Subgroups — C₇₃×#25620 #32935024

Order 18688.

1136 conjugacy classes of subgroups.

The subgroup lattice has 462 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×#3151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2641	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2006	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1998	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1963	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1883	C₂	1	4	yes	maximal, complemented
9	C₇₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	4	yes	—
11	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
12	#553×C₇₃	—	2	2	no	—
13	#553×C₇₃	—	2	4	no	—
14	#552×C₇₃	—	2	2	no	—
15	#541×C₇₃	—	2	1	no	—
16	#540×C₇₃	—	2	1	no	—
17	#537×C₇₃	C₂²	1	2	yes	—
18	#532×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
20	#529×C₇₃	—	2	2	no	—
21	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
22	#520×C₇₃	C₂²	1	2	yes	—
23	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
24	#496×C₇₃	—	2	2	no	—
25	#493×C₇₃	—	2	1	no	—
26	#492×C₇₃	—	2	1	no	—
27	#460×C₇₃	—	2	2	no	—
28	#459×C₇₃	—	2	2	no	—
29	#423×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#104×C₇₃	C₂²	1	2	yes	—
31	C₂×#104×C₇₃	C₂²	1	4	yes	—
32	#418×C₇₃	C₂²	1	2	yes	—
33	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
34	#394×C₇₃	—	2	4	no	—
35	#390×C₇₃	C₂²	1	4	yes	—
36	#376×C₇₃	C₂²	1	1	yes	characteristic
37	#343×C₇₃	C₂²	1	4	yes	—
38	#339×C₇₃	C₂²	1	2	yes	—
39	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
40	C₂×#41×C₇₃	C₂³	1	2	yes	—
41	C₂²×D₄×C₇₃	—	2	2	no	—
42	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
43	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
44	AGL(1,ℤ/8)×C₇₃	—	4	4	no	—
45	AGL(1,ℤ/8)×C₇₃	—	4	4	no	—
46	C₂×SD₁₆×C₇₃	—	2	2	no	—
47	C₂×SD₁₆×C₇₃	—	2	4	no	—
48	C₂×D₈×C₇₃	—	2	2	no	—
49	C₂×D₈×C₇₃	—	2	4	no	—
50	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
51	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
53	#127×C₇₃	—	2	2	no	—
54	#127×C₇₃	—	2	1	no	—
55	#127×C₇₃	—	2	1	no	—
56	#127×C₇₃	D₄	1	1	yes	characteristic
57	#126×C₇₃	—	2	4	no	—
58	#126×C₇₃	—	2	4	no	—
59	#125×C₇₃	—	2	4	no	—
60	#125×C₇₃	—	2	1	no	—
61	#125×C₇₃	—	2	1	no	—
62	#125×C₇₃	—	2	2	no	—
63	#124×C₇₃	D₄	1	2	yes	—
64	#123×C₇₃	—	2	4	no	—
65	#123×C₇₃	—	2	4	no	—
66	C₂²⋊Q₈×C₇₃	—	2	2	no	—
67	C₂²⋊Q₈×C₇₃	—	2	2	no	—
68	#121×C₇₃	—	2	4	no	—
69	#121×C₇₃	—	2	2	no	—
70	#121×C₇₃	—	2	2	no	—
71	#121×C₇₃	—	2	2	no	—
72	#121×C₇₃	—	2	4	no	—
73	C₄×Q₈×C₇₃	—	2	2	no	—
74	C₄×Q₈×C₇₃	D₄	1	2	yes	—
75	C₄×D₄×C₇₃	—	2	4	no	—
76	C₄×D₄×C₇₃	—	2	2	no	—
77	C₄×D₄×C₇₃	—	2	2	no	—
78	C₄×D₄×C₇₃	—	2	4	no	—
79	C₄×D₄×C₇₃	—	2	2	no	—
80	C₄×D₄×C₇₃	D₄	1	2	yes	—
81	#117×C₇₃	—	2	4	no	—
82	#117×C₇₃	—	2	2	no	—
83	#117×C₇₃	—	2	1	no	—
84	#117×C₇₃	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
86	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
87	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
89	C₂×C₄²×C₇₃	—	2	1	no	—
90	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₇₃	—	2	2	no	—
93	#104×C₇₃	—	2	4	no	—
94	#104×C₇₃	—	4	4	no	—
