Subgroups — #13128565

Order 1664.

1142 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719511	C₂	1	4	yes	maximal, complemented
3	#11719510	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719503	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#88180	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719324	C₂	1	2	yes	maximal, complemented
8	#11719323	C₂	1	2	yes	maximal, complemented
9	#11719321	C₂	1	2	yes	maximal, complemented
10	#11719319	C₂	1	2	yes	maximal, complemented
11	#11719316	C₂	1	2	yes	maximal, complemented
12	#11719308	C₂	1	2	yes	maximal, complemented
13	#11719305	C₂	1	2	yes	maximal, complemented
14	#11719301	C₂	1	2	yes	maximal, complemented
15	#11719209	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719205	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719200	C₂	1	4	yes	maximal, complemented
18	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
20	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×#6129	C₂²	1	4	yes	complemented
22	C₂×#6127	C₂²	1	1	yes	characteristic
23	C₁₃×#121	C₂²	1	2	yes	—
24	C₁₃×#121	C₂²	1	2	yes	—
25	C₁₃×#121	C₂²	1	2	yes	—
26	C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	#88207	C₂²	1	4	yes	—
30	#88207	C₂²	1	2	yes	—
31	C₂×C₂²⋊Dic₁₃	C₂²	1	4	yes	—
32	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
33	#88194	C₂²	1	2	yes	complemented
34	#88193	C₂²	1	4	yes	complemented
35	#88193	C₂²	1	4	yes	complemented
36	#88192	C₂²	1	2	yes	complemented
37	#88192	C₂²	1	2	yes	complemented
38	#88192	C₂²	1	4	yes	complemented
39	#88190	C₂²	1	2	yes	complemented
40	#88190	C₂²	1	4	yes	complemented
41	#88189	C₂²	1	4	yes	complemented
42	#88189	C₂²	1	4	yes	complemented
43	D₄×Dic₁₃	C₂²	1	2	yes	complemented
44	D₄×Dic₁₃	C₂²	1	2	yes	complemented
45	D₄×Dic₁₃	C₂²	1	2	yes	complemented
46	D₄×Dic₁₃	C₂²	1	2	yes	complemented
47	D₄×Dic₁₃	C₂²	1	4	yes	complemented
48	#88184	C₂²	1	1	yes	characteristic, complemented
49	#88184	C₂²	1	1	yes	characteristic, complemented
50	#88183	C₂²	1	2	yes	—
51	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	—
52	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
53	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
54	#88180	C₂²	1	2	yes	—
55	#88180	C₂²	1	1	yes	characteristic
56	#88180	C₂²	1	1	yes	characteristic
57	#88180	C₂²	1	1	yes	characteristic
58	#88180	C₂²	1	2	yes	complemented
59	#88180	C₂²	1	1	yes	characteristic, complemented
60	#88180	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
63	#88178	C₂²	1	4	yes	—
64	#88178	C₂²	1	1	yes	characteristic, complemented
65	#88178	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×Dic₁₃	C₂²	1	2	yes	complemented
67	#88147	C₂²	1	2	yes	complemented
68	#88146	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
70	#88144	C₂²	1	2	yes	complemented
71	#88144	C₂²	1	2	yes	complemented
72	#88142	C₂²	1	2	yes	complemented
73	#88142	C₂²	1	2	yes	complemented
74	#88141	C₂²	1	2	yes	complemented
