Subgroups — C₄×#11718668 #15870481

Order 3328.

1000 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718668	C₂	1	1	yes	maximal, characteristic
2	C₄×#88123	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115788	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115594	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115407	C₂	1	2	yes	maximal, complemented
6	#13115083	C₂	1	2	yes	maximal
7	#13114836	C₂	1	1	yes	maximal, characteristic
8	C₄×#88047	C₂	1	2	yes	maximal, complemented
9	C₄×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88072	C₂	1	2	yes	maximal
11	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	—	2	1	no	—
16	C₂×#88123	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₂₆	—	2	1	no	—
18	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
22	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
23	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
24	C₄³×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×#88072	C₂²	1	2	yes	—
26	C₂×#88072	C₂²	1	2	yes	—
27	#11718668	C₄	1	8	yes	direct product factor
28	C₂×#88047	C₂²	1	2	yes	—
29	C₂×#88047	C₂²	1	2	yes	—
30	#11718596	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₁₃	—	2	1	no	—
32	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
33	#11718590	—	2	1	no	—
34	#11718589	—	2	1	no	—
35	#11718589	C₂²	1	2	yes	—
36	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
38	C₂×C₄×#1055	C₂²	1	2	yes	—
39	#11718121	C₂²	1	2	yes	—
40	#11718121	C₂²	1	2	yes	—
41	#11718121	C₂²	1	2	yes	—
42	#11718121	C₂²	1	2	yes	—
43	#11718116	C₂²	1	2	yes	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂²×Dic₂₆	—	2	1	no	—
49	C₄×D₄×C₁₃	—	2	2	no	—
50	C₄×D₄×C₁₃	—	2	2	no	—
51	C₄×D₄×C₁₃	—	2	2	no	—
52	C₄×D₄×C₁₃	—	2	2	no	—
53	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
54	C₄×D₄×C₁₃	Q₈	1	4	yes	complemented
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	—	2	1	no	—
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	—	4	4	no	—
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊Dic₁₃	—	2	1	no	—
73	C₂×C₄⋊Dic₁₃	—	2	1	no	—
74	C₂×C₄⋊Dic₁₃	—	2	1	no	—
75	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
76	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
77	C₂×#6101	—	2	2	no	—
78	C₂×C₄×Dic₁₃	—	2	2	no	—
79	C₂²×#1055	C₂³	1	2	yes	—
80	C₂²×#1055	C₂³	1	2	yes	—
81	#88123	—	2	2	no	—
82	#88123	C₂×C₄	1	4	yes	complemented
83	C₄×Dic₂₆	—	4	4	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	1	no	—
87	#88072	—	2	4	no	—
88	#88072	C₂×C₄	1	8	yes	—
89	#88071	—	2	2	no	—
90	#88071	—	2	2	no	—
91	#88047	—	2	4	no	—
92	#88047	C₂×C₄	1	8	yes	complemented
93	C₄⋊#1055	—	2	2	no	—
94	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
95	C₄×#1055	—	2	4	no	—
96	C₄×#474	—	13	1	no	maximal, Sylow
97	C₂⁴×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
103	C₂×D₄×C₁₃	#41	1	2	yes	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂²×Dic₁₃	—	2	2	no	—
124	C₂²×Dic₁₃	—	2	2	no	—
125	C₂×Dic₂₆	—	2	4	no	—
126	C₂×Dic₂₆	—	4	2	no	—
127	C₂×Dic₂₆	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
132	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
