Subgroups — C₇₃×#25744 #32935148

Order 18688.

1606 conjugacy classes of subgroups.

The subgroup lattice has 498 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
2	C₇₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#455×C₇₃	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2004	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1965	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1962	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#104×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	2	yes	—
11	C₂×#137×C₇₃	C₂²	1	2	yes	—
12	C₂×#137×C₇₃	C₂²	1	4	yes	complemented
13	#550×C₇₃	—	2	2	no	—
14	D₄²×C₇₃	—	2	4	no	—
15	D₄²×C₇₃	—	2	2	no	—
16	#535×C₇₃	—	2	2	no	—
17	#535×C₇₃	C₂²	1	2	yes	—
18	#532×C₇₃	—	2	1	no	—
19	#532×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×#127×C₇₃	—	2	1	no	—
22	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×#124×C₇₃	C₂²	1	4	yes	complemented
24	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
25	#497×C₇₃	—	2	2	no	—
26	#494×C₇₃	—	2	1	no	—
27	#492×C₇₃	—	2	1	no	—
28	#462×C₇₃	—	2	2	no	—
29	#461×C₇₃	—	2	2	no	—
30	#455×C₇₃	—	2	16	no	—
31	#423×C₇₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#104×C₇₃	C₂²	1	2	yes	—
33	C₂×#104×C₇₃	C₂²	1	4	yes	complemented
34	#419×C₇₃	C₂²	1	2	yes	complemented
35	C₂×#100×C₇₃	C₂²	1	4	yes	complemented
36	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
37	#390×C₇₃	—	2	4	no	—
38	C₄³×C₇₃	C₂²	1	1	yes	characteristic, complemented
39	#339×C₇₃	C₂²	1	2	yes	complemented
40	H(5,𝔽₂)×C₇₃	—	2	8	no	—
41	H(5,𝔽₂)×C₇₃	—	4	4	no	—
42	C₂×#41×C₇₃	—	2	2	no	—
43	C₂×#41×C₇₃	—	2	2	no	—
44	C₂×#41×C₇₃	C₂³	1	2	yes	—
45	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
47	C₂²×D₄×C₇₃	—	2	4	no	—
48	C₂²×D₄×C₇₃	—	2	4	no	—
49	C₂²×D₄×C₇₃	—	2	2	no	—
50	C₂²×D₄×C₇₃	—	2	2	no	—
51	C₂²×D₄×C₇₃	D₄	1	4	yes	—
52	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
53	#137×C₇₃	—	2	8	no	—
54	#137×C₇₃	—	2	8	no	—
55	#137×C₇₃	—	4	4	no	—
56	C₂×Q₁₆×C₇₃	—	2	2	no	—
57	C₂×Q₁₆×C₇₃	—	2	4	no	—
58	C₂×SD₁₆×C₇₃	—	2	2	no	—
59	C₂×SD₁₆×C₇₃	—	2	4	no	—
60	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
61	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
62	C₄⋊Q₈×C₇₃	—	2	2	no	—
63	C₄⋊Q₈×C₇₃	—	2	1	no	—
64	C₄⋊Q₈×C₇₃	—	2	1	no	—
65	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
66	#127×C₇₃	—	2	4	no	—
67	#127×C₇₃	—	2	2	no	—
68	#127×C₇₃	—	2	1	no	—
69	#127×C₇₃	—	2	1	no	—
70	#127×C₇₃	—	2	2	no	—
71	#127×C₇₃	D₄	1	1	yes	characteristic
72	#124×C₇₃	—	2	2	no	—
73	#124×C₇₃	—	2	8	no	—
74	#124×C₇₃	—	4	4	no	—
75	#124×C₇₃	D₄	1	2	yes	—
76	#121×C₇₃	—	2	4	no	—
77	#121×C₇₃	—	2	8	no	—
78	#121×C₇₃	—	2	2	no	—
79	#121×C₇₃	—	2	4	no	—
80	#120×C₇₃	—	2	8	no	—
81	#120×C₇₃	—	2	4	no	—
82	C₄×Q₈×C₇₃	D₄	1	2	yes	—
83	C₄×D₄×C₇₃	—	2	4	no	—
84	C₄×D₄×C₇₃	—	2	2	no	—
85	C₄×D₄×C₇₃	—	2	2	no	—
86	C₄×D₄×C₇₃	D₄	1	2	yes	—
87	#117×C₇₃	—	2	1	no	—
