Subgroups — C₇₃×#25639 #32935043

Order 18688.

1198 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#496×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#464×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2015	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2012	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1879	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
16	#559×C₇₃	—	2	4	no	—
17	#559×C₇₃	—	2	4	no	—
18	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#124×C₇₃	—	2	1	no	—
20	C₂×#124×C₇₃	C₂²	1	2	yes	—
21	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#123×C₇₃	—	2	2	no	—
23	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₇₃	—	2	1	no	—
26	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
27	#496×C₇₃	—	2	4	no	—
28	#464×C₇₃	—	2	4	no	—
29	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#103×C₇₃	C₂²	1	2	yes	—
32	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₇₃	C₂²	1	2	yes	—
34	C₂×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
36	#397×C₇₃	—	2	1	no	—
37	#393×C₇₃	—	2	1	no	—
38	#391×C₇₃	C₂²	1	2	yes	—
39	#390×C₇₃	C₂²	1	2	yes	—
40	#388×C₇₃	—	2	2	no	—
41	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	#340×C₇₃	C₂²	1	2	yes	—
43	#336×C₇₃	C₂²	1	2	yes	—
44	#336×C₇₃	C₂²	1	2	yes	—
45	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₇₃	—	2	1	no	—
49	C₂²×D₄×C₇₃	—	2	1	no	—
50	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₇₃	—	2	2	no	—
53	C₂×Q₁₆×C₇₃	—	2	2	no	—
54	C₂×Q₁₆×C₇₃	—	4	2	no	—
55	C₂×SD₁₆×C₇₃	—	2	2	no	—
56	C₂×SD₁₆×C₇₃	—	2	4	no	—
57	C₂×SD₁₆×C₇₃	—	2	4	no	—
58	C₂×SD₁₆×C₇₃	—	4	2	no	—
59	C₂×SD₁₆×C₇₃	—	4	2	no	—
60	C₂×D₈×C₇₃	—	2	4	no	—
61	C₂×D₈×C₇₃	—	2	4	no	—
62	C₂×D₈×C₇₃	—	4	2	no	—
63	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
66	#127×C₇₃	—	2	2	no	—
67	#127×C₇₃	D₄	1	4	yes	—
68	#124×C₇₃	—	2	8	no	—
69	#124×C₇₃	—	2	4	no	—
70	#124×C₇₃	—	2	4	no	—
71	#124×C₇₃	—	2	2	no	—
72	#124×C₇₃	—	2	2	no	—
73	#123×C₇₃	—	2	16	no	—
74	C₄×Q₈×C₇₃	—	2	2	no	—
75	C₄×Q₈×C₇₃	—	2	2	no	—
76	C₄×Q₈×C₇₃	—	2	2	no	—
77	C₄×Q₈×C₇₃	D₄	1	4	yes	—
78	C₄×D₄×C₇₃	—	2	8	no	—
79	C₄×D₄×C₇₃	—	2	4	no	—
80	C₄×D₄×C₇₃	—	2	4	no	—
81	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
93	C₂×C₄²×C₇₃	—	2	1	no	—
94	C₂×C₄²×C₇₃	—	2	1	no	—
95	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₇₃	—	2	2	no	—
98	#103×C₇₃	—	2	4	no	—
99	#103×C₇₃	—	2	2	no	—
100	#102×C₇₃	—	2	2	no	—
101	#102×C₇₃	—	4	2	no	—
102	#102×C₇₃	—	4	2	no	—
103	#97×C₇₃	—	2	2	no	—
104	#95×C₇₃	—	2	1	no	—
105	#95×C₇₃	—	2	2	no	—
106	#95×C₇₃	—	2	2	no	—
107	C₂⁴×C₇₃	—	2	2	no	—
108	C₂⁴×C₇₃	—	2	1	no	—
109	C₂×Q₈×C₇₃	—	2	2	no	—
110	C₂×Q₈×C₇₃	—	2	1	no	—
