Subgroups — C₇₃×#25750 #32935154

Order 18688.

1452 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3499	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	C₂×#456×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₂×#454×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2658	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2005	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2003	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1966	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1963	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₇₃	C₂²	1	2	yes	—
13	C₂×#137×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#137×C₇₃	C₂²	1	2	yes	—
15	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
17	D₄×Q₈×C₇₃	—	2	2	no	—
18	#547×C₇₃	—	2	2	no	—
19	#547×C₇₃	—	2	4	no	—
20	#536×C₇₃	—	2	2	no	—
21	#536×C₇₃	C₂²	1	2	yes	—
22	#532×C₇₃	—	2	1	no	—
23	#532×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₇₃	—	2	1	no	—
25	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
26	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#124×C₇₃	C₂²	1	2	yes	—
28	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
29	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
30	#497×C₇₃	—	2	1	no	—
31	#496×C₇₃	—	2	1	no	—
32	#495×C₇₃	—	2	2	no	—
33	#464×C₇₃	—	2	2	no	—
34	#463×C₇₃	—	2	2	no	—
35	#456×C₇₃	—	2	8	no	—
36	#454×C₇₃	—	2	8	no	—
37	#423×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×#104×C₇₃	C₂²	1	2	yes	—
39	C₂×#104×C₇₃	C₂²	1	2	yes	—
40	C₂×#104×C₇₃	C₂²	1	2	yes	—
41	#419×C₇₃	C₂²	1	1	yes	characteristic
42	#418×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×#101×C₇₃	C₂²	1	2	yes	—
44	C₂×#101×C₇₃	C₂²	1	2	yes	—
45	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
46	#399×C₇₃	—	2	4	no	—
47	#376×C₇₃	C₂²	1	1	yes	characteristic
48	#339×C₇₃	C₂²	1	2	yes	—
49	2₋¹⁺⁴×C₇₃	—	2	4	no	—
50	2₋¹⁺⁴×C₇₃	—	2	4	no	—
51	2₋¹⁺⁴×C₇₃	—	4	2	no	—
52	2₋¹⁺⁴×C₇₃	—	4	2	no	—
53	C₂×#41×C₇₃	—	2	2	no	—
54	C₂×#41×C₇₃	—	2	2	no	—
55	C₂×#41×C₇₃	—	2	4	no	—
56	C₂×#41×C₇₃	C₂³	1	2	yes	—
57	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₇₃	—	2	2	no	—
59	C₂²×Q₈×C₇₃	—	2	2	no	—
60	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
63	#137×C₇₃	—	2	4	no	—
64	#137×C₇₃	—	2	4	no	—
65	#137×C₇₃	—	4	2	no	—
66	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
67	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
68	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
69	C₂×Q₁₆×C₇₃	—	2	1	no	—
70	C₂×Q₁₆×C₇₃	—	2	2	no	—
71	C₂×SD₁₆×C₇₃	—	2	1	no	—
72	C₂×SD₁₆×C₇₃	—	2	2	no	—
73	C₂×SD₁₆×C₇₃	—	2	1	no	—
74	C₂×SD₁₆×C₇₃	—	2	2	no	—
75	C₂×D₈×C₇₃	—	2	1	no	—
76	C₂×D₈×C₇₃	—	2	2	no	—
77	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
80	C₄⋊Q₈×C₇₃	—	2	4	no	—