75	#88140	C₂²	1	4	yes	complemented
76	#88139	C₂²	1	4	yes	complemented
77	#88137	C₂²	1	4	yes	complemented
78	#88135	C₂²	1	4	yes	complemented
79	#88133	C₂²	1	4	yes	complemented
80	#88133	C₂²	1	4	yes	complemented
81	#88132	C₂²	1	4	yes	complemented
82	#88131	C₂²	1	4	yes	complemented
83	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
84	C₂⁴×C₁₃	C₂³	1	2	yes	—
85	C₂×D₄×C₁₃	—	2	4	no	—
86	C₂×D₄×C₁₃	—	4	4	no	—
87	C₂×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂×D₄×C₁₃	C₂³	1	2	yes	—
89	C₂×D₄×C₁₃	C₂³	1	4	yes	—
90	C₂×D₄×C₁₃	C₂³	1	4	yes	—
91	C₂²×C₄×C₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
100	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
101	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
104	C₂²×Dic₁₃	C₂³	1	2	yes	—
105	C₂²×Dic₁₃	C₂³	1	4	yes	—
106	C₂²×Dic₁₃	C₂³	1	4	yes	—
107	C₂²×Dic₁₃	C₂³	1	2	yes	—
108	#6129	—	4	8	no	—
109	#6127	—	2	4	no	—
110	C₂×D₅₂	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂³	1	2	yes	—
112	C₂×C₄×D₁₃	C₂³	1	4	yes	—
113	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
114	C₂×Dic₂₆	C₂³	1	4	yes	—
115	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
121	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
123	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
125	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
126	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
127	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
128	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
129	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
130	#6103	C₂³	1	2	yes	—
131	#6103	C₂³	1	2	yes	—
132	#6103	C₂³	1	4	yes	—
133	C₄⋊Dic₁₃	C₂³	1	2	yes	—
134	C₄⋊Dic₁₃	C₂³	1	2	yes	—
135	C₄⋊Dic₁₃	C₂³	1	4	yes	—
136	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
142	#6101	C₂³	1	2	yes	—
143	#6101	C₂³	1	4	yes	—
144	#6101	C₂³	1	2	yes	—
145	#6101	C₂³	1	4	yes	—
146	#6101	C₂³	1	4	yes	—
147	C₄×Dic₁₃	C₂³	1	2	yes	—
148	C₄×Dic₁₃	C₂³	1	4	yes	—
149	C₄×Dic₁₃	C₂³	1	2	yes	—
150	C₄×Dic₁₃	C₂³	1	2	yes	—
151	C₄×Dic₁₃	C₂³	1	2	yes	—
152	C₄×Dic₁₃	C₂³	1	2	yes	—
153	#3494	—	13	1	no	maximal, Sylow
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	2	4	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	2	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂³×C₁₃	C₂⁴	1	4	yes	—
162	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂²×D₁₃	C₂⁴	1	2	yes	—
165	D₄×C₁₃	—	2	8	no	—
166	D₄×C₁₃	—	2	4	no	—
167	D₄×C₁₃	—	2	4	no	—
168	D₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	#41	1	4	yes	complemented
176	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²⋊D₁₃	—	2	4	no	—
182	C₂²⋊D₁₃	—	2	4	no	—
183	C₂²⋊D₁₃	—	4	4	no	—
184	C₂²⋊D₁₃	—	4	2	no	—
185	C₂²⋊D₁₃	—	4	4	no	—
186	C₂×Dic₁₃	—	2	4	no	—
187	C₂×Dic₁₃	—	4	4	no	—
188	C₂×Dic₁₃	—	4	4	no	—
189	C₂×Dic₁₃	—	4	2	no	—
190	C₂×Dic₁₃	C₂⁴	1	2	yes	—
191	C₂×Dic₁₃	C₂⁴	1	2	yes	—
192	C₂×Dic₁₃	C₂⁴	1	2	yes	—
193	C₂×Dic₁₃	C₂⁴	1	2	yes	—
194	C₂×Dic₁₃	C₂⁴	1	2	yes	—
