Subgroups — C₇₃×#25743 #32935147

Order 18688.

1592 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3153	C₂	1	2	yes	maximal, complemented
3	C₂×#455×C₇₃	C₂	1	2	yes	maximal, complemented
4	C₂×#453×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2544	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2007	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2006	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1980	C₂	1	2	yes	maximal, complemented
9	C₄×#100×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	2	yes	—
11	C₂×#137×C₇₃	C₂²	1	4	yes	complemented
12	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	4	yes	complemented
13	#547×C₇₃	—	2	2	no	—
14	#546×C₇₃	—	2	4	no	—
15	D₄²×C₇₃	—	2	2	no	—
16	#537×C₇₃	C₂²	1	2	yes	—
17	#534×C₇₃	—	2	2	no	—
18	#532×C₇₃	C₂²	1	2	yes	—
19	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×#121×C₇₃	—	2	2	no	—
23	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
24	#497×C₇₃	—	2	2	no	—
25	#496×C₇₃	—	2	2	no	—
26	#495×C₇₃	—	2	4	no	—
27	#455×C₇₃	—	2	8	no	—
28	#453×C₇₃	—	2	8	no	—
29	C₂×#104×C₇₃	C₂²	1	4	yes	complemented
30	C₂×#104×C₇₃	C₂²	1	4	yes	complemented
31	C₂×#100×C₇₃	C₂²	1	2	yes	—
32	C₄×M₁₆×C₇₃	C₂²	1	2	yes	complemented
33	#394×C₇₃	—	2	2	no	—
34	#391×C₇₃	C₂²	1	1	yes	characteristic, complemented
35	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
36	#386×C₇₃	—	2	2	no	—
37	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	#343×C₇₃	C₂²	1	2	yes	complemented
39	H(5,𝔽₂)×C₇₃	—	2	4	no	—
40	H(5,𝔽₂)×C₇₃	—	2	4	no	—
41	H(5,𝔽₂)×C₇₃	—	4	4	no	—
42	C₂×#41×C₇₃	—	2	4	no	—
43	C₂×#41×C₇₃	C₂³	1	4	yes	—
44	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₇₃	—	2	4	no	—
46	C₂²×D₄×C₇₃	—	2	2	no	—
47	C₂²×D₄×C₇₃	—	2	4	no	—
48	C₂²×D₄×C₇₃	—	2	2	no	—
49	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇₃	D₄	1	2	yes	—
52	#137×C₇₃	—	2	8	no	—
53	#137×C₇₃	—	4	4	no	—
54	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
55	AGL(1,ℤ/8)×C₇₃	—	4	4	no	—
56	C₂×Q₁₆×C₇₃	—	2	4	no	—
57	C₂×SD₁₆×C₇₃	—	2	4	no	—
58	C₂×SD₁₆×C₇₃	—	2	4	no	—
59	C₂×D₈×C₇₃	—	2	4	no	—
60	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
61	C₄⋊Q₈×C₇₃	D₄	1	2	yes	complemented
62	#127×C₇₃	—	2	4	no	—
63	#127×C₇₃	D₄	1	2	yes	complemented
64	#124×C₇₃	—	2	4	no	—
65	#124×C₇₃	—	2	2	no	—
66	#124×C₇₃	—	2	2	no	—
67	#124×C₇₃	D₄	1	4	yes	complemented
68	#123×C₇₃	—	2	8	no	—
69	C₂²⋊Q₈×C₇₃	—	2	4	no	—
70	#121×C₇₃	—	2	4	no	—
