Subgroups — C₇₃×#25751 #32935155

Order 18688.

1474 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3500	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#456×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₂×#455×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×#2004	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1967	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	1	yes	characteristic
13	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#137×C₇₃	C₂²	1	2	yes	—
15	C₂×#137×C₇₃	C₂²	1	2	yes	—
16	C₂×#137×C₇₃	C₂²	1	2	yes	complemented
17	#548×C₇₃	—	2	2	no	—
18	#546×C₇₃	—	2	2	no	—
19	#546×C₇₃	—	2	4	no	—
20	#536×C₇₃	—	2	1	no	—
21	#536×C₇₃	C₂²	1	1	yes	characteristic
22	#535×C₇₃	—	2	1	no	—
23	#535×C₇₃	C₂²	1	1	yes	characteristic
24	#532×C₇₃	—	2	1	no	—
25	#532×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
27	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#124×C₇₃	—	2	1	no	—
29	C₂×#124×C₇₃	C₂²	1	2	yes	—
30	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
31	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
32	#497×C₇₃	—	2	1	no	—
33	#497×C₇₃	—	2	1	no	—
34	#494×C₇₃	—	2	1	no	—
35	#492×C₇₃	—	2	1	no	—
36	#462×C₇₃	—	2	2	no	—
37	#461×C₇₃	—	2	2	no	—
38	#456×C₇₃	—	2	8	no	—
39	#455×C₇₃	—	2	8	no	—
40	#423×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×#104×C₇₃	C₂²	1	2	yes	—
42	C₂×#104×C₇₃	C₂²	1	2	yes	—
43	C₂×#104×C₇₃	C₂²	1	2	yes	complemented
44	#419×C₇₃	C₂²	1	2	yes	complemented
45	C₂×#101×C₇₃	C₂²	1	2	yes	complemented
46	C₂×#100×C₇₃	C₂²	1	2	yes	—
47	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
48	#399×C₇₃	—	2	4	no	—
49	#376×C₇₃	C₂²	1	1	yes	characteristic, complemented
50	#339×C₇₃	C₂²	1	2	yes	complemented
51	2₋¹⁺⁴×C₇₃	—	2	4	no	—
52	2₋¹⁺⁴×C₇₃	—	4	2	no	—
53	H(5,𝔽₂)×C₇₃	—	2	4	no	—
54	H(5,𝔽₂)×C₇₃	—	4	2	no	—
55	C₂×#41×C₇₃	—	2	1	no	—
56	C₂×#41×C₇₃	—	2	1	no	—
57	C₂×#41×C₇₃	—	2	1	no	—
58	C₂×#41×C₇₃	—	2	1	no	—
59	C₂×#41×C₇₃	—	2	2	no	—
60	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
61	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
62	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₇₃	—	2	1	no	—
64	C₂²×Q₈×C₇₃	—	2	1	no	—
65	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
66	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₇₃	—	2	2	no	—
68	C₂²×D₄×C₇₃	—	2	1	no	—
69	C₂²×D₄×C₇₃	—	2	1	no	—
70	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
71	#137×C₇₃	—	2	4	no	—
72	#137×C₇₃	—	2	4	no	—
73	#137×C₇₃	—	2	4	no	—
74	#137×C₇₃	—	2	4	no	—
75	#137×C₇₃	—	4	2	no	—
76	#137×C₇₃	—	4	2	no	—
77	C₂×Q₁₆×C₇₃	—	2	2	no	—
78	C₂×Q₁₆×C₇₃	—	2	2	no	—
79	C₂×Q₁₆×C₇₃	—	2	2	no	—
80	C₂×SD₁₆×C₇₃	—	2	2	no	—
81	C₂×SD₁₆×C₇₃	—	2	2	no	—
82	C₂×SD₁₆×C₇₃	—	2	2	no	—
