Subgroups — C₂×#13116563 #16015846

Order 3328.

1154 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88158	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88052	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116563	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718089	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6127	—	2	1	no	—
7	C₂²×C₁₃×M₁₆	—	2	1	no	—
8	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×Dic₅₂	C₄	1	1	yes	characteristic
10	C₂×#88158	—	2	1	no	—
11	C₂×#88158	—	2	2	no	—
12	C₂×#88158	—	2	2	no	—
13	C₂×#88158	—	2	1	no	—
14	C₂×#88158	C₄	1	2	yes	—
15	C₂×#88158	C₄	1	4	yes	—
16	C₂×#88158	C₂²	1	2	yes	—
17	C₂×#88158	C₂²	1	4	yes	—
18	C₂²×D₁₀₄	C₄	1	1	yes	characteristic
19	C₂²×#6095	—	2	1	no	—
20	C₂×C₁₃×#108	—	2	2	no	—
21	C₂×C₁₃×#108	—	2	1	no	—
22	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#108	C₂²	1	4	yes	complemented
24	C₂×#88052	—	2	1	no	—
25	C₂×#88052	—	2	1	no	—
26	C₂×#88052	—	2	2	no	—
27	C₂×#88052	C₂²	1	4	yes	complemented
28	C₂²×#6090	C₂²	1	2	yes	complemented
29	#11718089	C₂²	1	16	yes	complemented
30	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
31	C₂²×C₂²⋊D₁₃	—	4	1	no	—
32	C₂×#6127	—	2	2	no	—
33	C₂×#6127	—	2	4	no	—
34	C₂×#6127	—	2	2	no	—
35	C₂×#6127	—	2	4	no	—
36	C₂×#6127	—	4	1	no	—
37	C₂×#6127	—	4	2	no	—
38	C₂×#6127	—	4	1	no	—
39	C₂×#6127	—	4	2	no	—
40	C₂²×D₅₂	—	2	1	no	—
41	C₂²×C₄×D₁₃	—	4	1	no	—
42	C₂²×Dic₂₆	—	2	1	no	—
43	C₂×C₁₃×M₁₆	—	2	2	no	—
44	C₂×C₁₃×M₁₆	—	2	4	no	—
45	C₂×C₁₃×M₁₆	—	4	1	no	—
46	C₂×C₁₃×M₁₆	—	4	2	no	—
47	C₂²×C₈×C₁₃	—	4	1	no	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	D₄	1	2	yes	—
54	C₂²×C₈×C₁₃	D₄	1	2	yes	—
55	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₂×Dic₅₂	—	2	2	no	—
59	C₂×Dic₅₂	—	2	1	no	—
60	C₂×Dic₅₂	C₂×C₄	1	2	yes	—
61	C₂×Dic₅₂	C₂×C₄	1	4	yes	—
62	#88158	—	2	4	no	—
63	#88158	—	2	4	no	—
64	#88158	—	2	4	no	—
65	#88158	—	2	2	no	—
66	#88158	—	2	4	no	—
67	#88158	—	2	2	no	—
68	#88158	—	2	4	no	—
69	#88158	C₂×C₄	1	4	yes	—
70	#88158	C₂×C₄	1	8	yes	—
71	#88158	C₂³	1	4	yes	—
72	C₂×D₁₀₄	—	2	2	no	—
73	C₂×D₁₀₄	—	2	1	no	—
74	C₂×D₁₀₄	C₂×C₄	1	2	yes	—
75	C₂×D₁₀₄	C₂×C₄	1	4	yes	—
76	C₂×#6095	—	2	4	no	—
77	C₂×#6095	—	2	2	no	—
78	C₂×#6095	—	2	2	no	—
79	C₂×#6095	—	2	4	no	—
80	C₁₃×#108	—	2	2	no	—
81	C₁₃×#108	—	2	4	no	—
82	C₁₃×#108	C₂³	1	4	yes	complemented
83	#88052	—	2	4	no	—
84	#88052	—	2	4	no	—
85	C₂×#6090	—	2	2	no	—
86	C₂×#6090	—	2	2	no	—
87	C₂×#6090	C₂³	1	4	yes	complemented
88	C₂×#2143	—	13	1	no	maximal, Sylow
89	C₂⁴×C₁₃	SD₁₆	1	1	yes	characteristic
90	C₂³×D₁₃	—	4	1	no	—
91	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	D₈	1	2	yes	—
97	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₂²⋊D₁₃	—	4	2	no	—
102	C₂×C₂²⋊D₁₃	—	4	4	no	—
103	C₂×C₂²⋊D₁₃	—	4	2	no	—
104	C₂×C₂²⋊D₁₃	—	4	4	no	—
105	C₂²×Dic₁₃	—	4	1	no	—