88	#117×C₇₃	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
91	C₂×C₄²×C₇₃	—	2	1	no	—
92	C₂×C₄²×C₇₃	—	2	2	no	—
93	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
94	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₃	—	2	2	no	—
96	#104×C₇₃	—	2	8	no	—
97	#104×C₇₃	D₄	1	8	yes	complemented
98	#103×C₇₃	—	2	4	no	—
99	#100×C₇₃	—	2	8	no	—
100	#97×C₇₃	—	2	1	no	—
101	C₄×C₈×C₇₃	—	2	1	no	—
102	C₂⁴×C₇₃	—	2	4	no	—
103	C₂⁴×C₇₃	C₂×D₄	1	4	yes	—
104	#41×C₇₃	—	2	2	no	—
105	#41×C₇₃	—	2	4	no	—
106	#41×C₇₃	—	2	4	no	—
107	#41×C₇₃	—	4	8	no	—
108	#41×C₇₃	—	4	4	no	—
109	#41×C₇₃	—	4	4	no	—
110	#41×C₇₃	C₂×D₄	1	4	yes	—
111	C₂×Q₈×C₇₃	—	2	2	no	—
112	C₂×Q₈×C₇₃	—	2	4	no	—
113	C₂×Q₈×C₇₃	—	2	2	no	—
114	C₂×Q₈×C₇₃	—	2	4	no	—
115	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
116	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₇₃	—	2	1	no	—
118	C₂×D₄×C₇₃	—	2	4	no	—
119	C₂×D₄×C₇₃	—	2	4	no	—
120	C₂×D₄×C₇₃	—	2	2	no	—
121	C₂×D₄×C₇₃	—	2	8	no	—
122	C₂×D₄×C₇₃	—	2	4	no	—
123	C₂×D₄×C₇₃	—	2	2	no	—
124	C₂×D₄×C₇₃	—	2	4	no	—
125	C₂×D₄×C₇₃	—	2	4	no	—
126	C₂×D₄×C₇₃	—	2	2	no	—
127	C₂×D₄×C₇₃	—	2	2	no	—
128	C₂×D₄×C₇₃	—	2	4	no	—
129	C₂×D₄×C₇₃	—	4	8	no	—
130	C₂×D₄×C₇₃	—	4	8	no	—
131	C₂×D₄×C₇₃	—	4	16	no	—
132	C₂×D₄×C₇₃	—	4	4	no	—
133	C₂×D₄×C₇₃	—	4	4	no	—
134	C₂×D₄×C₇₃	—	8	8	no	—
135	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₃	—	2	1	no	—
138	C₂²×C₄×C₇₃	—	2	4	no	—
139	C₂²×C₄×C₇₃	—	2	2	no	—
140	C₂²×C₄×C₇₃	—	2	2	no	—
141	C₂²×C₄×C₇₃	—	2	2	no	—
142	C₂²×C₄×C₇₃	—	2	2	no	—
143	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₇₃	—	4	8	no	—
146	Q₁₆×C₇₃	—	4	4	no	—
147	SD₁₆×C₇₃	—	4	8	no	—
148	SD₁₆×C₇₃	—	4	4	no	—
149	M₁₆×C₇₃	—	2	2	no	—
150	M₁₆×C₇₃	—	2	4	no	—
151	M₁₆×C₇₃	C₂×D₄	1	4	yes	complemented
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×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	C₄⋊C₄×C₇₃	—	4	2	no	—
158	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
159	C₂²⋊C₄×C₇₃	—	2	8	no	—
160	C₂²⋊C₄×C₇₃	—	2	1	no	—
161	C₂²⋊C₄×C₇₃	—	2	2	no	—
162	C₂²⋊C₄×C₇₃	—	2	4	no	—
163	C₂²⋊C₄×C₇₃	—	4	16	no	—
164	C₄²×C₇₃	—	2	2	no	—
165	C₄²×C₇₃	—	2	1	no	—
166	C₄²×C₇₃	—	2	2	no	—
167	C₄²×C₇₃	—	4	4	no	—
168	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₇₃	C₂×D₄	1	2	yes	—
171	C₄²×C₇₃	C₂×D₄	1	4	yes	complemented
172	C₂³×C₇₃	—	2	1	no	—
173	C₂³×C₇₃	—	2	4	no	—
174	C₂³×C₇₃	—	2	2	no	—
175	C₂³×C₇₃	—	2	8	no	—
176	C₂³×C₇₃	—	4	8	no	—
177	C₂³×C₇₃	—	4	8	no	—
178	C₂³×C₇₃	—	8	8	no	—
179	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₇₃	—	2	1	no	—
181	Q₈×C₇₃	—	2	4	no	—
182	Q₈×C₇₃	—	4	2	no	—
183	Q₈×C₇₃	—	4	2	no	—
184	Q₈×C₇₃	—	4	4	no	—
185	Q₈×C₇₃	#127	1	2	yes	—
186	D₄×C₇₃	—	2	4	no	—
187	D₄×C₇₃	—	2	1	no	—
188	D₄×C₇₃	—	2	4	no	—
189	D₄×C₇₃	—	4	8	no	—
190	D₄×C₇₃	—	4	8	no	—
191	D₄×C₇₃	—	4	4	no	—
192	D₄×C₇₃	—	4	2	no	—
193	D₄×C₇₃	—	4	2	no	—
194	D₄×C₇₃	—	4	4	no	—
195	D₄×C₇₃	—	4	8	no	—
196	D₄×C₇₃	—	4	4	no	—
