Subgroups — #13128797

Order 1664.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719534	C₂	1	2	yes	maximal, complemented
3	#11719290	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719289	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719287	C₂	1	2	yes	maximal, complemented
6	#11719265	C₂	1	4	yes	maximal, complemented
7	#11719257	C₂	1	2	yes	maximal, complemented
8	#11719255	C₂	1	2	yes	maximal, complemented
9	D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719250	C₂	1	2	yes	maximal, complemented
11	D₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719237	C₂	1	2	yes	maximal, complemented
13	#11719232	C₂	1	4	yes	maximal, complemented
14	#11719184	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719184	C₂	1	2	yes	maximal, complemented
16	#11719182	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#88129	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₃	C₂²	1	2	yes	—
20	C₂×#6127	C₂²	1	2	yes	complemented
21	C₂²×D₅₂	C₂²	1	2	yes	—
22	C₂²×Dic₂₆	C₂²	1	2	yes	complemented
23	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
28	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
29	C₁₃×#117	C₂²	1	2	yes	complemented
30	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄²×C₁₃	C₂²	1	2	yes	complemented
32	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	#88201	C₂²	1	2	yes	complemented
34	#88200	C₂²	1	2	yes	complemented
35	#88193	C₂²	1	4	yes	complemented
36	#88191	C₂²	1	4	yes	complemented
37	D₄×Dic₁₃	C₂²	1	2	yes	—
38	#88184	C₂²	1	2	yes	—
39	#88184	C₂²	1	1	yes	characteristic
40	#88184	C₂²	1	2	yes	complemented
41	#88184	C₂²	1	2	yes	complemented
42	#88183	C₂²	1	4	yes	complemented
43	#88183	C₂²	1	2	yes	complemented
44	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
45	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
46	C₂×#6103	C₂²	1	4	yes	complemented
47	C₂×#6103	C₂²	1	4	yes	complemented
48	#88178	C₂²	1	2	yes	complemented
49	#88178	C₂²	1	1	yes	characteristic, complemented
50	#88152	C₂²	1	4	yes	complemented
51	#88150	C₂²	1	4	yes	complemented
52	#88149	C₂²	1	2	yes	—
53	#88148	C₂²	1	4	yes	complemented
54	#88148	C₂²	1	4	yes	complemented
55	#88147	C₂²	1	2	yes	complemented
56	#88146	C₂²	1	2	yes	complemented
57	#88142	C₂²	1	2	yes	complemented
58	#88139	C₂²	1	4	yes	complemented
59	#88138	C₂²	1	4	yes	complemented
60	#88136	C₂²	1	4	yes	—
61	#88135	C₂²	1	4	yes	complemented
62	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
63	#88132	C₂²	1	4	yes	complemented
64	#88130	C₂²	1	2	yes	complemented
65	#88130	C₂²	1	4	yes	complemented
66	#88129	C₂²	1	1	yes	characteristic
67	#88129	C₂²	1	2	yes	—
68	#88129	C₂²	1	2	yes	complemented
69	#88129	C₂²	1	4	yes	complemented
70	#88129	C₂²	1	2	yes	complemented
71	#88129	C₂²	1	4	yes	complemented
72	#88128	C₂²	1	1	yes	characteristic
73	C₄×D₅₂	C₂²	1	1	yes	characteristic
74	C₄×D₅₂	C₂²	1	2	yes	complemented
75	C₄×D₅₂	C₂²	1	2	yes	complemented
76	C₄×D₅₂	C₂²	1	2	yes	complemented