133	C₁₃×C₄⋊C₄	#41	1	2	yes	—
134	C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₁₃×C₂²⋊C₄	—	2	4	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	1	no	—
140	C₄²×C₁₃	—	2	1	no	—
141	C₄²×C₁₃	—	4	1	no	—
142	C₄²×C₁₃	—	4	2	no	—
143	C₄²×C₁₃	—	4	2	no	—
144	C₄²×C₁₃	—	4	2	no	—
145	C₄²×C₁₃	D₈	1	4	yes	—
146	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
147	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
148	C₄²×C₁₃	#41	1	2	yes	—
149	C₄²×C₁₃	#41	1	2	yes	—
150	C₄⋊Dic₁₃	—	2	4	no	—
151	C₄⋊Dic₁₃	—	2	2	no	—
152	C₄⋊Dic₁₃	—	2	2	no	—
153	C₄⋊Dic₁₃	—	2	2	no	—
154	C₄⋊Dic₁₃	—	4	2	no	—
155	C₄⋊Dic₁₃	—	4	2	no	—
156	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
157	#6101	—	4	4	no	—
158	C₄×Dic₁₃	—	4	4	no	—
159	C₂×#1055	—	2	2	no	—
160	C₂×#1055	—	2	2	no	—
161	C₂×#1055	—	2	2	no	—
162	C₂×#1055	—	2	2	no	—
163	C₂×#1055	—	2	2	no	—
164	C₂×#1055	C₂²×C₄	1	4	yes	—
165	C₂×#474	—	13	1	no	—
166	C₄×C₄⋊Q₈	—	13	1	no	—
167	C₄²×D₄	D₁₃	1	1	yes	characteristic
168	#1988	—	13	1	no	—
169	#1947	—	13	1	no	—
170	#1918	—	13	2	no	—
171	#1862	—	13	2	no	—
172	#1802	—	13	1	no	—
173	C₄×#107	—	13	2	no	—
174	C₄×C₄⋊C₈	—	13	1	no	—
175	C₄×#102	—	13	2	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	2	2	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	C₄×Q₈	1	4	yes	complemented
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	4	8	no	—
201	C₂×C₄×C₁₃	—	4	1	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	8	no	—
208	C₂×C₄×C₁₃	—	4	8	no	—
209	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
212	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
213	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
214	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
215	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
216	C₂×C₄×C₁₃	#135	1	2	yes	—
217	C₂×C₄×C₁₃	#137	1	2	yes	—
218	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×Dic₁₃	—	2	4	no	—
225	C₂×Dic₁₃	—	4	2	no	—
226	C₂×Dic₁₃	—	4	2	no	—
227	C₂×Dic₁₃	—	4	2	no	—
228	C₂×Dic₁₃	—	4	2	no	—
229	C₂×Dic₁₃	—	4	2	no	—
230	Dic₂₆	—	4	8	no	—
231	#1055	—	2	4	no	—
232	#1055	—	4	2	no	—
233	C₂×C₄⋊Q₈	—	13	1	no	—
234	C₂×C₄×Q₈	—	26	1	no	—
235	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
238	C₂²×C₄²	—	2	1	no	—
239	#474	—	13	8	no	—
240	C₂×#107	—	13	2	no	—
241	C₂×#107	—	13	2	no	—
242	C₂×C₄⋊C₈	—	13	1	no	—
243	C₂×C₄⋊C₈	—	13	1	no	—
244	C₂×#102	—	13	2	no	—
245	C₂×#102	—	13	2	no	—
246	C₂×C₄×C₈	—	13	2	no	—
247	#391	—	26	1	no	—
248	#389	—	13	2	no	—
249	#389	—	26	1	no	—
250	#384	—	13	1	no	—
251	C₄×C₄⋊C₄	—	13	2	no	—
252	C₄×C₄⋊C₄	—	26	1	no	—
253	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
254	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
256	C₄×C₂²⋊C₄	—	2	1	no	—
257	C₄×C₂²⋊C₄	—	2	1	no	—
258	C₄×C₂²⋊C₄	—	2	1	no	—
259	C₄³	C₂×D₁₃	1	1	yes	characteristic
260	#340	—	13	2	no	—
261	#340	—	13	2	no	—
262	#340	—	13	2	no	—
263	#340	—	13	2	no	—
264	#336	—	13	2	no	—
265	C₂²×C₁₃	—	2	4	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
274	C₂²×C₁₃	#525	1	1	yes	characteristic
275	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
276	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
