Subgroups — #24921986

Order 10624.

1160 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128445	C₂	1	2	yes	maximal, complemented
2	#19128443	C₂	1	2	yes	maximal, complemented
3	#19128434	C₂	1	2	yes	maximal, complemented
4	#19128357	C₂	1	2	yes	maximal, complemented
5	#19128346	C₂	1	2	yes	maximal, complemented
6	#19128339	C₂	1	4	yes	maximal, complemented
7	#19128335	C₂	1	2	yes	maximal, complemented
8	#19128325	C₂	1	2	yes	maximal, complemented
9	#19128288	C₂	1	2	yes	maximal, complemented
10	#19128284	C₂	1	4	yes	maximal, complemented
11	#19128264	C₂	1	2	yes	maximal, complemented
12	#19128259	C₂	1	2	yes	maximal, complemented
13	#19128235	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14581780	C₂	1	1	yes	maximal, characteristic, complemented
15	#532×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13050589	C₂²	1	2	yes	complemented
17	C₂²×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₃₃₂	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₈₃	C₂²	1	4	yes	complemented
20	C₂×D₄×D₈₃	C₂²	1	2	yes	complemented
21	#14581788	C₂²	1	2	yes	—
22	#14581787	C₂²	1	4	yes	complemented
23	#14581786	C₂²	1	2	yes	complemented
24	#14581784	C₂²	1	1	yes	characteristic, complemented
25	#14581781	C₂²	1	4	yes	complemented
26	#14581780	C₂²	1	2	yes	complemented
27	#14581780	C₂²	1	2	yes	complemented
28	#14581780	C₂²	1	1	yes	characteristic, complemented
29	#14581780	C₂²	1	2	yes	complemented
30	#14581780	C₂²	1	2	yes	complemented
31	#14581779	C₂²	1	2	yes	complemented
32	#14581778	C₂²	1	4	yes	complemented
33	#14581778	C₂²	1	4	yes	complemented
34	#14581777	C₂²	1	4	yes	complemented
35	#14581776	C₂²	1	4	yes	complemented
36	#14581775	C₂²	1	2	yes	complemented
37	#14581775	C₂²	1	4	yes	complemented
38	#14581774	C₂²	1	4	yes	complemented
39	#14581772	C₂²	1	2	yes	complemented
40	#14581771	C₂²	1	1	yes	characteristic, complemented
41	#14581769	C₂²	1	4	yes	complemented
42	#14581768	C₂²	1	4	yes	complemented
43	#14581767	C₂²	1	2	yes	—
44	#14581766	C₂²	1	1	yes	characteristic
45	#14581766	C₂²	1	4	yes	complemented
46	#14581765	C₂²	1	4	yes	complemented
47	#14581764	C₂²	1	4	yes	complemented
48	#14581764	C₂²	1	4	yes	complemented
49	#14581764	C₂²	1	4	yes	complemented
50	#14581762	C₂²	1	4	yes	complemented
51	#14581762	C₂²	1	4	yes	complemented
52	#14581760	C₂²	1	4	yes	complemented
53	#14581760	C₂²	1	4	yes	complemented
54	#14581760	C₂²	1	4	yes	complemented
55	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
56	#14581757	C₂²	1	2	yes	complemented
57	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₈₃	C₂²	1	4	yes	complemented
