Subgroups — #15845367

Order 3328.

618 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	#13125422	C₂	1	1	yes	maximal, characteristic, complemented
2	#13124624	C₂	1	2	yes	maximal
3	#13114294	C₂	1	2	yes	maximal, complemented
4	#13114287	C₂	1	2	yes	maximal, complemented
5	#13114240	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114235	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114206	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114201	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11718050	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113491	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	#11719175	C₂²	1	2	yes	—
14	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₈×D₄×C₁₃	—	2	1	no	—
17	C₈×D₄×C₁₃	—	2	1	no	—
18	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#431	—	2	1	no	—
21	C₁₃×#431	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	—	2	1	no	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	#11718894	—	2	2	no	—
25	#11718777	—	2	1	no	—
26	#11718777	—	2	1	no	—
27	#11718683	—	2	2	no	—
28	#11718682	C₂²	1	2	yes	—
29	#11718681	C₂²	1	2	yes	—
30	#11718670	—	2	2	no	—
31	#11718669	C₂²	1	2	yes	—
32	#11718668	C₂²	1	2	yes	—
33	#11718659	—	2	2	no	—
34	C₂×C₄⋊#1055	C₂²	1	2	yes	—
35	#11718360	C₂²	1	1	yes	characteristic
36	C₄×Dic₅₂	—	2	1	no	—
37	C₄×Dic₅₂	—	2	1	no	—
38	#11718343	C₂²	1	1	yes	characteristic
39	#11718342	C₂²	1	2	yes	—
40	#11718074	C₂²	1	2	yes	—
41	#11718074	C₂²	1	2	yes	—
42	#11718073	C₂²	1	2	yes	—
43	#11718073	C₂²	1	2	yes	—
44	#11718050	C₂²	1	1	yes	characteristic
45	#11718050	C₂²	1	1	yes	characteristic
46	#11718050	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	—	2	1	no	—
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
53	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
57	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×#117	—	2	1	no	—
59	C₁₃×#117	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	#88180	—	2	2	no	—
63	#88178	—	2	2	no	—
64	#88178	—	2	2	no	—
65	C₂²×#1055	—	2	2	no	—
66	C₂×Dic₅₂	—	2	1	no	—
67	C₂×Dic₅₂	—	2	1	no	—
68	#88124	—	2	2	no	—
69	#88123	C₂³	1	2	yes	—
70	#88123	C₂³	1	2	yes	—
71	C₄×Dic₂₆	—	2	2	no	—
72	C₄×Dic₂₆	—	2	2	no	—
73	C₁₃×C₄⋊C₈	—	2	1	no	—
74	C₁₃×C₄⋊C₈	—	2	1	no	—
75	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₂²⋊C₈	—	2	1	no	—
78	C₁₃×C₂²⋊C₈	—	2	1	no	—
79	C₁₃×C₂²⋊C₈	—	2	1	no	—
80	C₄×C₈×C₁₃	—	2	1	no	—
81	C₄×C₈×C₁₃	—	2	1	no	—
82	C₄×C₈×C₁₃	—	2	1	no	—
83	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	#88075	—	2	2	no	—
88	#88075	—	2	2	no	—
89	#88072	—	2	2	no	—
90	#88072	—	2	2	no	—
91	#88058	—	2	1	no	—
92	#88058	—	2	1	no	—
93	#88056	—	2	2	no	—
94	#88056	—	2	2	no	—
95	#88048	—	2	2	no	—
96	#88048	—	2	2	no	—
97	#88047	—	2	2	no	—
98	#88047	—	2	2	no	—
99	C₄⋊#1055	—	2	2	no	—
100	C₄⋊#1055	C₂³	1	2	yes	—
101	C₄⋊#1055	C₂³	1	2	yes	—
102	#19126	—	13	1	no	maximal, Sylow
103	C₁₃×#41	—	2	2	no	—
104	C₁₃×#41	Q₁₆	1	4	yes	complemented
105	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂×Dic₂₆	—	2	2	no	—
115	C₂×Dic₂₆	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	4	1	no	—
120	C₂×C₈×C₁₃	—	4	2	no	—
121	C₂×C₈×C₁₃	—	4	2	no	—
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
130	C₁₃×C₂²⋊C₄	—	2	1	no	—
131	C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₄²×C₁₃	—	2	1	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	#41	1	1	yes	characteristic
139	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₂²⋊Dic₁₃	—	4	2	no	—
141	C₄⋊Dic₁₃	—	2	2	no	—
142	C₄⋊Dic₁₃	—	2	2	no	—
143	C₄⋊Dic₁₃	—	2	2	no	—
144	C₄⋊Dic₁₃	—	2	2	no	—
