Subgroups — C₇₃×#25749 #32935153

Order 18688.

1652 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3498	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×#455×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₂×#453×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2657	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2004	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2002	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1965	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×H(5,𝔽₂)×C₇₃	C₂²	1	2	yes	—
13	C₂×#137×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#137×C₇₃	C₂²	1	2	yes	complemented
15	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	complemented
17	#550×C₇₃	—	2	2	no	—
18	D₄²×C₇₃	—	2	4	no	—
19	D₄²×C₇₃	—	2	2	no	—
20	#535×C₇₃	—	2	2	no	—
21	#535×C₇₃	C₂²	1	2	yes	—
22	#532×C₇₃	—	2	1	no	—
23	#532×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#127×C₇₃	—	2	1	no	—
25	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#127×C₇₃	C₂²	1	2	yes	complemented
27	C₂×#124×C₇₃	C₂²	1	2	yes	complemented
28	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic, complemented
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	#455×C₇₃	—	2	8	no	—
36	#453×C₇₃	—	2	8	no	—
37	#423×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#104×C₇₃	C₂²	1	2	yes	—
39	C₂×#104×C₇₃	C₂²	1	2	yes	complemented
40	C₂×#104×C₇₃	C₂²	1	2	yes	complemented
41	#419×C₇₃	C₂²	1	1	yes	characteristic, complemented
42	#418×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#100×C₇₃	C₂²	1	2	yes	complemented
44	C₂×#100×C₇₃	C₂²	1	2	yes	complemented
45	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	#392×C₇₃	—	2	4	no	—
47	#376×C₇₃	C₂²	1	1	yes	characteristic, complemented
48	#339×C₇₃	C₂²	1	2	yes	complemented
49	H(5,𝔽₂)×C₇₃	—	2	4	no	—
50	H(5,𝔽₂)×C₇₃	—	2	4	no	—
51	H(5,𝔽₂)×C₇₃	—	4	2	no	—
52	H(5,𝔽₂)×C₇₃	—	4	2	no	—
53	C₂×#41×C₇₃	—	2	2	no	—
54	C₂×#41×C₇₃	—	2	2	no	—
55	C₂×#41×C₇₃	C₂³	1	2	yes	—
56	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₇₃	—	2	4	no	—
59	C₂²×D₄×C₇₃	—	2	4	no	—
60	C₂²×D₄×C₇₃	—	2	2	no	—
61	C₂²×D₄×C₇₃	—	2	2	no	—
62	C₂²×D₄×C₇₃	—	2	4	no	—
63	C₂²×D₄×C₇₃	D₄	1	4	yes	—
64	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
66	#137×C₇₃	—	2	4	no	—
67	#137×C₇₃	—	2	4	no	—
68	#137×C₇₃	—	4	2	no	—
69	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
70	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
71	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
72	C₂×Q₁₆×C₇₃	—	2	1	no	—
73	C₂×Q₁₆×C₇₃	—	2	2	no	—
74	C₂×SD₁₆×C₇₃	—	2	1	no	—
75	C₂×SD₁₆×C₇₃	—	2	2	no	—
76	C₂×SD₁₆×C₇₃	—	2	1	no	—