71	#121×C₇₃	—	2	4	no	—
72	#121×C₇₃	—	2	4	no	—
73	#121×C₇₃	—	2	2	no	—
74	#121×C₇₃	—	2	4	no	—
75	#121×C₇₃	—	2	2	no	—
76	#120×C₇₃	—	2	8	no	—
77	C₄×D₄×C₇₃	—	2	2	no	—
78	C₄×D₄×C₇₃	—	2	2	no	—
79	C₄×D₄×C₇₃	—	2	2	no	—
80	C₄×D₄×C₇₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
82	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
90	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
93	#104×C₇₃	—	2	8	no	—
94	#104×C₇₃	—	2	8	no	—
95	#100×C₇₃	D₄	1	8	yes	complemented
96	#97×C₇₃	—	2	2	no	—
97	C₄×C₈×C₇₃	—	2	2	no	—
98	#95×C₇₃	—	2	1	no	—
99	#95×C₇₃	—	2	2	no	—
100	C₂⁴×C₇₃	—	2	4	no	—
101	C₂⁴×C₇₃	—	2	1	no	—
102	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
103	#41×C₇₃	—	2	4	no	—
104	#41×C₇₃	—	2	4	no	—
105	#41×C₇₃	—	2	4	no	—
106	#41×C₇₃	—	2	4	no	—
107	#41×C₇₃	—	4	8	no	—
108	#41×C₇₃	—	4	8	no	—
109	C₂×Q₈×C₇₃	—	2	2	no	—
110	C₂×Q₈×C₇₃	—	2	2	no	—
111	C₂×Q₈×C₇₃	—	2	2	no	—
112	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
113	C₂×D₄×C₇₃	—	2	8	no	—
114	C₂×D₄×C₇₃	—	2	4	no	—
115	C₂×D₄×C₇₃	—	2	4	no	—
116	C₂×D₄×C₇₃	—	2	2	no	—
117	C₂×D₄×C₇₃	—	2	2	no	—
118	C₂×D₄×C₇₃	—	2	2	no	—
119	C₂×D₄×C₇₃	—	2	2	no	—
120	C₂×D₄×C₇₃	—	2	2	no	—
121	C₂×D₄×C₇₃	—	2	2	no	—
122	C₂×D₄×C₇₃	—	2	2	no	—
123	C₂×D₄×C₇₃	—	4	4	no	—
124	C₂×D₄×C₇₃	—	4	8	no	—
125	C₂×D₄×C₇₃	—	4	8	no	—
126	C₂×D₄×C₇₃	—	4	8	no	—
127	C₂×D₄×C₇₃	—	4	8	no	—
128	C₂×D₄×C₇₃	—	4	4	no	—
129	C₂×D₄×C₇₃	—	8	4	no	—
130	C₂×D₄×C₇₃	—	8	2	no	—
131	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
132	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₇₃	—	2	4	no	—
134	C₂²×C₄×C₇₃	—	2	1	no	—
135	C₂²×C₄×C₇₃	—	2	2	no	—
136	C₂²×C₄×C₇₃	—	2	4	no	—
137	C₂²×C₄×C₇₃	—	2	2	no	—
138	C₂²×C₄×C₇₃	—	2	1	no	—
139	C₂²×C₄×C₇₃	—	2	1	no	—
140	C₂²×C₄×C₇₃	—	8	2	no	—
141	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₇₃	—	4	8	no	—
146	SD₁₆×C₇₃	—	4	8	no	—
147	SD₁₆×C₇₃	—	4	8	no	—
148	D₈×C₇₃	—	4	8	no	—
149	M₁₆×C₇₃	—	2	4	no	—
150	M₁₆×C₇₃	C₂×D₄	1	8	yes	complemented
151	C₂×C₈×C₇₃	—	2	4	no	—
152	C₄⋊C₄×C₇₃	—	2	4	no	—
153	C₄⋊C₄×C₇₃	—	2	2	no	—
154	C₄⋊C₄×C₇₃	—	2	2	no	—
155	C₄⋊C₄×C₇₃	—	2	2	no	—
156	C₄⋊C₄×C₇₃	—	4	2	no	—
157	C₂²⋊C₄×C₇₃	—	2	8	no	—
158	C₂²⋊C₄×C₇₃	—	2	4	no	—
159	C₂²⋊C₄×C₇₃	—	2	4	no	—
160	C₂²⋊C₄×C₇₃	—	2	4	no	—
161	C₂²⋊C₄×C₇₃	—	4	4	no	—
162	C₂²⋊C₄×C₇₃	—	4	2	no	—
163	C₂²⋊C₄×C₇₃	—	4	1	no	—
164	C₂²⋊C₄×C₇₃	—	4	1	no	—
165	C₂²⋊C₄×C₇₃	—	8	2	no	—
166	C₄²×C₇₃	—	2	2	no	—
167	C₄²×C₇₃	—	2	2	no	—
