Subgroups — C₇₃×#25617 #32935021

Order 18688.

1106 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2861	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2007	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2006	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1998	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1962	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1883	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1882	C₂	1	2	yes	maximal, complemented
11	C₄×#104×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₇₃	C₂²	1	2	yes	—
13	C₂×#137×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
15	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	1	yes	characteristic
16	#553×C₇₃	—	2	2	no	—
17	#553×C₇₃	—	2	4	no	—
18	#552×C₇₃	—	2	2	no	—
19	#541×C₇₃	—	2	1	no	—
20	#540×C₇₃	—	2	1	no	—
21	#537×C₇₃	C₂²	1	2	yes	—
22	#532×C₇₃	C₂²	1	1	yes	characteristic
23	#529×C₇₃	—	2	2	no	—
24	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
26	#520×C₇₃	C₂²	1	2	yes	—
27	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
28	#497×C₇₃	—	2	1	no	—
29	#496×C₇₃	—	2	1	no	—
30	#495×C₇₃	—	2	2	no	—
31	#464×C₇₃	—	2	2	no	—
32	#463×C₇₃	—	2	2	no	—
33	#423×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×#104×C₇₃	C₂²	1	2	yes	—
35	C₂×#104×C₇₃	C₂²	1	2	yes	—
36	C₂×#104×C₇₃	C₂²	1	2	yes	—
37	#419×C₇₃	C₂²	1	1	yes	characteristic
38	#418×C₇₃	C₂²	1	1	yes	characteristic
39	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
40	#391×C₇₃	C₂²	1	2	yes	—
41	#390×C₇₃	C₂²	1	2	yes	—
42	#388×C₇₃	—	2	4	no	—
43	C₄³×C₇₃	C₂²	1	1	yes	characteristic
44	#343×C₇₃	C₂²	1	2	yes	—
45	#343×C₇₃	C₂²	1	2	yes	—
46	#339×C₇₃	C₂²	1	2	yes	—
47	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
48	C₂×#41×C₇₃	C₂³	1	2	yes	—
49	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
51	#137×C₇₃	—	2	4	no	—
52	#137×C₇₃	—	4	2	no	—
53	#137×C₇₃	—	4	2	no	—
54	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
55	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
56	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
57	C₂×Q₁₆×C₇₃	—	2	1	no	—
58	C₂×Q₁₆×C₇₃	—	2	2	no	—
59	C₂×SD₁₆×C₇₃	—	2	1	no	—
60	C₂×SD₁₆×C₇₃	—	2	2	no	—
61	C₂×SD₁₆×C₇₃	—	2	1	no	—
62	C₂×SD₁₆×C₇₃	—	2	2	no	—
63	C₂×D₈×C₇₃	—	2	1	no	—
64	C₂×D₈×C₇₃	—	2	2	no	—
65	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
69	#127×C₇₃	D₄	1	1	yes	characteristic
70	#126×C₇₃	—	2	4	no	—
71	#126×C₇₃	—	2	4	no	—
72	#125×C₇₃	—	2	4	no	—
73	#125×C₇₃	—	2	1	no	—
74	#125×C₇₃	—	2	1	no	—
75	#125×C₇₃	—	2	2	no	—
76	#124×C₇₃	—	2	2	no	—
77	#124×C₇₃	—	2	1	no	—
78	#124×C₇₃	—	2	1	no	—
79	#124×C₇₃	D₄	1	2	yes	—
80	#123×C₇₃	—	2	4	no	—
81	#123×C₇₃	—	2	4	no	—
82	C₂²⋊Q₈×C₇₃	—	2	2	no	—
83	C₂²⋊Q₈×C₇₃	—	2	2	no	—
84	#121×C₇₃	—	2	4	no	—
85	#121×C₇₃	—	2	2	no	—
86	#121×C₇₃	—	2	2	no	—
87	#121×C₇₃	—	2	2	no	—
88	#121×C₇₃	—	2	4	no	—
89	C₄×Q₈×C₇₃	—	2	2	no	—
90	C₄×Q₈×C₇₃	D₄	1	2	yes	—
91	C₄×D₄×C₇₃	—	2	4	no	—
92	C₄×D₄×C₇₃	—	2	2	no	—