77	C₂×SD₁₆×C₇₃	—	2	2	no	—
78	C₂×D₈×C₇₃	—	2	1	no	—
79	C₂×D₈×C₇₃	—	2	2	no	—
80	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
83	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic, complemented
84	#127×C₇₃	—	2	4	no	—
85	#127×C₇₃	—	2	2	no	—
86	#127×C₇₃	—	2	1	no	—
87	#127×C₇₃	—	2	1	no	—
88	#127×C₇₃	—	2	2	no	—
89	#127×C₇₃	—	2	4	no	—
90	#127×C₇₃	—	4	2	no	—
91	#127×C₇₃	D₄	1	1	yes	characteristic, complemented
92	#124×C₇₃	—	2	2	no	—
93	#124×C₇₃	—	2	2	no	—
94	#124×C₇₃	—	2	1	no	—
95	#124×C₇₃	—	2	1	no	—
96	#124×C₇₃	—	2	4	no	—
97	#124×C₇₃	—	4	2	no	—
98	#124×C₇₃	D₄	1	2	yes	complemented
99	#121×C₇₃	—	2	4	no	—
100	#121×C₇₃	—	2	8	no	—
101	#121×C₇₃	—	2	2	no	—
102	#121×C₇₃	—	2	4	no	—
103	#120×C₇₃	—	2	8	no	—
104	#120×C₇₃	—	2	4	no	—
105	C₄×Q₈×C₇₃	D₄	1	2	yes	complemented
106	C₄×D₄×C₇₃	—	2	4	no	—
107	C₄×D₄×C₇₃	—	2	2	no	—
108	C₄×D₄×C₇₃	—	2	2	no	—
109	C₄×D₄×C₇₃	D₄	1	2	yes	complemented
110	#117×C₇₃	—	2	1	no	—
111	#117×C₇₃	C₂³	1	1	yes	characteristic
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	#100×C₇₃	—	2	4	no	—
124	#100×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	4	no	—
129	C₂⁴×C₇₃	—	2	1	no	—
130	C₂⁴×C₇₃	C₂×D₄	1	4	yes	—
131	#41×C₇₃	—	2	2	no	—
132	#41×C₇₃	—	2	2	no	—
133	#41×C₇₃	—	2	2	no	—
134	#41×C₇₃	—	2	2	no	—
135	#41×C₇₃	—	2	2	no	—
136	#41×C₇₃	—	4	4	no	—
137	#41×C₇₃	—	4	4	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	1	no	—
142	C₂×Q₈×C₇₃	—	2	1	no	—
143	C₂×Q₈×C₇₃	—	2	2	no	—
144	C₂×Q₈×C₇₃	—	2	2	no	—
145	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
146	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₇₃	—	2	1	no	—
148	C₂×D₄×C₇₃	—	2	4	no	—
149	C₂×D₄×C₇₃	—	2	4	no	—
150	C₂×D₄×C₇₃	—	2	2	no	—
151	C₂×D₄×C₇₃	—	2	8	no	—
152	C₂×D₄×C₇₃	—	2	4	no	—
153	C₂×D₄×C₇₃	—	2	2	no	—
154	C₂×D₄×C₇₃	—	2	4	no	—
155	C₂×D₄×C₇₃	—	2	2	no	—
156	C₂×D₄×C₇₃	—	2	2	no	—
157	C₂×D₄×C₇₃	—	2	2	no	—
158	C₂×D₄×C₇₃	—	2	2	no	—
159	C₂×D₄×C₇₃	—	2	1	no	—
160	C₂×D₄×C₇₃	—	2	1	no	—
161	C₂×D₄×C₇₃	—	2	2	no	—
162	C₂×D₄×C₇₃	—	2	2	no	—
163	C₂×D₄×C₇₃	—	2	2	no	—
164	C₂×D₄×C₇₃	—	2	2	no	—
165	C₂×D₄×C₇₃	—	4	4	no	—
166	C₂×D₄×C₇₃	—	4	4	no	—
167	C₂×D₄×C₇₃	—	4	8	no	—
168	C₂×D₄×C₇₃	—	4	8	no	—
169	C₂×D₄×C₇₃	—	4	8	no	—
170	C₂×D₄×C₇₃	—	4	4	no	—
171	C₂×D₄×C₇₃	—	4	4	no	—
172	C₂×D₄×C₇₃	—	8	8	no	—
173	C₂×D₄×C₇₃	—	8	4	no	—
174	C₂×D₄×C₇₃	—	8	8	no	—
175	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₃	—	2	1	no	—
178	C₂²×C₄×C₇₃	—	2	4	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	—	2	1	no	—
183	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
185	Q₁₆×C₇₃	—	4	4	no	—
186	Q₁₆×C₇₃	—	4	2	no	—
187	SD₁₆×C₇₃	—	4	4	no	—
188	SD₁₆×C₇₃	—	4	4	no	—