83	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
84	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
85	C₄⋊Q₈×C₇₃	—	2	1	no	—
86	C₄⋊Q₈×C₇₃	—	2	4	no	—
87	C₄⋊Q₈×C₇₃	—	2	2	no	—
88	C₄⋊Q₈×C₇₃	—	2	1	no	—
89	C₄⋊Q₈×C₇₃	—	2	1	no	—
90	C₄⋊Q₈×C₇₃	—	4	2	no	—
91	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
92	#127×C₇₃	—	2	1	no	—
93	#127×C₇₃	D₄	1	1	yes	characteristic
94	#124×C₇₃	—	2	4	no	—
95	#124×C₇₃	—	2	1	no	—
96	#124×C₇₃	—	2	1	no	—
97	#124×C₇₃	—	2	1	no	—
98	#124×C₇₃	—	2	1	no	—
99	#124×C₇₃	—	2	2	no	—
100	#124×C₇₃	—	2	4	no	—
101	#124×C₇₃	—	4	2	no	—
102	#124×C₇₃	D₄	1	1	yes	characteristic
103	#124×C₇₃	D₄	1	1	yes	characteristic
104	#123×C₇₃	—	2	4	no	—
105	#123×C₇₃	—	2	2	no	—
106	C₂²⋊Q₈×C₇₃	—	2	4	no	—
107	C₂²⋊Q₈×C₇₃	—	2	2	no	—
108	#121×C₇₃	—	2	4	no	—
109	#121×C₇₃	—	2	4	no	—
110	#121×C₇₃	—	2	2	no	—
111	#121×C₇₃	—	2	2	no	—
112	#120×C₇₃	—	2	4	no	—
113	#120×C₇₃	—	2	2	no	—
114	C₄×Q₈×C₇₃	D₄	1	2	yes	—
115	C₄×D₄×C₇₃	—	2	4	no	—
116	C₄×D₄×C₇₃	—	2	2	no	—
117	C₄×D₄×C₇₃	—	2	2	no	—
118	C₄×D₄×C₇₃	D₄	1	2	yes	—
119	#117×C₇₃	—	2	1	no	—
120	#117×C₇₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
122	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
124	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₇₃	D₄	1	4	yes	—
126	C₂×C₄²×C₇₃	—	2	1	no	—
127	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₇₃	—	2	2	no	—
130	#104×C₇₃	—	2	4	no	—
131	#104×C₇₃	—	2	4	no	—
132	#104×C₇₃	D₄	1	8	yes	complemented
133	#103×C₇₃	—	2	4	no	—
134	#101×C₇₃	—	2	4	no	—
135	#100×C₇₃	—	2	4	no	—
136	#97×C₇₃	—	2	1	no	—
137	C₄×C₈×C₇₃	—	2	1	no	—
138	#95×C₇₃	—	2	2	no	—
139	C₂⁴×C₇₃	—	2	2	no	—
140	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
141	#41×C₇₃	—	2	2	no	—
142	#41×C₇₃	—	2	2	no	—
143	#41×C₇₃	—	2	2	no	—
144	#41×C₇₃	—	2	2	no	—
145	#41×C₇₃	—	2	2	no	—
146	#41×C₇₃	—	4	4	no	—
147	#41×C₇₃	—	4	8	no	—
148	#41×C₇₃	—	4	4	no	—
149	#41×C₇₃	—	4	2	no	—
150	#41×C₇₃	—	4	2	no	—
151	#41×C₇₃	—	4	2	no	—
152	#41×C₇₃	—	4	2	no	—
153	#41×C₇₃	C₂×D₄	1	4	yes	—
154	C₂×Q₈×C₇₃	—	2	2	no	—
155	C₂×Q₈×C₇₃	—	2	2	no	—
156	C₂×Q₈×C₇₃	—	2	1	no	—
157	C₂×Q₈×C₇₃	—	2	1	no	—
158	C₂×Q₈×C₇₃	—	2	2	no	—
159	C₂×Q₈×C₇₃	—	2	2	no	—
160	C₂×Q₈×C₇₃	—	2	2	no	—
161	C₂×Q₈×C₇₃	—	2	2	no	—
162	C₂×Q₈×C₇₃	—	2	2	no	—
163	C₂×Q₈×C₇₃	—	2	2	no	—
164	C₂×Q₈×C₇₃	—	2	2	no	—
165	C₂×Q₈×C₇₃	—	4	4	no	—
166	C₂×Q₈×C₇₃	—	4	2	no	—
167	C₂×Q₈×C₇₃	—	4	2	no	—
168	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
169	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
170	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
171	C₂×D₄×C₇₃	—	2	1	no	—
172	C₂×D₄×C₇₃	—	2	2	no	—
173	C₂×D₄×C₇₃	—	2	2	no	—
174	C₂×D₄×C₇₃	—	2	2	no	—
175	C₂×D₄×C₇₃	—	2	1	no	—
176	C₂×D₄×C₇₃	—	2	1	no	—
177	C₂×D₄×C₇₃	—	2	4	no	—
178	C₂×D₄×C₇₃	—	2	2	no	—
