Subgroups — C₇₃×#25580 #32934984

Order 18688.

1162 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#489×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#464×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2540	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2001	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2000	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1875	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1873	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	1	yes	characteristic
14	#556×C₇₃	—	2	4	no	—
15	#556×C₇₃	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#126×C₇₃	—	2	2	no	—
18	C₂×#124×C₇₃	—	2	1	no	—
19	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
22	C₂×#121×C₇₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₇₃	—	2	1	no	—
24	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#117×C₇₃	C₂²	1	2	yes	—
27	#489×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	2	yes	—
31	C₂×#103×C₇₃	C₂²	1	2	yes	—
32	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₇₃	C₂²	1	2	yes	—
34	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
37	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
38	#399×C₇₃	—	2	1	no	—
39	#392×C₇₃	—	2	1	no	—
40	#390×C₇₃	—	2	2	no	—
41	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	#340×C₇₃	C₂²	1	2	yes	—
43	#340×C₇₃	C₂²	1	2	yes	—
44	#340×C₇₃	C₂²	1	2	yes	—
45	C₂²×Q₈×C₇₃	—	2	1	no	—
46	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₇₃	—	2	2	no	—
49	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
52	C₂×Q₁₆×C₇₃	—	2	2	no	—
53	C₂×Q₁₆×C₇₃	—	4	2	no	—
54	C₂×SD₁₆×C₇₃	—	2	2	no	—
55	C₂×SD₁₆×C₇₃	—	4	2	no	—
56	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₇₃	—	2	2	no	—
60	C₄⋊Q₈×C₇₃	D₄	1	4	yes	complemented
61	#126×C₇₃	—	2	16	no	—
62	#124×C₇₃	—	2	8	no	—
63	#124×C₇₃	—	2	2	no	—
64	#124×C₇₃	—	2	2	no	—
65	C₂²⋊Q₈×C₇₃	—	2	4	no	—
66	C₂²⋊Q₈×C₇₃	—	2	4	no	—
67	C₂²⋊Q₈×C₇₃	—	2	4	no	—
68	C₂²⋊Q₈×C₇₃	—	4	2	no	—
69	#121×C₇₃	—	2	4	no	—
70	#121×C₇₃	—	4	2	no	—
71	C₄×Q₈×C₇₃	—	2	8	no	—
72	C₄×Q₈×C₇₃	—	2	2	no	—
73	C₄×Q₈×C₇₃	D₄	1	4	yes	complemented
74	C₄×D₄×C₇₃	—	2	2	no	—
75	C₄×D₄×C₇₃	—	2	2	no	—
76	#117×C₇₃	—	2	4	no	—
77	#117×C₇₃	—	2	4	no	—
78	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
79	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
82	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
93	C₂×C₄²×C₇₃	—	2	2	no	—
94	C₂×C₄²×C₇₃	—	2	1	no	—
95	C₂×C₄²×C₇₃	—	2	1	no	—
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₇₃	—	2	2	no	—
98	#103×C₇₃	—	2	2	no	—
99	#103×C₇₃	—	2	4	no	—
100	#103×C₇₃	—	2	4	no	—
101	#102×C₇₃	—	2	2	no	—
102	#102×C₇₃	—	2	4	no	—
103	C₂²⋊C₈×C₇₃	—	4	2	no	—
104	C₂²⋊C₈×C₇₃	—	4	2	no	—
105	#97×C₇₃	—	2	2	no	—
106	#95×C₇₃	—	2	1	no	—
107	C₂⁴×C₇₃	—	2	1	no	—
108	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₇₃	—	2	4	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	4	no	—
118	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₇₃	—	2	2	no	—
120	C₂×D₄×C₇₃	—	2	1	no	—
121	C₂×D₄×C₇₃	—	2	1	no	—
122	C₂×D₄×C₇₃	—	2	2	no	—
123	C₂×D₄×C₇₃	—	2	2	no	—
124	C₂×D₄×C₇₃	—	4	2	no	—
125	C₂×D₄×C₇₃	—	4	4	no	—
126	C₂×D₄×C₇₃	—	4	4	no	—
127	C₂×D₄×C₇₃	—	8	2	no	—
128	C₂²×C₄×C₇₃	—	2	2	no	—
129	C₂²×C₄×C₇₃	—	2	1	no	—