277	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
278	C₂²×C₁₃	#575	1	1	yes	characteristic
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	1	no	—
284	C₄×C₁₃	—	4	2	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	C₄×D₈	1	4	yes	—
287	C₄×C₁₃	#474	1	4	yes	complemented
288	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
289	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
290	C₄×C₁₃	#529	1	1	yes	characteristic
291	C₄×C₁₃	#533	1	1	yes	characteristic
292	Dic₁₃	—	4	4	no	—
293	Dic₁₃	—	8	2	no	—
294	C₂²×Q₈	—	26	1	no	—
295	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	—	2	1	no	—
299	C₂²×C₈	—	13	2	no	—
300	C₂²×C₈	—	13	2	no	—
301	C₄⋊Q₈	—	13	4	no	—
302	C₄⋊Q₈	—	26	2	no	—
303	C₄×Q₈	—	52	4	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	Dic₂₆	1	4	yes	complemented
309	C₄×D₄	C₄×D₁₃	1	4	yes	—
310	C₂×C₄⋊C₄	—	13	2	no	—
311	C₂×C₄⋊C₄	—	13	2	no	—
312	C₂×C₄⋊C₄	—	26	1	no	—
313	C₂×C₄⋊C₄	—	26	2	no	—
314	C₂×C₄⋊C₄	—	26	1	no	—
315	C₂×C₄⋊C₄	—	26	1	no	—
316	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	4	4	no	—
326	C₂×C₄²	—	26	2	no	—
327	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
328	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
329	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
330	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
331	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
332	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
334	#107	—	13	8	no	—
335	#107	—	26	4	no	—
336	C₄⋊C₈	—	13	4	no	—
337	C₄⋊C₈	—	26	2	no	—
338	#102	—	13	8	no	—
339	#102	—	26	4	no	—
340	C₄×C₈	—	26	4	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	#95	—	2	1	no	—
344	#95	—	26	2	no	—
345	#95	—	26	2	no	—
346	C₂×C₁₃	—	4	4	no	—
347	C₂×C₁₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
348	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
349	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
350	C₂×C₁₃	C₂×#474	1	1	yes	characteristic
351	C₂×C₁₃	#3076	1	1	yes	characteristic
352	C₂×C₁₃	#3100	1	1	yes	characteristic
353	C₂×C₁₃	#3107	1	1	yes	characteristic
354	C₂⁴	—	2	1	no	—
355	C₂×Q₈	—	26	4	no	—
356	C₂×Q₈	—	52	2	no	—
357	C₂×Q₈	—	52	2	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	C₂×Dic₂₆	1	2	yes	—
362	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
363	C₂×D₄	#6127	1	2	yes	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	26	2	no	—
377	C₂²×C₄	—	26	2	no	—
378	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
385	C₂×C₈	—	13	4	no	—
386	C₂×C₈	—	26	2	no	—
387	C₂×C₈	—	26	2	no	—
388	C₂×C₈	—	26	2	no	—
389	C₂×C₈	—	26	2	no	—
390	C₂×C₈	—	26	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	13	4	no	—
395	C₄⋊C₄	—	26	4	no	—
396	C₄⋊C₄	—	26	2	no	—
397	C₄⋊C₄	—	26	2	no	—
398	C₄⋊C₄	—	26	2	no	—
399	C₄⋊C₄	—	52	2	no	—
400	C₄⋊C₄	—	52	4	no	—
401	C₄⋊C₄	—	52	2	no	—
402	C₄⋊C₄	C₂×Dic₂₆	1	2	yes	—
403	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
404	C₄⋊C₄	#6127	1	2	yes	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	4	1	no	—
413	C₄²	—	4	2	no	—
414	C₄²	—	4	2	no	—
415	C₄²	—	4	2	no	—
416	C₄²	—	52	4	no	—
417	C₄²	#6104	1	4	yes	—
418	C₄²	C₂×Dic₂₆	1	2	yes	—
419	C₄²	C₂×C₄×D₁₃	1	2	yes	—