179	C₂×D₄×C₇₃	—	2	2	no	—
180	C₂×D₄×C₇₃	—	2	1	no	—
181	C₂×D₄×C₇₃	—	2	1	no	—
182	C₂×D₄×C₇₃	—	2	2	no	—
183	C₂×D₄×C₇₃	—	4	4	no	—
184	C₂×D₄×C₇₃	—	4	8	no	—
185	C₂×D₄×C₇₃	—	4	2	no	—
186	C₂×D₄×C₇₃	—	4	2	no	—
187	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
188	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₃	—	2	1	no	—
191	C₂²×C₄×C₇₃	—	2	2	no	—
192	C₂²×C₄×C₇₃	—	2	2	no	—
193	C₂²×C₄×C₇₃	—	2	2	no	—
194	C₂²×C₄×C₇₃	—	2	2	no	—
195	C₂²×C₄×C₇₃	—	2	1	no	—
196	C₂²×C₄×C₇₃	—	2	1	no	—
197	C₂²×C₄×C₇₃	—	2	2	no	—
198	C₂²×C₄×C₇₃	—	2	2	no	—
199	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
202	Q₁₆×C₇₃	—	4	4	no	—
203	Q₁₆×C₇₃	—	4	4	no	—
204	Q₁₆×C₇₃	—	4	4	no	—
205	SD₁₆×C₇₃	—	4	4	no	—
206	SD₁₆×C₇₃	—	4	4	no	—
207	SD₁₆×C₇₃	—	4	4	no	—
208	M₁₆×C₇₃	—	2	2	no	—
209	M₁₆×C₇₃	—	2	2	no	—
210	M₁₆×C₇₃	—	2	2	no	—
211	M₁₆×C₇₃	C₂×D₄	1	4	yes	—
212	C₂×C₈×C₇₃	—	2	2	no	—
213	C₂×C₈×C₇₃	—	2	2	no	—
214	C₄⋊C₄×C₇₃	—	2	4	no	—
215	C₄⋊C₄×C₇₃	—	2	2	no	—
216	C₄⋊C₄×C₇₃	—	2	2	no	—
217	C₄⋊C₄×C₇₃	—	4	8	no	—
218	C₄⋊C₄×C₇₃	—	4	2	no	—
219	C₄⋊C₄×C₇₃	—	4	2	no	—
220	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
221	C₂²⋊C₄×C₇₃	—	2	4	no	—
222	C₂²⋊C₄×C₇₃	—	2	4	no	—
223	C₂²⋊C₄×C₇₃	—	2	1	no	—
224	C₂²⋊C₄×C₇₃	—	2	2	no	—
225	C₂²⋊C₄×C₇₃	—	2	4	no	—
226	C₂²⋊C₄×C₇₃	—	2	4	no	—
227	C₂²⋊C₄×C₇₃	—	2	2	no	—
228	C₂²⋊C₄×C₇₃	—	2	2	no	—
229	C₂²⋊C₄×C₇₃	—	4	8	no	—
230	C₄²×C₇₃	—	2	2	no	—
231	C₄²×C₇₃	—	2	1	no	—
232	C₄²×C₇₃	—	2	2	no	—
233	C₄²×C₇₃	C₂×D₄	1	4	yes	—
234	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₇₃	C₂×D₄	1	2	yes	—
237	C₂³×C₇₃	—	2	1	no	—
238	C₂³×C₇₃	—	2	2	no	—
239	C₂³×C₇₃	—	2	1	no	—
240	C₂³×C₇₃	—	2	1	no	—
241	C₂³×C₇₃	—	2	4	no	—
242	C₂³×C₇₃	—	4	4	no	—
243	C₂³×C₇₃	—	4	4	no	—
244	C₂³×C₇₃	—	8	4	no	—
245	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
246	Q₈×C₇₃	—	2	1	no	—
247	Q₈×C₇₃	—	2	2	no	—
248	Q₈×C₇₃	—	2	2	no	—
249	Q₈×C₇₃	—	4	4	no	—
250	Q₈×C₇₃	—	4	1	no	—
251	Q₈×C₇₃	—	4	1	no	—
252	Q₈×C₇₃	—	4	2	no	—
253	Q₈×C₇₃	—	4	2	no	—
254	Q₈×C₇₃	—	4	2	no	—
255	Q₈×C₇₃	—	4	2	no	—
256	Q₈×C₇₃	—	4	2	no	—
257	Q₈×C₇₃	#127	1	2	yes	—
258	D₄×C₇₃	—	2	4	no	—
259	D₄×C₇₃	—	2	1	no	—
260	D₄×C₇₃	—	2	2	no	—
261	D₄×C₇₃	—	2	2	no	—
262	D₄×C₇₃	—	4	4	no	—
263	D₄×C₇₃	—	4	4	no	—
264	D₄×C₇₃	—	4	4	no	—
265	D₄×C₇₃	—	4	2	no	—
266	D₄×C₇₃	—	4	2	no	—
267	D₄×C₇₃	—	4	1	no	—
268	D₄×C₇₃	—	4	1	no	—
269	D₄×C₇₃	—	4	2	no	—
270	D₄×C₇₃	—	8	2	no	—
271	D₄×C₇₃	—	8	4	no	—
272	D₄×C₇₃	#127	1	2	yes	—
273	C₂×C₄×C₇₃	—	2	1	no	—
274	C₂×C₄×C₇₃	—	2	4	no	—
275	C₂×C₄×C₇₃	—	2	2	no	—
276	C₂×C₄×C₇₃	—	2	1	no	—
277	C₂×C₄×C₇₃	—	2	2	no	—
278	C₂×C₄×C₇₃	—	2	1	no	—
279	C₂×C₄×C₇₃	—	2	4	no	—
280	C₂×C₄×C₇₃	—	2	4	no	—
281	C₂×C₄×C₇₃	—	4	2	no	—
282	C₂×C₄×C₇₃	—	4	4	no	—
283	C₂×C₄×C₇₃	—	4	4	no	—
284	C₂×C₄×C₇₃	—	4	4	no	—