189	SD₁₆×C₇₃	—	4	2	no	—
190	SD₁₆×C₇₃	—	4	2	no	—
191	D₈×C₇₃	—	4	4	no	—
192	D₈×C₇₃	—	4	2	no	—
193	M₁₆×C₇₃	—	2	2	no	—
194	M₁₆×C₇₃	—	2	2	no	—
195	M₁₆×C₇₃	—	2	2	no	—
196	M₁₆×C₇₃	C₂×D₄	1	4	yes	complemented
197	C₂×C₈×C₇₃	—	2	2	no	—
198	C₂×C₈×C₇₃	—	2	1	no	—
199	C₂×C₈×C₇₃	—	2	1	no	—
200	C₄⋊C₄×C₇₃	—	2	2	no	—
201	C₄⋊C₄×C₇₃	—	2	2	no	—
202	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
203	C₂²⋊C₄×C₇₃	—	2	8	no	—
204	C₂²⋊C₄×C₇₃	—	2	1	no	—
205	C₂²⋊C₄×C₇₃	—	2	2	no	—
206	C₂²⋊C₄×C₇₃	—	2	4	no	—
207	C₂²⋊C₄×C₇₃	—	4	8	no	—
208	C₂²⋊C₄×C₇₃	—	4	2	no	—
209	C₂²⋊C₄×C₇₃	—	4	2	no	—
210	C₄²×C₇₃	—	2	2	no	—
211	C₄²×C₇₃	—	2	1	no	—
212	C₄²×C₇₃	—	2	2	no	—
213	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₇₃	C₂×D₄	1	2	yes	—
216	C₄²×C₇₃	C₂×D₄	1	4	yes	complemented
217	C₂³×C₇₃	—	2	1	no	—
218	C₂³×C₇₃	—	2	4	no	—
219	C₂³×C₇₃	—	2	2	no	—
220	C₂³×C₇₃	—	2	4	no	—
221	C₂³×C₇₃	—	2	4	no	—
222	C₂³×C₇₃	—	4	8	no	—
223	C₂³×C₇₃	—	4	8	no	—
224	C₂³×C₇₃	—	4	4	no	—
225	C₂³×C₇₃	—	4	1	no	—
226	C₂³×C₇₃	—	4	2	no	—
227	C₂³×C₇₃	—	8	8	no	—
228	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
229	Q₈×C₇₃	—	2	1	no	—
230	Q₈×C₇₃	—	2	2	no	—
231	Q₈×C₇₃	—	2	2	no	—
232	Q₈×C₇₃	—	4	1	no	—
233	Q₈×C₇₃	—	4	1	no	—
234	Q₈×C₇₃	—	4	2	no	—
235	Q₈×C₇₃	#127	1	2	yes	—
236	D₄×C₇₃	—	2	4	no	—
237	D₄×C₇₃	—	2	1	no	—
238	D₄×C₇₃	—	2	2	no	—
239	D₄×C₇₃	—	2	2	no	—
240	D₄×C₇₃	—	4	8	no	—
241	D₄×C₇₃	—	4	8	no	—
242	D₄×C₇₃	—	4	4	no	—
243	D₄×C₇₃	—	4	8	no	—
244	D₄×C₇₃	—	4	2	no	—
245	D₄×C₇₃	—	4	2	no	—
246	D₄×C₇₃	—	4	2	no	—
247	D₄×C₇₃	—	4	1	no	—
248	D₄×C₇₃	—	4	2	no	—
249	D₄×C₇₃	—	4	1	no	—
250	D₄×C₇₃	—	4	2	no	—
251	D₄×C₇₃	—	4	2	no	—
252	D₄×C₇₃	—	4	2	no	—
253	D₄×C₇₃	—	8	4	no	—
254	D₄×C₇₃	—	8	8	no	—
255	D₄×C₇₃	—	8	16	no	—
256	D₄×C₇₃	#127	1	2	yes	—
257	C₂×C₄×C₇₃	—	2	1	no	—
258	C₂×C₄×C₇₃	—	2	4	no	—
259	C₂×C₄×C₇₃	—	2	2	no	—
260	C₂×C₄×C₇₃	—	2	2	no	—
261	C₂×C₄×C₇₃	—	2	4	no	—
262	C₂×C₄×C₇₃	—	4	2	no	—
263	C₂×C₄×C₇₃	—	4	8	no	—
264	C₂×C₄×C₇₃	—	4	4	no	—
265	C₂×C₄×C₇₃	—	4	4	no	—
266	C₂×C₄×C₇₃	—	4	2	no	—
267	C₂×C₄×C₇₃	—	4	2	no	—
268	C₂×C₄×C₇₃	—	4	1	no	—
269	C₂×C₄×C₇₃	—	4	2	no	—
270	C₂×C₄×C₇₃	#120	1	2	yes	—
271	C₂×C₄×C₇₃	#120	1	2	yes	—
272	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
276	C₈×C₇₃	—	2	4	no	—
277	C₈×C₇₃	—	4	1	no	—
278	C₈×C₇₃	—	4	1	no	—
279	C₂²×C₇₃	—	2	2	no	—
280	C₂²×C₇₃	—	2	2	no	—
281	C₂²×C₇₃	—	4	2	no	—
282	C₂²×C₇₃	—	4	2	no	—
283	C₂²×C₇₃	—	4	4	no	—
284	C₂²×C₇₃	—	4	8	no	—
285	C₂²×C₇₃	—	4	4	no	—
286	C₂²×C₇₃	—	8	4	no	—
287	C₂²×C₇₃	—	8	4	no	—
288	C₂²×C₇₃	—	8	4	no	—
289	C₂²×C₇₃	—	8	1	no	—
290	C₂²×C₇₃	—	8	2	no	—
291	C₂²×C₇₃	—	16	8	no	—
292	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