130	C₂²×C₄×C₇₃	—	2	1	no	—
131	C₂²×C₄×C₇₃	—	2	2	no	—
132	C₂²×C₄×C₇₃	—	2	2	no	—
133	C₂²×C₄×C₇₃	—	2	2	no	—
134	C₂²×C₄×C₇₃	—	2	2	no	—
135	C₂²×C₄×C₇₃	—	2	2	no	—
136	C₂²×C₄×C₇₃	—	2	2	no	—
137	C₂²×C₄×C₇₃	—	2	2	no	—
138	C₂²×C₄×C₇₃	—	2	1	no	—
139	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
143	Q₁₆×C₇₃	—	4	4	no	—
144	SD₁₆×C₇₃	—	4	4	no	—
145	C₂×C₈×C₇₃	—	2	2	no	—
146	C₂×C₈×C₇₃	—	2	1	no	—
147	C₂×C₈×C₇₃	—	2	1	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₂×C₈×C₇₃	—	2	2	no	—
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₄⋊C₄×C₇₃	—	2	8	no	—
153	C₄⋊C₄×C₇₃	—	2	4	no	—
154	C₄⋊C₄×C₇₃	—	2	4	no	—
155	C₄⋊C₄×C₇₃	—	2	2	no	—
156	C₄⋊C₄×C₇₃	—	2	1	no	—
157	C₄⋊C₄×C₇₃	—	2	2	no	—
158	C₄⋊C₄×C₇₃	—	2	2	no	—
159	C₄⋊C₄×C₇₃	—	4	4	no	—
160	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
162	C₄⋊C₄×C₇₃	#41	1	4	yes	—
163	C₂²⋊C₄×C₇₃	—	2	8	no	—
164	C₂²⋊C₄×C₇₃	—	2	8	no	—
165	C₂²⋊C₄×C₇₃	—	2	4	no	—
166	C₂²⋊C₄×C₇₃	—	4	4	no	—
167	C₂²⋊C₄×C₇₃	—	4	4	no	—
168	C₂²⋊C₄×C₇₃	—	4	2	no	—
169	C₂²⋊C₄×C₇₃	—	4	2	no	—
170	C₄²×C₇₃	—	2	8	no	—
171	C₄²×C₇₃	—	2	4	no	—
172	C₄²×C₇₃	—	8	1	no	—
173	C₄²×C₇₃	C₂×D₄	1	2	yes	—
174	C₄²×C₇₃	C₂×D₄	1	2	yes	—
175	C₂³×C₇₃	—	2	2	no	—
176	C₂³×C₇₃	—	2	2	no	—
177	C₂³×C₇₃	—	2	2	no	—
178	C₂³×C₇₃	—	2	2	no	—
179	C₂³×C₇₃	—	2	2	no	—
180	C₂³×C₇₃	—	2	2	no	—
181	C₂³×C₇₃	—	2	2	no	—
182	C₂³×C₇₃	—	4	1	no	—
183	C₂³×C₇₃	—	4	2	no	—
184	C₂³×C₇₃	—	4	2	no	—
185	C₂³×C₇₃	—	4	1	no	—
186	C₂³×C₇₃	—	4	1	no	—
187	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₇₃	—	2	2	no	—
189	Q₈×C₇₃	—	2	2	no	—
190	Q₈×C₇₃	—	4	8	no	—
191	Q₈×C₇₃	—	4	2	no	—
192	Q₈×C₇₃	—	4	1	no	—
193	Q₈×C₇₃	—	4	1	no	—
194	Q₈×C₇₃	—	4	2	no	—
195	D₄×C₇₃	—	4	4	no	—
196	D₄×C₇₃	—	4	1	no	—
197	D₄×C₇₃	—	4	1	no	—
198	D₄×C₇₃	—	4	2	no	—
199	D₄×C₇₃	—	8	8	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	2	1	no	—
202	C₂×C₄×C₇₃	—	2	1	no	—
203	C₂×C₄×C₇₃	—	2	2	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	2	no	—
206	C₂×C₄×C₇₃	—	2	4	no	—
207	C₂×C₄×C₇₃	—	2	4	no	—
208	C₂×C₄×C₇₃	—	2	2	no	—
209	C₂×C₄×C₇₃	—	2	2	no	—
210	C₂×C₄×C₇₃	—	4	2	no	—
211	C₂×C₄×C₇₃	—	4	2	no	—
212	C₂×C₄×C₇₃	—	4	4	no	—
213	C₂×C₄×C₇₃	—	4	2	no	—
214	C₂×C₄×C₇₃	—	4	1	no	—
215	C₂×C₄×C₇₃	—	4	1	no	—
216	C₂×C₄×C₇₃	—	4	2	no	—
217	C₂×C₄×C₇₃	—	4	2	no	—
218	C₂×C₄×C₇₃	—	4	2	no	—
219	C₂×C₄×C₇₃	—	4	2	no	—
220	C₂×C₄×C₇₃	—	4	1	no	—
221	C₂×C₄×C₇₃	—	4	2	no	—
222	C₂×C₄×C₇₃	#120	1	2	yes	—
223	C₂×C₄×C₇₃	#120	1	2	yes	—
224	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
227	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
228	C₈×C₇₃	—	4	1	no	—
229	C₈×C₇₃	—	4	1	no	—
230	C₈×C₇₃	—	4	2	no	—
231	C₂²×C₇₃	—	4	2	no	—
232	C₂²×C₇₃	—	4	2	no	—
233	C₂²×C₇₃	—	4	2	no	—
234	C₂²×C₇₃	—	4	2	no	—
235	C₂²×C₇₃	—	4	2	no	—
236	C₂²×C₇₃	—	4	2	no	—
237	C₂²×C₇₃	—	4	2	no	—
238	C₂²×C₇₃	—	8	1	no	—
239	C₂²×C₇₃	—	8	1	no	—
240	C₂²×C₇₃	—	8	1	no	—
241	C₂²×C₇₃	—	8	2	no	—
242	C₂²×C₇₃	—	8	2	no	—
243	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
244	C₂²×C₇₃	#546	1	2	yes	—
245	C₂²×C₇₃	#575	1	2	yes	—
246	C₂²×C₇₃	#577	1	1	yes	characteristic
247	C₂²×C₇₃	#578	1	1	yes	characteristic
248	C₄×C₇₃	—	2	2	no	—
249	C₄×C₇₃	—	2	2	no	—
250	C₄×C₇₃	—	4	2	no	—
251	C₄×C₇₃	—	4	2	no	—
252	C₄×C₇₃	—	4	4	no	—
253	C₄×C₇₃	—	4	2	no	—
254	C₄×C₇₃	—	4	4	no	—