77	#88126	C₂²	1	4	yes	complemented
78	#88126	C₂²	1	2	yes	complemented
79	#88124	C₂²	1	1	yes	characteristic, complemented
80	#88123	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₂₆	C₂²	1	2	yes	complemented
83	C₂³×D₁₃	C₂³	1	4	yes	—
84	C₁₃×#41	—	2	4	no	—
85	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₃	C₂³	1	2	yes	—
87	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
89	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
97	C₂²×Dic₁₃	C₂³	1	4	yes	—
98	D₄×D₁₃	—	2	8	no	—
99	#6127	—	4	4	no	—
100	C₂×D₅₂	—	4	4	no	—
101	C₂×D₅₂	C₂³	1	1	yes	characteristic
102	C₂×D₅₂	C₂³	1	2	yes	—
103	C₂×D₅₂	C₂³	1	2	yes	—
104	C₂×D₅₂	C₂³	1	2	yes	—
105	C₂×D₅₂	C₂³	1	4	yes	—
106	C₂×C₄×D₁₃	C₂³	1	2	yes	—
107	C₂×C₄×D₁₃	C₂³	1	4	yes	—
108	C₂×C₄×D₁₃	C₂³	1	4	yes	—
109	C₂×Dic₂₆	—	4	4	no	—
110	C₂×Dic₂₆	C₂³	1	2	yes	—
111	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
112	C₂×Dic₂₆	C₂³	1	4	yes	—
113	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₄²×C₁₃	C₂³	1	2	yes	—
122	C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₄²×C₁₃	C₂³	1	2	yes	—
125	C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
128	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
129	#6103	C₂³	1	4	yes	—
130	#6103	C₂³	1	2	yes	—
131	#6103	C₂³	1	2	yes	—
132	#6103	C₂³	1	4	yes	—
133	#6103	C₂³	1	2	yes	—
134	#6103	C₂³	1	4	yes	—
135	#6103	C₂³	1	4	yes	—
136	#6103	C₂³	1	2	yes	—
137	#6103	C₂³	1	4	yes	—
138	#6103	C₂³	1	4	yes	—
139	#6103	C₂³	1	4	yes	—
140	#6103	C₂³	1	4	yes	—
141	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₁₃	C₂³	1	2	yes	—
144	C₄⋊Dic₁₃	C₂³	1	2	yes	—
145	#6101	C₂³	1	2	yes	—
146	#6101	C₂³	1	4	yes	—
147	#6101	C₂³	1	2	yes	—
148	#6101	C₂³	1	2	yes	—
149	#6101	C₂³	1	4	yes	—
150	#6101	C₂³	1	2	yes	—
151	C₄×Dic₁₃	C₂³	1	4	yes	—
152	C₄×Dic₁₃	C₂³	1	2	yes	—
153	#3514	—	13	1	no	maximal, Sylow
154	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂³×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×D₁₃	—	2	8	no	—
157	C₂²×D₁₃	—	4	4	no	—
158	C₂²×D₁₃	—	4	4	no	—
159	C₂²×D₁₃	C₂⁴	1	2	yes	—
160	C₂²×D₁₃	C₂⁴	1	4	yes	—
161	Q₈×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	2	4	no	—
163	D₄×C₁₃	#41	1	4	yes	complemented
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂²⋊D₁₃	—	2	8	no	—
180	C₂²⋊D₁₃	—	4	4	no	—
181	C₂²⋊D₁₃	—	4	2	no	—
182	C₂×Dic₁₃	—	4	4	no	—
183	C₂×Dic₁₃	C₂⁴	1	2	yes	—
184	C₂×Dic₁₃	C₂⁴	1	2	yes	—
185	C₂×Dic₁₃	C₂⁴	1	4	yes	—
186	C₂×Dic₁₃	C₂⁴	1	2	yes	—
187	D₅₂	—	2	4	no	—
188	D₅₂	—	2	2	no	—
189	D₅₂	—	2	4	no	—
190	D₅₂	—	4	4	no	—
191	D₅₂	—	4	2	no	—
192	C₄×D₁₃	—	2	4	no	—
193	C₄×D₁₃	—	4	4	no	—
194	C₄×D₁₃	—	4	4	no	—
195	Dic₂₆	—	2	2	no	—
196	Dic₂₆	—	2	4	no	—
197	Dic₂₆	—	4	4	no	—
198	#559	—	13	1	no	—
199	#556	—	13	1	no	—
200	#555	—	13	2	no	—
201	#551	—	13	4	no	—
202	D₄×Q₈	—	13	1	no	—
203	#548	—	13	2	no	—
204	#546	—	13	2	no	—
205	#546	—	13	2	no	—
206	D₄²	—	13	1	no	—
207	#542	—	13	2	no	—
208	#538	—	13	4	no	—
209	#532	—	13	1	no	—
210	#529	—	13	2	no	—
211	#529	—	13	1	no	—
212	C₂×#124	—	13	2	no	—