93	C₄×D₄×C₇₃	—	2	2	no	—
94	C₄×D₄×C₇₃	—	2	4	no	—
95	C₄×D₄×C₇₃	—	2	2	no	—
96	C₄×D₄×C₇₃	D₄	1	2	yes	—
97	#117×C₇₃	—	2	4	no	—
98	#117×C₇₃	—	2	2	no	—
99	#117×C₇₃	—	2	1	no	—
100	#117×C₇₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
102	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
103	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
104	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
105	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
106	C₂×C₄²×C₇₃	—	2	1	no	—
107	C₂×C₄²×C₇₃	—	2	2	no	—
108	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
109	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₇₃	—	2	2	no	—
111	#104×C₇₃	—	2	4	no	—
112	#104×C₇₃	—	4	2	no	—
113	#104×C₇₃	—	4	2	no	—
114	#103×C₇₃	—	2	2	no	—
115	#102×C₇₃	—	2	2	no	—
116	#97×C₇₃	—	2	1	no	—
117	C₄×C₈×C₇₃	—	2	1	no	—
118	#95×C₇₃	—	2	4	no	—
119	C₂⁴×C₇₃	—	2	1	no	—
120	#41×C₇₃	—	2	2	no	—
121	#41×C₇₃	—	2	2	no	—
122	#41×C₇₃	—	2	2	no	—
123	#41×C₇₃	—	2	2	no	—
124	#41×C₇₃	—	2	2	no	—
125	#41×C₇₃	—	2	2	no	—
126	C₂×Q₈×C₇₃	—	2	1	no	—
127	C₂×Q₈×C₇₃	—	2	1	no	—
128	C₂×Q₈×C₇₃	—	2	2	no	—
129	C₂×Q₈×C₇₃	—	2	2	no	—
130	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
131	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₇₃	—	2	1	no	—
133	C₂×D₄×C₇₃	—	2	2	no	—
134	C₂×D₄×C₇₃	—	2	4	no	—
135	C₂×D₄×C₇₃	—	2	2	no	—
136	C₂×D₄×C₇₃	—	2	1	no	—
137	C₂×D₄×C₇₃	—	2	1	no	—
138	C₂×D₄×C₇₃	—	2	2	no	—
139	C₂×D₄×C₇₃	—	2	2	no	—
140	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₃	—	2	2	no	—
143	C₂²×C₄×C₇₃	—	2	4	no	—
144	C₂²×C₄×C₇₃	—	2	1	no	—
145	C₂²×C₄×C₇₃	—	2	2	no	—
146	C₂²×C₄×C₇₃	—	2	2	no	—
147	C₂²×C₄×C₇₃	—	2	1	no	—
148	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
151	Q₁₆×C₇₃	—	4	4	no	—
152	Q₁₆×C₇₃	—	4	2	no	—
153	SD₁₆×C₇₃	—	4	4	no	—
154	SD₁₆×C₇₃	—	4	4	no	—
155	SD₁₆×C₇₃	—	4	2	no	—
156	SD₁₆×C₇₃	—	4	2	no	—
157	D₈×C₇₃	—	4	4	no	—
158	D₈×C₇₃	—	4	2	no	—
159	M₁₆×C₇₃	—	2	2	no	—
160	M₁₆×C₇₃	—	2	2	no	—
161	M₁₆×C₇₃	—	2	2	no	—
162	M₁₆×C₇₃	#41	1	4	yes	—
163	C₂×C₈×C₇₃	—	2	2	no	—
164	C₂×C₈×C₇₃	—	2	1	no	—
165	C₂×C₈×C₇₃	—	2	1	no	—
166	C₄⋊C₄×C₇₃	—	2	4	no	—
167	C₄⋊C₄×C₇₃	—	2	4	no	—
168	C₄⋊C₄×C₇₃	—	2	4	no	—
169	C₄⋊C₄×C₇₃	—	2	4	no	—
170	C₄⋊C₄×C₇₃	—	2	2	no	—
171	C₄⋊C₄×C₇₃	—	2	2	no	—
172	C₄⋊C₄×C₇₃	—	2	2	no	—
173	C₄⋊C₄×C₇₃	—	2	2	no	—
174	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
175	C₂²⋊C₄×C₇₃	—	2	4	no	—
176	C₂²⋊C₄×C₇₃	—	2	4	no	—
177	C₂²⋊C₄×C₇₃	—	2	4	no	—
178	C₂²⋊C₄×C₇₃	—	2	1	no	—
179	C₂²⋊C₄×C₇₃	—	2	2	no	—
180	C₂²⋊C₄×C₇₃	—	2	2	no	—
181	C₂²⋊C₄×C₇₃	—	2	2	no	—
182	C₂²⋊C₄×C₇₃	—	4	8	no	—
183	C₂²⋊C₄×C₇₃	—	4	2	no	—
184	C₂²⋊C₄×C₇₃	—	4	2	no	—
185	C₄²×C₇₃	—	2	4	no	—
186	C₄²×C₇₃	—	2	2	no	—
187	C₄²×C₇₃	—	2	1	no	—
188	C₄²×C₇₃	—	2	2	no	—
189	C₄²×C₇₃	—	2	2	no	—
190	C₄²×C₇₃	—	4	4	no	—
191	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₇₃	C₂×D₄	1	2	yes	—
194	C₂³×C₇₃	—	2	2	no	—
195	C₂³×C₇₃	—	2	1	no	—
196	C₂³×C₇₃	—	4	4	no	—
197	C₂³×C₇₃	—	4	1	no	—