81	C₄⋊Q₈×C₇₃	—	2	2	no	—
82	C₄⋊Q₈×C₇₃	—	2	1	no	—
83	C₄⋊Q₈×C₇₃	—	2	1	no	—
84	C₄⋊Q₈×C₇₃	—	2	2	no	—
85	C₄⋊Q₈×C₇₃	—	2	4	no	—
86	C₄⋊Q₈×C₇₃	—	4	2	no	—
87	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
88	#127×C₇₃	D₄	1	1	yes	characteristic
89	#124×C₇₃	—	2	2	no	—
90	#124×C₇₃	—	2	4	no	—
91	#124×C₇₃	—	2	2	no	—
92	#124×C₇₃	—	2	1	no	—
93	#124×C₇₃	—	2	1	no	—
94	#124×C₇₃	—	4	2	no	—
95	#124×C₇₃	D₄	1	2	yes	—
96	#123×C₇₃	—	2	8	no	—
97	#123×C₇₃	—	2	4	no	—
98	C₂²⋊Q₈×C₇₃	—	2	8	no	—
99	C₂²⋊Q₈×C₇₃	—	2	4	no	—
100	#121×C₇₃	—	2	4	no	—
101	#121×C₇₃	—	2	2	no	—
102	C₄×Q₈×C₇₃	D₄	1	2	yes	—
103	C₄×D₄×C₇₃	—	2	4	no	—
104	C₄×D₄×C₇₃	—	2	2	no	—
105	C₄×D₄×C₇₃	—	2	2	no	—
106	C₄×D₄×C₇₃	D₄	1	2	yes	—
107	#117×C₇₃	—	2	1	no	—
108	#117×C₇₃	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
110	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
111	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
112	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
113	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
114	C₂×C₄²×C₇₃	—	2	1	no	—
115	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
116	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
117	C₄⋊C₈×C₇₃	—	2	2	no	—
118	#104×C₇₃	—	2	4	no	—
119	#104×C₇₃	—	2	4	no	—
120	#104×C₇₃	D₄	1	8	yes	complemented
121	#103×C₇₃	—	2	2	no	—
122	#102×C₇₃	—	2	2	no	—
123	#101×C₇₃	—	2	4	no	—
124	#101×C₇₃	—	2	4	no	—
125	#97×C₇₃	—	2	1	no	—
126	C₄×C₈×C₇₃	—	2	1	no	—
127	#95×C₇₃	—	2	2	no	—
128	C₂⁴×C₇₃	—	2	1	no	—
129	#41×C₇₃	—	2	2	no	—
130	#41×C₇₃	—	2	2	no	—
131	#41×C₇₃	—	2	2	no	—
132	#41×C₇₃	—	2	2	no	—
133	#41×C₇₃	—	2	2	no	—
134	#41×C₇₃	—	4	4	no	—
135	#41×C₇₃	—	4	4	no	—
136	#41×C₇₃	—	4	8	no	—
137	#41×C₇₃	—	4	8	no	—
138	#41×C₇₃	—	4	4	no	—
139	#41×C₇₃	—	4	4	no	—
140	#41×C₇₃	C₂×D₄	1	4	yes	—
141	C₂×Q₈×C₇₃	—	2	4	no	—
142	C₂×Q₈×C₇₃	—	2	2	no	—
143	C₂×Q₈×C₇₃	—	2	2	no	—
144	C₂×Q₈×C₇₃	—	2	2	no	—
145	C₂×Q₈×C₇₃	—	2	2	no	—
146	C₂×Q₈×C₇₃	—	2	2	no	—
147	C₂×Q₈×C₇₃	—	2	2	no	—
148	C₂×Q₈×C₇₃	—	2	1	no	—
149	C₂×Q₈×C₇₃	—	2	1	no	—
150	C₂×Q₈×C₇₃	—	2	2	no	—
151	C₂×Q₈×C₇₃	—	2	2	no	—
152	C₂×Q₈×C₇₃	—	4	4	no	—
153	C₂×Q₈×C₇₃	—	4	4	no	—
154	C₂×Q₈×C₇₃	—	4	4	no	—
155	C₂×Q₈×C₇₃	—	4	4	no	—
156	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
157	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₇₃	—	2	1	no	—
159	C₂×D₄×C₇₃	—	2	4	no	—
160	C₂×D₄×C₇₃	—	2	2	no	—
161	C₂×D₄×C₇₃	—	2	2	no	—
162	C₂×D₄×C₇₃	—	2	1	no	—
163	C₂×D₄×C₇₃	—	2	1	no	—
164	C₂×D₄×C₇₃	—	2	2	no	—
165	C₂×D₄×C₇₃	—	2	2	no	—
166	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₃	—	2	1	no	—
169	C₂²×C₄×C₇₃	—	2	4	no	—
170	C₂²×C₄×C₇₃	—	2	4	no	—
171	C₂²×C₄×C₇₃	—	2	2	no	—
172	C₂²×C₄×C₇₃	—	2	2	no	—
173	C₂²×C₄×C₇₃	—	2	2	no	—
174	C₂²×C₄×C₇₃	—	2	1	no	—
175	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