197	D₄×C₇₃	—	8	4	no	—
198	D₄×C₇₃	—	8	8	no	—
199	D₄×C₇₃	#127	1	2	yes	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	2	4	no	—
202	C₂×C₄×C₇₃	—	2	4	no	—
203	C₂×C₄×C₇₃	—	2	2	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	4	no	—
206	C₂×C₄×C₇₃	—	4	8	no	—
207	C₂×C₄×C₇₃	—	4	4	no	—
208	C₂×C₄×C₇₃	—	4	2	no	—
209	C₂×C₄×C₇₃	—	4	2	no	—
210	C₂×C₄×C₇₃	—	4	4	no	—
211	C₂×C₄×C₇₃	—	4	2	no	—
212	C₂×C₄×C₇₃	—	4	4	no	—
213	C₂×C₄×C₇₃	#120	1	2	yes	—
214	C₂×C₄×C₇₃	#120	1	2	yes	—
215	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
219	C₈×C₇₃	—	2	4	no	—
220	C₈×C₇₃	—	4	2	no	—
221	C₂²×C₇₃	—	2	2	no	—
222	C₂²×C₇₃	—	2	2	no	—
223	C₂²×C₇₃	—	4	2	no	—
224	C₂²×C₇₃	—	4	2	no	—
225	C₂²×C₇₃	—	4	4	no	—
226	C₂²×C₇₃	—	4	8	no	—
227	C₂²×C₇₃	—	4	4	no	—
228	C₂²×C₇₃	—	8	8	no	—
229	C₂²×C₇₃	—	16	8	no	—
230	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
231	C₂²×C₇₃	D₄²	1	2	yes	—
232	C₄×C₇₃	—	2	2	no	—
233	C₄×C₇₃	—	2	2	no	—
234	C₄×C₇₃	—	4	4	no	—
235	C₄×C₇₃	—	4	2	no	—
236	C₄×C₇₃	—	4	2	no	—
237	C₄×C₇₃	—	8	2	no	—
238	C₄×C₇₃	#455	1	4	yes	complemented
239	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
240	C₄×C₇₃	#535	1	1	yes	characteristic
241	C₄×C₇₃	D₄²	1	2	yes	—
242	#25744	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂×C₇₃	—	2	2	no	—
244	C₂×C₇₃	—	4	2	no	—
245	C₂×C₇₃	—	8	4	no	—
246	C₂×C₇₃	—	8	2	no	—
247	C₂×C₇₃	#2433	1	1	yes	characteristic
248	C₂×C₇₃	C₂×#455	1	2	yes	—
249	#3498	C₂×C₇₃	1	1	yes	characteristic
250	#3152	C₂×C₇₃	1	1	yes	characteristic, complemented
251	#3039	C₂×C₇₃	1	1	yes	characteristic, complemented
252	C₂×#455	C₂×C₇₃	1	4	yes	complemented
253	#2858	C₂×C₇₃	1	1	yes	characteristic, complemented
254	#2004	C₂×C₇₃	1	4	yes	complemented
255	#1965	C₂×C₇₃	1	1	yes	characteristic, complemented
256	#1962	C₂×C₇₃	1	1	yes	characteristic, complemented
257	C₄×#104	C₂×C₇₃	1	1	yes	characteristic, complemented
258	C₇₃	#25744	1	1	yes	characteristic, direct product factor, Sylow
259	C₂×H(5,𝔽₂)	C₂²×C₇₃	1	2	yes	—
260	C₂×#137	C₂²×C₇₃	1	2	yes	—
261	C₂×#137	C₂²×C₇₃	1	4	yes	complemented
262	#550	—	2	2	no	—
263	D₄²	—	2	4	no	—
264	D₄²	—	2	2	no	—
265	#535	—	2	2	no	—
266	#535	C₂²×C₇₃	1	2	yes	—
267	#532	—	2	1	no	—
268	#532	C₂²×C₇₃	1	1	yes	characteristic
269	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
270	C₂×#127	—	2	1	no	—
271	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
272	C₂×#124	C₂²×C₇₃	1	4	yes	complemented
273	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
274	#497	—	2	2	no	—
275	#494	—	2	1	no	—
276	#492	—	2	1	no	—
277	#462	—	2	2	no	—
278	#461	—	2	2	no	—
279	#455	—	2	16	no	—
280	#423	C₂²×C₇₃	1	1	yes	characteristic, complemented
281	C₂×#104	C₂²×C₇₃	1	2	yes	—
282	C₂×#104	C₂²×C₇₃	1	4	yes	complemented
283	#419	C₂²×C₇₃	1	2	yes	complemented
284	C₂×#100	C₂²×C₇₃	1	4	yes	complemented
285	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
286	#390	—	2	4	no	—