95	#102×C₇₃	—	2	4	no	—
96	#97×C₇₃	—	2	1	no	—
97	C₄×C₈×C₇₃	—	2	1	no	—
98	#95×C₇₃	—	2	2	no	—
99	C₂⁴×C₇₃	—	2	2	no	—
100	#41×C₇₃	—	2	2	no	—
101	#41×C₇₃	—	2	4	no	—
102	#41×C₇₃	—	2	4	no	—
103	#41×C₇₃	—	2	2	no	—
104	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₇₃	—	2	1	no	—
107	C₂×D₄×C₇₃	—	2	2	no	—
108	C₂×D₄×C₇₃	—	2	4	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	4	no	—
113	C₂×D₄×C₇₃	—	2	4	no	—
114	C₂×D₄×C₇₃	—	4	2	no	—
115	C₂×D₄×C₇₃	—	4	2	no	—
116	C₂×D₄×C₇₃	—	8	4	no	—
117	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₃	—	2	4	no	—
120	C₂²×C₄×C₇₃	—	2	1	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	2	2	no	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
127	SD₁₆×C₇₃	—	4	8	no	—
128	SD₁₆×C₇₃	—	4	4	no	—
129	D₈×C₇₃	—	4	8	no	—
130	D₈×C₇₃	—	4	4	no	—
131	M₁₆×C₇₃	—	2	2	no	—
132	M₁₆×C₇₃	—	2	4	no	—
133	M₁₆×C₇₃	#41	1	4	yes	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₄⋊C₄×C₇₃	—	2	4	no	—
137	C₄⋊C₄×C₇₃	—	2	4	no	—
138	C₄⋊C₄×C₇₃	—	2	4	no	—
139	C₄⋊C₄×C₇₃	—	2	4	no	—
140	C₄⋊C₄×C₇₃	—	2	2	no	—
141	C₄⋊C₄×C₇₃	—	2	2	no	—
142	C₄⋊C₄×C₇₃	—	2	2	no	—
143	C₄⋊C₄×C₇₃	—	2	2	no	—
144	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
145	C₂²⋊C₄×C₇₃	—	2	4	no	—
146	C₂²⋊C₄×C₇₃	—	2	4	no	—
147	C₂²⋊C₄×C₇₃	—	2	4	no	—
148	C₂²⋊C₄×C₇₃	—	2	1	no	—
149	C₂²⋊C₄×C₇₃	—	2	2	no	—
150	C₂²⋊C₄×C₇₃	—	2	2	no	—
151	C₂²⋊C₄×C₇₃	—	2	2	no	—
152	C₂²⋊C₄×C₇₃	—	8	8	no	—
153	C₄²×C₇₃	—	2	4	no	—
154	C₄²×C₇₃	—	2	2	no	—
155	C₄²×C₇₃	—	2	1	no	—
156	C₄²×C₇₃	—	2	2	no	—
157	C₄²×C₇₃	—	2	2	no	—
158	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₇₃	C₂×D₄	1	2	yes	—
161	C₂³×C₇₃	—	2	2	no	—
162	C₂³×C₇₃	—	2	1	no	—
163	C₂³×C₇₃	—	4	8	no	—
164	C₂³×C₇₃	—	4	2	no	—
165	C₂³×C₇₃	—	4	4	no	—
166	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₇₃	—	2	1	no	—
168	Q₈×C₇₃	—	2	1	no	—
169	Q₈×C₇₃	—	2	4	no	—
170	D₄×C₇₃	—	2	1	no	—
171	D₄×C₇₃	—	2	1	no	—
172	D₄×C₇₃	—	2	4	no	—
173	D₄×C₇₃	—	4	2	no	—
174	D₄×C₇₃	—	4	4	no	—
175	D₄×C₇₃	—	4	2	no	—
176	D₄×C₇₃	—	4	2	no	—
177	D₄×C₇₃	—	4	4	no	—
178	D₄×C₇₃	—	8	2	no	—
179	D₄×C₇₃	—	8	4	no	—
180	D₄×C₇₃	—	8	4	no	—
181	D₄×C₇₃	—	8	4	no	—
182	C₂×C₄×C₇₃	—	2	2	no	—
183	C₂×C₄×C₇₃	—	2	2	no	—
184	C₂×C₄×C₇₃	—	2	1	no	—
185	C₂×C₄×C₇₃	—	2	4	no	—
186	C₂×C₄×C₇₃	—	4	2	no	—
187	C₂×C₄×C₇₃	—	4	2	no	—
188	C₂×C₄×C₇₃	—	4	2	no	—
189	C₂×C₄×C₇₃	—	4	2	no	—
190	C₂×C₄×C₇₃	—	4	4	no	—
191	C₂×C₄×C₇₃	—	4	4	no	—
192	C₂×C₄×C₇₃	—	4	2	no	—
193	C₂×C₄×C₇₃	—	8	2	no	—
194	C₂×C₄×C₇₃	—	8	4	no	—
195	C₂×C₄×C₇₃	#120	1	2	yes	—
196	C₂×C₄×C₇₃	#120	1	2	yes	—
197	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
200	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
201	C₈×C₇₃	—	2	4	no	—
202	C₈×C₇₃	—	4	2	no	—
203	C₂²×C₇₃	—	2	2	no	—
204	C₂²×C₇₃	—	4	2	no	—
205	C₂²×C₇₃	—	4	1	no	—
206	C₂²×C₇₃	—	4	2	no	—
207	C₂²×C₇₃	—	4	2	no	—
208	C₂²×C₇₃	—	4	2	no	—
209	C₂²×C₇₃	—	8	8	no	—
210	C₂²×C₇₃	—	8	2	no	—
211	C₂²×C₇₃	—	8	4	no	—
212	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
213	C₂²×C₇₃	#550	1	2	yes	—
214	C₄×C₇₃	—	2	2	no	—
215	C₄×C₇₃	—	2	2	no	—
216	C₄×C₇₃	—	4	2	no	—
217	C₄×C₇₃	—	4	1	no	—
218	C₄×C₇₃	—	4	4	no	—
219	C₄×C₇₃	—	4	2	no	—