145	#6101	—	4	2	no	—
146	#6101	—	4	2	no	—
147	C₄×Dic₁₃	—	4	2	no	—
148	C₂×#1055	—	2	2	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	4	4	no	—
151	Dic₅₂	—	4	2	no	—
152	Dic₅₂	—	4	2	no	—
153	#3170	—	13	1	no	—
154	#3076	—	13	2	no	—
155	C₈×#41	D₁₃	1	1	yes	characteristic
156	#1684	—	13	2	no	—
157	#1683	—	13	2	no	—
158	#1676	—	13	1	no	—
159	#1675	—	13	1	no	—
160	#1670	—	13	1	no	—
161	#1669	—	13	1	no	—
162	C₂×#335	—	13	1	no	—
163	#1542	—	13	2	no	—
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	#121	1	1	yes	characteristic
166	Q₈×C₁₃	—	2	1	no	—
167	Q₈×C₁₃	C₂×Q₁₆	1	2	yes	—
168	D₄×C₁₃	—	2	4	no	—
169	D₄×C₁₃	—	2	1	no	—
170	D₄×C₁₃	C₂×Q₁₆	1	2	yes	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
185	C₂×C₄×C₁₃	#135	1	2	yes	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×Dic₁₃	—	4	2	no	—
190	C₂×Dic₁₃	—	4	2	no	—
191	Dic₂₆	—	4	2	no	—
192	Dic₂₆	—	4	2	no	—
193	Dic₂₆	—	8	2	no	—
194	C₈×C₁₃	—	2	1	no	—
195	C₈×C₁₃	—	2	1	no	—
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	4	1	no	—
198	C₈×C₁₃	—	4	1	no	—
199	C₈×C₁₃	#135	1	2	yes	—
200	#1055	—	4	2	no	—
201	#1055	—	4	2	no	—
202	#533	—	13	2	no	—
203	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
204	#500	—	13	1	no	—
205	#494	—	13	1	no	—
206	#487	—	13	2	no	—
207	#479	—	26	2	no	—
208	#478	—	26	2	no	—
209	#477	—	13	2	no	—
210	#476	—	13	2	no	—
211	#475	—	13	2	no	—
212	#474	—	13	2	no	—
213	#467	—	26	1	no	—
214	#467	—	26	1	no	—
215	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
216	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
217	C₄×Q₁₆	—	26	1	no	—
218	C₄×Q₁₆	—	26	1	no	—
219	C₈×D₄	—	2	1	no	—
220	C₈×D₄	—	2	1	no	—
221	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
222	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
223	#431	—	2	1	no	—
224	#431	C₂×D₁₃	1	1	yes	characteristic
225	#427	—	26	2	no	—
226	C₂×C₄⋊C₈	—	13	2	no	—
227	#416	—	26	2	no	—
228	C₂×C₄×C₈	—	2	1	no	—
229	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
230	#335	—	13	1	no	—
231	#335	—	13	1	no	—
232	#335	—	13	2	no	—
233	#333	—	13	2	no	—
234	#333	—	13	2	no	—
235	#332	—	13	2	no	—
236	#332	—	13	2	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	#467	1	2	yes	—
243	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	4	1	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	#467	1	2	yes	—
251	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
252	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
253	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
254	C₄×C₁₃	#575	1	1	yes	characteristic
255	Dic₁₃	—	8	2	no	—
256	Dic₁₃	—	8	2	no	—
257	C₂×#41	D₅₂	1	1	yes	characteristic
258	C₂×Q₁₆	—	26	1	no	—
259	C₂×Q₁₆	—	26	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	26	2	no	—
263	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
264	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
265	C₄⋊Q₈	—	13	2	no	—
266	C₄⋊Q₈	—	13	2	no	—
267	#125	—	26	2	no	—
268	C₂²⋊Q₈	—	26	2	no	—
269	C₂²⋊Q₈	—	26	2	no	—
270	C₄×Q₈	—	26	2	no	—
271	C₄×Q₈	—	26	2	no	—
272	C₄×Q₈	D₅₂	1	1	yes	characteristic
273	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	D₅₂	1	1	yes	characteristic
277	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
278	#117	—	2	1	no	—
279	#117	—	26	2	no	—
280	#117	D₅₂	1	1	yes	characteristic
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
283	#107	—	26	1	no	—
284	#107	—	26	1	no	—
285	#107	—	26	2	no	—
286	#107	—	26	2	no	—
287	#106	—	26	2	no	—
288	#106	—	26	2	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	13	2	no	—
292	C₄⋊C₈	—	13	2	no	—
293	C₄⋊C₈	—	26	2	no	—