195	C₂×Dic₁₃	C₂⁴	1	2	yes	—
196	C₂×Dic₁₃	C₂⁴	1	2	yes	—
197	D₅₂	—	2	2	no	—
198	C₄×D₁₃	—	2	4	no	—
199	C₄×D₁₃	—	4	4	no	—
200	Dic₂₆	—	2	2	no	—
201	Dic₂₆	—	4	4	no	—
202	#555	—	13	2	no	—
203	#553	—	13	2	no	—
204	#553	—	13	2	no	—
205	#551	—	13	4	no	—
206	#547	—	13	2	no	—
207	#546	—	13	4	no	—
208	#544	—	13	1	no	—
209	#542	—	13	2	no	—
210	#540	—	13	2	no	—
211	#535	—	13	1	no	—
212	#532	—	13	2	no	—
213	#529	—	13	2	no	—
214	#525	—	13	1	no	—
215	C₂×#121	D₁₃	1	1	yes	characteristic, complemented
216	#520	—	13	1	no	—
217	#518	—	13	1	no	—
218	C₂×#117	—	13	1	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	—	2	1	no	—
222	C₂²×C₁₃	—	2	1	no	—
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	—	2	4	no	—
225	C₂²×C₁₃	—	2	4	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	4	no	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	4	4	no	—
230	C₂²×C₁₃	—	8	4	no	—
231	C₂²×C₁₃	C₂×#41	1	2	yes	—
232	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
233	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
234	C₂×D₁₃	—	2	2	no	—
235	C₂×D₁₃	—	2	2	no	—
236	C₂×D₁₃	—	2	2	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	—	2	4	no	—
240	C₄×C₁₃	C₂×#41	1	2	yes	—
241	C₄×C₁₃	C₂×#41	1	2	yes	—
242	Dic₁₃	—	2	2	no	—
243	Dic₁₃	—	2	2	no	—
244	Dic₁₃	—	2	2	no	—
245	Dic₁₃	—	2	2	no	—
246	Dic₁₃	—	2	2	no	—
247	Dic₁₃	—	2	2	no	—
248	Dic₁₃	—	2	2	no	—
249	C₂×#41	—	13	4	no	—
250	C₂×#41	—	13	1	no	—
251	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
252	C₂²×D₄	C₂×D₁₃	1	2	yes	—
253	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
254	C₄⋊Q₈	—	13	2	no	—
255	C₄⋊Q₈	—	13	2	no	—
256	#127	—	13	2	no	—
257	#126	—	13	4	no	—
258	#126	—	13	4	no	—
259	#125	—	13	2	no	—
260	#125	—	13	2	no	—
261	#124	—	13	2	no	—
262	#124	—	13	4	no	—
263	#124	—	13	4	no	—
264	#123	—	13	4	no	—
265	#123	—	13	4	no	—
266	#123	—	13	2	no	—
267	#123	—	13	4	no	—
268	#123	—	13	4	no	—
269	C₂²⋊Q₈	—	13	1	no	—
270	C₂²⋊Q₈	—	13	1	no	—
271	C₂²⋊Q₈	—	13	4	no	—
272	C₂²⋊Q₈	—	13	4	no	—
273	#121	—	13	4	no	—
274	#121	—	13	2	no	—
275	#121	—	13	2	no	—
276	#121	—	13	4	no	—
277	#121	—	13	4	no	—
278	#121	—	13	1	no	—
279	#121	—	13	1	no	—
280	#121	C₂×D₁₃	1	2	yes	—
281	#121	C₂×D₁₃	1	2	yes	—
282	#121	C₂×D₁₃	1	2	yes	—
283	#121	C₂×D₁₃	1	2	yes	—
284	#120	—	13	2	no	—
285	#120	—	13	4	no	—
286	C₄×Q₈	—	13	2	no	—
287	C₄×D₄	—	13	2	no	—
288	C₄×D₄	—	13	2	no	—
289	C₄×D₄	—	13	2	no	—
290	C₄×D₄	—	13	2	no	—
291	C₄×D₄	—	13	4	no	—
292	C₄×D₄	—	13	4	no	—
293	C₄×D₄	—	13	2	no	—
294	C₄×D₄	—	13	2	no	—
295	C₄×D₄	—	13	2	no	—
296	C₄×D₄	—	13	4	no	—
297	#117	—	13	1	no	—
298	#117	—	13	1	no	—
299	#117	—	13	2	no	—
300	#117	—	13	2	no	—
301	#117	—	13	1	no	—
302	#117	—	13	1	no	—
303	#117	—	13	1	no	—
304	#117	—	13	2	no	—
305	#117	—	13	4	no	—
306	C₂×C₄⋊C₄	—	13	1	no	—
307	C₂×C₄⋊C₄	—	13	1	no	—
308	C₂×C₄⋊C₄	—	13	2	no	—
309	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	13	2	no	—
311	C₂×C₂²⋊C₄	—	13	4	no	—
312	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