168	C₄²×C₇₃	C₂×D₄	1	2	yes	—
169	C₄²×C₇₃	C₂×D₄	1	2	yes	—
170	C₂³×C₇₃	—	2	2	no	—
171	C₂³×C₇₃	—	2	2	no	—
172	C₂³×C₇₃	—	2	4	no	—
173	C₂³×C₇₃	—	4	2	no	—
174	C₂³×C₇₃	—	4	2	no	—
175	C₂³×C₇₃	—	4	8	no	—
176	C₂³×C₇₃	—	4	2	no	—
177	C₂³×C₇₃	—	4	2	no	—
178	C₂³×C₇₃	—	4	1	no	—
179	C₂³×C₇₃	—	4	1	no	—
180	C₂³×C₇₃	—	4	1	no	—
181	C₂³×C₇₃	—	8	4	no	—
182	C₂³×C₇₃	—	8	4	no	—
183	C₂³×C₇₃	#127	1	4	yes	—
184	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₇₃	—	2	4	no	—
186	Q₈×C₇₃	—	2	4	no	—
187	Q₈×C₇₃	—	4	4	no	—
188	D₄×C₇₃	—	2	8	no	—
189	D₄×C₇₃	—	2	4	no	—
190	D₄×C₇₃	—	2	4	no	—
191	D₄×C₇₃	—	4	4	no	—
192	D₄×C₇₃	—	4	16	no	—
193	D₄×C₇₃	—	4	4	no	—
194	D₄×C₇₃	—	4	4	no	—
195	D₄×C₇₃	—	4	4	no	—
196	D₄×C₇₃	—	8	2	no	—
197	D₄×C₇₃	—	8	4	no	—
198	D₄×C₇₃	—	8	8	no	—
199	C₂×C₄×C₇₃	—	2	2	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	2	4	no	—
202	C₂×C₄×C₇₃	—	4	1	no	—
203	C₂×C₄×C₇₃	—	4	1	no	—
204	C₂×C₄×C₇₃	—	4	4	no	—
205	C₂×C₄×C₇₃	—	4	8	no	—
206	C₂×C₄×C₇₃	—	4	1	no	—
207	C₂×C₄×C₇₃	—	4	1	no	—
208	C₂×C₄×C₇₃	—	4	4	no	—
209	C₂×C₄×C₇₃	—	4	4	no	—
210	C₂×C₄×C₇₃	—	4	2	no	—
211	C₂×C₄×C₇₃	—	4	1	no	—
212	C₂×C₄×C₇₃	—	4	1	no	—
213	C₂×C₄×C₇₃	—	4	1	no	—
214	C₂×C₄×C₇₃	—	4	1	no	—
215	C₂×C₄×C₇₃	—	4	1	no	—
216	C₂×C₄×C₇₃	—	4	1	no	—
217	C₂×C₄×C₇₃	—	8	2	no	—
218	C₂×C₄×C₇₃	#120	1	2	yes	—
219	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
220	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
221	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
224	C₈×C₇₃	—	2	8	no	—
225	C₂²×C₇₃	—	2	1	no	—
226	C₂²×C₇₃	—	2	1	no	—
227	C₂²×C₇₃	—	2	4	no	—
228	C₂²×C₇₃	—	4	4	no	—
229	C₂²×C₇₃	—	4	2	no	—
230	C₂²×C₇₃	—	4	2	no	—
231	C₂²×C₇₃	—	4	4	no	—
232	C₂²×C₇₃	—	4	4	no	—
233	C₂²×C₇₃	—	4	4	no	—
234	C₂²×C₇₃	—	8	2	no	—
235	C₂²×C₇₃	—	8	2	no	—
236	C₂²×C₇₃	—	8	2	no	—
237	C₂²×C₇₃	—	8	1	no	—
238	C₂²×C₇₃	—	8	1	no	—
239	C₂²×C₇₃	—	8	1	no	—
240	C₂²×C₇₃	—	16	8	no	—
241	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
242	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
243	C₂²×C₇₃	#535	1	1	yes	characteristic
244	C₄×C₇₃	—	2	2	no	—
245	C₄×C₇₃	—	2	1	no	—
246	C₄×C₇₃	—	2	1	no	—
247	C₄×C₇₃	—	4	2	no	—
248	C₄×C₇₃	—	4	4	no	—
249	C₄×C₇₃	—	4	2	no	—
250	C₄×C₇₃	—	8	1	no	—
251	C₄×C₇₃	—	8	1	no	—
252	C₄×C₇₃	D₄²	1	4	yes	—
253	#25743	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂×C₇₃	—	2	1	no	—
255	C₂×C₇₃	—	2	1	no	—
256	C₂×C₇₃	—	4	4	no	—
257	C₂×C₇₃	—	8	4	no	—
258	C₂×C₇₃	—	16	1	no	—