106	#6127	—	2	4	no	—
107	#6127	—	2	8	no	—
108	#6127	—	2	4	no	—
109	#6127	—	4	4	no	—
110	#6127	—	4	4	no	—
111	#6127	—	4	4	no	—
112	#6127	—	4	4	no	—
113	#6127	—	4	2	no	—
114	#6127	—	4	2	no	—
115	#6127	—	4	4	no	—
116	C₂×D₅₂	—	2	4	no	—
117	C₂×D₅₂	—	2	2	no	—
118	C₂×D₅₂	—	4	2	no	—
119	C₂×D₅₂	—	4	1	no	—
120	C₂×C₄×D₁₃	—	4	4	no	—
121	C₂×C₄×D₁₃	—	4	2	no	—
122	C₂×C₄×D₁₃	—	4	4	no	—
123	C₂×C₄×D₁₃	—	4	2	no	—
124	C₂×Dic₂₆	—	2	4	no	—
125	C₂×Dic₂₆	—	2	2	no	—
126	C₂×Dic₂₆	—	4	2	no	—
127	C₂×Dic₂₆	—	4	1	no	—
128	C₁₃×M₁₆	—	2	4	no	—
129	C₁₃×M₁₆	—	4	4	no	—
130	C₁₃×M₁₆	—	4	2	no	—
131	C₂×C₈×C₁₃	—	4	4	no	—
132	C₂×C₈×C₁₃	—	4	2	no	—
133	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
134	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
136	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
139	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
140	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
151	Dic₅₂	—	2	2	no	—
152	Dic₅₂	—	2	4	no	—
153	Dic₅₂	C₂²×C₄	1	4	yes	—
154	D₁₀₄	—	2	2	no	—
155	D₁₀₄	—	2	4	no	—
156	D₁₀₄	C₂²×C₄	1	4	yes	—
157	#6095	—	2	4	no	—
158	#6095	—	2	8	no	—
159	#6095	—	2	4	no	—
160	#6090	—	2	4	no	—
161	C₂²×#135	—	13	1	no	—
162	C₂²×M₃₂	—	13	1	no	—
163	C₂²×#108	D₁₃	1	1	yes	characteristic, complemented
164	#2143	—	13	8	no	—
165	C₂×#359	—	13	4	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	#102	1	1	yes	characteristic
168	C₂³×C₁₃	#102	1	1	yes	characteristic
169	C₂³×C₁₃	#102	1	2	yes	—
170	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
171	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
172	C₂²×D₁₃	—	4	4	no	—
173	C₂²×D₁₃	—	4	2	no	—
174	C₂²×D₁₃	—	8	4	no	—
175	C₂×C₄×C₁₃	#102	1	2	yes	—
176	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
177	C₂×C₄×C₁₃	#102	1	2	yes	—
178	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
179	C₂×C₄×C₁₃	#102	1	2	yes	—
180	C₂×C₄×C₁₃	#102	1	2	yes	—
181	C₂×C₄×C₁₃	#102	1	2	yes	—
182	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
188	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
191	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₂²⋊D₁₃	—	4	4	no	—
194	C₂²⋊D₁₃	—	4	8	no	—
195	C₂²⋊D₁₃	—	4	4	no	—
196	C₂×Dic₁₃	—	4	4	no	—
197	C₂×Dic₁₃	—	4	2	no	—
198	D₅₂	—	2	4	no	—
199	D₅₂	—	4	4	no	—
200	D₅₂	—	4	2	no	—
201	C₄×D₁₃	—	4	4	no	—
202	C₄×D₁₃	—	4	8	no	—
203	C₄×D₁₃	—	4	4	no	—
204	Dic₂₆	—	2	4	no	—
205	Dic₂₆	—	4	4	no	—
206	Dic₂₆	—	4	2	no	—
207	C₈×C₁₃	—	4	4	no	—
208	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
210	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
212	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
213	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂²×#41	—	26	1	no	—
215	C₂×#135	—	13	2	no	—
216	C₂×#135	—	13	4	no	—
217	C₂×#135	—	13	2	no	—
218	C₂×#135	—	13	4	no	—
219	C₂×#135	—	26	1	no	—
220	C₂×#135	—	26	2	no	—
