	C₂×C₄×C₈	—	13	1	no	—
215	C₂×C₄×C₈	—	13	1	no	—
216	C₄⋊C₁₆	—	13	2	no	—
217	C₄⋊C₁₆	—	13	2	no	—
218	C₄⋊C₁₆	—	13	2	no	—
219	C₂²⋊C₁₆	—	13	2	no	—
220	C₂²⋊C₁₆	—	13	2	no	—
221	C₂²⋊C₁₆	—	13	2	no	—
222	#346	—	13	2	no	—
223	#346	—	13	2	no	—
224	C₄×C₁₆	—	13	1	no	—
225	C₄×C₁₆	—	13	1	no	—
226	C₄×C₁₆	—	13	2	no	—
227	C₄×C₁₆	—	13	1	no	—
228	C₄×C₁₆	—	13	1	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	C₂×M₃₂	1	2	yes	—
235	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
236	C₂×D₁₃	—	2	1	no	—
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	2	1	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
244	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
245	Dic₁₃	—	2	1	no	—
246	Dic₁₃	—	2	1	no	—
247	Dic₁₃	—	2	1	no	—
248	Dic₁₃	—	2	1	no	—
249	Dic₁₃	C₂×M₃₂	1	2	yes	—
250	Dic₁₃	C₂×M₃₂	1	2	yes	—
251	Dic₁₃	#504	1	2	yes	—
252	C₂×#41	—	13	1	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	C₂×#261	1	1	yes	characteristic
258	C₂²×C₈	C₂×#261	1	1	yes	characteristic
259	C₄×Q₈	—	13	1	no	—
260	C₄×Q₈	—	13	1	no	—
261	C₄×D₄	—	13	1	no	—
262	C₄×D₄	—	13	1	no	—
263	C₄×D₄	—	13	1	no	—
264	C₄×D₄	—	13	1	no	—
265	C₄×D₄	—	13	1	no	—
266	C₄×D₄	C₂×#261	1	1	yes	characteristic
267	#117	—	13	1	no	—
268	#117	—	13	1	no	—
269	#117	—	13	1	no	—
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	—	13	1	no	—
272	C₂×C₄²	—	13	1	no	—
273	M₃₂	—	26	4	no	—
274	M₃₂	—	26	4	no	—
275	C₂×C₁₆	—	13	2	no	—
276	C₂×C₁₆	—	13	2	no	—
277	C₂×C₁₆	—	13	2	no	—
278	C₂×C₁₆	—	13	2	no	—
279	C₂×C₁₆	—	26	4	no	—
280	C₄⋊C₈	—	13	1	no	—
281	C₄⋊C₈	—	13	1	no	—
282	C₄⋊C₈	—	13	1	no	—
283	C₄⋊C₈	—	13	1	no	—
284	C₄⋊C₈	—	13	1	no	—
285	C₄⋊C₈	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	C₂×#261	1	1	yes	characteristic
291	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
292	C₄×C₈	—	13	1	no	—
293	C₄×C₈	—	13	1	no	—
294	C₄×C₈	—	13	1	no	—
295	C₄×C₈	—	13	1	no	—
296	C₄×C₈	—	13	1	no	—
297	C₄×C₈	—	13	1	no	—
298	C₄×C₈	—	13	1	no	—
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	C₂×#261	1	1	yes	characteristic
302	C₂×C₁₃	—	2	2	no	—
303	C₂×C₁₃	—	4	1	no	—
304	C₂×C₁₃	C₈×#41	1	1	yes	characteristic
305	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
306	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
307	D₁₃	—	4	1	no	—
308	#41	—	26	4	no	—
309	C₂×Q₈	—	13	1	no	—
310	C₂×D₄	—	13	1	no	—
311	C₂×D₄	—	13	1	no	—
312	C₂×D₄	D₁₃⋊C₈	1	1	yes	characteristic
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
321	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	13	1	no	—
325	C₂×C₈	—	13	1	no	—
326	C₂×C₈	—	13	1	no	—
327	C₂×C₈	—	13	1	no	—
328	C₂×C₈	—	26	2	no	—
329	C₂×C₈	—	26	2	no	—
330	C₂×C₈	—	26	2	no	—
331	C₂×C₈	—	26	2	no	—
332	C₂×C₈	C₂²×#261	1	1	yes	characteristic
333	C₂×C₈	C₂²×#261	1	1	yes	characteristic
334	C₂×C₈	C₂²×#261	1	1	yes	characteristic
335	C₂×C₈	C₂²×#261	1	1	yes	characteristic
336	C₄⋊C₄	—	13	1	no	—
337	C₄⋊C₄	—	13	1	no	—
338	C₄⋊C₄	—	13	1	no	—
339	C₄⋊C₄	—	13	1	no	—
