Subgroups — #15831279

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719175	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718586	C₂	1	1	yes	maximal, characteristic
3	#13113527	C₂	1	4	yes	maximal, complemented
4	#13113522	C₂	1	2	yes	maximal, complemented
5	#13113518	C₂	1	2	yes	maximal, complemented
6	#13113494	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₁₃×M₁₆	—	2	1	no	—
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88180	—	2	1	no	—
11	C₂×#88178	—	2	1	no	—
12	C₂×#88178	C₄	1	2	yes	—
13	#11719175	—	2	1	no	—
14	#11719175	—	2	1	no	—
15	#11719175	—	2	1	no	—
16	#11719175	—	2	1	no	—
17	#11719175	C₄	1	2	yes	—
18	#11719175	C₄	1	2	yes	—
19	#11719175	C₂²	1	2	yes	—
20	#11719175	C₂²	1	2	yes	—
21	C₂×#88124	—	2	1	no	—
22	C₂×#88123	C₂²	1	1	yes	characteristic
23	C₂×#88123	C₂²	1	1	yes	characteristic
24	C₂×C₄×Dic₂₆	—	2	1	no	—
25	C₂×C₄×Dic₂₆	C₄	1	2	yes	—
26	C₁₃×#423	—	2	1	no	—
27	C₁₃×#423	—	2	1	no	—
28	C₁₃×#423	C₂²	1	2	yes	—
29	C₁₃×#423	C₂²	1	2	yes	—
30	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
32	C₂×C₂²⋊#1055	—	2	1	no	—
33	#11718586	—	2	1	no	—
34	#11718586	—	2	1	no	—
35	#11718586	C₂²	1	2	yes	—
36	#11718586	C₂²	1	2	yes	—
37	C₂×C₄⋊#1055	C₂²	1	2	yes	—
38	C₂×C₄×#1055	—	2	1	no	—
39	#11718078	C₂²	1	8	yes	complemented
40	#11718073	C₂²	1	8	yes	complemented
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂²×Dic₂₆	—	2	1	no	—
45	C₂²×Dic₂₆	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×M₁₆	—	2	2	no	—
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	4	4	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
63	#88180	—	2	2	no	—
64	#88180	—	2	2	no	—
65	#88180	—	2	2	no	—
66	#88180	—	2	2	no	—
67	C₂×C₄⋊Dic₁₃	—	2	1	no	—
68	C₂×C₄⋊Dic₁₃	—	2	1	no	—
69	C₂×C₄⋊Dic₁₃	—	2	1	no	—
70	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
71	#88178	—	2	2	no	—
72	#88178	—	2	2	no	—
73	#88178	—	2	2	no	—
74	#88178	—	2	2	no	—
75	#88178	—	2	2	no	—
76	#88178	—	2	2	no	—
77	#88178	C₂×C₄	1	4	yes	—
78	#88178	C₂×C₄	1	4	yes	—
79	C₂×#6101	—	2	2	no	—
80	C₂×#6101	—	2	2	no	—
81	C₂×C₄×Dic₁₃	—	2	2	no	—
82	C₂²×#1055	—	2	2	no	—
83	#88124	—	2	2	no	—
84	#88124	—	2	2	no	—
85	#88124	—	2	2	no	—
86	#88124	—	2	2	no	—
87	#88123	—	2	1	no	—
88	#88123	—	2	1	no	—
89	#88123	—	2	1	no	—
90	#88123	—	2	1	no	—
91	#88123	C₂×C₄	1	2	yes	—
92	#88123	C₂×C₄	1	2	yes	—
93	#88123	C₂³	1	2	yes	—
94	#88123	C₂³	1	2	yes	—
95	C₄×Dic₂₆	—	2	2	no	—
96	C₄×Dic₂₆	—	2	2	no	—
97	C₄×Dic₂₆	—	2	2	no	—
98	C₄×Dic₂₆	—	2	2	no	—
99	C₄×Dic₂₆	—	2	2	no	—
100	C₄×Dic₂₆	—	2	2	no	—
101	C₄×Dic₂₆	C₂×C₄	1	4	yes	—
102	C₄×Dic₂₆	C₂×C₄	1	4	yes	—
103	C₁₃×C₄⋊C₈	—	2	2	no	—