285	C₂×C₄×C₇₃	—	4	4	no	—
286	C₂×C₄×C₇₃	—	4	1	no	—
287	C₂×C₄×C₇₃	—	4	1	no	—
288	C₂×C₄×C₇₃	—	4	1	no	—
289	C₂×C₄×C₇₃	—	4	1	no	—
290	C₂×C₄×C₇₃	—	4	2	no	—
291	C₂×C₄×C₇₃	—	4	2	no	—
292	C₂×C₄×C₇₃	—	4	2	no	—
293	C₂×C₄×C₇₃	—	8	2	no	—
294	C₂×C₄×C₇₃	#120	1	2	yes	—
295	C₂×C₄×C₇₃	#120	1	2	yes	—
296	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
300	C₈×C₇₃	—	2	4	no	—
301	C₈×C₇₃	—	4	2	no	—
302	C₂²×C₇₃	—	2	2	no	—
303	C₂²×C₇₃	—	2	2	no	—
304	C₂²×C₇₃	—	4	2	no	—
305	C₂²×C₇₃	—	4	1	no	—
306	C₂²×C₇₃	—	4	1	no	—
307	C₂²×C₇₃	—	4	2	no	—
308	C₂²×C₇₃	—	4	2	no	—
309	C₂²×C₇₃	—	4	4	no	—
310	C₂²×C₇₃	—	4	2	no	—
311	C₂²×C₇₃	—	8	4	no	—
312	C₂²×C₇₃	—	16	4	no	—
313	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
314	C₂²×C₇₃	D₄²	1	2	yes	—
315	C₄×C₇₃	—	2	2	no	—
316	C₄×C₇₃	—	2	2	no	—
317	C₄×C₇₃	—	2	2	no	—
318	C₄×C₇₃	—	4	4	no	—
319	C₄×C₇₃	—	4	2	no	—
320	C₄×C₇₃	—	4	1	no	—
321	C₄×C₇₃	—	4	1	no	—
322	C₄×C₇₃	—	4	2	no	—
323	C₄×C₇₃	—	8	2	no	—
324	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
325	C₄×C₇₃	#535	1	1	yes	characteristic
326	C₄×C₇₃	D₄²	1	2	yes	—
327	#25751	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
328	C₂×C₇₃	—	2	2	no	—
329	C₂×C₇₃	—	4	2	no	—
330	C₂×C₇₃	—	8	1	no	—
331	C₂×C₇₃	—	8	2	no	—
332	C₂×C₇₃	—	8	1	no	—
333	C₂×C₇₃	#2433	1	1	yes	characteristic
334	C₂×C₇₃	#3022	1	2	yes	—
335	#3500	C₂×C₇₃	1	1	yes	characteristic
336	#3152	C₂×C₇₃	1	1	yes	characteristic, complemented
337	#3039	C₂×C₇₃	1	1	yes	characteristic, complemented
338	C₂×#456	C₂×C₇₃	1	2	yes	complemented
339	C₂×#455	C₂×C₇₃	1	2	yes	complemented
340	#2658	C₂×C₇₃	1	1	yes	characteristic, complemented
341	#2005	C₂×C₇₃	1	2	yes	complemented
342	#2004	C₂×C₇₃	1	2	yes	complemented
343	#1967	C₂×C₇₃	1	1	yes	characteristic, complemented
344	#1963	C₂×C₇₃	1	1	yes	characteristic, complemented
345	#1759	C₂×C₇₃	1	1	yes	characteristic, complemented
346	C₇₃	#25751	1	1	yes	characteristic, direct product factor, Sylow
347	C₂×2₋¹⁺⁴	C₂²×C₇₃	1	1	yes	characteristic
348	C₂×H(5,𝔽₂)	C₂²×C₇₃	1	1	yes	characteristic
349	C₂×#137	C₂²×C₇₃	1	2	yes	—
350	C₂×#137	C₂²×C₇₃	1	2	yes	—
351	C₂×#137	C₂²×C₇₃	1	2	yes	complemented
352	#548	—	2	2	no	—
353	#546	—	2	2	no	—
354	#546	—	2	4	no	—
355	#536	—	2	1	no	—
356	#536	C₂²×C₇₃	1	1	yes	characteristic
357	#535	—	2	1	no	—
358	#535	C₂²×C₇₃	1	1	yes	characteristic
359	#532	—	2	1	no	—
360	#532	C₂²×C₇₃	1	1	yes	characteristic
361	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
362	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	complemented
363	C₂×#124	—	2	1	no	—
364	C₂×#124	C₂²×C₇₃	1	2	yes	—
365	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
366	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
367	#497	—	2	1	no	—
368	#497	—	2	1	no	—
369	#494	—	2	1	no	—