111	C₂×Q₈×C₇₃	—	2	1	no	—
112	C₂×Q₈×C₇₃	—	2	1	no	—
113	C₂×Q₈×C₇₃	—	2	2	no	—
114	C₂×Q₈×C₇₃	—	2	2	no	—
115	C₂×Q₈×C₇₃	—	2	2	no	—
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	—	4	2	no	—
118	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₇₃	—	2	4	no	—
120	C₂×D₄×C₇₃	—	2	4	no	—
121	C₂×D₄×C₇₃	—	2	2	no	—
122	C₂×D₄×C₇₃	—	2	1	no	—
123	C₂×D₄×C₇₃	—	2	1	no	—
124	C₂×D₄×C₇₃	—	2	2	no	—
125	C₂×D₄×C₇₃	—	2	2	no	—
126	C₂×D₄×C₇₃	—	2	2	no	—
127	C₂×D₄×C₇₃	—	2	2	no	—
128	C₂×D₄×C₇₃	—	2	2	no	—
129	C₂×D₄×C₇₃	—	2	2	no	—
130	C₂×D₄×C₇₃	—	4	4	no	—
131	C₂×D₄×C₇₃	—	8	1	no	—
132	C₂×D₄×C₇₃	—	8	1	no	—
133	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₇₃	—	2	1	no	—
135	C₂²×C₄×C₇₃	—	2	1	no	—
136	C₂²×C₄×C₇₃	—	2	8	no	—
137	C₂²×C₄×C₇₃	—	2	1	no	—
138	C₂²×C₄×C₇₃	—	2	2	no	—
139	C₂²×C₄×C₇₃	—	8	2	no	—
140	C₂²×C₄×C₇₃	—	8	2	no	—
141	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
146	Q₁₆×C₇₃	—	4	4	no	—
147	SD₁₆×C₇₃	—	4	8	no	—
148	SD₁₆×C₇₃	—	4	4	no	—
149	D₈×C₇₃	—	4	8	no	—
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₂×C₈×C₇₃	—	2	1	no	—
153	C₂×C₈×C₇₃	—	2	1	no	—
154	C₂×C₈×C₇₃	—	2	2	no	—
155	C₂×C₈×C₇₃	—	2	2	no	—
156	C₂×C₈×C₇₃	#41	1	4	yes	—
157	C₄⋊C₄×C₇₃	—	2	4	no	—
158	C₄⋊C₄×C₇₃	—	2	2	no	—
159	C₄⋊C₄×C₇₃	—	2	4	no	—
160	C₄⋊C₄×C₇₃	—	2	1	no	—
161	C₄⋊C₄×C₇₃	—	2	2	no	—
162	C₄⋊C₄×C₇₃	—	2	2	no	—
163	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₇₃	—	2	8	no	—
165	C₂²⋊C₄×C₇₃	—	2	8	no	—
166	C₂²⋊C₄×C₇₃	—	2	8	no	—
167	C₂²⋊C₄×C₇₃	—	4	4	no	—
168	C₂²⋊C₄×C₇₃	—	4	2	no	—
169	C₂²⋊C₄×C₇₃	—	4	2	no	—
170	C₂²⋊C₄×C₇₃	—	8	2	no	—
171	C₄²×C₇₃	—	2	4	no	—
172	C₄²×C₇₃	—	2	2	no	—
173	C₄²×C₇₃	—	2	2	no	—
174	C₄²×C₇₃	—	8	1	no	—
175	C₄²×C₇₃	C₂×D₄	1	2	yes	—
176	C₄²×C₇₃	C₂×D₄	1	2	yes	—
177	C₂³×C₇₃	—	2	4	no	—
178	C₂³×C₇₃	—	4	2	no	—
179	C₂³×C₇₃	—	4	2	no	—
180	C₂³×C₇₃	—	4	2	no	—
181	C₂³×C₇₃	—	4	2	no	—
182	C₂³×C₇₃	—	4	2	no	—
183	C₂³×C₇₃	—	4	2	no	—
184	C₂³×C₇₃	—	4	1	no	—
185	C₂³×C₇₃	—	4	2	no	—
186	C₂³×C₇₃	—	4	2	no	—
187	C₂³×C₇₃	—	4	1	no	—
188	C₂³×C₇₃	—	4	1	no	—
189	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₇₃	—	2	2	no	—
191	Q₈×C₇₃	—	2	2	no	—
192	Q₈×C₇₃	—	4	4	no	—
193	Q₈×C₇₃	—	4	2	no	—
194	Q₈×C₇₃	—	4	1	no	—
195	Q₈×C₇₃	—	4	1	no	—
196	Q₈×C₇₃	—	4	2	no	—
197	D₄×C₇₃	—	2	4	no	—
198	D₄×C₇₃	—	2	4	no	—
199	D₄×C₇₃	—	4	8	no	—
200	D₄×C₇₃	—	4	2	no	—
201	D₄×C₇₃	—	4	1	no	—
202	D₄×C₇₃	—	4	2	no	—
203	D₄×C₇₃	—	4	1	no	—
204	D₄×C₇₃	—	4	2	no	—
205	D₄×C₇₃	—	8	4	no	—
206	C₂×C₄×C₇₃	—	2	2	no	—
207	C₂×C₄×C₇₃	—	2	1	no	—
208	C₂×C₄×C₇₃	—	2	1	no	—
209	C₂×C₄×C₇₃	—	2	2	no	—
210	C₂×C₄×C₇₃	—	2	2	no	—
211	C₂×C₄×C₇₃	—	2	2	no	—
212	C₂×C₄×C₇₃	—	2	2	no	—
213	C₂×C₄×C₇₃	—	2	2	no	—
214	C₂×C₄×C₇₃	—	2	2	no	—
215	C₂×C₄×C₇₃	—	2	2	no	—