313	C₂×C₄²	—	13	2	no	—
314	C₂×C₁₃	—	2	2	no	—
315	C₂×C₁₃	—	2	2	no	—
316	C₂×C₁₃	—	4	1	no	—
317	C₂×C₁₃	—	4	4	no	—
318	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
319	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
320	C₂×C₁₃	#585	1	1	yes	characteristic
321	D₁₃	—	4	2	no	—
322	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
323	C₂⁴	C₂²×D₁₃	1	2	yes	—
324	#41	—	26	4	no	—
325	#41	—	52	8	no	—
326	C₂×Q₈	—	13	1	no	—
327	C₂×Q₈	—	13	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	13	2	no	—
331	C₂×D₄	—	13	2	no	—
332	C₂×D₄	—	13	2	no	—
333	C₂×D₄	—	13	4	no	—
334	C₂×D₄	—	13	4	no	—
335	C₂×D₄	—	13	1	no	—
336	C₂×D₄	C₂²×D₁₃	1	2	yes	—
337	C₂×D₄	C₂²×D₁₃	1	2	yes	—
338	C₂×D₄	C₂²×D₁₃	1	4	yes	—
339	C₂×D₄	C₂²×D₁₃	1	4	yes	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	13	2	no	—
342	C₂²×C₄	—	13	2	no	—
343	C₂²×C₄	—	13	4	no	—
344	C₂²×C₄	—	13	4	no	—
345	C₂²×C₄	—	13	2	no	—
346	C₂²×C₄	—	13	4	no	—
347	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
353	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
354	C₄⋊C₄	—	13	1	no	—
355	C₄⋊C₄	—	13	1	no	—
356	C₄⋊C₄	—	13	1	no	—
357	C₄⋊C₄	—	13	1	no	—
358	C₄⋊C₄	—	13	2	no	—
359	C₄⋊C₄	—	13	2	no	—
360	C₄⋊C₄	—	13	4	no	—
361	C₄⋊C₄	—	13	2	no	—
362	C₄⋊C₄	—	13	1	no	—
363	C₄⋊C₄	—	13	1	no	—
364	C₄⋊C₄	—	13	4	no	—
365	C₄⋊C₄	—	13	4	no	—
366	C₄⋊C₄	—	13	4	no	—
367	C₄⋊C₄	—	13	2	no	—
368	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
369	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
370	C₂²⋊C₄	—	13	2	no	—
371	C₂²⋊C₄	—	13	2	no	—
372	C₂²⋊C₄	—	13	2	no	—
373	C₂²⋊C₄	—	13	2	no	—
374	C₂²⋊C₄	—	13	2	no	—
375	C₂²⋊C₄	—	13	4	no	—
376	C₂²⋊C₄	—	13	4	no	—
377	C₂²⋊C₄	—	13	4	no	—
378	C₂²⋊C₄	—	13	2	no	—
379	C₂²⋊C₄	—	13	4	no	—
380	C₂²⋊C₄	—	13	2	no	—
381	C₂²⋊C₄	—	13	4	no	—
382	C₂²⋊C₄	—	13	2	no	—
383	C₂²⋊C₄	—	13	2	no	—
384	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
385	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
386	C₄²	—	13	2	no	—
387	C₄²	—	13	2	no	—
388	C₄²	—	13	2	no	—
389	C₄²	—	13	2	no	—
390	C₄²	—	13	4	no	—
391	C₄²	—	13	2	no	—
392	C₁₃	#3494	1	1	yes	characteristic, complemented, Sylow
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	13	2	no	—
400	C₂³	C₂³×D₁₃	1	1	yes	characteristic
401	C₂³	C₂³×D₁₃	1	4	yes	—
402	C₂³	C₂³×D₁₃	1	1	yes	characteristic
403	C₂³	C₂³×D₁₃	1	1	yes	characteristic
404	Q₈	—	26	2	no	—
405	Q₈	—	52	4	no	—
406	D₄	—	2	8	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	26	4	no	—
411	D₄	—	26	4	no	—
412	D₄	—	26	2	no	—
413	D₄	—	52	2	no	—
414	D₄	—	52	4	no	—
415	D₄	—	52	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	13	2	no	—
423	C₂×C₄	—	13	2	no	—
424	C₂×C₄	—	13	2	no	—
425	C₂×C₄	—	13	2	no	—
426	C₂×C₄	—	13	2	no	—
427	C₂×C₄	—	13	2	no	—
428	C₂×C₄	—	13	2	no	—
429	C₂×C₄	—	26	4	no	—
430	C₂×C₄	—	26	4	no	—
431	C₂×C₄	—	52	4	no	—
432	C₂×C₄	—	52	4	no	—
433	C₂×C₄	—	52	2	no	—
434	C₂×C₄	—	52	4	no	—
435	C₂×C₄	#6129	1	4	yes	complemented