370	#492	—	2	1	no	—
371	#462	—	2	2	no	—
372	#461	—	2	2	no	—
373	#456	—	2	8	no	—
374	#455	—	2	8	no	—
375	#423	C₂²×C₇₃	1	1	yes	characteristic, complemented
376	C₂×#104	C₂²×C₇₃	1	2	yes	—
377	C₂×#104	C₂²×C₇₃	1	2	yes	—
378	C₂×#104	C₂²×C₇₃	1	2	yes	complemented
379	#419	C₂²×C₇₃	1	2	yes	complemented
380	C₂×#101	C₂²×C₇₃	1	2	yes	complemented
381	C₂×#100	C₂²×C₇₃	1	2	yes	—
382	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
383	#399	—	2	4	no	—
384	#376	C₂²×C₇₃	1	1	yes	characteristic, complemented
385	#339	C₂²×C₇₃	1	2	yes	complemented
386	2₋¹⁺⁴	—	2	4	no	—
387	2₋¹⁺⁴	—	4	2	no	—
388	H(5,𝔽₂)	—	2	4	no	—
389	H(5,𝔽₂)	—	4	2	no	—
390	C₂×#41	—	2	1	no	—
391	C₂×#41	—	2	1	no	—
392	C₂×#41	—	2	1	no	—
393	C₂×#41	—	2	1	no	—
394	C₂×#41	—	2	2	no	—
395	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
396	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
397	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
398	C₂²×Q₈	—	2	1	no	—
399	C₂²×Q₈	—	2	1	no	—
400	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
401	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
402	C₂²×D₄	—	2	2	no	—
403	C₂²×D₄	—	2	1	no	—
404	C₂²×D₄	—	2	1	no	—
405	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
406	#137	—	2	4	no	—
407	#137	—	2	4	no	—
408	#137	—	2	4	no	—
409	#137	—	2	4	no	—
410	#137	—	4	2	no	—
411	#137	—	4	2	no	—
412	C₂×Q₁₆	—	2	2	no	—
413	C₂×Q₁₆	—	2	2	no	—
414	C₂×Q₁₆	—	2	2	no	—
415	C₂×SD₁₆	—	2	2	no	—
416	C₂×SD₁₆	—	2	2	no	—
417	C₂×SD₁₆	—	2	2	no	—
418	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
419	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
420	C₄⋊Q₈	—	2	1	no	—
421	C₄⋊Q₈	—	2	4	no	—
422	C₄⋊Q₈	—	2	2	no	—
423	C₄⋊Q₈	—	2	1	no	—
424	C₄⋊Q₈	—	2	1	no	—
425	C₄⋊Q₈	—	4	2	no	—
426	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
427	#127	—	2	1	no	—
428	#127	D₄×C₇₃	1	1	yes	characteristic
429	#124	—	2	4	no	—
430	#124	—	2	1	no	—
431	#124	—	2	1	no	—
432	#124	—	2	1	no	—
433	#124	—	2	1	no	—
434	#124	—	2	2	no	—
435	#124	—	2	4	no	—
436	#124	—	4	2	no	—
437	#124	D₄×C₇₃	1	1	yes	characteristic
438	#124	D₄×C₇₃	1	1	yes	characteristic
439	#123	—	2	4	no	—
440	#123	—	2	2	no	—
441	C₂²⋊Q₈	—	2	4	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	#121	—	2	4	no	—
444	#121	—	2	4	no	—
445	#121	—	2	2	no	—
446	#121	—	2	2	no	—
447	#120	—	2	4	no	—
448	#120	—	2	2	no	—
449	C₄×Q₈	D₄×C₇₃	1	2	yes	—
450	C₄×D₄	—	2	4	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	D₄×C₇₃	1	2	yes	—
454	#117	—	2	1	no	—
455	#117	C₂³×C₇₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	—	2	4	no	—
457	C₂×C₄⋊C₄	—	2	2	no	—
458	C₂×C₂²⋊C₄	—	2	4	no	—
459	C₂×C₂²⋊C₄	—	2	4	no	—
460	C₂×C₂²⋊C₄	D₄×C₇₃	1	4	yes	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