59	#14581754	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₈₃	C₂²	1	4	yes	complemented
62	#14581749	C₂²	1	2	yes	complemented
63	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	2	yes	complemented
64	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	4	yes	complemented
65	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	2	yes	complemented
66	C₂×#41×C₈₃	C₂²	1	2	yes	complemented
67	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
68	#127×C₈₃	C₂²	1	1	yes	characteristic, complemented
69	#124×C₈₃	C₂²	1	2	yes	complemented
70	#121×C₈₃	C₂²	1	2	yes	complemented
71	#121×C₈₃	C₂²	1	2	yes	complemented
72	C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
73	C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
74	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₈₃	C₂³	1	2	yes	—
76	C₂³×D₈₃	C₂³	1	4	yes	—
77	#13050589	—	4	4	no	—
78	C₂×Dic₁₆₆	—	4	2	no	—
79	C₂×Dic₁₆₆	C₂³	1	2	yes	—
80	C₂×Dic₁₆₆	C₂³	1	2	yes	—
81	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
82	C₂×D₃₃₂	—	4	2	no	—
83	C₂×D₃₃₂	C₂³	1	2	yes	—
84	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
85	C₂×D₃₃₂	C₂³	1	2	yes	—
86	C₂×D₃₃₂	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
92	D₄×D₈₃	—	4	4	no	—
93	D₄×D₈₃	—	4	8	no	—
94	C₂²×Dic₈₃	C₂³	1	4	yes	—
95	C₂²×Dic₈₃	C₂³	1	2	yes	—
96	C₂×C₄×D₈₃	C₂³	1	2	yes	—
97	C₂×C₄×D₈₃	C₂³	1	4	yes	—
98	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₈₃	C₂³	1	4	yes	—
100	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
101	Dic₈₃⋊C₄	C₂³	1	2	yes	—
102	Dic₈₃⋊C₄	C₂³	1	2	yes	—
103	Dic₈₃⋊C₄	C₂³	1	4	yes	—
104	Dic₈₃⋊C₄	C₂³	1	2	yes	—
105	Dic₈₃⋊C₄	C₂³	1	2	yes	—
106	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
107	C₂²⋊Dic₈₃	C₂³	1	4	yes	—
108	C₂²⋊Dic₈₃	C₂³	1	4	yes	—
109	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
110	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
111	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
112	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
113	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
114	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
115	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
116	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
119	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
120	C₄×Dic₈₃	C₂³	1	4	yes	—
121	C₄×Dic₈₃	C₂³	1	2	yes	—
122	#41×C₈₃	—	4	4	no	—
123	C₂×Q₈×C₈₃	C₂³	1	2	yes	—
124	C₂×D₄×C₈₃	C₂³	1	4	yes	—
125	C₂×D₄×C₈₃	C₂³	1	2	yes	—
126	C₂×D₄×C₈₃	C₂³	1	2	yes	—
127	C₂×D₄×C₈₃	C₂³	1	2	yes	—
128	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₈₃	C₂³	1	4	yes	—