104	C₁₃×C₄⋊C₈	—	2	2	no	—
105	C₁₃×C₄⋊C₈	—	2	2	no	—
106	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
107	C₂²⋊#1055	—	2	2	no	—
108	C₂²⋊#1055	—	2	2	no	—
109	C₄⋊#1055	—	2	2	no	—
110	C₄⋊#1055	C₂³	1	4	yes	—
111	C₄×#1055	—	2	2	no	—
112	C₄×#1055	—	2	2	no	—
113	#17708	—	13	1	no	maximal, Sylow
114	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
127	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×Dic₁₃	—	2	2	no	—
138	C₂²×Dic₁₃	—	2	2	no	—
139	C₂×Dic₂₆	—	2	2	no	—
140	C₂×Dic₂₆	—	2	2	no	—
141	C₂×Dic₂₆	—	2	2	no	—
142	C₂×Dic₂₆	—	4	4	no	—
143	C₂×Dic₂₆	—	4	4	no	—
144	C₂×Dic₂₆	C₂²×C₄	1	4	yes	—
145	C₁₃×M₁₆	—	4	4	no	—
146	C₁₃×M₁₆	—	4	4	no	—
147	C₂×C₈×C₁₃	—	2	4	no	—
148	C₂×C₈×C₁₃	—	4	4	no	—
149	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂²⋊Dic₁₃	—	2	4	no	—
166	C₂²⋊Dic₁₃	—	2	4	no	—
167	C₄⋊Dic₁₃	—	2	2	no	—
168	C₄⋊Dic₁₃	—	2	2	no	—
169	C₄⋊Dic₁₃	—	2	2	no	—
170	C₄⋊Dic₁₃	—	2	2	no	—
171	C₄⋊Dic₁₃	—	2	2	no	—
172	C₄⋊Dic₁₃	—	2	2	no	—
173	C₄⋊Dic₁₃	—	2	2	no	—
174	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
175	#6101	—	2	4	no	—
176	#6101	—	2	4	no	—
177	#6101	—	2	4	no	—
178	#6101	—	2	4	no	—
179	C₄×Dic₁₃	—	2	4	no	—
180	C₄×Dic₁₃	—	2	4	no	—
181	C₂×#1055	—	2	4	no	—
182	C₂×#1055	—	4	4	no	—
183	C₂×#533	—	13	1	no	—
184	C₂×#431	—	13	1	no	—
185	C₂×#423	D₁₃	1	1	yes	characteristic
186	#1550	—	13	4	no	—
187	#1549	—	13	2	no	—
188	#1548	—	13	2	no	—
189	#1542	—	13	4	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	#103	1	4	yes	—
193	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	#103	1	4	yes	—
209	C₂×C₄×C₁₃	#103	1	4	yes	—
210	C₂×C₄×C₁₃	#103	1	4	yes	—
211	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
221	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
222	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
223	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
224	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
225	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
226	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×Dic₁₃	—	2	4	no	—
230	C₂×Dic₁₃	—	2	4	no	—
231	C₂×Dic₁₃	—	4	4	no	—
232	C₂×Dic₁₃	—	4	4	no	—
233	Dic₂₆	—	4	4	no	—
234	Dic₂₆	—	4	4	no	—
235	Dic₂₆	—	4	4	no	—
236	Dic₂₆	—	4	4	no	—
237	C₈×C₁₃	—	4	4	no	—
238	#1055	—	4	4	no	—
239	C₂²×M₁₆	—	2	1	no	—
240	#533	—	13	2	no	—
241	#533	—	13	2	no	—
242	#533	—	13	2	no	—
243	#533	—	13	2	no	—
244	#533	—	26	1	no	—
245	#533	—	26	1	no	—
246	#533	—	26	1	no	—
247	#533	—	26	1	no	—
248	C₂×C₄⋊Q₈	—	13	1	no	—
249	C₂×C₄⋊Q₈	—	13	1	no	—
250	C₂×#125	—	26	1	no	—
251	C₂×C₂²⋊Q₈	—	13	2	no	—
252	C₂×C₂²⋊Q₈	—	26	1	no	—
253	C₂×C₄×Q₈	—	13	2	no	—
254	C₂×C₄×Q₈	—	26	1	no	—