259	C₂×C₇₃	#2433	1	1	yes	characteristic
260	C₂×C₇₃	#3018	1	1	yes	characteristic
261	C₂×C₇₃	#3019	1	1	yes	characteristic
262	#3496	C₂×C₇₃	1	1	yes	characteristic, complemented
263	#3153	C₂×C₇₃	1	2	yes	complemented
264	C₂×#455	C₂×C₇₃	1	2	yes	complemented
265	C₂×#453	C₂×C₇₃	1	2	yes	complemented
266	#2544	C₂×C₇₃	1	1	yes	characteristic, complemented
267	#2007	C₂×C₇₃	1	2	yes	complemented
268	#2006	C₂×C₇₃	1	2	yes	complemented
269	#1980	C₂×C₇₃	1	2	yes	complemented
270	C₄×#100	C₂×C₇₃	1	1	yes	characteristic, complemented
271	C₇₃	#25743	1	1	yes	characteristic, direct product factor, Sylow
272	C₂×H(5,𝔽₂)	C₂²×C₇₃	1	2	yes	—
273	C₂×#137	C₂²×C₇₃	1	4	yes	complemented
274	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	4	yes	complemented
275	#547	—	2	2	no	—
276	#546	—	2	4	no	—
277	D₄²	—	2	2	no	—
278	#537	C₂²×C₇₃	1	2	yes	—
279	#534	—	2	2	no	—
280	#532	C₂²×C₇₃	1	2	yes	—
281	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
282	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
283	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic, complemented
284	C₂×#121	—	2	2	no	—
285	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
286	#497	—	2	2	no	—
287	#496	—	2	2	no	—
288	#495	—	2	4	no	—
289	#455	—	2	8	no	—
290	#453	—	2	8	no	—
291	C₂×#104	C₂²×C₇₃	1	4	yes	complemented
292	C₂×#104	C₂²×C₇₃	1	4	yes	complemented
293	C₂×#100	C₂²×C₇₃	1	2	yes	—
294	C₄×M₁₆	C₂²×C₇₃	1	2	yes	complemented
295	#394	—	2	2	no	—
296	#391	C₂²×C₇₃	1	1	yes	characteristic, complemented
297	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
298	#386	—	2	2	no	—
299	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
300	#343	C₂²×C₇₃	1	2	yes	complemented
301	H(5,𝔽₂)	—	2	4	no	—
302	H(5,𝔽₂)	—	2	4	no	—
303	H(5,𝔽₂)	—	4	4	no	—
304	C₂×#41	—	2	4	no	—
305	C₂×#41	C₂³×C₇₃	1	4	yes	—
306	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
307	C₂²×D₄	—	2	4	no	—
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	—	2	4	no	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
313	C₂³×C₄	D₄×C₇₃	1	2	yes	—
314	#137	—	2	8	no	—
315	#137	—	4	4	no	—
316	AGL(1,ℤ/8)	—	2	8	no	—
317	AGL(1,ℤ/8)	—	4	4	no	—
318	C₂×Q₁₆	—	2	4	no	—
319	C₂×SD₁₆	—	2	4	no	—
320	C₂×SD₁₆	—	2	4	no	—
321	C₂×D₈	—	2	4	no	—
322	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
323	C₄⋊Q₈	D₄×C₇₃	1	2	yes	complemented
324	#127	—	2	4	no	—
325	#127	D₄×C₇₃	1	2	yes	complemented
326	#124	—	2	4	no	—
327	#124	—	2	2	no	—