216	C₂×C₄×C₇₃	—	2	2	no	—
217	C₂×C₄×C₇₃	—	4	2	no	—
218	C₂×C₄×C₇₃	—	4	1	no	—
219	C₂×C₄×C₇₃	—	4	1	no	—
220	C₂×C₄×C₇₃	—	4	1	no	—
221	C₂×C₄×C₇₃	—	4	2	no	—
222	C₂×C₄×C₇₃	—	4	2	no	—
223	C₂×C₄×C₇₃	—	4	2	no	—
224	C₂×C₄×C₇₃	—	4	2	no	—
225	C₂×C₄×C₇₃	—	8	8	no	—
226	C₂×C₄×C₇₃	#120	1	2	yes	—
227	C₂×C₄×C₇₃	#120	1	2	yes	—
228	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
231	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
232	C₈×C₇₃	—	2	4	no	—
233	C₈×C₇₃	—	4	1	no	—
234	C₈×C₇₃	—	4	1	no	—
235	C₂²×C₇₃	—	4	4	no	—
236	C₂²×C₇₃	—	4	4	no	—
237	C₂²×C₇₃	—	4	4	no	—
238	C₂²×C₇₃	—	8	2	no	—
239	C₂²×C₇₃	—	8	2	no	—
240	C₂²×C₇₃	—	8	2	no	—
241	C₂²×C₇₃	—	8	2	no	—
242	C₂²×C₇₃	—	8	2	no	—
243	C₂²×C₇₃	—	8	2	no	—
244	C₂²×C₇₃	—	8	1	no	—
245	C₂²×C₇₃	—	8	1	no	—
246	C₂²×C₇₃	—	8	1	no	—
247	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
248	C₂²×C₇₃	#550	1	2	yes	—
249	C₂²×C₇₃	#575	1	2	yes	—
250	C₂²×C₇₃	#576	1	1	yes	characteristic
251	C₂²×C₇₃	#577	1	1	yes	characteristic
252	C₄×C₇₃	—	2	2	no	—
253	C₄×C₇₃	—	2	2	no	—
254	C₄×C₇₃	—	4	2	no	—
255	C₄×C₇₃	—	4	2	no	—
256	C₄×C₇₃	—	4	2	no	—
257	C₄×C₇₃	—	4	2	no	—
258	C₄×C₇₃	—	8	2	no	—
259	C₄×C₇₃	—	8	1	no	—
260	C₄×C₇₃	#532	1	1	yes	characteristic
261	C₄×C₇₃	#535	1	1	yes	characteristic
262	C₄×C₇₃	#546	1	2	yes	—
263	#25639	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂×C₇₃	—	8	4	no	—
265	C₂×C₇₃	—	16	1	no	—
266	C₂×C₇₃	#2431	1	1	yes	characteristic
267	C₂×C₇₃	#3005	1	1	yes	characteristic
268	C₂×C₇₃	#3012	1	1	yes	characteristic
269	C₂×C₇₃	#3401	1	2	yes	—
270	C₂×C₇₃	#3403	1	2	yes	—
271	C₂×#559	C₂×C₇₃	1	1	yes	characteristic, complemented
272	C₂×#496	C₂×C₇₃	1	1	yes	characteristic
273	C₂×#464	C₂×C₇₃	1	1	yes	characteristic, complemented
274	#2592	C₂×C₇₃	1	1	yes	characteristic, complemented
275	#2015	C₂×C₇₃	1	2	yes	complemented
276	#2012	C₂×C₇₃	1	2	yes	complemented
277	#1985	C₂×C₇₃	1	1	yes	characteristic, complemented
278	#1982	C₂×C₇₃	1	1	yes	characteristic, complemented
279	#1879	C₂×C₇₃	1	2	yes	complemented
280	#1877	C₂×C₇₃	1	2	yes	complemented
281	#1763	C₂×C₇₃	1	1	yes	characteristic, complemented
282	C₇₃	#25639	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
284	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
285	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
286	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
287	#559	—	2	4	no	—
288	#559	—	2	4	no	—
289	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
290	C₂×#124	—	2	1	no	—
291	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
292	C₂×#124	C₂²×C₇₃	1	2	yes	—
293	C₂×#123	—	2	2	no	—
294	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