293	C₂²×C₇₃	D₄²	1	2	yes	—
294	C₄×C₇₃	—	2	2	no	—
295	C₄×C₇₃	—	2	2	no	—
296	C₄×C₇₃	—	2	2	no	—
297	C₄×C₇₃	—	4	4	no	—
298	C₄×C₇₃	—	4	2	no	—
299	C₄×C₇₃	—	4	2	no	—
300	C₄×C₇₃	—	8	1	no	—
301	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
302	C₄×C₇₃	#535	1	1	yes	characteristic
303	C₄×C₇₃	D₄²	1	2	yes	—
304	#25749	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
305	C₂×C₇₃	—	2	2	no	—
306	C₂×C₇₃	—	4	2	no	—
307	C₂×C₇₃	—	8	4	no	—
308	C₂×C₇₃	—	8	2	no	—
309	C₂×C₇₃	—	16	1	no	—
310	C₂×C₇₃	#2433	1	1	yes	characteristic
311	C₂×C₇₃	#3019	1	2	yes	—
312	#3498	C₂×C₇₃	1	1	yes	characteristic, complemented
313	#3153	C₂×C₇₃	1	1	yes	characteristic, complemented
314	#3040	C₂×C₇₃	1	1	yes	characteristic, complemented
315	C₂×#455	C₂×C₇₃	1	2	yes	complemented
316	C₂×#453	C₂×C₇₃	1	2	yes	complemented
317	#2657	C₂×C₇₃	1	1	yes	characteristic, complemented
318	#2004	C₂×C₇₃	1	2	yes	complemented
319	#2002	C₂×C₇₃	1	2	yes	complemented
320	#1965	C₂×C₇₃	1	1	yes	characteristic, complemented
321	#1963	C₂×C₇₃	1	1	yes	characteristic, complemented
322	#1759	C₂×C₇₃	1	1	yes	characteristic, complemented
323	C₇₃	#25749	1	1	yes	characteristic, direct product factor, Sylow
324	C₂×H(5,𝔽₂)	C₂²×C₇₃	1	2	yes	—
325	C₂×#137	C₂²×C₇₃	1	1	yes	characteristic
326	C₂×#137	C₂²×C₇₃	1	2	yes	complemented
327	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	1	yes	characteristic
328	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	complemented
329	#550	—	2	2	no	—
330	D₄²	—	2	4	no	—
331	D₄²	—	2	2	no	—
332	#535	—	2	2	no	—
333	#535	C₂²×C₇₃	1	2	yes	—
334	#532	—	2	1	no	—
335	#532	C₂²×C₇₃	1	1	yes	characteristic
336	C₂×#127	—	2	1	no	—
337	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
338	C₂×#127	C₂²×C₇₃	1	2	yes	complemented
339	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic, complemented
340	C₂×#124	C₂²×C₇₃	1	2	yes	complemented
341	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
342	#497	—	2	1	no	—
343	#496	—	2	1	no	—
344	#495	—	2	2	no	—
345	#464	—	2	2	no	—
346	#463	—	2	2	no	—
347	#455	—	2	8	no	—
348	#453	—	2	8	no	—
349	#423	C₂²×C₇₃	1	1	yes	characteristic, complemented
350	C₂×#104	C₂²×C₇₃	1	2	yes	—
351	C₂×#104	C₂²×C₇₃	1	2	yes	complemented
352	C₂×#104	C₂²×C₇₃	1	2	yes	complemented
353	#419	C₂²×C₇₃	1	1	yes	characteristic, complemented
354	#418	C₂²×C₇₃	1	1	yes	characteristic, complemented
355	C₂×#100	C₂²×C₇₃	1	2	yes	complemented
356	C₂×#100	C₂²×C₇₃	1	2	yes	complemented
357	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
358	#392	—	2	4	no	—
359	#376	C₂²×C₇₃	1	1	yes	characteristic, complemented
360	#339	C₂²×C₇₃	1	2	yes	complemented