221	C₂×#135	—	26	2	no	—
222	C₂×#135	—	26	1	no	—
223	C₂²×Q₁₆	—	13	1	no	—
224	C₂²×SD₁₆	—	26	1	no	—
225	C₂²×D₈	—	13	1	no	—
226	C₂²×M₁₆	—	2	1	no	—
227	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
228	C₂×M₃₂	—	13	4	no	—
229	C₂×M₃₂	—	26	1	no	—
230	C₂×M₃₂	—	26	1	no	—
231	C₂×M₃₂	—	26	2	no	—
232	C₂²×C₁₆	—	13	2	no	—
233	C₂×#108	—	2	2	no	—
234	C₂×#108	—	2	1	no	—
235	C₂×#108	C₂×D₁₃	1	2	yes	complemented
236	C₂×#108	C₂×D₁₃	1	4	yes	complemented
237	#359	—	13	16	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	C₂×#102	1	2	yes	—
244	C₂²×C₁₃	C₂×#102	1	2	yes	—
245	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
246	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
247	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
248	C₂×D₁₃	—	4	4	no	—
249	C₂×D₁₃	—	8	8	no	—
250	C₂×D₁₃	—	8	4	no	—
251	C₄×C₁₃	C₂×#102	1	2	yes	—
252	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
253	C₄×C₁₃	C₂×#102	1	2	yes	—
254	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
255	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
256	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
257	Dic₁₃	—	4	4	no	—
258	C₂×#41	—	26	2	no	—
259	C₂×#41	—	26	4	no	—
260	C₂×#41	—	26	4	no	—
261	C₂×#41	—	26	2	no	—
262	C₂×#41	—	52	2	no	—
263	C₂×#41	—	52	1	no	—
264	C₂×#41	—	52	1	no	—
265	C₂×#41	—	52	2	no	—
266	C₂²×Q₈	—	26	1	no	—
267	C₂²×D₄	—	26	1	no	—
268	C₂²×D₄	—	52	1	no	—
269	C₂³×C₄	—	52	1	no	—
270	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
271	#135	—	13	4	no	—
272	#135	—	13	8	no	—
273	#135	—	13	4	no	—
274	#135	—	26	4	no	—
275	#135	—	26	4	no	—
276	#135	—	26	4	no	—
277	#135	—	26	2	no	—
278	#135	—	26	4	no	—
279	#135	—	26	2	no	—
280	#135	—	26	4	no	—
281	C₂×Q₁₆	—	13	2	no	—
282	C₂×Q₁₆	—	13	4	no	—
283	C₂×Q₁₆	—	26	2	no	—
284	C₂×Q₁₆	—	26	1	no	—
285	C₂×SD₁₆	—	26	4	no	—
286	C₂×SD₁₆	—	26	2	no	—
287	C₂×SD₁₆	—	26	2	no	—
288	C₂×SD₁₆	—	26	4	no	—
289	C₂×D₈	—	13	2	no	—
290	C₂×D₈	—	13	4	no	—
291	C₂×D₈	—	26	2	no	—
292	C₂×D₈	—	26	1	no	—
293	C₂×M₁₆	—	2	4	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	4	2	no	—
296	C₂×M₁₆	—	4	1	no	—
297	C₂²×C₈	—	4	1	no	—
298	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
299	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
300	C₂²×C₈	C₄×D₁₃	1	2	yes	—
301	C₂²×C₈	D₅₂	1	1	yes	characteristic
302	C₂²×C₈	D₅₂	1	1	yes	characteristic
303	C₂²×C₈	D₅₂	1	2	yes	—
304	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
305	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
307	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
308	M₃₂	—	26	4	no	—
309	M₃₂	—	26	4	no	—
310	C₂×C₁₆	—	13	4	no	—
311	C₂×C₁₆	—	26	2	no	—
312	C₂×C₁₆	—	26	2	no	—
313	#108	—	2	2	no	—
314	#108	—	2	4	no	—
315	#108	C₂²×D₁₃	1	4	yes	complemented
316	C₂×C₁₃	—	2	2	no	—
317	C₂×C₁₃	—	2	1	no	—
318	C₂×C₁₃	—	2	2	no	—