294	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
295	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
296	#103	—	26	2	no	—
297	#103	—	26	2	no	—
298	#103	—	26	2	no	—
299	#103	—	26	2	no	—
300	#102	—	26	2	no	—
301	#102	—	26	2	no	—
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
309	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
312	C₂×C₁₃	—	2	2	no	—
313	C₂×C₁₃	—	4	2	no	—
314	C₂×C₁₃	#3035	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#467	1	1	yes	characteristic
316	C₂×C₁₃	#3067	1	1	yes	characteristic
317	#41	—	2	2	no	—
318	#41	Dic₅₂	1	4	yes	complemented
319	C₂×Q₈	—	26	2	no	—
320	C₂×Q₈	—	26	2	no	—
321	C₂×Q₈	C₂×D₅₂	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
328	C₂²×C₄	#6127	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
330	Q₁₆	—	52	2	no	—
331	Q₁₆	—	52	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	26	2	no	—
339	C₂×C₈	—	26	2	no	—
340	C₂×C₈	—	52	4	no	—
341	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	26	2	no	—
348	C₄⋊C₄	—	26	2	no	—
349	C₄⋊C₄	—	26	2	no	—
350	C₄⋊C₄	—	26	2	no	—
351	C₄⋊C₄	—	52	2	no	—
352	C₄⋊C₄	—	52	2	no	—
353	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
354	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	52	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	52	2	no	—
363	C₄²	C₂×D₅₂	1	1	yes	characteristic
364	C₄²	#6127	1	1	yes	characteristic
365	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
366	C₄²	C₂³×D₁₃	1	1	yes	characteristic
367	C₁₃	#19126	1	1	yes	characteristic, complemented, Sylow
368	C₂³	—	2	1	no	—
369	C₂³	#88184	1	1	yes	characteristic
370	Q₈	—	2	1	no	—
371	Q₈	—	52	2	no	—
372	Q₈	—	52	2	no	—
373	Q₈	—	104	2	no	—
374	Q₈	C₂×Dic₅₂	1	2	yes	—
375	D₄	—	2	4	no	—
376	D₄	—	2	1	no	—
377	D₄	C₂×Dic₅₂	1	2	yes	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	52	2	no	—
389	C₂×C₄	—	52	2	no	—
390	C₂×C₄	#88158	1	2	yes	—
391	C₂×C₄	C₂×Dic₅₂	1	2	yes	—
392	C₂×C₄	#88184	1	1	yes	characteristic
393	C₂×C₄	#88184	1	1	yes	characteristic
394	C₂×C₄	#88184	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
396	C₂×C₄	C₂×#6127	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	4	1	no	—
402	C₈	—	4	1	no	—
403	C₈	—	52	2	no	—
404	C₈	—	52	2	no	—
405	C₈	#88204	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	#11718777	1	2	yes	—
412	C₂²	C₂×#88184	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	104	2	no	—
420	C₄	—	104	2	no	—
421	C₄	#11718777	1	2	yes	—
422	C₄	C₂×#88158	1	1	yes	characteristic
423	C₄	C₂²×Dic₅₂	1	1	yes	characteristic
424	C₄	C₂×#88204	1	1	yes	characteristic
425	C₄	#11719527	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	4	2	no	—
428	C₂	#13124291	1	1	yes	characteristic
429	C₂	C₂×#11718777	1	1	yes	characteristic
430	C₂	#13124556	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88184
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×#41	C₂
socle	C₂²×C₁₃	C₂×#121
prime radical	C₂×C₁₃×#41	D₄
hypercenter	C₈×#41	D₁₃
hypocenter	C₁₃	#19126
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #13125422	C₂	semidirect
3. #13114294	C₂	semidirect
4. #13114287	C₂	semidirect
5. #13114240	C₂	semidirect
6. #13114235	C₂	semidirect
7. #13114206	C₂	semidirect
8. #13114201	C₂	semidirect
9. C₂×#11718050	C₂	semidirect
10. #13113491	C₂	semidirect
104. C₁₃×#41	Q₁₆	semidirect
318. #41	Dic₅₂	semidirect
367. C₁₃	#19126	semidirect

Maximal subgroups

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

subgroup	index
#13125422	2
#13124624	2
#13114294	2
#13114287	2
#13114240	2
#13114235	2
#13114206	2
#13114201	2
C₂×#11718050	2
#13113491	2
C₈×C₁₃×#41	2
#19126	13