213	#518	—	13	2	no	—
214	C₄×#41	D₁₃	1	1	yes	characteristic, complemented
215	C₂²×C₁₃	—	2	2	no	—
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	1	no	—
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	C₂×#41	1	4	yes	—
221	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
222	C₂×D₁₃	—	2	2	no	—
223	C₂×D₁₃	—	2	4	no	—
224	C₂×D₁₃	—	2	4	no	—
225	C₂×D₁₃	—	2	2	no	—
226	C₂×D₁₃	—	2	4	no	—
227	C₂×D₁₃	—	2	2	no	—
228	C₂×D₁₃	—	8	8	no	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	2	no	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	C₂×#41	1	2	yes	—
237	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
238	Dic₁₃	—	2	2	no	—
239	Dic₁₃	—	2	2	no	—
240	Dic₁₃	—	2	4	no	—
241	Dic₁₃	—	2	2	no	—
242	C₂×#41	—	13	2	no	—
243	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
244	C₂²×Q₈	—	13	2	no	—
245	C₂²×D₄	—	13	2	no	—
246	C₂²×D₄	—	13	2	no	—
247	C₄⋊Q₈	—	13	2	no	—
248	C₄⋊Q₈	—	13	1	no	—
249	#127	—	13	1	no	—
250	#126	—	13	4	no	—
251	#126	—	13	4	no	—
252	#126	—	13	2	no	—
253	#125	—	13	1	no	—
254	#124	—	13	2	no	—
255	#124	—	13	4	no	—
256	#124	—	13	1	no	—
257	#124	—	13	2	no	—
258	#124	—	13	4	no	—
259	#124	—	13	2	no	—
260	#124	—	13	2	no	—
261	#124	—	13	4	no	—
262	#123	—	13	2	no	—
263	#123	—	13	4	no	—
264	#123	—	13	4	no	—
265	#123	—	13	4	no	—
266	C₂²⋊Q₈	—	13	2	no	—
267	C₂²⋊Q₈	—	13	2	no	—
268	C₂²⋊Q₈	—	13	1	no	—
269	C₂²⋊Q₈	—	13	4	no	—
270	C₂²⋊Q₈	—	13	4	no	—
271	#121	—	13	4	no	—
272	#121	—	13	2	no	—
273	#121	—	13	1	no	—
274	#121	—	13	2	no	—
275	#121	—	13	2	no	—
276	#121	—	13	2	no	—
277	#121	—	13	4	no	—
278	#120	—	13	4	no	—
279	#120	—	13	4	no	—
280	C₄×Q₈	—	13	2	no	—
281	C₄×Q₈	—	13	1	no	—
282	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
283	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
284	C₄×D₄	—	13	2	no	—
285	C₄×D₄	—	13	4	no	—
286	C₄×D₄	—	13	2	no	—
287	C₄×D₄	—	13	2	no	—
288	C₄×D₄	—	13	4	no	—
289	C₄×D₄	—	13	2	no	—
290	C₄×D₄	—	13	1	no	—
291	C₄×D₄	—	13	2	no	—
292	C₄×D₄	—	13	2	no	—
293	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
294	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
295	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
296	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
297	#117	—	13	2	no	—
298	#117	—	13	2	no	—
299	#117	—	13	4	no	—
300	#117	C₂×D₁₃	1	2	yes	complemented
301	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
302	C₂×C₂²⋊C₄	—	13	4	no	—
303	C₂×C₂²⋊C₄	—	13	4	no	—
304	C₂×C₂²⋊C₄	—	13	4	no	—
305	C₂×C₄²	C₂×D₁₃	1	2	yes	complemented
306	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
307	C₂×C₁₃	—	2	4	no	—
308	C₂×C₁₃	—	4	1	no	—
309	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
310	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₁₃	#585	1	1	yes	characteristic
312	D₁₃	—	4	4	no	—
313	D₁₃	—	4	2	no	—
314	C₂⁴	—	13	4	no	—
315	#41	—	2	4	no	—
316	#41	—	52	4	no	—
317	C₂×Q₈	—	13	1	no	—
318	C₂×Q₈	—	13	2	no	—
319	C₂×Q₈	—	13	4	no	—
320	C₂×Q₈	—	52	4	no	—
321	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