255	C₄×C₇₃	—	8	1	no	—
256	C₄×C₇₃	#532	1	1	yes	characteristic
257	C₄×C₇₃	#535	1	1	yes	characteristic
258	C₄×C₇₃	#550	1	2	yes	—
259	#25580	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂×C₇₃	—	8	2	no	—
261	C₂×C₇₃	—	16	1	no	—
262	C₂×C₇₃	#2431	1	1	yes	characteristic
263	C₂×C₇₃	#3005	1	1	yes	characteristic
264	C₂×C₇₃	#3013	1	1	yes	characteristic
265	C₂×C₇₃	#3311	1	2	yes	—
266	C₂×C₇₃	#3313	1	2	yes	—
267	C₂×#556	C₂×C₇₃	1	1	yes	characteristic, complemented
268	C₂×#489	C₂×C₇₃	1	1	yes	characteristic, complemented
269	C₂×#464	C₂×C₇₃	1	1	yes	characteristic, complemented
270	#2540	C₂×C₇₃	1	1	yes	characteristic
271	#2001	C₂×C₇₃	1	2	yes	complemented
272	#2000	C₂×C₇₃	1	2	yes	complemented
273	#1987	C₂×C₇₃	1	1	yes	characteristic, complemented
274	#1955	C₂×C₇₃	1	1	yes	characteristic, complemented
275	#1875	C₂×C₇₃	1	2	yes	complemented
276	#1873	C₂×C₇₃	1	2	yes	complemented
277	#1763	C₂×C₇₃	1	1	yes	characteristic, complemented
278	C₇₃	#25580	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
280	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
281	#556	—	2	4	no	—
282	#556	—	2	4	no	—
283	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
284	C₂×#126	—	2	2	no	—
285	C₂×#124	—	2	1	no	—
286	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
287	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
288	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
289	C₂×#121	C₂²×C₇₃	1	2	yes	—
290	C₂×C₄×Q₈	—	2	1	no	—
291	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
293	C₂×#117	C₂²×C₇₃	1	2	yes	—
294	#489	—	2	4	no	—
295	#464	—	2	4	no	—
296	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
297	C₂×#103	C₂²×C₇₃	1	2	yes	—
298	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
299	C₂×#103	C₂²×C₇₃	1	2	yes	—
300	C₂×#102	C₂²×C₇₃	1	2	yes	—
301	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
302	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
304	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
305	#399	—	2	1	no	—
306	#392	—	2	1	no	—
307	#390	—	2	2	no	—
308	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
309	#340	C₂²×C₇₃	1	2	yes	—
310	#340	C₂²×C₇₃	1	2	yes	—
311	#340	C₂²×C₇₃	1	2	yes	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
314	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
317	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
319	C₂×Q₁₆	—	2	2	no	—
320	C₂×Q₁₆	—	4	2	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×SD₁₆	—	4	2	no	—
323	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
326	C₄⋊Q₈	—	2	2	no	—
327	C₄⋊Q₈	D₄×C₇₃	1	4	yes	complemented
328	#126	—	2	16	no	—
329	#124	—	2	8	no	—
330	#124	—	2	2	no	—
331	#124	—	2	2	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	C₂²⋊Q₈	—	2	4	no	—
334	C₂²⋊Q₈	—	2	4	no	—
335	C₂²⋊Q₈	—	4	2	no	—
336	#121	—	2	4	no	—
337	#121	—	4	2	no	—
338	C₄×Q₈	—	2	8	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	D₄×C₇₃	1	4	yes	complemented
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	#117	—	2	4	no	—
344	#117	—	2	4	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
364	C₄⋊C₈	—	2	2	no	—
365	#103	—	2	2	no	—
366	#103	—	2	4	no	—
367	#103	—	2	4	no	—
368	#102	—	2	2	no	—
369	#102	—	2	4	no	—
370	C₂²⋊C₈	—	4	2	no	—