198	C₂³×C₇₃	—	4	2	no	—
199	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₇₃	—	2	1	no	—
201	Q₈×C₇₃	—	2	1	no	—
202	Q₈×C₇₃	—	2	2	no	—
203	Q₈×C₇₃	—	2	2	no	—
204	Q₈×C₇₃	—	4	1	no	—
205	Q₈×C₇₃	—	4	1	no	—
206	Q₈×C₇₃	—	4	2	no	—
207	D₄×C₇₃	—	2	1	no	—
208	D₄×C₇₃	—	2	1	no	—
209	D₄×C₇₃	—	2	2	no	—
210	D₄×C₇₃	—	2	2	no	—
211	D₄×C₇₃	—	4	2	no	—
212	D₄×C₇₃	—	4	2	no	—
213	D₄×C₇₃	—	4	2	no	—
214	D₄×C₇₃	—	4	1	no	—
215	D₄×C₇₃	—	4	1	no	—
216	D₄×C₇₃	—	4	2	no	—
217	D₄×C₇₃	—	8	2	no	—
218	D₄×C₇₃	—	8	4	no	—
219	C₂×C₄×C₇₃	—	2	4	no	—
220	C₂×C₄×C₇₃	—	2	2	no	—
221	C₂×C₄×C₇₃	—	2	2	no	—
222	C₂×C₄×C₇₃	—	2	1	no	—
223	C₂×C₄×C₇₃	—	2	4	no	—
224	C₂×C₄×C₇₃	—	4	2	no	—
225	C₂×C₄×C₇₃	—	4	2	no	—
226	C₂×C₄×C₇₃	—	4	2	no	—
227	C₂×C₄×C₇₃	—	4	2	no	—
228	C₂×C₄×C₇₃	—	4	2	no	—
229	C₂×C₄×C₇₃	—	4	2	no	—
230	C₂×C₄×C₇₃	—	4	4	no	—
231	C₂×C₄×C₇₃	—	4	1	no	—
232	C₂×C₄×C₇₃	—	4	2	no	—
233	C₂×C₄×C₇₃	—	8	2	no	—
234	C₂×C₄×C₇₃	—	8	4	no	—
235	C₂×C₄×C₇₃	#120	1	2	yes	—
236	C₂×C₄×C₇₃	#120	1	2	yes	—
237	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
240	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
241	C₈×C₇₃	—	2	4	no	—
242	C₈×C₇₃	—	4	1	no	—
243	C₈×C₇₃	—	4	1	no	—
244	C₂²×C₇₃	—	2	2	no	—
245	C₂²×C₇₃	—	4	2	no	—
246	C₂²×C₇₃	—	4	1	no	—
247	C₂²×C₇₃	—	4	2	no	—
248	C₂²×C₇₃	—	4	2	no	—
249	C₂²×C₇₃	—	4	2	no	—
250	C₂²×C₇₃	—	8	4	no	—
251	C₂²×C₇₃	—	8	1	no	—
252	C₂²×C₇₃	—	8	2	no	—
253	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
254	C₂²×C₇₃	#550	1	2	yes	—
255	C₄×C₇₃	—	2	2	no	—
256	C₄×C₇₃	—	2	2	no	—
257	C₄×C₇₃	—	4	4	no	—
258	C₄×C₇₃	—	4	2	no	—
259	C₄×C₇₃	—	4	1	no	—
260	C₄×C₇₃	—	4	4	no	—
261	C₄×C₇₃	—	4	2	no	—
262	C₄×C₇₃	—	8	1	no	—
263	C₄×C₇₃	#532	1	1	yes	characteristic
264	C₄×C₇₃	#535	1	1	yes	characteristic
265	C₄×C₇₃	#546	1	2	yes	—
266	#25617	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂×C₇₃	—	2	2	no	—
268	C₂×C₇₃	—	8	2	no	—
269	C₂×C₇₃	—	8	1	no	—
270	C₂×C₇₃	—	16	1	no	—
271	C₂×C₇₃	#2431	1	1	yes	characteristic
272	C₂×C₇₃	#3018	1	2	yes	—
273	#3512	C₂×C₇₃	1	1	yes	characteristic, complemented
274	#3153	C₂×C₇₃	1	1	yes	characteristic, complemented
275	#3040	C₂×C₇₃	1	1	yes	characteristic, complemented
276	#2861	C₂×C₇₃	1	1	yes	characteristic, complemented
277	#2007	C₂×C₇₃	1	2	yes	complemented
278	#2006	C₂×C₇₃	1	2	yes	complemented
279	#1998	C₂×C₇₃	1	1	yes	characteristic, complemented
280	#1962	C₂×C₇₃	1	1	yes	characteristic, complemented
281	#1883	C₂×C₇₃	1	2	yes	complemented
282	#1882	C₂×C₇₃	1	2	yes	complemented
283	C₄×#104	C₂×C₇₃	1	1	yes	characteristic, complemented
284	C₇₃	#25617	1	1	yes	characteristic, direct product factor, Sylow
285	C₂×#137	C₂²×C₇₃	1	2	yes	—
286	C₂×#137	C₂²×C₇₃	1	1	yes	characteristic
287	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
288	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	1	yes	characteristic
289	#553	—	2	2	no	—
290	#553	—	2	4	no	—
291	#552	—	2	2	no	—
292	#541	—	2	1	no	—
293	#540	—	2	1	no	—
294	#537	C₂²×C₇₃	1	2	yes	—