178	Q₁₆×C₇₃	—	4	4	no	—
179	Q₁₆×C₇₃	—	4	2	no	—
180	SD₁₆×C₇₃	—	4	4	no	—
181	SD₁₆×C₇₃	—	4	4	no	—
182	SD₁₆×C₇₃	—	4	2	no	—
183	SD₁₆×C₇₃	—	4	2	no	—
184	D₈×C₇₃	—	4	4	no	—
185	D₈×C₇₃	—	4	2	no	—
186	M₁₆×C₇₃	—	2	2	no	—
187	M₁₆×C₇₃	—	2	2	no	—
188	M₁₆×C₇₃	—	2	2	no	—
189	M₁₆×C₇₃	C₂×D₄	1	4	yes	—
190	C₂×C₈×C₇₃	—	2	2	no	—
191	C₂×C₈×C₇₃	—	2	1	no	—
192	C₂×C₈×C₇₃	—	2	1	no	—
193	C₄⋊C₄×C₇₃	—	2	8	no	—
194	C₄⋊C₄×C₇₃	—	2	2	no	—
195	C₄⋊C₄×C₇₃	—	2	4	no	—
196	C₄⋊C₄×C₇₃	—	2	4	no	—
197	C₄⋊C₄×C₇₃	—	2	2	no	—
198	C₄⋊C₄×C₇₃	—	4	8	no	—
199	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
200	C₂²⋊C₄×C₇₃	—	2	8	no	—
201	C₂²⋊C₄×C₇₃	—	2	1	no	—
202	C₂²⋊C₄×C₇₃	—	2	2	no	—
203	C₂²⋊C₄×C₇₃	—	2	4	no	—
204	C₂²⋊C₄×C₇₃	—	4	8	no	—
205	C₂²⋊C₄×C₇₃	—	4	2	no	—
206	C₂²⋊C₄×C₇₃	—	4	2	no	—
207	C₄²×C₇₃	—	2	2	no	—
208	C₄²×C₇₃	—	2	1	no	—
209	C₄²×C₇₃	—	2	2	no	—
210	C₄²×C₇₃	C₂×D₄	1	4	yes	—
211	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₇₃	C₂×D₄	1	2	yes	—
214	C₂³×C₇₃	—	2	1	no	—
215	C₂³×C₇₃	—	2	2	no	—
216	C₂³×C₇₃	—	4	4	no	—
217	C₂³×C₇₃	—	4	1	no	—
218	C₂³×C₇₃	—	4	2	no	—
219	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₇₃	—	2	1	no	—
221	Q₈×C₇₃	—	2	2	no	—
222	Q₈×C₇₃	—	2	2	no	—
223	Q₈×C₇₃	—	4	8	no	—
224	Q₈×C₇₃	—	4	2	no	—
225	Q₈×C₇₃	—	4	2	no	—
226	Q₈×C₇₃	—	4	2	no	—
227	Q₈×C₇₃	—	4	2	no	—
228	Q₈×C₇₃	—	4	1	no	—
229	Q₈×C₇₃	—	4	1	no	—
230	Q₈×C₇₃	—	4	2	no	—
231	Q₈×C₇₃	#127	1	2	yes	—
232	D₄×C₇₃	—	2	4	no	—
233	D₄×C₇₃	—	2	1	no	—
234	D₄×C₇₃	—	2	2	no	—
235	D₄×C₇₃	—	2	2	no	—
236	D₄×C₇₃	—	4	4	no	—
237	D₄×C₇₃	—	4	8	no	—
238	D₄×C₇₃	—	4	2	no	—
239	D₄×C₇₃	—	4	2	no	—
240	D₄×C₇₃	—	4	1	no	—
241	D₄×C₇₃	—	4	1	no	—
242	D₄×C₇₃	—	4	2	no	—
243	D₄×C₇₃	#127	1	2	yes	—
244	C₂×C₄×C₇₃	—	2	1	no	—
245	C₂×C₄×C₇₃	—	2	4	no	—
246	C₂×C₄×C₇₃	—	2	2	no	—
247	C₂×C₄×C₇₃	—	2	2	no	—
248	C₂×C₄×C₇₃	—	2	4	no	—
249	C₂×C₄×C₇₃	—	2	4	no	—
250	C₂×C₄×C₇₃	—	2	4	no	—
251	C₂×C₄×C₇₃	—	2	4	no	—
252	C₂×C₄×C₇₃	—	4	2	no	—
253	C₂×C₄×C₇₃	—	4	4	no	—
254	C₂×C₄×C₇₃	—	4	8	no	—
255	C₂×C₄×C₇₃	—	4	4	no	—
256	C₂×C₄×C₇₃	—	4	8	no	—
257	C₂×C₄×C₇₃	—	4	2	no	—
258	C₂×C₄×C₇₃	—	4	2	no	—
259	C₂×C₄×C₇₃	—	4	1	no	—
260	C₂×C₄×C₇₃	—	4	2	no	—
261	C₂×C₄×C₇₃	#120	1	2	yes	—
262	C₂×C₄×C₇₃	#120	1	2	yes	—
263	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
267	C₈×C₇₃	—	2	4	no	—
268	C₈×C₇₃	—	4	1	no	—
269	C₈×C₇₃	—	4	1	no	—
270	C₂²×C₇₃	—	2	2	no	—
271	C₂²×C₇₃	—	2	2	no	—
272	C₂²×C₇₃	—	4	2	no	—
273	C₂²×C₇₃	—	4	2	no	—
274	C₂²×C₇₃	—	4	4	no	—
275	C₂²×C₇₃	—	8	4	no	—
276	C₂²×C₇₃	—	8	1	no	—
277	C₂²×C₇₃	—	8	2	no	—
278	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
279	C₂²×C₇₃	D₄²	1	2	yes	—
280	C₄×C₇₃	—	2	2	no	—
281	C₄×C₇₃	—	2	2	no	—
282	C₄×C₇₃	—	2	2	no	—
283	C₄×C₇₃	—	4	4	no	—
284	C₄×C₇₃	—	4	4	no	—
285	C₄×C₇₃	—	4	2	no	—
286	C₄×C₇₃	—	4	2	no	—
287	C₄×C₇₃	—	8	1	no	—