255	C₂×#117	—	26	1	no	—
256	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
257	#431	—	13	2	no	—
258	#431	—	13	2	no	—
259	#431	—	26	1	no	—
260	#431	—	26	1	no	—
261	#423	—	2	1	no	—
262	#423	—	2	1	no	—
263	#423	C₂×D₁₃	1	2	yes	—
264	#423	C₂×D₁₃	1	2	yes	—
265	C₂×C₄⋊C₈	—	2	1	no	—
266	C₂×C₄⋊C₈	—	13	2	no	—
267	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
268	C₂×C₂²⋊C₈	—	26	1	no	—
269	C₂×C₄×C₈	—	26	1	no	—
270	#333	—	13	8	no	—
271	#332	—	13	8	no	—
272	C₂²×C₁₃	—	2	1	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	—	2	1	no	—
276	C₂²×C₁₃	—	2	1	no	—
277	C₂²×C₁₃	—	2	1	no	—
278	C₂²×C₁₃	—	4	4	no	—
279	C₂²×C₁₃	C₂×#103	1	2	yes	—
280	C₂²×C₁₃	C₂×#103	1	2	yes	—
281	C₂²×C₁₃	C₂×#103	1	2	yes	—
282	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	—	2	1	no	—
287	C₄×C₁₃	—	2	1	no	—
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	#413	1	2	yes	—
290	C₄×C₁₃	C₂×#103	1	2	yes	—
291	C₄×C₁₃	C₂×#103	1	2	yes	—
292	C₄×C₁₃	C₂×#103	1	2	yes	—
293	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
294	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
295	C₄×C₁₃	#575	1	2	yes	—
296	Dic₁₃	—	4	4	no	—
297	Dic₁₃	—	4	4	no	—
298	C₂²×Q₈	—	13	2	no	—
299	C₂²×Q₈	—	26	1	no	—
300	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
301	C₂³×C₄	D₅₂	1	1	yes	characteristic
302	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	4	4	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	26	2	no	—
308	C₄⋊Q₈	—	13	2	no	—
309	C₄⋊Q₈	—	13	2	no	—
310	C₄⋊Q₈	—	13	2	no	—
311	C₄⋊Q₈	—	13	2	no	—
312	C₄⋊Q₈	—	26	1	no	—
313	C₄⋊Q₈	—	26	1	no	—
314	C₄⋊Q₈	—	26	1	no	—
315	C₄⋊Q₈	—	26	1	no	—
316	#125	—	26	2	no	—
317	#125	—	26	2	no	—
318	#125	—	26	2	no	—
319	#125	—	26	2	no	—
320	C₂²⋊Q₈	—	13	4	no	—
321	C₂²⋊Q₈	—	13	4	no	—
322	C₂²⋊Q₈	—	26	2	no	—
323	C₂²⋊Q₈	—	26	2	no	—
324	C₂²⋊Q₈	—	26	2	no	—
325	C₂²⋊Q₈	—	26	2	no	—
326	C₂²⋊Q₈	—	26	2	no	—
327	C₂²⋊Q₈	—	26	2	no	—
328	C₄×Q₈	—	13	4	no	—
329	C₄×Q₈	—	13	4	no	—
330	C₄×Q₈	—	26	2	no	—
331	C₄×Q₈	—	26	2	no	—
332	C₄×Q₈	—	26	2	no	—
333	C₄×Q₈	—	26	2	no	—
334	C₄×Q₈	—	26	2	no	—
335	C₄×Q₈	—	26	2	no	—
336	#117	—	26	2	no	—
337	#117	—	26	2	no	—
338	#117	—	26	2	no	—
339	#117	—	26	2	no	—
340	C₂×C₄⋊C₄	—	13	2	no	—
341	C₂×C₄⋊C₄	—	26	2	no	—
342	C₂×C₄⋊C₄	—	26	2	no	—
343	C₂×C₄⋊C₄	—	26	1	no	—
344	C₂×C₄⋊C₄	—	26	1	no	—
345	C₂×C₄⋊C₄	—	26	1	no	—
346	C₂×C₂²⋊C₄	—	26	2	no	—
347	C₂×C₄²	—	26	2	no	—
348	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
349	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
350	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
351	C₂×C₄²	D₅₂	1	1	yes	characteristic
352	C₂×C₄²	D₅₂	1	1	yes	characteristic