463	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
464	C₄⋊C₈	—	2	2	no	—
465	#104	—	2	4	no	—
466	#104	—	2	4	no	—
467	#104	D₄×C₇₃	1	8	yes	complemented
468	#103	—	2	4	no	—
469	#101	—	2	4	no	—
470	#100	—	2	4	no	—
471	#97	—	2	1	no	—
472	C₄×C₈	—	2	1	no	—
473	#95	—	2	2	no	—
474	C₂⁴	—	2	2	no	—
475	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
476	#41	—	2	2	no	—
477	#41	—	2	2	no	—
478	#41	—	2	2	no	—
479	#41	—	2	2	no	—
480	#41	—	2	2	no	—
481	#41	—	4	4	no	—
482	#41	—	4	8	no	—
483	#41	—	4	4	no	—
484	#41	—	4	2	no	—
485	#41	—	4	2	no	—
486	#41	—	4	2	no	—
487	#41	—	4	2	no	—
488	#41	C₂×D₄×C₇₃	1	4	yes	—
489	C₂×Q₈	—	2	2	no	—
490	C₂×Q₈	—	2	2	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	2	no	—
494	C₂×Q₈	—	2	2	no	—
495	C₂×Q₈	—	2	2	no	—
496	C₂×Q₈	—	2	2	no	—
497	C₂×Q₈	—	2	2	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	—	4	4	no	—
501	C₂×Q₈	—	4	2	no	—
502	C₂×Q₈	—	4	2	no	—
503	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
504	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
505	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	4	4	no	—
519	C₂×D₄	—	4	8	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
523	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
524	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
535	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
537	Q₁₆	—	4	4	no	—
538	Q₁₆	—	4	4	no	—
539	Q₁₆	—	4	4	no	—
540	SD₁₆	—	4	4	no	—
541	SD₁₆	—	4	4	no	—
542	SD₁₆	—	4	4	no	—
543	M₁₆	—	2	2	no	—
544	M₁₆	—	2	2	no	—
545	M₁₆	—	2	2	no	—
546	M₁₆	C₂×D₄×C₇₃	1	4	yes	—
547	C₂×C₈	—	2	2	no	—
548	C₂×C₈	—	2	2	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	4	8	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	4	8	no	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	2	no	—
568	C₄²	C₂×D₄×C₇₃	1	4	yes	—
569	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
570	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
571	C₄²	C₂×D₄×C₇₃	1	2	yes	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	4	4	no	—
578	C₂³	—	4	4	no	—
579	C₂³	—	8	4	no	—
580	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
581	Q₈	—	2	1	no	—
582	Q₈	—	2	2	no	—
583	Q₈	—	2	2	no	—
584	Q₈	—	4	4	no	—
585	Q₈	—	4	1	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	4	2	no	—
589	Q₈	—	4	2	no	—
590	Q₈	—	4	2	no	—
591	Q₈	—	4	2	no	—
592	Q₈	#127×C₇₃	1	2	yes	—
593	D₄	—	2	4	no	—
594	D₄	—	2	1	no	—
595	D₄	—	2	2	no	—
596	D₄	—	2	2	no	—
597	D₄	—	4	4	no	—
598	D₄	—	4	4	no	—
599	D₄	—	4	4	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	2	no	—
605	D₄	—	8	2	no	—
606	D₄	—	8	4	no	—
607	D₄	#127×C₇₃	1	2	yes	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	4	4	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	8	2	no	—