295	#532	C₂²×C₇₃	1	1	yes	characteristic
296	#529	—	2	2	no	—
297	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
298	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
299	#520	C₂²×C₇₃	1	2	yes	—
300	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
301	#497	—	2	1	no	—
302	#496	—	2	1	no	—
303	#495	—	2	2	no	—
304	#464	—	2	2	no	—
305	#463	—	2	2	no	—
306	#423	C₂²×C₇₃	1	1	yes	characteristic
307	C₂×#104	C₂²×C₇₃	1	2	yes	—
308	C₂×#104	C₂²×C₇₃	1	2	yes	—
309	C₂×#104	C₂²×C₇₃	1	2	yes	—
310	#419	C₂²×C₇₃	1	1	yes	characteristic
311	#418	C₂²×C₇₃	1	1	yes	characteristic
312	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
313	#391	C₂²×C₇₃	1	2	yes	—
314	#390	C₂²×C₇₃	1	2	yes	—
315	#388	—	2	4	no	—
316	C₄³	C₂²×C₇₃	1	1	yes	characteristic
317	#343	C₂²×C₇₃	1	2	yes	—
318	#343	C₂²×C₇₃	1	2	yes	—
319	#339	C₂²×C₇₃	1	2	yes	—
320	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
321	C₂×#41	C₂³×C₇₃	1	2	yes	—
322	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
323	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
324	#137	—	2	4	no	—
325	#137	—	4	2	no	—
326	#137	—	4	2	no	—
327	AGL(1,ℤ/8)	—	2	4	no	—
328	AGL(1,ℤ/8)	—	4	2	no	—
329	AGL(1,ℤ/8)	—	4	2	no	—
330	C₂×Q₁₆	—	2	1	no	—
331	C₂×Q₁₆	—	2	2	no	—
332	C₂×SD₁₆	—	2	1	no	—
333	C₂×SD₁₆	—	2	2	no	—
334	C₂×SD₁₆	—	2	1	no	—
335	C₂×SD₁₆	—	2	2	no	—
336	C₂×D₈	—	2	1	no	—
337	C₂×D₈	—	2	2	no	—
338	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
339	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
340	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
341	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
342	#127	D₄×C₇₃	1	1	yes	characteristic
343	#126	—	2	4	no	—
344	#126	—	2	4	no	—
345	#125	—	2	4	no	—
346	#125	—	2	1	no	—
347	#125	—	2	1	no	—
348	#125	—	2	2	no	—
349	#124	—	2	2	no	—
350	#124	—	2	1	no	—
351	#124	—	2	1	no	—
352	#124	D₄×C₇₃	1	2	yes	—
353	#123	—	2	4	no	—
354	#123	—	2	4	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	#121	—	2	4	no	—
358	#121	—	2	2	no	—
359	#121	—	2	2	no	—
360	#121	—	2	2	no	—
361	#121	—	2	4	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	D₄×C₇₃	1	2	yes	—
364	C₄×D₄	—	2	4	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	D₄×C₇₃	1	2	yes	—
370	#117	—	2	4	no	—
371	#117	—	2	2	no	—
372	#117	—	2	1	no	—
373	#117	C₂³×C₇₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	4	no	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	—	2	2	no	—
381	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
382	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
383	C₄⋊C₈	—	2	2	no	—
384	#104	—	2	4	no	—
385	#104	—	4	2	no	—
386	#104	—	4	2	no	—
387	#103	—	2	2	no	—
388	#102	—	2	2	no	—
389	#97	—	2	1	no	—
390	C₄×C₈	—	2	1	no	—
391	#95	—	2	4	no	—
392	C₂⁴	—	2	1	no	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
404	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
414	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