295	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
296	C₂×C₄×D₄	—	2	1	no	—
297	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
298	#496	—	2	4	no	—
299	#464	—	2	4	no	—
300	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
301	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
302	C₂×#103	C₂²×C₇₃	1	2	yes	—
303	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
304	C₂×#102	C₂²×C₇₃	1	2	yes	—
305	C₂×#102	C₂²×C₇₃	1	2	yes	—
306	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
307	#397	—	2	1	no	—
308	#393	—	2	1	no	—
309	#391	C₂²×C₇₃	1	2	yes	—
310	#390	C₂²×C₇₃	1	2	yes	—
311	#388	—	2	2	no	—
312	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
313	#340	C₂²×C₇₃	1	2	yes	—
314	#336	C₂²×C₇₃	1	2	yes	—
315	#336	C₂²×C₇₃	1	2	yes	—
316	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
317	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
318	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
322	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
323	C₂³×C₄	—	2	2	no	—
324	C₂×Q₁₆	—	2	2	no	—
325	C₂×Q₁₆	—	4	2	no	—
326	C₂×SD₁₆	—	2	2	no	—
327	C₂×SD₁₆	—	2	4	no	—
328	C₂×SD₁₆	—	2	4	no	—
329	C₂×SD₁₆	—	4	2	no	—
330	C₂×SD₁₆	—	4	2	no	—
331	C₂×D₈	—	2	4	no	—
332	C₂×D₈	—	2	4	no	—
333	C₂×D₈	—	4	2	no	—
334	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
337	#127	—	2	2	no	—
338	#127	D₄×C₇₃	1	4	yes	—
339	#124	—	2	8	no	—
340	#124	—	2	4	no	—
341	#124	—	2	4	no	—
342	#124	—	2	2	no	—
343	#124	—	2	2	no	—
344	#123	—	2	16	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	D₄×C₇₃	1	4	yes	—
349	C₄×D₄	—	2	8	no	—
350	C₄×D₄	—	2	4	no	—
351	C₄×D₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
354	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
367	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
368	C₄⋊C₈	—	2	2	no	—
369	#103	—	2	4	no	—
370	#103	—	2	2	no	—
371	#102	—	2	2	no	—
372	#102	—	4	2	no	—
373	#102	—	4	2	no	—
374	#97	—	2	2	no	—
375	#95	—	2	1	no	—
376	#95	—	2	2	no	—
377	#95	—	2	2	no	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	2	1	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	4	2	no	—
389	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	4	4	no	—
402	C₂×D₄	—	8	1	no	—
403	C₂×D₄	—	8	1	no	—
404	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	8	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	8	2	no	—
411	C₂²×C₄	—	8	2	no	—
412	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
414	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
417	Q₁₆	—	4	4	no	—
418	SD₁₆	—	4	8	no	—
419	SD₁₆	—	4	4	no	—
420	D₈	—	4	8	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	#41×C₇₃	1	4	yes	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	8	2	no	—