353	C₂×C₄²	D₅₂	1	1	yes	characteristic
354	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
355	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
356	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
358	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
359	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
360	C₄⋊C₈	—	2	2	no	—
361	C₄⋊C₈	—	2	2	no	—
362	C₄⋊C₈	—	2	2	no	—
363	C₄⋊C₈	—	13	4	no	—
364	C₄⋊C₈	—	26	2	no	—
365	C₄⋊C₈	C₂²×D₁₃	1	4	yes	—
366	C₂²⋊C₈	—	26	2	no	—
367	C₂²⋊C₈	—	26	2	no	—
368	C₄×C₈	—	26	2	no	—
369	C₄×C₈	—	26	2	no	—
370	C₂×C₁₃	—	2	2	no	—
371	C₂×C₁₃	—	2	2	no	—
372	C₂×C₁₃	—	2	2	no	—
373	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
374	C₂×C₁₃	C₂²×#103	1	1	yes	characteristic
375	C₂×C₁₃	#2896	1	1	yes	characteristic
376	C₂⁴	#6103	1	1	yes	characteristic
377	C₂×Q₈	—	13	4	no	—
378	C₂×Q₈	—	26	2	no	—
379	C₂×Q₈	—	26	2	no	—
380	C₂×Q₈	—	26	2	no	—
381	C₂×Q₈	—	52	4	no	—
382	C₂×Q₈	—	52	4	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	26	2	no	—
386	C₂²×C₄	—	26	2	no	—
387	C₂²×C₄	#6103	1	1	yes	characteristic
388	C₂²×C₄	#6103	1	1	yes	characteristic
389	C₂²×C₄	#6103	1	1	yes	characteristic
390	C₂²×C₄	#6103	1	1	yes	characteristic
391	C₂²×C₄	#6103	1	1	yes	characteristic
392	C₂²×C₄	#6103	1	1	yes	characteristic
393	C₂²×C₄	#6103	1	1	yes	characteristic
394	C₂²×C₄	#6103	1	1	yes	characteristic
395	C₂²×C₄	#6103	1	1	yes	characteristic
396	C₂²×C₄	#6105	1	4	yes	—
397	C₂²×C₄	#6107	1	4	yes	—
398	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
407	M₁₆	—	4	4	no	—
408	M₁₆	—	4	4	no	—
409	C₂×C₈	—	2	4	no	—
410	C₂×C₈	—	4	4	no	—
411	C₂×C₈	—	26	4	no	—
412	C₂×C₈	—	52	4	no	—
413	C₄⋊C₄	—	13	4	no	—
414	C₄⋊C₄	—	26	2	no	—
415	C₄⋊C₄	—	26	2	no	—
416	C₄⋊C₄	—	26	2	no	—
417	C₄⋊C₄	—	26	4	no	—
418	C₄⋊C₄	—	26	4	no	—
419	C₄⋊C₄	—	26	4	no	—
420	C₄⋊C₄	—	26	4	no	—
421	C₄⋊C₄	—	26	2	no	—
422	C₄⋊C₄	—	26	2	no	—
423	C₄⋊C₄	—	26	2	no	—
424	C₄⋊C₄	—	26	2	no	—
425	C₂²⋊C₄	—	26	4	no	—
426	C₂²⋊C₄	—	26	4	no	—
427	C₄²	—	26	4	no	—
428	C₄²	—	26	4	no	—
429	C₄²	#6103	1	1	yes	characteristic
430	C₄²	#6103	1	1	yes	characteristic
431	C₄²	#6103	1	1	yes	characteristic
432	C₄²	#6103	1	1	yes	characteristic
433	C₄²	#6103	1	1	yes	characteristic
434	C₄²	#6103	1	1	yes	characteristic
435	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
436	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
437	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
438	C₄²	C₂×D₅₂	1	1	yes	characteristic
439	C₄²	C₂×D₅₂	1	1	yes	characteristic
440	C₄²	C₂×D₅₂	1	1	yes	characteristic
441	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
442	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