361	H(5,𝔽₂)	—	2	4	no	—
362	H(5,𝔽₂)	—	2	4	no	—
363	H(5,𝔽₂)	—	4	2	no	—
364	H(5,𝔽₂)	—	4	2	no	—
365	C₂×#41	—	2	2	no	—
366	C₂×#41	—	2	2	no	—
367	C₂×#41	C₂³×C₇₃	1	2	yes	—
368	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
369	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
370	C₂²×D₄	—	2	4	no	—
371	C₂²×D₄	—	2	4	no	—
372	C₂²×D₄	—	2	2	no	—
373	C₂²×D₄	—	2	2	no	—
374	C₂²×D₄	—	2	4	no	—
375	C₂²×D₄	D₄×C₇₃	1	4	yes	—
376	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
377	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
378	#137	—	2	4	no	—
379	#137	—	2	4	no	—
380	#137	—	4	2	no	—
381	AGL(1,ℤ/8)	—	2	4	no	—
382	AGL(1,ℤ/8)	—	2	4	no	—
383	AGL(1,ℤ/8)	—	4	2	no	—
384	C₂×Q₁₆	—	2	1	no	—
385	C₂×Q₁₆	—	2	2	no	—
386	C₂×SD₁₆	—	2	1	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×SD₁₆	—	2	1	no	—
389	C₂×SD₁₆	—	2	2	no	—
390	C₂×D₈	—	2	1	no	—
391	C₂×D₈	—	2	2	no	—
392	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
393	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
394	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
395	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic, complemented
396	#127	—	2	4	no	—
397	#127	—	2	2	no	—
398	#127	—	2	1	no	—
399	#127	—	2	1	no	—
400	#127	—	2	2	no	—
401	#127	—	2	4	no	—
402	#127	—	4	2	no	—
403	#127	D₄×C₇₃	1	1	yes	characteristic, complemented
404	#124	—	2	2	no	—
405	#124	—	2	2	no	—
406	#124	—	2	1	no	—
407	#124	—	2	1	no	—
408	#124	—	2	4	no	—
409	#124	—	4	2	no	—
410	#124	D₄×C₇₃	1	2	yes	complemented
411	#121	—	2	4	no	—
412	#121	—	2	8	no	—
413	#121	—	2	2	no	—
414	#121	—	2	4	no	—
415	#120	—	2	8	no	—
416	#120	—	2	4	no	—
417	C₄×Q₈	D₄×C₇₃	1	2	yes	complemented
418	C₄×D₄	—	2	4	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	D₄×C₇₃	1	2	yes	complemented
422	#117	—	2	1	no	—
423	#117	C₂³×C₇₃	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	—	2	4	no	—
425	C₂×C₂²⋊C₄	—	2	2	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
428	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
429	C₄⋊C₈	—	2	2	no	—
430	#104	—	2	4	no	—
431	#104	—	2	4	no	—
432	#104	D₄×C₇₃	1	8	yes	complemented
433	#103	—	2	2	no	—
434	#102	—	2	2	no	—
435	#100	—	2	4	no	—
436	#100	—	2	4	no	—
437	#97	—	2	1	no	—
438	C₄×C₈	—	2	1	no	—
439	#95	—	2	2	no	—
440	C₂⁴	—	2	4	no	—
441	C₂⁴	—	2	1	no	—
442	C₂⁴	C₂×D₄×C₇₃	1	4	yes	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	4	4	no	—
449	#41	—	4	4	no	—
450	#41	—	4	4	no	—
451	#41	—	4	4	no	—
452	#41	C₂×D₄×C₇₃	1	4	yes	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
458	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	4	4	no	—
478	C₂×D₄	—	4	4	no	—