220	C₄×C₇₃	—	8	2	no	—
221	C₄×C₇₃	#532	1	1	yes	characteristic
222	C₄×C₇₃	#535	1	1	yes	characteristic
223	C₄×C₇₃	#546	1	2	yes	—
224	#25620	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂×C₇₃	—	2	2	no	—
226	C₂×C₇₃	—	8	2	no	—
227	C₂×C₇₃	—	8	1	no	—
228	C₂×C₇₃	—	16	2	no	—
229	C₂×C₇₃	#2431	1	1	yes	characteristic
230	C₂×C₇₃	#3021	1	2	yes	—
231	#3512	C₂×C₇₃	1	1	yes	characteristic, complemented
232	#3151	C₂×C₇₃	1	1	yes	characteristic, complemented
233	#3038	C₂×C₇₃	1	1	yes	characteristic, complemented
234	#2641	C₂×C₇₃	1	1	yes	characteristic, complemented
235	#2006	C₂×C₇₃	1	4	yes	complemented
236	#1998	C₂×C₇₃	1	1	yes	characteristic, complemented
237	#1963	C₂×C₇₃	1	1	yes	characteristic, complemented
238	#1883	C₂×C₇₃	1	4	yes	complemented
239	#1759	C₂×C₇₃	1	1	yes	characteristic, complemented
240	C₇₃	#25620	1	1	yes	characteristic, direct product factor, Sylow
241	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	4	yes	—
242	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
243	#553	—	2	2	no	—
244	#553	—	2	4	no	—
245	#552	—	2	2	no	—
246	#541	—	2	1	no	—
247	#540	—	2	1	no	—
248	#537	C₂²×C₇₃	1	2	yes	—
249	#532	C₂²×C₇₃	1	1	yes	characteristic
250	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
251	#529	—	2	2	no	—
252	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
253	#520	C₂²×C₇₃	1	2	yes	—
254	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
255	#496	—	2	2	no	—
256	#493	—	2	1	no	—
257	#492	—	2	1	no	—
258	#460	—	2	2	no	—
259	#459	—	2	2	no	—
260	#423	C₂²×C₇₃	1	1	yes	characteristic
261	C₂×#104	C₂²×C₇₃	1	2	yes	—
262	C₂×#104	C₂²×C₇₃	1	4	yes	—
263	#418	C₂²×C₇₃	1	2	yes	—
264	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
265	#394	—	2	4	no	—
266	#390	C₂²×C₇₃	1	4	yes	—
267	#376	C₂²×C₇₃	1	1	yes	characteristic
268	#343	C₂²×C₇₃	1	4	yes	—
269	#339	C₂²×C₇₃	1	2	yes	—
270	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
271	C₂×#41	C₂³×C₇₃	1	2	yes	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
274	AGL(1,ℤ/8)	—	2	8	no	—
275	AGL(1,ℤ/8)	—	4	4	no	—
276	AGL(1,ℤ/8)	—	4	4	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×SD₁₆	—	2	4	no	—
279	C₂×D₈	—	2	2	no	—
280	C₂×D₈	—	2	4	no	—
281	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
282	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
283	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
284	#127	—	2	2	no	—
285	#127	—	2	1	no	—
286	#127	—	2	1	no	—
287	#127	D₄×C₇₃	1	1	yes	characteristic
288	#126	—	2	4	no	—
289	#126	—	2	4	no	—
290	#125	—	2	4	no	—
291	#125	—	2	1	no	—
292	#125	—	2	1	no	—
293	#125	—	2	2	no	—
294	#124	D₄×C₇₃	1	2	yes	—
295	#123	—	2	4	no	—
296	#123	—	2	4	no	—
297	C₂²⋊Q₈	—	2	2	no	—
298	C₂²⋊Q₈	—	2	2	no	—
299	#121	—	2	4	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	#121	—	2	2	no	—
303	#121	—	2	4	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	D₄×C₇₃	1	2	yes	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	D₄×C₇₃	1	2	yes	—
312	#117	—	2	4	no	—
313	#117	—	2	2	no	—
314	#117	—	2	1	no	—
315	#117	C₂³×C₇₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