443	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
444	C₄²	C₂³×D₁₃	1	1	yes	characteristic
445	C₁₃	#17708	1	1	yes	characteristic, complemented, Sylow
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	#88050	1	4	yes	—
449	C₂³	C₂×#6103	1	1	yes	characteristic
450	C₂³	C₂×#6103	1	1	yes	characteristic
451	C₂³	C₂×#6103	1	1	yes	characteristic
452	Q₈	—	52	4	no	—
453	Q₈	—	52	4	no	—
454	Q₈	—	52	4	no	—
455	Q₈	—	52	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	26	4	no	—
469	C₂×C₄	—	26	4	no	—
470	C₂×C₄	—	52	4	no	—
471	C₂×C₄	—	52	4	no	—
472	C₂×C₄	#88050	1	4	yes	—
473	C₂×C₄	#88050	1	4	yes	—
474	C₂×C₄	#88050	1	4	yes	—
475	C₂×C₄	C₂×#6103	1	1	yes	characteristic
476	C₂×C₄	C₂×#6103	1	1	yes	characteristic
477	C₂×C₄	C₂×#6103	1	1	yes	characteristic
478	C₂×C₄	C₂×#6103	1	1	yes	characteristic
479	C₂×C₄	C₂×#6103	1	1	yes	characteristic
480	C₂×C₄	C₂×#6103	1	1	yes	characteristic
481	C₂×C₄	C₂×#6103	1	1	yes	characteristic
482	C₂×C₄	C₂×#6103	1	1	yes	characteristic
483	C₂×C₄	C₂×#6103	1	1	yes	characteristic
484	C₂×C₄	C₂×#6105	1	2	yes	—
485	C₂×C₄	C₂×#6105	1	2	yes	—
486	C₂×C₄	C₂×#6105	1	2	yes	—
487	C₂×C₄	C₂×#6107	1	2	yes	—
488	C₂×C₄	C₂×#6107	1	2	yes	—
489	C₂×C₄	C₂×#6107	1	2	yes	—
490	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
492	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
493	C₈	—	4	4	no	—
494	C₈	—	52	4	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	4	4	no	—
502	C₂²	C₂×#88050	1	2	yes	—
503	C₂²	C₂×#88050	1	2	yes	—
504	C₂²	C₂×#88050	1	2	yes	—
505	C₂²	C₂²×#6103	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	52	4	no	—
513	C₄	—	52	4	no	—
514	C₄	C₂×#88050	1	2	yes	—
515	C₄	C₂×#88050	1	2	yes	—
516	C₄	C₂×#88050	1	2	yes	—
517	C₄	#11718793	1	2	yes	—
518	C₄	#11719453	1	2	yes	—
519	C₄	C₂²×#6105	1	1	yes	characteristic
520	C₄	C₂²×#6107	1	1	yes	characteristic
521	C₂	—	2	2	no	—
522	C₂	—	2	2	no	—
523	C₂	—	2	2	no	—
524	C₂	C₂×#11718793	1	1	yes	characteristic
525	C₂	C₂²×#88050	1	1	yes	characteristic
526	C₂	#13123356	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#6103
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#423	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#423	D₁₃
hypocenter	C₁₃	#17708
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #13113527	C₂	semidirect
4. #13113522	C₂	semidirect
5. #13113518	C₂	semidirect
6. #13113494	C₂	semidirect
39. #11718078	C₂²	semidirect
40. #11718073	C₂²	semidirect
445. C₁₃	#17708	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719175	2
C₂×#11718586	2
#13113527	2
#13113522	2
#13113518	2
#13113494	2
C₂×C₁₃×#423	2
#17708	13