288	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
289	C₄×C₇₃	#535	1	1	yes	characteristic
290	C₄×C₇₃	D₄²	1	2	yes	—
291	#25750	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂×C₇₃	—	2	2	no	—
293	C₂×C₇₃	—	4	2	no	—
294	C₂×C₇₃	—	8	2	no	—
295	C₂×C₇₃	—	16	1	no	—
296	C₂×C₇₃	#2433	1	1	yes	characteristic
297	C₂×C₇₃	#3020	1	2	yes	—
298	#3499	C₂×C₇₃	1	1	yes	characteristic, complemented
299	#3153	C₂×C₇₃	1	1	yes	characteristic, complemented
300	#3040	C₂×C₇₃	1	1	yes	characteristic, complemented
301	C₂×#456	C₂×C₇₃	1	2	yes	complemented
302	C₂×#454	C₂×C₇₃	1	2	yes	complemented
303	#2658	C₂×C₇₃	1	1	yes	characteristic, complemented
304	#2005	C₂×C₇₃	1	2	yes	complemented
305	#2003	C₂×C₇₃	1	2	yes	complemented
306	#1966	C₂×C₇₃	1	1	yes	characteristic, complemented
307	#1963	C₂×C₇₃	1	1	yes	characteristic, complemented
308	#1759	C₂×C₇₃	1	1	yes	characteristic, complemented
309	C₇₃	#25750	1	1	yes	characteristic, direct product factor, Sylow
310	C₂×2₋¹⁺⁴	C₂²×C₇₃	1	2	yes	—
311	C₂×#137	C₂²×C₇₃	1	1	yes	characteristic
312	C₂×#137	C₂²×C₇₃	1	2	yes	—
313	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	1	yes	characteristic
314	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
315	D₄×Q₈	—	2	2	no	—
316	#547	—	2	2	no	—
317	#547	—	2	4	no	—
318	#536	—	2	2	no	—
319	#536	C₂²×C₇₃	1	2	yes	—
320	#532	—	2	1	no	—
321	#532	C₂²×C₇₃	1	1	yes	characteristic
322	C₂×C₄⋊Q₈	—	2	1	no	—
323	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
324	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
325	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
326	C₂×#124	C₂²×C₇₃	1	2	yes	—
327	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
328	#497	—	2	1	no	—
329	#496	—	2	1	no	—
330	#495	—	2	2	no	—
331	#464	—	2	2	no	—
332	#463	—	2	2	no	—
333	#456	—	2	8	no	—
334	#454	—	2	8	no	—
335	#423	C₂²×C₇₃	1	1	yes	characteristic
336	C₂×#104	C₂²×C₇₃	1	2	yes	—
337	C₂×#104	C₂²×C₇₃	1	2	yes	—
338	C₂×#104	C₂²×C₇₃	1	2	yes	—
339	#419	C₂²×C₇₃	1	1	yes	characteristic
340	#418	C₂²×C₇₃	1	1	yes	characteristic
341	C₂×#101	C₂²×C₇₃	1	2	yes	—
342	C₂×#101	C₂²×C₇₃	1	2	yes	—
343	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
344	#399	—	2	4	no	—
345	#376	C₂²×C₇₃	1	1	yes	characteristic
346	#339	C₂²×C₇₃	1	2	yes	—
347	2₋¹⁺⁴	—	2	4	no	—
348	2₋¹⁺⁴	—	2	4	no	—
349	2₋¹⁺⁴	—	4	2	no	—
350	2₋¹⁺⁴	—	4	2	no	—
351	C₂×#41	—	2	2	no	—
352	C₂×#41	—	2	2	no	—
353	C₂×#41	—	2	4	no	—
354	C₂×#41	C₂³×C₇₃	1	2	yes	—
355	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
356	C₂²×Q₈	—	2	2	no	—
357	C₂²×Q₈	—	2	2	no	—
358	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
360	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
361	#137	—	2	4	no	—
362	#137	—	2	4	no	—
363	#137	—	4	2	no	—
364	AGL(1,ℤ/8)	—	2	4	no	—