328	#124	—	2	2	no	—
329	#124	D₄×C₇₃	1	4	yes	complemented
330	#123	—	2	8	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	#121	—	2	4	no	—
333	#121	—	2	4	no	—
334	#121	—	2	4	no	—
335	#121	—	2	2	no	—
336	#121	—	2	4	no	—
337	#121	—	2	2	no	—
338	#120	—	2	8	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	—	2	4	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
352	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
355	#104	—	2	8	no	—
356	#104	—	2	8	no	—
357	#100	D₄×C₇₃	1	8	yes	complemented
358	#97	—	2	2	no	—
359	C₄×C₈	—	2	2	no	—
360	#95	—	2	1	no	—
361	#95	—	2	2	no	—
362	C₂⁴	—	2	4	no	—
363	C₂⁴	—	2	1	no	—
364	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
365	#41	—	2	4	no	—
366	#41	—	2	4	no	—
367	#41	—	2	4	no	—
368	#41	—	2	4	no	—
369	#41	—	4	8	no	—
370	#41	—	4	8	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	4	8	no	—
388	C₂×D₄	—	4	8	no	—
389	C₂×D₄	—	4	8	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	8	4	no	—
392	C₂×D₄	—	8	2	no	—
393	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
394	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	8	2	no	—
403	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
407	Q₁₆	—	4	8	no	—
408	SD₁₆	—	4	8	no	—
409	SD₁₆	—	4	8	no	—
410	D₈	—	4	8	no	—
411	M₁₆	—	2	4	no	—
412	M₁₆	C₂×D₄×C₇₃	1	8	yes	complemented
413	C₂×C₈	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	4	2	no	—
425	C₂²⋊C₄	—	4	1	no	—
426	C₂²⋊C₄	—	4	1	no	—
427	C₂²⋊C₄	—	8	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	C₂×D₄×C₇₃	1	2	yes	—
431	C₄²	C₂×D₄×C₇₃	1	2	yes	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	8	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	8	4	no	—
444	C₂³	—	8	4	no	—
445	C₂³	#127×C₇₃	1	4	yes	—
446	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
447	Q₈	—	2	4	no	—
448	Q₈	—	2	4	no	—
449	Q₈	—	4	4	no	—
450	D₄	—	2	8	no	—
451	D₄	—	2	4	no	—
452	D₄	—	2	4	no	—
453	D₄	—	4	4	no	—
454	D₄	—	4	16	no	—
455	D₄	—	4	4	no	—
456	D₄	—	4	4	no	—
457	D₄	—	4	4	no	—
458	D₄	—	8	2	no	—
459	D₄	—	8	4	no	—
460	D₄	—	8	8	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	8	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	#120×C₇₃	1	2	yes	—
481	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
482	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
485	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
486	C₈	—	2	8	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	16	8	no	—