422	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
424	Q₁₆	—	4	4	no	—
425	Q₁₆	—	4	2	no	—
426	SD₁₆	—	4	4	no	—
427	SD₁₆	—	4	4	no	—
428	SD₁₆	—	4	2	no	—
429	SD₁₆	—	4	2	no	—
430	D₈	—	4	4	no	—
431	D₈	—	4	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	#41×C₇₃	1	4	yes	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	4	8	no	—
456	C₂²⋊C₄	—	4	2	no	—
457	C₂²⋊C₄	—	4	2	no	—
458	C₄²	—	2	4	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	4	4	no	—
464	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
465	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
466	C₄²	C₂×D₄×C₇₃	1	2	yes	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	2	no	—
472	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
473	Q₈	—	2	1	no	—
474	Q₈	—	2	1	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	2	2	no	—
477	Q₈	—	4	1	no	—
478	Q₈	—	4	1	no	—
479	Q₈	—	4	2	no	—
480	D₄	—	2	1	no	—
481	D₄	—	2	1	no	—
482	D₄	—	2	2	no	—
483	D₄	—	2	2	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	1	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	2	no	—
490	D₄	—	8	2	no	—
491	D₄	—	8	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	8	2	no	—
507	C₂×C₄	—	8	4	no	—
508	C₂×C₄	#120×C₇₃	1	2	yes	—
509	C₂×C₄	#120×C₇₃	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
513	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
514	C₈	—	2	4	no	—
515	C₈	—	4	1	no	—
516	C₈	—	4	1	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	8	4	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	1	no	—
526	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
527	C₂²	#550×C₇₃	1	2	yes	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	8	1	no	—
536	C₄	#532×C₇₃	1	1	yes	characteristic
537	C₄	#535×C₇₃	1	1	yes	characteristic
538	C₄	#546×C₇₃	1	2	yes	—
539	C₂	—	2	2	no	—
540	C₂	—	8	2	no	—
541	C₂	—	8	1	no	—
542	C₂	—	16	1	no	—
543	C₂	C₇₃×#2431	1	1	yes	characteristic
544	C₂	C₇₃×#3018	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3512	C₂	semidirect
2. C₇₃×#3153	C₂	semidirect
3. C₇₃×#3040	C₂	semidirect
4. C₇₃×#2861	C₂	semidirect
5. C₇₃×#2007	C₂	semidirect
6. C₇₃×#2006	C₂	semidirect
7. C₇₃×#1998	C₂	semidirect
8. C₇₃×#1962	C₂	semidirect
9. C₇₃×#1883	C₂	semidirect
10. C₇₃×#1882	C₂	semidirect
11. C₄×#104×C₇₃	C₂	semidirect
266. #25617	C₇₃	direct (N × H)
273. #3512	C₂×C₇₃	semidirect
274. #3153	C₂×C₇₃	semidirect
275. #3040	C₂×C₇₃	semidirect
276. #2861	C₂×C₇₃	semidirect
277. #2007	C₂×C₇₃	semidirect
278. #2006	C₂×C₇₃	semidirect
279. #1998	C₂×C₇₃	semidirect
280. #1962	C₂×C₇₃	semidirect
281. #1883	C₂×C₇₃	semidirect
282. #1882	C₂×C₇₃	semidirect
283. C₄×#104	C₂×C₇₃	semidirect
284. C₇₃	#25617	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#3512	2
C₇₃×#3153	2
C₇₃×#3040	2
C₇₃×#2861	2
C₇₃×#2007	2
C₇₃×#2006	2
C₇₃×#1998	2
C₇₃×#1962	2
C₇₃×#1883	2
C₇₃×#1882	2
C₄×#104×C₇₃	2
#25617	73

Subgroups — C73×#25617 #32935021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25617 #32935021