287	C₄³	C₂²×C₇₃	1	1	yes	characteristic, complemented
288	#339	C₂²×C₇₃	1	2	yes	complemented
289	H(5,𝔽₂)	—	2	8	no	—
290	H(5,𝔽₂)	—	4	4	no	—
291	C₂×#41	—	2	2	no	—
292	C₂×#41	—	2	2	no	—
293	C₂×#41	C₂³×C₇₃	1	2	yes	—
294	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
295	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
296	C₂²×D₄	—	2	4	no	—
297	C₂²×D₄	—	2	4	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	D₄×C₇₃	1	4	yes	—
301	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
302	#137	—	2	8	no	—
303	#137	—	2	8	no	—
304	#137	—	4	4	no	—
305	C₂×Q₁₆	—	2	2	no	—
306	C₂×Q₁₆	—	2	4	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂×SD₁₆	—	2	4	no	—
309	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
310	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
315	#127	—	2	4	no	—
316	#127	—	2	2	no	—
317	#127	—	2	1	no	—
318	#127	—	2	1	no	—
319	#127	—	2	2	no	—
320	#127	D₄×C₇₃	1	1	yes	characteristic
321	#124	—	2	2	no	—
322	#124	—	2	8	no	—
323	#124	—	4	4	no	—
324	#124	D₄×C₇₃	1	2	yes	—
325	#121	—	2	4	no	—
326	#121	—	2	8	no	—
327	#121	—	2	2	no	—
328	#121	—	2	4	no	—
329	#120	—	2	8	no	—
330	#120	—	2	4	no	—
331	C₄×Q₈	D₄×C₇₃	1	2	yes	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	D₄×C₇₃	1	2	yes	—
336	#117	—	2	1	no	—
337	#117	C₂³×C₇₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	8	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
343	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
344	C₄⋊C₈	—	2	2	no	—
345	#104	—	2	8	no	—
346	#104	D₄×C₇₃	1	8	yes	complemented
347	#103	—	2	4	no	—
348	#100	—	2	8	no	—
349	#97	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	C₂×D₄×C₇₃	1	4	yes	—
353	#41	—	2	2	no	—
354	#41	—	2	4	no	—
355	#41	—	2	4	no	—
356	#41	—	4	8	no	—
357	#41	—	4	4	no	—
358	#41	—	4	4	no	—
359	#41	C₂×D₄×C₇₃	1	4	yes	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
365	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	4	8	no	—
379	C₂×D₄	—	4	8	no	—
380	C₂×D₄	—	4	16	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	8	8	no	—
384	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
385	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
394	Q₁₆	—	4	8	no	—
395	Q₁₆	—	4	4	no	—
396	SD₁₆	—	4	8	no	—
397	SD₁₆	—	4	4	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	4	no	—
400	M₁₆	C₂×D₄×C₇₃	1	4	yes	complemented
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	4	16	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	4	4	no	—
417	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₇₃	1	2	yes	—
420	C₄²	C₂×D₄×C₇₃	1	4	yes	complemented
421	C₂³	—	2	1	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	8	no	—
425	C₂³	—	4	8	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	8	8	no	—
428	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
429	Q₈	—	2	1	no	—
430	Q₈	—	2	4	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	4	no	—