319	C₂×C₁₃	—	2	1	no	—
320	C₂×C₁₃	#2143	1	2	yes	complemented
321	C₂×C₁₃	C₂²×#102	1	1	yes	characteristic
322	D₁₃	—	8	4	no	—
323	C₂⁴	—	52	1	no	—
324	C₂⁴	#6106	1	1	yes	characteristic
325	#41	—	26	8	no	—
326	#41	—	26	4	no	—
327	#41	—	26	4	no	—
328	#41	—	52	4	no	—
329	#41	—	52	2	no	—
330	#41	—	52	4	no	—
331	#41	—	52	2	no	—
332	#41	—	52	4	no	—
333	#41	—	52	4	no	—
334	#41	—	52	4	no	—
335	C₂×Q₈	—	26	4	no	—
336	C₂×Q₈	—	26	2	no	—
337	C₂×Q₈	—	52	2	no	—
338	C₂×Q₈	—	52	1	no	—
339	C₂×D₄	—	26	4	no	—
340	C₂×D₄	—	26	2	no	—
341	C₂×D₄	—	52	2	no	—
342	C₂×D₄	—	52	4	no	—
343	C₂×D₄	—	52	2	no	—
344	C₂×D₄	—	52	4	no	—
345	C₂×D₄	—	52	2	no	—
346	C₂×D₄	—	52	1	no	—
347	C₂²×C₄	—	52	1	no	—
348	C₂²×C₄	—	52	4	no	—
349	C₂²×C₄	—	52	2	no	—
350	C₂²×C₄	—	52	4	no	—
351	C₂²×C₄	—	52	2	no	—
352	C₂²×C₄	#6103	1	1	yes	characteristic
353	C₂²×C₄	#6103	1	1	yes	characteristic
354	C₂²×C₄	#6103	1	2	yes	—
355	C₂²×C₄	#6104	1	2	yes	—
356	C₂²×C₄	#6104	1	1	yes	characteristic
357	C₂²×C₄	#6104	1	1	yes	characteristic
358	C₂²×C₄	#6106	1	1	yes	characteristic
359	C₂²×C₄	#6106	1	2	yes	—
360	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
361	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
362	Q₁₆	—	13	4	no	—
363	Q₁₆	—	26	2	no	—
364	Q₁₆	—	26	4	no	—
365	SD₁₆	—	26	4	no	—
366	SD₁₆	—	26	8	no	—
367	SD₁₆	—	26	4	no	—
368	D₈	—	13	4	no	—
369	D₈	—	26	2	no	—
370	D₈	—	26	4	no	—
371	M₁₆	—	2	4	no	—
372	M₁₆	—	4	4	no	—
373	M₁₆	—	4	2	no	—
374	C₂×C₈	—	4	4	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	#6103	1	2	yes	—
377	C₂×C₈	#6103	1	1	yes	characteristic
378	C₂×C₈	#6103	1	2	yes	—
379	C₂×C₈	#6103	1	1	yes	characteristic
380	C₂×C₈	#6103	1	2	yes	—
381	C₂×C₈	#6103	1	2	yes	—
382	C₂×C₈	#6103	1	2	yes	—
383	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
384	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
385	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
386	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
387	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
388	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
389	C₂×C₈	C₂×D₅₂	1	2	yes	—
390	C₂×C₈	C₂×D₅₂	1	2	yes	—
391	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
392	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
393	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
394	C₁₆	—	26	4	no	—
395	C₁₃	C₂×#2143	1	1	yes	characteristic, complemented, Sylow
396	C₂³	—	4	2	no	—
397	C₂³	—	52	4	no	—
398	C₂³	—	52	2	no	—
399	C₂³	—	104	4	no	—
400	C₂³	#88049	1	1	yes	characteristic
401	C₂³	#88049	1	1	yes	characteristic
402	C₂³	#88049	1	2	yes	—
403	C₂³	C₂×#6106	1	1	yes	characteristic
404	C₂³	C₂×#6106	1	2	yes	—
405	Q₈	—	26	4	no	—
406	Q₈	—	52	4	no	—
407	Q₈	—	52	2	no	—
408	D₄	—	26	4	no	—
409	D₄	—	52	4	no	—
410	D₄	—	52	8	no	—
411	D₄	—	52	4	no	—
412	D₄	—	52	4	no	—
413	D₄	—	52	2	no	—