420	C₄²	#6127	1	2	yes	—
421	C₄²	#6127	1	2	yes	—
422	C₁₃	C₄×#474	1	1	yes	characteristic, complemented, Sylow
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
431	Q₈	—	52	8	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	2	no	—
434	D₄	—	2	2	no	—
435	D₄	C₄×Dic₂₆	1	4	yes	complemented
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	26	4	no	—
458	C₂×C₄	—	52	2	no	—
459	C₂×C₄	—	52	2	no	—
460	C₂×C₄	—	52	2	no	—
461	C₂×C₄	—	52	2	no	—
462	C₂×C₄	—	52	2	no	—
463	C₂×C₄	#88178	1	2	yes	—
464	C₂×C₄	#88178	1	2	yes	—
465	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
466	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
467	C₂×C₄	C₂×#6104	1	2	yes	—
468	C₂×C₄	C₂×#6104	1	2	yes	—
469	C₂×C₄	C₂×#6104	1	2	yes	—
470	C₂×C₄	#88204	1	2	yes	—
471	C₂×C₄	#88205	1	2	yes	—
472	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
473	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
474	C₂×C₄	C₂×#6127	1	1	yes	characteristic
475	C₂×C₄	C₂×#6127	1	1	yes	characteristic
476	C₂×C₄	C₂×#6127	1	1	yes	characteristic
477	C₂×C₄	C₂×#6127	1	1	yes	characteristic
478	C₈	—	26	4	no	—
479	C₈	—	52	2	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂×#88178	1	1	yes	characteristic
488	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
489	C₂²	#11719496	1	1	yes	characteristic
490	C₂²	C₂²×#6104	1	1	yes	characteristic
491	C₂²	C₂×#88204	1	1	yes	characteristic
492	C₂²	#11719527	1	1	yes	characteristic
493	C₂²	C₂×#88205	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	52	4	no	—
502	C₄	—	104	2	no	—
503	C₄	#11718668	1	4	yes	direct product factor
504	C₄	C₄×#6104	1	4	yes	—
505	C₄	C₂×C₄×Dic₂₆	1	1	yes	characteristic
506	C₄	#11719175	1	1	yes	characteristic
507	C₄	C₄×#6127	1	1	yes	characteristic
508	C₄	#11719184	1	1	yes	characteristic
509	C₂	—	4	4	no	—
510	C₂	C₄×#88178	1	1	yes	characteristic
511	C₂	C₂×C₄×#6104	1	1	yes	characteristic
512	C₂	C₄×#88205	1	1	yes	characteristic
513	C₂	C₂×#11718668	1	1	yes	characteristic
514	C₂	#13124624	1	1	yes	characteristic
515	C₂	#13124836	1	1	yes	characteristic
516	C₂	#13124907	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄²×D₄×C₁₃	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×D₄×C₁₃	C₂³
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄²×D₄	D₁₃
hypocenter	C₁₃	C₄×#474
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
2. C₄×#88123	C₂	semidirect
3. #13115788	C₂	semidirect
4. #13115594	C₂	semidirect
5. #13115407	C₂	semidirect
8. C₄×#88047	C₂	semidirect
9. C₄×C₄⋊#1055	C₂	semidirect
27. #11718668	C₄	direct (N × H)
54. C₄×D₄×C₁₃	Q₈	semidirect
82. #88123	C₂×C₄	semidirect
92. #88047	C₂×C₄	semidirect
94. C₄⋊#1055	C₂×C₄	semidirect
187. D₄×C₁₃	C₄×Q₈	semidirect
287. C₄×C₁₃	#474	semidirect
308. C₄×D₄	Dic₂₆	semidirect
422. C₁₃	C₄×#474	semidirect
435. D₄	C₄×Dic₂₆	semidirect
503. C₄	#11718668	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11718668	2
C₄×#88123	2
#13115788	2
#13115594	2
#13115407	2
#13115083	2
#13114836	2
C₄×#88047	2
C₄×C₄⋊#1055	2
C₄×#88072	2
C₄²×D₄×C₁₃	2
C₄×#474	13

Subgroups — C4×#11718668 #15870481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718668 #15870481