132	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
133	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
135	C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
136	C₄²×C₈₃	C₂³	1	1	yes	characteristic
137	C₄²×C₈₃	C₂³	1	1	yes	characteristic
138	C₄²×C₈₃	C₂³	1	1	yes	characteristic
139	C₄²×C₈₃	C₂³	1	1	yes	characteristic
140	C₂³×C₈₃	C₂⁴	1	4	yes	—
141	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
142	C₂²×D₈₃	—	2	4	no	—
143	C₂²×D₈₃	—	4	4	no	—
144	C₂²×D₈₃	—	4	4	no	—
145	C₂²×D₈₃	—	4	2	no	—
146	C₂²×D₈₃	—	4	4	no	—
147	C₂²×D₈₃	—	4	2	no	—
148	C₂²×D₈₃	C₂⁴	1	2	yes	—
149	C₂²×D₈₃	C₂⁴	1	4	yes	—
150	Q₈×C₈₃	—	4	2	no	—
151	D₄×C₈₃	—	2	8	no	—
152	D₄×C₈₃	—	2	4	no	—
153	D₄×C₈₃	—	4	2	no	—
154	D₄×C₈₃	—	4	2	no	—
155	C₂×C₄×C₈₃	—	2	2	no	—
156	C₂×C₄×C₈₃	—	2	2	no	—
157	C₂×C₄×C₈₃	—	4	1	no	—
158	C₂×C₄×C₈₃	—	4	4	no	—
159	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₈₃	C₂⁴	1	4	yes	—
165	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₈₃	—	2	4	no	—
167	C₂²⋊D₈₃	—	4	4	no	—
168	C₂²⋊D₈₃	—	4	4	no	—
169	C₂²⋊D₈₃	—	4	4	no	—
170	C₂²⋊D₈₃	—	4	4	no	—
171	C₂×Dic₈₃	—	4	2	no	—
172	C₂×Dic₈₃	—	4	4	no	—
173	C₂×Dic₈₃	C₂⁴	1	2	yes	—
174	C₂×Dic₈₃	C₂⁴	1	4	yes	—
175	C₂×Dic₈₃	C₂⁴	1	2	yes	—
176	C₂×Dic₈₃	C₂⁴	1	2	yes	—
177	D₃₃₂	—	2	4	no	—
178	D₃₃₂	—	4	4	no	—
179	D₃₃₂	—	4	2	no	—
180	D₃₃₂	—	4	1	no	—
181	C₄×D₈₃	—	2	4	no	—
182	C₄×D₈₃	—	4	4	no	—
183	Dic₁₆₆	—	2	4	no	—
184	Dic₁₆₆	—	4	2	no	—
185	Dic₁₆₆	—	4	1	no	—
186	C₂²×C₈₃	—	2	1	no	—
187	C₂²×C₈₃	—	2	1	no	—
188	C₂²×C₈₃	—	2	4	no	—
189	C₂²×C₈₃	—	2	4	no	—
190	C₂²×C₈₃	—	2	4	no	—
191	C₂²×C₈₃	H(5,𝔽₂)	1	2	yes	—
192	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
193	C₂×D₈₃	—	2	2	no	—
194	C₂×D₈₃	—	2	4	no	—
195	C₂×D₈₃	—	2	4	no	—
196	C₂×D₈₃	—	2	2	no	—
197	C₂×D₈₃	—	2	2	no	—
198	C₂×D₈₃	—	2	4	no	—
199	C₂×D₈₃	—	8	4	no	—
200	C₂×D₈₃	—	8	8	no	—
201	C₄×C₈₃	—	2	1	no	—
202	C₄×C₈₃	—	2	4	no	—
203	C₄×C₈₃	—	2	1	no	—
204	C₄×C₈₃	—	2	1	no	—
205	C₄×C₈₃	—	2	1	no	—
206	C₄×C₈₃	—	2	1	no	—
207	C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
208	Dic₈₃	—	2	4	no	—
209	Dic₈₃	—	2	2	no	—
210	Dic₈₃	—	2	2	no	—
211	Dic₈₃	—	2	2	no	—
212	C₂×C₈₃	—	2	2	no	—
213	C₂×C₈₃	—	4	4	no	—
214	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₈₃	#585	1	1	yes	characteristic
217	D₈₃	—	4	2	no	—
218	D₈₃	—	4	4	no	—
219	#3558	—	83	1	no	maximal, Sylow
220	C₈₃	#3558	1	1	yes	characteristic, complemented, Sylow
221	#562	—	83	2	no	—
222	H(3,𝔽₄)	—	83	2	no	—
223	#559	—	83	2	no	—
224	#548	—	83	2	no	—
225	#546	—	83	4	no	—
226	#546	—	83	2	no	—
227	D₄²	—	83	2	no	—
228	#542	—	83	2	no	—
229	#538	—	83	2	no	—