414	C₂×C₄	—	52	4	no	—
415	C₂×C₄	—	52	2	no	—
416	C₂×C₄	—	52	4	no	—
417	C₂×C₄	—	52	8	no	—
418	C₂×C₄	—	52	4	no	—
419	C₂×C₄	#88049	1	1	yes	characteristic
420	C₂×C₄	#88049	1	2	yes	—
421	C₂×C₄	#88049	1	2	yes	—
422	C₂×C₄	#88049	1	1	yes	characteristic
423	C₂×C₄	#88049	1	2	yes	—
424	C₂×C₄	#88049	1	2	yes	—
425	C₂×C₄	#88049	1	2	yes	—
426	C₂×C₄	C₂×#6103	1	2	yes	—
427	C₂×C₄	C₂×#6103	1	1	yes	characteristic
428	C₂×C₄	C₂×#6103	1	2	yes	—
429	C₂×C₄	C₂×#6103	1	1	yes	characteristic
430	C₂×C₄	C₂×#6104	1	2	yes	—
431	C₂×C₄	C₂×#6104	1	2	yes	—
432	C₂×C₄	C₂×#6104	1	1	yes	characteristic
433	C₂×C₄	C₂×#6104	1	1	yes	characteristic
434	C₂×C₄	C₂×#6106	1	2	yes	—
435	C₂×C₄	C₂×#6106	1	1	yes	characteristic
436	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
437	C₈	—	4	4	no	—
438	C₈	C₂×#6103	1	1	yes	characteristic
439	C₈	C₂×#6103	1	2	yes	—
440	C₈	C₂×#6103	1	1	yes	characteristic
441	C₈	C₂×#6103	1	2	yes	—
442	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
443	C₈	C₂²×D₅₂	1	1	yes	characteristic
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	52	4	no	—
450	C₂²	—	104	8	no	—
451	C₂²	—	104	4	no	—
452	C₂²	C₂×#88049	1	2	yes	—
453	C₂²	C₂×#88049	1	2	yes	—
454	C₂²	C₂×#88049	1	1	yes	characteristic
455	C₂²	C₂×#88049	1	1	yes	characteristic
456	C₂²	C₂²×#6106	1	1	yes	characteristic
457	C₄	—	52	4	no	—
458	C₄	C₂×#88049	1	2	yes	—
459	C₄	C₂×#88049	1	1	yes	characteristic
460	C₄	C₂×#88049	1	2	yes	—
461	C₄	C₂×#88049	1	1	yes	characteristic
462	C₄	C₂²×#6103	1	1	yes	characteristic
463	C₄	C₂²×#6104	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	2	1	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	2	no	—
468	C₂	—	104	4	no	—
469	C₂	#13116563	1	2	yes	direct product factor
470	C₂	C₂²×#88049	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#6104
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×#108	C₂
socle	C₂²×C₁₃	C₂×#102
prime radical	C₂²×#88158	C₂
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×#108	D₁₃
hypocenter	C₁₃	C₂×#2143
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
2. C₂²×#88052	C₂	semidirect
3. #13116563	C₂	direct (N × H)
4. C₂×#11718089	C₂	semidirect
5. C₂²×C₁₃×#108	C₂	semidirect
22. C₂×C₁₃×#108	C₂²	semidirect
23. C₂×C₁₃×#108	C₂²	semidirect
27. C₂×#88052	C₂²	semidirect
28. C₂²×#6090	C₂²	semidirect
29. #11718089	C₂²	semidirect
82. C₁₃×#108	C₂³	semidirect
87. C₂×#6090	C₂³	semidirect
163. C₂²×#108	D₁₃	semidirect
235. C₂×#108	C₂×D₁₃	semidirect
236. C₂×#108	C₂×D₁₃	semidirect
315. #108	C₂²×D₁₃	semidirect
320. C₂×C₁₃	#2143	semidirect
395. C₁₃	C₂×#2143	semidirect
469. C₂	#13116563	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88158	2
C₂²×#88052	2
#13116563	2
C₂×#11718089	2
C₂²×C₁₃×#108	2
C₂×#2143	13

Subgroups — C2×#13116563 #16015846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116563 #16015846