322	C₂×D₄	—	13	4	no	—
323	C₂×D₄	—	13	2	no	—
324	C₂×D₄	—	13	4	no	—
325	C₂×D₄	—	13	2	no	—
326	C₂×D₄	—	13	1	no	—
327	C₂×D₄	—	13	2	no	—
328	C₂×D₄	—	13	2	no	—
329	C₂×D₄	—	13	4	no	—
330	C₂×D₄	—	26	8	no	—
331	C₂×D₄	—	52	4	no	—
332	C₂×D₄	C₂²×D₁₃	1	2	yes	—
333	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
334	C₂²×C₄	—	13	4	no	—
335	C₂²×C₄	—	13	2	no	—
336	C₂²×C₄	—	13	4	no	—
337	C₂²×C₄	—	13	4	no	—
338	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
339	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
341	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
343	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
344	C₄⋊C₄	—	13	2	no	—
345	C₄⋊C₄	—	13	2	no	—
346	C₄⋊C₄	—	13	2	no	—
347	C₄⋊C₄	—	13	2	no	—
348	C₄⋊C₄	—	13	4	no	—
349	C₄⋊C₄	—	13	1	no	—
350	C₄⋊C₄	—	13	1	no	—
351	C₄⋊C₄	—	13	2	no	—
352	C₄⋊C₄	—	13	4	no	—
353	C₄⋊C₄	—	13	2	no	—
354	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
355	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
357	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
358	C₂²⋊C₄	—	13	4	no	—
359	C₂²⋊C₄	—	13	2	no	—
360	C₂²⋊C₄	—	13	2	no	—
361	C₂²⋊C₄	—	13	4	no	—
362	C₂²⋊C₄	—	13	2	no	—
363	C₂²⋊C₄	—	13	2	no	—
364	C₂²⋊C₄	—	13	4	no	—
365	C₂²⋊C₄	—	13	4	no	—
366	C₂²⋊C₄	—	13	4	no	—
367	C₂²⋊C₄	—	13	4	no	—
368	C₂²⋊C₄	—	13	4	no	—
369	C₂²⋊C₄	—	13	4	no	—
370	C₂²⋊C₄	—	13	2	no	—
371	C₂²⋊C₄	—	13	4	no	—
372	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
373	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
375	C₄²	—	13	4	no	—
376	C₄²	—	13	2	no	—
377	C₄²	C₂²×D₁₃	1	1	yes	characteristic
378	C₄²	C₂²×D₁₃	1	2	yes	—
379	C₄²	C₂²×D₁₃	1	1	yes	characteristic
380	C₄²	C₂²×D₁₃	1	1	yes	characteristic
381	C₄²	C₂²×D₁₃	1	1	yes	characteristic
382	C₄²	C₂²×D₁₃	1	2	yes	—
383	C₄²	C₂²×D₁₃	1	2	yes	—
384	C₁₃	#3514	1	1	yes	characteristic, complemented, Sylow
385	C₂³	—	13	2	no	—
386	C₂³	—	13	4	no	—
387	C₂³	—	26	8	no	—
388	C₂³	—	52	4	no	—
389	C₂³	—	52	4	no	—
390	C₂³	C₂³×D₁₃	1	1	yes	characteristic
391	C₂³	C₂³×D₁₃	1	2	yes	—
392	Q₈	—	2	2	no	—
393	Q₈	—	26	2	no	—
394	Q₈	—	26	4	no	—
395	Q₈	—	52	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	26	8	no	—
398	D₄	—	26	4	no	—
399	D₄	—	26	2	no	—
400	D₄	—	26	4	no	—
401	D₄	—	52	2	no	—
402	D₄	—	52	4	no	—
403	D₄	—	52	2	no	—
404	D₄	—	52	4	no	—
405	D₄	#6127	1	4	yes	complemented
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	13	2	no	—
413	C₂×C₄	—	13	2	no	—
414	C₂×C₄	—	13	2	no	—
415	C₂×C₄	—	13	4	no	—
416	C₂×C₄	—	26	4	no	—
417	C₂×C₄	—	52	4	no	—
418	C₂×C₄	—	52	4	no	—
419	C₂×C₄	—	52	4	no	—
420	C₂×C₄	C₂³×D₁₃	1	2	yes	—
421	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₁₃	1	2	yes	—
424	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₁₃	1	2	yes	—
427	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	26	2	no	—
435	C₂²	—	26	4	no	—
436	C₂²	—	26	4	no	—
437	C₂²	—	26	2	no	—
438	C₂²	—	26	4	no	—
439	C₂²	—	26	2	no	—
440	C₂²	—	104	8	no	—
441	C₂²	C₂×#6127	1	4	yes	—