436	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
437	C₂×C₄	C₂³×D₁₃	1	4	yes	—
438	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	8	4	no	—
453	C₂²	—	26	2	no	—
454	C₂²	—	26	2	no	—
455	C₂²	—	26	2	no	—
456	C₂²	C₂×#6129	1	2	yes	—
457	C₂²	#88251	1	2	yes	—
458	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	4	no	—
462	C₄	—	26	2	no	—
463	C₄	—	26	2	no	—
464	C₄	—	26	2	no	—
465	C₄	—	26	2	no	—
466	C₄	—	26	2	no	—
467	C₄	—	26	2	no	—
468	C₄	—	26	2	no	—
469	C₄	C₂×#6129	1	2	yes	—
470	C₄	C₂×#6129	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	2	2	no	—
473	C₂	—	4	1	no	—
474	C₂	—	4	4	no	—
475	C₂	—	52	2	no	—
476	C₂	C₂²×#6129	1	1	yes	characteristic
477	C₂	C₂×#88251	1	1	yes	characteristic
478	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₂×C₁₃×#121	C₂
hypercenter	C₂×#121	D₁₃
hypocenter	C₁₃	#3494
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#121	C₂	semidirect
2. #11719511	C₂	semidirect
3. #11719510	C₂	semidirect
4. #11719503	C₂	semidirect
5. #11719496	C₂	semidirect
6. C₂×#88180	C₂	semidirect
7. #11719324	C₂	semidirect
8. #11719323	C₂	semidirect
9. #11719321	C₂	semidirect
10. #11719319	C₂	semidirect
11. #11719316	C₂	semidirect
12. #11719308	C₂	semidirect
13. #11719305	C₂	semidirect
14. #11719301	C₂	semidirect
15. #11719209	C₂	semidirect
16. #11719205	C₂	semidirect
17. #11719200	C₂	semidirect
21. C₂×#6129	C₂²	semidirect
33. #88194	C₂²	semidirect
34. #88193	C₂²	semidirect
35. #88193	C₂²	semidirect
36. #88192	C₂²	semidirect
37. #88192	C₂²	semidirect
38. #88192	C₂²	semidirect
39. #88190	C₂²	semidirect
40. #88190	C₂²	semidirect
41. #88189	C₂²	semidirect
42. #88189	C₂²	semidirect
43. D₄×Dic₁₃	C₂²	semidirect
44. D₄×Dic₁₃	C₂²	semidirect
45. D₄×Dic₁₃	C₂²	semidirect
46. D₄×Dic₁₃	C₂²	semidirect
47. D₄×Dic₁₃	C₂²	semidirect
48. #88184	C₂²	semidirect
49. #88184	C₂²	semidirect
52. C₄×C₂²⋊D₁₃	C₂²	semidirect
53. C₄×C₂²⋊D₁₃	C₂²	semidirect
58. #88180	C₂²	semidirect
59. #88180	C₂²	semidirect
60. #88180	C₂²	semidirect
61. C₂×C₄⋊Dic₁₃	C₂²	semidirect
62. C₂×C₄⋊Dic₁₃	C₂²	semidirect
64. #88178	C₂²	semidirect
65. #88178	C₂²	semidirect
66. C₂×C₄×Dic₁₃	C₂²	semidirect
67. #88147	C₂²	semidirect
68. #88146	C₂²	semidirect
69. C₄⋊C₄×D₁₃	C₂²	semidirect
70. #88144	C₂²	semidirect
71. #88144	C₂²	semidirect
72. #88142	C₂²	semidirect
73. #88142	C₂²	semidirect
74. #88141	C₂²	semidirect
75. #88140	C₂²	semidirect
76. #88139	C₂²	semidirect
77. #88137	C₂²	semidirect
78. #88135	C₂²	semidirect
79. #88133	C₂²	semidirect
80. #88133	C₂²	semidirect
81. #88132	C₂²	semidirect
82. #88131	C₂²	semidirect
175. C₂×C₄×C₁₃	#41	semidirect
215. C₂×#121	D₁₃	semidirect
392. C₁₃	#3494	semidirect
435. C₂×C₄	#6129	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#121	2
#11719511	2
#11719510	2
#11719503	2
#11719496	2
C₂×#88180	2
#11719324	2
#11719323	2
#11719321	2
#11719319	2
#11719316	2
#11719308	2
#11719305	2
#11719301	2
#11719209	2
#11719205	2
#11719200	2
#3494	13