442	C₄²	—	2	4	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	8	1	no	—
446	C₄²	C₂×D₄×C₇₃	1	2	yes	—
447	C₄²	C₂×D₄×C₇₃	1	2	yes	—
448	C₂³	—	2	4	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
461	Q₈	—	2	2	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	4	4	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	2	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	4	no	—
470	D₄	—	4	8	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	2	no	—
476	D₄	—	8	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	8	8	no	—
497	C₂×C₄	#120×C₇₃	1	2	yes	—
498	C₂×C₄	#120×C₇₃	1	2	yes	—
499	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
501	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
502	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
503	C₈	—	2	4	no	—
504	C₈	—	4	1	no	—
505	C₈	—	4	1	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	1	no	—
518	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
519	C₂²	#550×C₇₃	1	2	yes	—
520	C₂²	#575×C₇₃	1	2	yes	—
521	C₂²	#576×C₇₃	1	1	yes	characteristic
522	C₂²	#577×C₇₃	1	1	yes	characteristic
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	8	2	no	—
530	C₄	—	8	1	no	—
531	C₄	#532×C₇₃	1	1	yes	characteristic
532	C₄	#535×C₇₃	1	1	yes	characteristic
533	C₄	#546×C₇₃	1	2	yes	—
534	C₂	—	8	4	no	—
535	C₂	—	16	1	no	—
536	C₂	C₇₃×#2431	1	1	yes	characteristic
537	C₂	C₇₃×#3005	1	1	yes	characteristic
538	C₂	C₇₃×#3012	1	1	yes	characteristic
539	C₂	C₇₃×#3401	1	2	yes	—
540	C₂	C₇₃×#3403	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#496×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×Q₈×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#559×C₇₃	C₂	semidirect
3. C₂×#464×C₇₃	C₂	semidirect
4. C₇₃×#2592	C₂	semidirect
5. C₇₃×#2015	C₂	semidirect
6. C₇₃×#2012	C₂	semidirect
7. C₇₃×#1985	C₂	semidirect
8. C₇₃×#1982	C₂	semidirect
9. C₇₃×#1879	C₂	semidirect
10. C₇₃×#1877	C₂	semidirect
11. C₇₃×#1763	C₂	semidirect
263. #25639	C₇₃	direct (N × H)
271. C₂×#559	C₂×C₇₃	semidirect
273. C₂×#464	C₂×C₇₃	semidirect
274. #2592	C₂×C₇₃	semidirect
275. #2015	C₂×C₇₃	semidirect
276. #2012	C₂×C₇₃	semidirect
277. #1985	C₂×C₇₃	semidirect
278. #1982	C₂×C₇₃	semidirect
279. #1879	C₂×C₇₃	semidirect
280. #1877	C₂×C₇₃	semidirect
281. #1763	C₂×C₇₃	semidirect
282. C₇₃	#25639	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×#559×C₇₃	2
C₂×#496×C₇₃	2
C₂×#464×C₇₃	2
C₇₃×#2592	2
C₇₃×#2015	2
C₇₃×#2012	2
C₇₃×#1985	2
C₇₃×#1982	2
C₇₃×#1879	2
C₇₃×#1877	2
C₇₃×#1763	2
#25639	73

Subgroups — C73×#25639 #32935043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25639 #32935043