230	#538	—	83	4	no	—
231	#535	—	83	2	no	—
232	#534	—	83	2	no	—
233	#532	D₈₃	1	1	yes	characteristic, complemented
234	#529	—	83	1	no	—
235	C₂×#124	—	83	1	no	—
236	C₂×#41	—	83	2	no	—
237	C₂×#41	C₂×D₈₃	1	2	yes	complemented
238	C₂²×Q₈	—	83	1	no	—
239	C₂²×D₄	—	83	4	no	—
240	C₂²×D₄	—	83	2	no	—
241	C₂²×D₄	—	83	1	no	—
242	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
243	#127	—	83	2	no	—
244	#127	C₂×D₈₃	1	1	yes	characteristic, complemented
245	#126	—	83	4	no	—
246	#126	—	83	2	no	—
247	#125	—	83	1	no	—
248	#124	—	83	4	no	—
249	#124	—	83	2	no	—
250	#124	—	83	4	no	—
251	#124	—	83	4	no	—
252	#124	—	83	2	no	—
253	#124	—	83	2	no	—
254	#124	—	83	2	no	—
255	#124	—	83	2	no	—
256	#124	—	83	1	no	—
257	#124	C₂×D₈₃	1	2	yes	complemented
258	#123	—	83	2	no	—
259	#123	—	83	4	no	—
260	#123	—	83	4	no	—
261	#123	—	83	4	no	—
262	#123	—	83	4	no	—
263	C₂²⋊Q₈	—	83	4	no	—
264	C₂²⋊Q₈	—	83	1	no	—
265	C₂²⋊Q₈	—	83	2	no	—
266	C₂²⋊Q₈	—	83	4	no	—
267	#121	—	83	4	no	—
268	#121	—	83	4	no	—
269	#121	—	83	4	no	—
270	#121	—	83	1	no	—
271	#121	—	83	4	no	—
272	#121	—	83	2	no	—
273	#121	—	83	4	no	—
274	#121	C₂×D₈₃	1	2	yes	complemented
275	#121	C₂×D₈₃	1	2	yes	complemented
276	#120	—	83	4	no	—
277	#120	—	83	4	no	—
278	#120	—	83	4	no	—
279	#120	—	83	4	no	—
280	#120	—	83	4	no	—
281	C₄×Q₈	—	83	2	no	—
282	C₄×Q₈	—	83	1	no	—
283	C₄×D₄	—	83	4	no	—
284	C₄×D₄	—	83	2	no	—
285	C₄×D₄	—	83	4	no	—
286	C₄×D₄	—	83	2	no	—
287	C₄×D₄	—	83	1	no	—
288	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
289	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
290	#117	—	83	2	no	—
291	C₂×C₂²⋊C₄	—	83	2	no	—
292	C₂×C₂²⋊C₄	—	83	2	no	—
293	C₂×C₂²⋊C₄	—	83	4	no	—
294	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic, complemented
295	C₂⁴	—	83	4	no	—
296	C₂⁴	—	83	2	no	—
297	#41	—	4	4	no	—
298	#41	—	332	4	no	—
299	C₂×Q₈	—	332	2	no	—
300	C₂×Q₈	—	83	1	no	—
301	C₂×Q₈	—	83	2	no	—
302	C₂×Q₈	—	83	2	no	—
303	C₂×Q₈	C₂²×D₈₃	1	2	yes	—
304	C₂×D₄	—	332	2	no	—
305	C₂×D₄	—	332	8	no	—
306	C₂×D₄	—	332	4	no	—
307	C₂×D₄	—	83	4	no	—
308	C₂×D₄	—	83	4	no	—
309	C₂×D₄	—	83	4	no	—
310	C₂×D₄	—	83	4	no	—
311	C₂×D₄	—	83	2	no	—
312	C₂×D₄	—	83	1	no	—
313	C₂×D₄	—	83	4	no	—
314	C₂×D₄	—	83	2	no	—
315	C₂×D₄	—	83	2	no	—
316	C₂×D₄	C₂²×D₈₃	1	4	yes	—
317	C₂×D₄	C₂²×D₈₃	1	2	yes	—
318	C₂×D₄	C₂²×D₈₃	1	2	yes	—
319	C₂×D₄	C₂²×D₈₃	1	2	yes	—
320	C₂²×C₄	—	83	2	no	—
321	C₂²×C₄	—	83	4	no	—
322	C₂²×C₄	—	83	4	no	—
323	C₂²×C₄	—	83	2	no	—
324	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₈₃	1	4	yes	—
328	C₄⋊C₄	—	83	2	no	—
329	C₄⋊C₄	—	83	2	no	—
330	C₄⋊C₄	—	83	2	no	—