442	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	26	2	no	—
451	C₄	—	26	4	no	—
452	C₄	—	26	2	no	—
453	C₄	—	26	2	no	—
454	C₄	C₂×#6127	1	2	yes	—
455	C₄	#88256	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	4	1	no	—
458	C₂	—	52	2	no	—
459	C₂	—	52	4	no	—
460	C₂	C₂²×#6127	1	1	yes	characteristic
461	C₂	C₂×#88256	1	1	yes	characteristic
462	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₄×C₁₃×#41	C₂
hypercenter	C₄×#41	D₁₃
hypocenter	C₁₃	#3514
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₃×#41	C₂	semidirect
2. #11719534	C₂	semidirect
3. #11719290	C₂	semidirect
4. #11719289	C₂	semidirect
5. #11719287	C₂	semidirect
6. #11719265	C₂	semidirect
7. #11719257	C₂	semidirect
8. #11719255	C₂	semidirect
9. D₄×D₅₂	C₂	semidirect
10. #11719250	C₂	semidirect
11. D₄×Dic₂₆	C₂	semidirect
12. #11719237	C₂	semidirect
13. #11719232	C₂	semidirect
14. #11719184	C₂	semidirect
15. #11719184	C₂	semidirect
16. #11719182	C₂	semidirect
17. C₂×#88129	C₂	semidirect
20. C₂×#6127	C₂²	semidirect
22. C₂²×Dic₂₆	C₂²	semidirect
23. C₄×Q₈×C₁₃	C₂²	semidirect
24. C₄×Q₈×C₁₃	C₂²	semidirect
27. C₄×D₄×C₁₃	C₂²	semidirect
28. C₄×D₄×C₁₃	C₂²	semidirect
29. C₁₃×#117	C₂²	semidirect
30. C₁₃×#117	C₂²	semidirect
31. C₂×C₄²×C₁₃	C₂²	semidirect
32. C₂×C₄²×C₁₃	C₂²	semidirect
33. #88201	C₂²	semidirect
34. #88200	C₂²	semidirect
35. #88193	C₂²	semidirect
36. #88191	C₂²	semidirect
40. #88184	C₂²	semidirect
41. #88184	C₂²	semidirect
42. #88183	C₂²	semidirect
43. #88183	C₂²	semidirect
44. C₄×C₂²⋊D₁₃	C₂²	semidirect
45. C₄×C₂²⋊D₁₃	C₂²	semidirect
46. C₂×#6103	C₂²	semidirect
47. C₂×#6103	C₂²	semidirect
48. #88178	C₂²	semidirect
49. #88178	C₂²	semidirect
50. #88152	C₂²	semidirect
51. #88150	C₂²	semidirect
53. #88148	C₂²	semidirect
54. #88148	C₂²	semidirect
55. #88147	C₂²	semidirect
56. #88146	C₂²	semidirect
57. #88142	C₂²	semidirect
58. #88139	C₂²	semidirect
59. #88138	C₂²	semidirect
61. #88135	C₂²	semidirect
62. C₂²⋊C₄×D₁₃	C₂²	semidirect
63. #88132	C₂²	semidirect
64. #88130	C₂²	semidirect
65. #88130	C₂²	semidirect
68. #88129	C₂²	semidirect
69. #88129	C₂²	semidirect
70. #88129	C₂²	semidirect
71. #88129	C₂²	semidirect
74. C₄×D₅₂	C₂²	semidirect
75. C₄×D₅₂	C₂²	semidirect
76. C₄×D₅₂	C₂²	semidirect
77. #88126	C₂²	semidirect
78. #88126	C₂²	semidirect
79. #88124	C₂²	semidirect
80. #88123	C₂²	semidirect
81. C₄×Dic₂₆	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
163. D₄×C₁₃	#41	semidirect
214. C₄×#41	D₁₃	semidirect
282. C₄×Q₈	C₂×D₁₃	semidirect
283. C₄×Q₈	C₂×D₁₃	semidirect
295. C₄×D₄	C₂×D₁₃	semidirect
296. C₄×D₄	C₂×D₁₃	semidirect
300. #117	C₂×D₁₃	semidirect
301. #117	C₂×D₁₃	semidirect
305. C₂×C₄²	C₂×D₁₃	semidirect
306. C₂×C₄²	C₂×D₁₃	semidirect
384. C₁₃	#3514	semidirect
405. D₄	#6127	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#41	2
#11719534	2
#11719290	2
#11719289	2
#11719287	2
#11719265	2
#11719257	2
#11719255	2
D₄×D₅₂	2
#11719250	2
D₄×Dic₂₆	2
#11719237	2
#11719232	2
#11719184	2
#11719182	2
C₂×#88129	2
#3514	13