434	Q₈	#127×C₇₃	1	2	yes	—
435	D₄	—	2	4	no	—
436	D₄	—	2	1	no	—
437	D₄	—	2	4	no	—
438	D₄	—	4	8	no	—
439	D₄	—	4	8	no	—
440	D₄	—	4	4	no	—
441	D₄	—	4	8	no	—
442	D₄	—	4	4	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	4	no	—
446	D₄	—	8	4	no	—
447	D₄	—	8	8	no	—
448	D₄	#127×C₇₃	1	2	yes	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	#120×C₇₃	1	2	yes	—
463	C₂×C₄	#120×C₇₃	1	2	yes	—
464	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
467	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
468	C₈	—	2	4	no	—
469	C₈	—	4	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	8	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	8	8	no	—
478	C₂²	—	16	8	no	—
479	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
480	C₂²	D₄²×C₇₃	1	2	yes	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	2	no	—
487	C₄	#455×C₇₃	1	4	yes	complemented
488	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
489	C₄	#535×C₇₃	1	1	yes	characteristic
490	C₄	D₄²×C₇₃	1	2	yes	—
491	C₂	—	2	2	no	—
492	C₂	—	4	2	no	—
493	C₂	—	8	4	no	—
494	C₂	—	8	2	no	—
495	C₂	C₇₃×#2433	1	1	yes	characteristic
496	C₂	C₂×#455×C₇₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#3498	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×#455×C₇₃	C₂	semidirect
5. C₇₃×#2858	C₂	semidirect
6. C₇₃×#2004	C₂	semidirect
7. C₇₃×#1965	C₂	semidirect
8. C₇₃×#1962	C₂	semidirect
9. C₄×#104×C₇₃	C₂	semidirect
12. C₂×#137×C₇₃	C₂²	semidirect
20. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
23. C₂×#124×C₇₃	C₂²	semidirect
31. #423×C₇₃	C₂²	semidirect
33. C₂×#104×C₇₃	C₂²	semidirect
34. #419×C₇₃	C₂²	semidirect
35. C₂×#100×C₇₃	C₂²	semidirect
36. C₄×M₁₆×C₇₃	C₂²	semidirect
38. C₄³×C₇₃	C₂²	semidirect
39. #339×C₇₃	C₂²	semidirect
97. #104×C₇₃	D₄	semidirect
151. M₁₆×C₇₃	C₂×D₄	semidirect
171. C₄²×C₇₃	C₂×D₄	semidirect
238. C₄×C₇₃	#455	semidirect
242. #25744	C₇₃	direct (N × H)
250. #3152	C₂×C₇₃	semidirect
251. #3039	C₂×C₇₃	semidirect
252. C₂×#455	C₂×C₇₃	semidirect
253. #2858	C₂×C₇₃	semidirect
254. #2004	C₂×C₇₃	semidirect
255. #1965	C₂×C₇₃	semidirect
256. #1962	C₂×C₇₃	semidirect
257. C₄×#104	C₂×C₇₃	semidirect
258. C₇₃	#25744	direct (N × H)
261. C₂×#137	C₂²×C₇₃	semidirect
269. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
272. C₂×#124	C₂²×C₇₃	semidirect
280. #423	C₂²×C₇₃	semidirect
282. C₂×#104	C₂²×C₇₃	semidirect
283. #419	C₂²×C₇₃	semidirect
284. C₂×#100	C₂²×C₇₃	semidirect
285. C₄×M₁₆	C₂²×C₇₃	semidirect
287. C₄³	C₂²×C₇₃	semidirect
288. #339	C₂²×C₇₃	semidirect
346. #104	D₄×C₇₃	semidirect
400. M₁₆	C₂×D₄×C₇₃	semidirect
420. C₄²	C₂×D₄×C₇₃	semidirect
487. C₄	#455×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×#3152	2
C₇₃×#3039	2
C₂×#455×C₇₃	2
C₇₃×#2858	2
C₇₃×#2004	2
C₇₃×#1965	2
C₇₃×#1962	2
C₄×#104×C₇₃	2
#25744	73

Subgroups — C73×#25744 #32935148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25744 #32935148