479	C₂×D₄	—	4	8	no	—
480	C₂×D₄	—	4	8	no	—
481	C₂×D₄	—	4	8	no	—
482	C₂×D₄	—	4	4	no	—
483	C₂×D₄	—	4	4	no	—
484	C₂×D₄	—	8	8	no	—
485	C₂×D₄	—	8	4	no	—
486	C₂×D₄	—	8	8	no	—
487	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
488	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
497	Q₁₆	—	4	4	no	—
498	Q₁₆	—	4	2	no	—
499	SD₁₆	—	4	4	no	—
500	SD₁₆	—	4	4	no	—
501	SD₁₆	—	4	2	no	—
502	SD₁₆	—	4	2	no	—
503	D₈	—	4	4	no	—
504	D₈	—	4	2	no	—
505	M₁₆	—	2	2	no	—
506	M₁₆	—	2	2	no	—
507	M₁₆	—	2	2	no	—
508	M₁₆	C₂×D₄×C₇₃	1	4	yes	complemented
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
515	C₂²⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	4	8	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	2	no	—
525	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
526	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
527	C₄²	C₂×D₄×C₇₃	1	2	yes	—
528	C₄²	C₂×D₄×C₇₃	1	4	yes	complemented
529	C₂³	—	2	1	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	4	8	no	—
535	C₂³	—	4	8	no	—
536	C₂³	—	4	4	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	8	8	no	—
540	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
541	Q₈	—	2	1	no	—
542	Q₈	—	2	2	no	—
543	Q₈	—	2	2	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	2	no	—
547	Q₈	#127×C₇₃	1	2	yes	—
548	D₄	—	2	4	no	—
549	D₄	—	2	1	no	—
550	D₄	—	2	2	no	—
551	D₄	—	2	2	no	—
552	D₄	—	4	8	no	—
553	D₄	—	4	8	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	8	no	—
556	D₄	—	4	2	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	1	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	2	no	—
565	D₄	—	8	4	no	—
566	D₄	—	8	8	no	—
567	D₄	—	8	16	no	—
568	D₄	#127×C₇₃	1	2	yes	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	8	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	#120×C₇₃	1	2	yes	—
583	C₂×C₄	#120×C₇₃	1	2	yes	—
584	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
586	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
587	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
588	C₈	—	2	4	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	8	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	8	4	no	—
599	C₂²	—	8	4	no	—
600	C₂²	—	8	4	no	—
601	C₂²	—	8	2	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	16	8	no	—
604	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
605	C₂²	D₄²×C₇₃	1	2	yes	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	4	4	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	—	8	1	no	—
613	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
614	C₄	#535×C₇₃	1	1	yes	characteristic
615	C₄	D₄²×C₇₃	1	2	yes	—