503	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
504	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
505	C₂²	#535×C₇₃	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	4	no	—
512	C₄	—	8	1	no	—
513	C₄	—	8	1	no	—
514	C₄	D₄²×C₇₃	1	4	yes	—
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	—	4	4	no	—
518	C₂	—	8	4	no	—
519	C₂	—	16	1	no	—
520	C₂	C₇₃×#2433	1	1	yes	characteristic
521	C₂	C₇₃×#3018	1	1	yes	characteristic
522	C₂	C₇₃×#3019	1	1	yes	characteristic

	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×#3496	C₂	semidirect
2. C₇₃×#3153	C₂	semidirect
3. C₂×#455×C₇₃	C₂	semidirect
4. C₂×#453×C₇₃	C₂	semidirect
5. C₇₃×#2544	C₂	semidirect
6. C₇₃×#2007	C₂	semidirect
7. C₇₃×#2006	C₂	semidirect
8. C₇₃×#1980	C₂	semidirect
9. C₄×#100×C₇₃	C₂	semidirect
11. C₂×#137×C₇₃	C₂²	semidirect
12. C₂×AGL(1,ℤ/8)×C₇₃	C₂²	semidirect
21. C₂×#124×C₇₃	C₂²	semidirect
29. C₂×#104×C₇₃	C₂²	semidirect
30. C₂×#104×C₇₃	C₂²	semidirect
32. C₄×M₁₆×C₇₃	C₂²	semidirect
34. #391×C₇₃	C₂²	semidirect
35. #390×C₇₃	C₂²	semidirect
37. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
38. #343×C₇₃	C₂²	semidirect
61. C₄⋊Q₈×C₇₃	D₄	semidirect
63. #127×C₇₃	D₄	semidirect
67. #124×C₇₃	D₄	semidirect
95. #100×C₇₃	D₄	semidirect
150. M₁₆×C₇₃	C₂×D₄	semidirect
253. #25743	C₇₃	direct (N × H)
262. #3496	C₂×C₇₃	semidirect
263. #3153	C₂×C₇₃	semidirect
264. C₂×#455	C₂×C₇₃	semidirect
265. C₂×#453	C₂×C₇₃	semidirect
266. #2544	C₂×C₇₃	semidirect
267. #2007	C₂×C₇₃	semidirect
268. #2006	C₂×C₇₃	semidirect
269. #1980	C₂×C₇₃	semidirect
270. C₄×#100	C₂×C₇₃	semidirect
271. C₇₃	#25743	direct (N × H)
273. C₂×#137	C₂²×C₇₃	semidirect
274. C₂×AGL(1,ℤ/8)	C₂²×C₇₃	semidirect
283. C₂×#124	C₂²×C₇₃	semidirect
291. C₂×#104	C₂²×C₇₃	semidirect
292. C₂×#104	C₂²×C₇₃	semidirect
294. C₄×M₁₆	C₂²×C₇₃	semidirect
296. #391	C₂²×C₇₃	semidirect
297. #390	C₂²×C₇₃	semidirect
299. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
300. #343	C₂²×C₇₃	semidirect
323. C₄⋊Q₈	D₄×C₇₃	semidirect
325. #127	D₄×C₇₃	semidirect
329. #124	D₄×C₇₃	semidirect
357. #100	D₄×C₇₃	semidirect
412. M₁₆	C₂×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×#3496	2
C₇₃×#3153	2
C₂×#455×C₇₃	2
C₂×#453×C₇₃	2
C₇₃×#2544	2
C₇₃×#2007	2
C₇₃×#2006	2
C₇₃×#1980	2
C₄×#100×C₇₃	2
#25743	73

Subgroups — C73×#25743 #32935147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25743 #32935147