331	C₄⋊C₄	—	83	2	no	—
332	C₄⋊C₄	—	83	4	no	—
333	C₄⋊C₄	—	83	1	no	—
334	C₄⋊C₄	—	83	4	no	—
335	C₄⋊C₄	—	83	1	no	—
336	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
337	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
338	C₂²⋊C₄	—	83	2	no	—
339	C₂²⋊C₄	—	83	4	no	—
340	C₂²⋊C₄	—	83	4	no	—
341	C₂²⋊C₄	—	83	2	no	—
342	C₂²⋊C₄	—	83	4	no	—
343	C₂²⋊C₄	—	83	4	no	—
344	C₂²⋊C₄	—	83	4	no	—
345	C₂²⋊C₄	—	83	4	no	—
346	C₂²⋊C₄	—	83	4	no	—
347	C₂²⋊C₄	—	83	4	no	—
348	C₂²⋊C₄	—	83	2	no	—
349	C₂²⋊C₄	—	83	2	no	—
350	C₂²⋊C₄	—	83	4	no	—
351	C₂²⋊C₄	—	83	2	no	—
352	C₂²⋊C₄	C₂²×D₈₃	1	4	yes	—
353	C₂²⋊C₄	C₂²×D₈₃	1	4	yes	—
354	C₄²	—	83	2	no	—
355	C₄²	—	83	4	no	—
356	C₄²	C₂²×D₈₃	1	1	yes	characteristic
357	C₄²	C₂²×D₈₃	1	1	yes	characteristic
358	C₄²	C₂²×D₈₃	1	1	yes	characteristic
359	C₄²	C₂²×D₈₃	1	1	yes	characteristic
360	C₂³	—	332	2	no	—
361	C₂³	—	332	4	no	—
362	C₂³	—	332	4	no	—
363	C₂³	—	332	2	no	—
364	C₂³	—	332	4	no	—
365	C₂³	—	83	4	no	—
366	C₂³	—	83	2	no	—
367	C₂³	—	166	4	no	—
368	C₂³	C₂³×D₈₃	1	4	yes	—
369	C₂³	C₂³×D₈₃	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	332	2	no	—
372	Q₈	—	332	1	no	—
373	Q₈	—	166	4	no	—
374	D₄	—	2	8	no	—
375	D₄	—	2	4	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	332	4	no	—
379	D₄	—	332	2	no	—
380	D₄	—	332	1	no	—
381	D₄	—	332	4	no	—
382	D₄	—	332	4	no	—
383	D₄	—	332	4	no	—
384	D₄	—	332	4	no	—
385	D₄	—	166	4	no	—
386	D₄	—	166	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	332	4	no	—
392	C₂×C₄	—	332	2	no	—
393	C₂×C₄	—	332	4	no	—
394	C₂×C₄	—	83	2	no	—
395	C₂×C₄	—	83	4	no	—
396	C₂×C₄	—	83	2	no	—
397	C₂×C₄	—	83	2	no	—
398	C₂×C₄	—	166	4	no	—
399	C₂×C₄	C₂³×D₈₃	1	4	yes	—
400	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
405	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	664	4	no	—
412	C₂²	—	664	8	no	—
413	C₂²	—	166	4	no	—
414	C₂²	—	166	2	no	—
415	C₂²	—	166	2	no	—
416	C₂²	—	166	4	no	—
417	C₂²	—	166	2	no	—
418	C₂²	—	166	4	no	—
419	C₂²	#14581837	1	2	yes	—
420	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	166	2	no	—
428	C₄	—	166	2	no	—
429	C₄	—	166	4	no	—
430	C₄	—	166	2	no	—
431	C₄	#14581838	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	4	4	no	—
434	C₂	—	332	4	no	—
435	C₂	—	332	2	no	—
436	C₂	C₂×#14581837	1	1	yes	characteristic
437	C₂	C₂×#14581838	1	1	yes	characteristic
438	C₂	#19128537	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#532×C₈₃	C₂
hypercenter	#532	D₈₃
hypocenter	C₈₃	#3558
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #19128445	C₂	semidirect
2. #19128443	C₂	semidirect
3. #19128434	C₂	semidirect
4. #19128357	C₂	semidirect