340	C₄⋊C₄	—	13	1	no	—
341	C₄⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
342	C₂²⋊C₄	—	13	1	no	—
343	C₂²⋊C₄	—	13	1	no	—
344	C₂²⋊C₄	—	13	1	no	—
345	C₂²⋊C₄	—	13	1	no	—
346	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
347	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
348	C₄²	—	13	1	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	—	13	1	no	—
352	C₄²	—	13	1	no	—
353	C₄²	—	13	1	no	—
354	C₄²	—	13	1	no	—
355	C₄²	—	13	1	no	—
356	C₄²	—	13	1	no	—
357	C₄²	C₂²×#261	1	1	yes	characteristic
358	C₁₆	—	13	4	no	—
359	C₁₆	—	26	2	no	—
360	C₁₆	—	26	2	no	—
361	C₁₆	—	26	2	no	—
362	C₁₃	#33479	1	1	yes	characteristic, complemented, Sylow
363	C₂³	—	13	1	no	—
364	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
365	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
366	Q₈	—	26	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	26	2	no	—
369	D₄	—	26	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	13	4	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	26	2	no	—
383	C₂×C₄	—	26	2	no	—
384	C₂×C₄	—	26	2	no	—
385	C₂×C₄	—	26	2	no	—
386	C₂×C₄	—	26	2	no	—
387	C₂×C₄	—	26	1	no	—
388	C₂×C₄	—	26	1	no	—
389	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
390	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
391	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
392	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
393	C₂×C₄	C₂³×#261	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	13	2	no	—
398	C₈	—	26	1	no	—
399	C₈	—	26	1	no	—
400	C₈	—	26	1	no	—
401	C₈	#88238	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	26	1	no	—
408	C₂²	—	26	1	no	—
409	C₂²	—	26	1	no	—
410	C₂²	D₁₃⋊M₃₂	1	2	yes	—
411	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	13	2	no	—
417	C₄	—	13	2	no	—
418	C₄	—	13	2	no	—
419	C₄	—	26	1	no	—
420	C₄	—	26	1	no	—
421	C₄	—	26	1	no	—
422	C₄	—	26	1	no	—
423	C₄	C₂×#88238	1	1	yes	characteristic
424	C₄	#41×#261	1	1	yes	characteristic
425	C₂	—	2	2	no	—
426	C₂	—	4	1	no	—
427	C₂	—	52	1	no	—
428	C₂	#13131641	1	1	yes	characteristic
429	C₂	C₂×D₁₃⋊M₃₂	1	1	yes	characteristic
430	C₂	D₁₃⋊#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₈×D₄×C₁₃	C₄
prime radical	C₂×#6129	C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	C₈×D₄	#261
hypocenter	C₁₃	#33479
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. #13131253	C₂	semidirect
2. #13131221	C₂	semidirect
3. #13131218	C₂	semidirect
4. #13131216	C₂	semidirect
5. #13131196	C₂	semidirect
6. #13131194	C₂	semidirect
7. #13131194	C₂	semidirect
8. #13131043	C₂	semidirect
9. #13131042	C₂	semidirect
10. C₂×#11718257	C₂	semidirect
147. #6092	#41	semidirect
177. C₂×Dic₁₃	M₃₂	semidirect
362. C₁₃	#33479	semidirect

Maximal subgroups

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

subgroup	index
#13131253	2
#13131221	2
#13131218	2
#13131216	2
#13131196	2
#13131194	2
#13131043	2
#13131042	2
C₂×#11718257	2
C₈×#6129	2
#33479	13