365	AGL(1,ℤ/8)	—	2	4	no	—
366	AGL(1,ℤ/8)	—	4	2	no	—
367	C₂×Q₁₆	—	2	1	no	—
368	C₂×Q₁₆	—	2	2	no	—
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×SD₁₆	—	2	2	no	—
371	C₂×SD₁₆	—	2	1	no	—
372	C₂×SD₁₆	—	2	2	no	—
373	C₂×D₈	—	2	1	no	—
374	C₂×D₈	—	2	2	no	—
375	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
376	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
377	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
378	C₄⋊Q₈	—	2	4	no	—
379	C₄⋊Q₈	—	2	2	no	—
380	C₄⋊Q₈	—	2	1	no	—
381	C₄⋊Q₈	—	2	1	no	—
382	C₄⋊Q₈	—	2	2	no	—
383	C₄⋊Q₈	—	2	4	no	—
384	C₄⋊Q₈	—	4	2	no	—
385	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
386	#127	D₄×C₇₃	1	1	yes	characteristic
387	#124	—	2	2	no	—
388	#124	—	2	4	no	—
389	#124	—	2	2	no	—
390	#124	—	2	1	no	—
391	#124	—	2	1	no	—
392	#124	—	4	2	no	—
393	#124	D₄×C₇₃	1	2	yes	—
394	#123	—	2	8	no	—
395	#123	—	2	4	no	—
396	C₂²⋊Q₈	—	2	8	no	—
397	C₂²⋊Q₈	—	2	4	no	—
398	#121	—	2	4	no	—
399	#121	—	2	2	no	—
400	C₄×Q₈	D₄×C₇₃	1	2	yes	—
401	C₄×D₄	—	2	4	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	D₄×C₇₃	1	2	yes	—
405	#117	—	2	1	no	—
406	#117	C₂³×C₇₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	—	2	4	no	—
408	C₂×C₄⋊C₄	—	2	4	no	—
409	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
410	C₂×C₂²⋊C₄	—	2	4	no	—
411	C₂×C₂²⋊C₄	—	2	2	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
414	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
415	C₄⋊C₈	—	2	2	no	—
416	#104	—	2	4	no	—
417	#104	—	2	4	no	—
418	#104	D₄×C₇₃	1	8	yes	complemented
419	#103	—	2	2	no	—
420	#102	—	2	2	no	—
421	#101	—	2	4	no	—
422	#101	—	2	4	no	—
423	#97	—	2	1	no	—
424	C₄×C₈	—	2	1	no	—
425	#95	—	2	2	no	—
426	C₂⁴	—	2	1	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	4	4	no	—
433	#41	—	4	4	no	—
434	#41	—	4	8	no	—
435	#41	—	4	8	no	—
436	#41	—	4	4	no	—
437	#41	—	4	4	no	—
438	#41	C₂×D₄×C₇₃	1	4	yes	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	4	4	no	—
451	C₂×Q₈	—	4	4	no	—
452	C₂×Q₈	—	4	4	no	—
453	C₂×Q₈	—	4	4	no	—
454	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
455	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
465	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
474	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
476	Q₁₆	—	4	4	no	—
477	Q₁₆	—	4	2	no	—
478	SD₁₆	—	4	4	no	—
479	SD₁₆	—	4	4	no	—
480	SD₁₆	—	4	2	no	—
481	SD₁₆	—	4	2	no	—
482	D₈	—	4	4	no	—
483	D₈	—	4	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	C₂×D₄×C₇₃	1	4	yes	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₄⋊C₄	—	2	8	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	4	8	no	—
497	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
498	C₂²⋊C₄	—	2	8	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	4	8	no	—
503	C₂²⋊C₄	—	4	2	no	—