319	C₂×C₂²⋊C₄	—	2	8	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
322	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
323	C₄⋊C₈	—	2	2	no	—
324	#104	—	2	4	no	—
325	#104	—	4	4	no	—
326	#102	—	2	4	no	—
327	#97	—	2	1	no	—
328	C₄×C₈	—	2	1	no	—
329	#95	—	2	2	no	—
330	C₂⁴	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	—	2	4	no	—
333	#41	—	2	4	no	—
334	#41	—	2	2	no	—
335	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
336	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	8	4	no	—
348	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
349	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
356	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
358	SD₁₆	—	4	8	no	—
359	SD₁₆	—	4	4	no	—
360	D₈	—	4	8	no	—
361	D₈	—	4	4	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	4	no	—
364	M₁₆	#41×C₇₃	1	4	yes	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	8	8	no	—
384	C₄²	—	2	4	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₇₃	1	2	yes	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	4	8	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	4	no	—
397	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
398	Q₈	—	2	1	no	—
399	Q₈	—	2	1	no	—
400	Q₈	—	2	4	no	—
401	D₄	—	2	1	no	—
402	D₄	—	2	1	no	—
403	D₄	—	2	4	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	4	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	4	no	—
409	D₄	—	8	2	no	—
410	D₄	—	8	4	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	2	no	—
425	C₂×C₄	—	8	4	no	—
426	C₂×C₄	#120×C₇₃	1	2	yes	—
427	C₂×C₄	#120×C₇₃	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
431	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
432	C₈	—	2	4	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	8	8	no	—
441	C₂²	—	8	4	no	—
442	C₂²	—	8	2	no	—
443	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
444	C₂²	#550×C₇₃	1	2	yes	—
445	C₄	—	2	2	no	—
446	C₄	—	2	2	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	8	2	no	—
452	C₄	#532×C₇₃	1	1	yes	characteristic
453	C₄	#535×C₇₃	1	1	yes	characteristic
454	C₄	#546×C₇₃	1	2	yes	—
455	C₂	—	2	2	no	—
456	C₂	—	8	2	no	—
457	C₂	—	8	1	no	—
458	C₂	—	16	2	no	—
459	C₂	C₇₃×#2431	1	1	yes	characteristic
460	C₂	C₇₃×#3021	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×#3151	C₂	semidirect
3. C₇₃×#3038	C₂	semidirect
4. C₇₃×#2641	C₂	semidirect
5. C₇₃×#2006	C₂	semidirect
6. C₇₃×#1998	C₂	semidirect
7. C₇₃×#1963	C₂	semidirect
8. C₇₃×#1883	C₂	semidirect
9. C₇₃×#1759	C₂	semidirect
224. #25620	C₇₃	direct (N × H)
231. #3512	C₂×C₇₃	semidirect
232. #3151	C₂×C₇₃	semidirect
233. #3038	C₂×C₇₃	semidirect
234. #2641	C₂×C₇₃	semidirect
235. #2006	C₂×C₇₃	semidirect
236. #1998	C₂×C₇₃	semidirect
237. #1963	C₂×C₇₃	semidirect
238. #1883	C₂×C₇₃	semidirect
239. #1759	C₂×C₇₃	semidirect
240. C₇₃	#25620	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×#3151	2
C₇₃×#3038	2
C₇₃×#2641	2
C₇₃×#2006	2
C₇₃×#1998	2
C₇₃×#1963	2
C₇₃×#1883	2
C₇₃×#1759	2
#25620	73

Subgroups — C73×#25620 #32935024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25620 #32935024