629	C₂×C₄	#120×C₇₃	1	2	yes	—
630	C₂×C₄	#120×C₇₃	1	2	yes	—
631	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
632	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
633	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
634	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
635	C₈	—	2	4	no	—
636	C₈	—	4	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	8	4	no	—
647	C₂²	—	16	4	no	—
648	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
649	C₂²	D₄²×C₇₃	1	2	yes	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	4	4	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	8	2	no	—
659	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
660	C₄	#535×C₇₃	1	1	yes	characteristic
661	C₄	D₄²×C₇₃	1	2	yes	—
662	C₂	—	2	2	no	—
663	C₂	—	4	2	no	—
664	C₂	—	8	2	no	—
665	C₂	—	8	1	no	—
666	C₂	—	8	1	no	—
667	C₂	C₇₃×#2433	1	1	yes	characteristic
668	C₂	C₇₃×#3022	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#3500	C₂
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
2. C₇₃×#3152	C₂	semidirect
3. C₇₃×#3039	C₂	semidirect
4. C₂×#456×C₇₃	C₂	semidirect
5. C₂×#455×C₇₃	C₂	semidirect
6. C₇₃×#2658	C₂	semidirect
7. C₇₃×#2005	C₂	semidirect
8. C₇₃×#2004	C₂	semidirect
9. C₇₃×#1967	C₂	semidirect
10. C₇₃×#1963	C₂	semidirect
11. C₇₃×#1759	C₂	semidirect
16. C₂×#137×C₇₃	C₂²	semidirect
26. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
27. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
40. #423×C₇₃	C₂²	semidirect
43. C₂×#104×C₇₃	C₂²	semidirect
44. #419×C₇₃	C₂²	semidirect
45. C₂×#101×C₇₃	C₂²	semidirect
47. C₄×M₁₆×C₇₃	C₂²	semidirect
49. #376×C₇₃	C₂²	semidirect
50. #339×C₇₃	C₂²	semidirect
132. #104×C₇₃	D₄	semidirect
327. #25751	C₇₃	direct (N × H)
336. #3152	C₂×C₇₃	semidirect
337. #3039	C₂×C₇₃	semidirect
338. C₂×#456	C₂×C₇₃	semidirect
339. C₂×#455	C₂×C₇₃	semidirect
340. #2658	C₂×C₇₃	semidirect
341. #2005	C₂×C₇₃	semidirect
342. #2004	C₂×C₇₃	semidirect
343. #1967	C₂×C₇₃	semidirect
344. #1963	C₂×C₇₃	semidirect
345. #1759	C₂×C₇₃	semidirect
346. C₇₃	#25751	direct (N × H)
351. C₂×#137	C₂²×C₇₃	semidirect
361. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
362. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
375. #423	C₂²×C₇₃	semidirect
378. C₂×#104	C₂²×C₇₃	semidirect
379. #419	C₂²×C₇₃	semidirect
380. C₂×#101	C₂²×C₇₃	semidirect
382. C₄×M₁₆	C₂²×C₇₃	semidirect
384. #376	C₂²×C₇₃	semidirect
385. #339	C₂²×C₇₃	semidirect
467. #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×#3500	2
C₇₃×#3152	2
C₇₃×#3039	2
C₂×#456×C₇₃	2
C₂×#455×C₇₃	2
C₇₃×#2658	2
C₇₃×#2005	2
C₇₃×#2004	2
C₇₃×#1967	2
C₇₃×#1963	2
C₇₃×#1759	2
#25751	73

Subgroups — C73×#25751 #32935155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25751 #32935155