504	C₂²⋊C₄	—	4	2	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	2	no	—
508	C₄²	C₂×D₄×C₇₃	1	4	yes	—
509	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
511	C₄²	C₂×D₄×C₇₃	1	2	yes	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
518	Q₈	—	2	1	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	4	8	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	4	2	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	2	no	—
529	Q₈	#127×C₇₃	1	2	yes	—
530	D₄	—	2	4	no	—
531	D₄	—	2	1	no	—
532	D₄	—	2	2	no	—
533	D₄	—	2	2	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	8	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	2	no	—
541	D₄	#127×C₇₃	1	2	yes	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	8	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	4	8	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	#120×C₇₃	1	2	yes	—
560	C₂×C₄	#120×C₇₃	1	2	yes	—
561	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
563	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
564	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
565	C₈	—	2	4	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	8	4	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	8	1	no	—
576	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
577	C₂²	D₄²×C₇₃	1	2	yes	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	2	no	—
585	C₄	—	8	1	no	—
586	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
587	C₄	#535×C₇₃	1	1	yes	characteristic
588	C₄	D₄²×C₇₃	1	2	yes	—
589	C₂	—	2	2	no	—
590	C₂	—	4	2	no	—
591	C₂	—	8	2	no	—
592	C₂	—	16	1	no	—
593	C₂	C₇₃×#2433	1	1	yes	characteristic
594	C₂	C₇₃×#3020	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×#3499	C₂	semidirect
2. C₇₃×#3153	C₂	semidirect
3. C₇₃×#3040	C₂	semidirect
4. C₂×#456×C₇₃	C₂	semidirect
5. C₂×#454×C₇₃	C₂	semidirect
6. C₇₃×#2658	C₂	semidirect
7. C₇₃×#2005	C₂	semidirect
8. C₇₃×#2003	C₂	semidirect
9. C₇₃×#1966	C₂	semidirect
10. C₇₃×#1963	C₂	semidirect
11. C₇₃×#1759	C₂	semidirect
120. #104×C₇₃	D₄	semidirect
291. #25750	C₇₃	direct (N × H)
298. #3499	C₂×C₇₃	semidirect
299. #3153	C₂×C₇₃	semidirect
300. #3040	C₂×C₇₃	semidirect
301. C₂×#456	C₂×C₇₃	semidirect
302. C₂×#454	C₂×C₇₃	semidirect
303. #2658	C₂×C₇₃	semidirect
304. #2005	C₂×C₇₃	semidirect
305. #2003	C₂×C₇₃	semidirect
306. #1966	C₂×C₇₃	semidirect
307. #1963	C₂×C₇₃	semidirect
308. #1759	C₂×C₇₃	semidirect
309. C₇₃	#25750	direct (N × H)
418. #104	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3499	2
C₇₃×#3153	2
C₇₃×#3040	2
C₂×#456×C₇₃	2
C₂×#454×C₇₃	2
C₇₃×#2658	2
C₇₃×#2005	2
C₇₃×#2003	2
C₇₃×#1966	2
C₇₃×#1963	2
C₇₃×#1759	2
#25750	73

Subgroups — C73×#25750 #32935154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25750 #32935154