371	C₂²⋊C₈	—	4	2	no	—
372	#97	—	2	2	no	—
373	#95	—	2	1	no	—
374	C₂⁴	—	2	1	no	—
375	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	4	4	no	—
385	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	4	4	no	—
394	C₂×D₄	—	8	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
410	Q₁₆	—	4	4	no	—
411	SD₁₆	—	4	4	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	4	4	no	—
427	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
428	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
429	C₄⋊C₄	#41×C₇₃	1	4	yes	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	—	4	4	no	—
435	C₂²⋊C₄	—	4	2	no	—
436	C₂²⋊C₄	—	4	2	no	—
437	C₄²	—	2	8	no	—
438	C₄²	—	2	4	no	—
439	C₄²	—	8	1	no	—
440	C₄²	C₂×D₄×C₇₃	1	2	yes	—
441	C₄²	C₂×D₄×C₇₃	1	2	yes	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
455	Q₈	—	2	2	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	4	8	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	4	1	no	—
460	Q₈	—	4	1	no	—
461	Q₈	—	4	2	no	—
462	D₄	—	4	4	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	2	no	—
466	D₄	—	8	8	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	#120×C₇₃	1	2	yes	—
490	C₂×C₄	#120×C₇₃	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
493	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
494	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
495	C₈	—	4	1	no	—
496	C₈	—	4	1	no	—
497	C₈	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	1	no	—
510	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
511	C₂²	#546×C₇₃	1	2	yes	—
512	C₂²	#575×C₇₃	1	2	yes	—
513	C₂²	#577×C₇₃	1	1	yes	characteristic
514	C₂²	#578×C₇₃	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	4	4	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	1	no	—
523	C₄	#532×C₇₃	1	1	yes	characteristic
524	C₄	#535×C₇₃	1	1	yes	characteristic
525	C₄	#550×C₇₃	1	2	yes	—
526	C₂	—	8	2	no	—
527	C₂	—	16	1	no	—
528	C₂	C₇₃×#2431	1	1	yes	characteristic
529	C₂	C₇₃×#3005	1	1	yes	characteristic
530	C₂	C₇₃×#3013	1	1	yes	characteristic
531	C₂	C₇₃×#3311	1	2	yes	—
532	C₂	C₇₃×#3313	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#2540	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#556×C₇₃	C₂	semidirect
2. C₂×#489×C₇₃	C₂	semidirect
3. C₂×#464×C₇₃	C₂	semidirect
5. C₇₃×#2001	C₂	semidirect
6. C₇₃×#2000	C₂	semidirect
7. C₇₃×#1987	C₂	semidirect
8. C₇₃×#1955	C₂	semidirect
9. C₇₃×#1875	C₂	semidirect
10. C₇₃×#1873	C₂	semidirect
11. C₇₃×#1763	C₂	semidirect
60. C₄⋊Q₈×C₇₃	D₄	semidirect
73. C₄×Q₈×C₇₃	D₄	semidirect
259. #25580	C₇₃	direct (N × H)
267. C₂×#556	C₂×C₇₃	semidirect
268. C₂×#489	C₂×C₇₃	semidirect
269. C₂×#464	C₂×C₇₃	semidirect
271. #2001	C₂×C₇₃	semidirect
272. #2000	C₂×C₇₃	semidirect
273. #1987	C₂×C₇₃	semidirect
274. #1955	C₂×C₇₃	semidirect
275. #1875	C₂×C₇₃	semidirect
276. #1873	C₂×C₇₃	semidirect
277. #1763	C₂×C₇₃	semidirect
278. C₇₃	#25580	direct (N × H)
327. C₄⋊Q₈	D₄×C₇₃	semidirect
340. C₄×Q₈	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₇₃	2
C₂×#489×C₇₃	2
C₂×#464×C₇₃	2
C₇₃×#2540	2
C₇₃×#2001	2
C₇₃×#2000	2
C₇₃×#1987	2
C₇₃×#1955	2
C₇₃×#1875	2
C₇₃×#1873	2
C₇₃×#1763	2
#25580	73

Subgroups — C73×#25580 #32934984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25580 #32934984