616	C₂	—	2	2	no	—
617	C₂	—	4	2	no	—
618	C₂	—	8	4	no	—
619	C₂	—	8	2	no	—
620	C₂	—	16	1	no	—
621	C₂	C₇₃×#2433	1	1	yes	characteristic
622	C₂	C₇₃×#3019	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×#3498	C₂	semidirect
2. C₇₃×#3153	C₂	semidirect
3. C₇₃×#3040	C₂	semidirect
4. C₂×#455×C₇₃	C₂	semidirect
5. C₂×#453×C₇₃	C₂	semidirect
6. C₇₃×#2657	C₂	semidirect
7. C₇₃×#2004	C₂	semidirect
8. C₇₃×#2002	C₂	semidirect
9. C₇₃×#1965	C₂	semidirect
10. C₇₃×#1963	C₂	semidirect
11. C₇₃×#1759	C₂	semidirect
14. C₂×#137×C₇₃	C₂²	semidirect
16. C₂×AGL(1,ℤ/8)×C₇₃	C₂²	semidirect
26. C₂×#127×C₇₃	C₂²	semidirect
27. C₂×#124×C₇₃	C₂²	semidirect
28. C₂×#124×C₇₃	C₂²	semidirect
37. #423×C₇₃	C₂²	semidirect
39. C₂×#104×C₇₃	C₂²	semidirect
40. C₂×#104×C₇₃	C₂²	semidirect
41. #419×C₇₃	C₂²	semidirect
42. #418×C₇₃	C₂²	semidirect
43. C₂×#100×C₇₃	C₂²	semidirect
44. C₂×#100×C₇₃	C₂²	semidirect
45. C₄×M₁₆×C₇₃	C₂²	semidirect
47. #376×C₇₃	C₂²	semidirect
48. #339×C₇₃	C₂²	semidirect
83. C₄⋊Q₈×C₇₃	D₄	semidirect
91. #127×C₇₃	D₄	semidirect
98. #124×C₇₃	D₄	semidirect
105. C₄×Q₈×C₇₃	D₄	semidirect
109. C₄×D₄×C₇₃	D₄	semidirect
120. #104×C₇₃	D₄	semidirect
196. M₁₆×C₇₃	C₂×D₄	semidirect
216. C₄²×C₇₃	C₂×D₄	semidirect
304. #25749	C₇₃	direct (N × H)
312. #3498	C₂×C₇₃	semidirect
313. #3153	C₂×C₇₃	semidirect
314. #3040	C₂×C₇₃	semidirect
315. C₂×#455	C₂×C₇₃	semidirect
316. C₂×#453	C₂×C₇₃	semidirect
317. #2657	C₂×C₇₃	semidirect
318. #2004	C₂×C₇₃	semidirect
319. #2002	C₂×C₇₃	semidirect
320. #1965	C₂×C₇₃	semidirect
321. #1963	C₂×C₇₃	semidirect
322. #1759	C₂×C₇₃	semidirect
323. C₇₃	#25749	direct (N × H)
326. C₂×#137	C₂²×C₇₃	semidirect
328. C₂×AGL(1,ℤ/8)	C₂²×C₇₃	semidirect
338. C₂×#127	C₂²×C₇₃	semidirect
339. C₂×#124	C₂²×C₇₃	semidirect
340. C₂×#124	C₂²×C₇₃	semidirect
349. #423	C₂²×C₇₃	semidirect
351. C₂×#104	C₂²×C₇₃	semidirect
352. C₂×#104	C₂²×C₇₃	semidirect
353. #419	C₂²×C₇₃	semidirect
354. #418	C₂²×C₇₃	semidirect
355. C₂×#100	C₂²×C₇₃	semidirect
356. C₂×#100	C₂²×C₇₃	semidirect
357. C₄×M₁₆	C₂²×C₇₃	semidirect
359. #376	C₂²×C₇₃	semidirect
360. #339	C₂²×C₇₃	semidirect
395. C₄⋊Q₈	D₄×C₇₃	semidirect
403. #127	D₄×C₇₃	semidirect
410. #124	D₄×C₇₃	semidirect
417. C₄×Q₈	D₄×C₇₃	semidirect
421. C₄×D₄	D₄×C₇₃	semidirect
432. #104	D₄×C₇₃	semidirect
508. M₁₆	C₂×D₄×C₇₃	semidirect
528. C₄²	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×#3498	2
C₇₃×#3153	2
C₇₃×#3040	2
C₂×#455×C₇₃	2
C₂×#453×C₇₃	2
C₇₃×#2657	2
C₇₃×#2004	2
C₇₃×#2002	2
C₇₃×#1965	2
C₇₃×#1963	2
C₇₃×#1759	2
#25749	73

Subgroups — C73×#25749 #32935153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25749 #32935153