5. #19128346	C₂	semidirect
6. #19128339	C₂	semidirect
7. #19128335	C₂	semidirect
8. #19128325	C₂	semidirect
9. #19128288	C₂	semidirect
10. #19128284	C₂	semidirect
11. #19128264	C₂	semidirect
12. #19128259	C₂	semidirect
13. #19128235	C₂	semidirect
14. C₂×#14581780	C₂	semidirect
15. #532×C₈₃	C₂	semidirect
16. C₂×#13050589	C₂²	semidirect
17. C₂²×Dic₁₆₆	C₂²	semidirect
19. C₂×D₄×D₈₃	C₂²	semidirect
20. C₂×D₄×D₈₃	C₂²	semidirect
22. #14581787	C₂²	semidirect
23. #14581786	C₂²	semidirect
24. #14581784	C₂²	semidirect
25. #14581781	C₂²	semidirect
26. #14581780	C₂²	semidirect
27. #14581780	C₂²	semidirect
28. #14581780	C₂²	semidirect
29. #14581780	C₂²	semidirect
30. #14581780	C₂²	semidirect
31. #14581779	C₂²	semidirect
32. #14581778	C₂²	semidirect
33. #14581778	C₂²	semidirect
34. #14581777	C₂²	semidirect
35. #14581776	C₂²	semidirect
36. #14581775	C₂²	semidirect
37. #14581775	C₂²	semidirect
38. #14581774	C₂²	semidirect
39. #14581772	C₂²	semidirect
40. #14581771	C₂²	semidirect
41. #14581769	C₂²	semidirect
42. #14581768	C₂²	semidirect
45. #14581766	C₂²	semidirect
46. #14581765	C₂²	semidirect
47. #14581764	C₂²	semidirect
48. #14581764	C₂²	semidirect
49. #14581764	C₂²	semidirect
50. #14581762	C₂²	semidirect
51. #14581762	C₂²	semidirect
52. #14581760	C₂²	semidirect
53. #14581760	C₂²	semidirect
54. #14581760	C₂²	semidirect
55. C₄×Dic₁₆₆	C₂²	semidirect
56. #14581757	C₂²	semidirect
57. C₄×D₃₃₂	C₂²	semidirect
58. D₄×Dic₈₃	C₂²	semidirect
59. #14581754	C₂²	semidirect
60. C₄×C₂²⋊D₈₃	C₂²	semidirect
61. C₄×C₂²⋊D₈₃	C₂²	semidirect
62. #14581749	C₂²	semidirect
63. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
64. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
65. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
66. C₂×#41×C₈₃	C₂²	semidirect
67. C₄⋊Q₈×C₈₃	C₂²	semidirect
68. #127×C₈₃	C₂²	semidirect
69. #124×C₈₃	C₂²	semidirect
70. #121×C₈₃	C₂²	semidirect
71. #121×C₈₃	C₂²	semidirect
72. C₄×D₄×C₈₃	C₂²	semidirect
73. C₄×D₄×C₈₃	C₂²	semidirect
74. C₂×C₄²×C₈₃	C₂²	semidirect
220. C₈₃	#3558	semidirect
233. #532	D₈₃	semidirect
237. C₂×#41	C₂×D₈₃	semidirect
242. C₄⋊Q₈	C₂×D₈₃	semidirect
244. #127	C₂×D₈₃	semidirect
257. #124	C₂×D₈₃	semidirect
274. #121	C₂×D₈₃	semidirect
275. #121	C₂×D₈₃	semidirect
288. C₄×D₄	C₂×D₈₃	semidirect
289. C₄×D₄	C₂×D₈₃	semidirect
294. C₂×C₄²	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128445	2
#19128443	2
#19128434	2
#19128357	2
#19128346	2
#19128339	2
#19128335	2
#19128325	2
#19128288	2
#19128284	2
#19128264	2
#19128259	2
#19128235	2
C₂×#14581780	2
#532×C₈₃	2
#3558	83