Subgroups — C₂×#22624255 #33993573

Order 18688.

8814 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624255	C₂	1	32	yes	maximal, direct product factor
2	C₂×#17989325	C₂	1	4	yes	maximal, complemented
3	C₂×#17989322	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17989257	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#17989232	C₂	1	2	yes	maximal, complemented
6	C₂×#17989225	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#17989222	C₂	1	2	yes	maximal, complemented
9	C₂×#17989221	C₂	1	2	yes	maximal, complemented
10	C₂×#17989190	C₂	1	2	yes	maximal, complemented
11	C₂×#17989188	C₂	1	2	yes	maximal, complemented
12	C₂×#17989151	C₂	1	2	yes	maximal, complemented
13	C₂×#17989150	C₂	1	2	yes	maximal, complemented
14	C₂×#17989145	C₂	1	4	yes	maximal, complemented
15	C₂×#127×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#17989124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#17989119	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#550×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11924027	C₂²	1	2	yes	complemented
20	C₂³×D₂₉₂	C₂²	1	2	yes	complemented
21	C₂²×D₄×D₇₃	C₂²	1	2	yes	complemented
22	C₂²×D₄×D₇₃	C₂²	1	4	yes	complemented
23	C₂²×D₄×D₇₃	C₂²	1	2	yes	complemented
24	C₂²×D₄×D₇₃	C₂²	1	2	yes	complemented
25	C₂²×D₄×D₇₃	C₂²	1	2	yes	complemented
26	#17989325	C₂²	1	64	yes	complemented
27	#17989322	C₂²	1	16	yes	complemented
28	#17989257	C₂²	1	16	yes	complemented
29	#17989232	C₂²	1	32	yes	complemented
30	#17989225	C₂²	1	32	yes	complemented
31	D₄×D₂₉₂	C₂²	1	16	yes	complemented
32	#17989222	C₂²	1	32	yes	complemented
33	#17989221	C₂²	1	32	yes	complemented
34	#17989190	C₂²	1	32	yes	complemented
35	#17989188	C₂²	1	32	yes	complemented
36	#17989151	C₂²	1	32	yes	complemented
37	#17989150	C₂²	1	32	yes	complemented
38	#17989145	C₂²	1	64	yes	complemented
39	C₂×#14556588	C₂²	1	1	yes	characteristic
40	C₂×#14556587	C₂²	1	2	yes	complemented
41	C₂×#14556587	C₂²	1	2	yes	complemented
42	C₂×#14556587	C₂²	1	2	yes	complemented
43	C₂×#14556587	C₂²	1	2	yes	complemented
44	#127×D₇₃	C₂²	1	16	yes	complemented
45	#17989124	C₂²	1	16	yes	complemented
46	#17989119	C₂²	1	16	yes	complemented
47	C₂×#14556586	C₂²	1	2	yes	complemented
48	C₂×#14556584	C₂²	1	2	yes	complemented
49	C₂×#14556582	C₂²	1	1	yes	characteristic, complemented
50	C₂×#14556582	C₂²	1	1	yes	characteristic, complemented
51	C₂×#14556580	C₂²	1	1	yes	characteristic, complemented
52	C₂×#14556580	C₂²	1	2	yes	complemented
53	C₂×#14556579	C₂²	1	2	yes	complemented
54	C₂×#14556578	C₂²	1	1	yes	characteristic, complemented
55	C₂×#14556576	C₂²	1	4	yes	complemented
56	C₂×#14556576	C₂²	1	2	yes	complemented
57	C₂×#14556575	C₂²	1	4	yes	complemented
58	C₂×#14556574	C₂²	1	4	yes	complemented
59	C₂×#14556573	C₂²	1	4	yes	complemented
60	C₂×#14556573	C₂²	1	2	yes	complemented
61	C₂×#14556571	C₂²	1	1	yes	characteristic, complemented
62	C₂×#14556567	C₂²	1	1	yes	characteristic, complemented
63	C₂×#14556566	C₂²	1	1	yes	characteristic
64	C₂×#14556566	C₂²	1	2	yes	complemented
65	C₂×#14556565	C₂²	1	4	yes	complemented
66	C₂×#14556565	C₂²	1	4	yes	complemented
67	C₂×#14556565	C₂²	1	2	yes	complemented
68	C₂×#14556564	C₂²	1	4	yes	complemented
69	C₂×#14556563	C₂²	1	4	yes	complemented
70	C₂×#14556563	C₂²	1	4	yes	complemented
71	C₂×#14556563	C₂²	1	4	yes	complemented
72	C₂×#14556562	C₂²	1	1	yes	characteristic
73	C₂×#14556562	C₂²	1	4	yes	complemented
74	C₂×#14556562	C₂²	1	2	yes	complemented
75	C₂×#14556561	C₂²	1	4	yes	complemented
76	C₂×#14556561	C₂²	1	4	yes	complemented
77	C₂×#14556559	C₂²	1	4	yes	complemented
78	C₂×#14556559	C₂²	1	4	yes	complemented
79	C₂×#14556559	C₂²	1	4	yes	complemented
80	C₂×#14556559	C₂²	1	4	yes	complemented
81	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×D₂₉₂	C₂²	1	2	yes	complemented
83	C₂×C₄×D₂₉₂	C₂²	1	2	yes	complemented
84	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
85	C₂×D₄×Dic₇₃	C₂²	1	2	yes	complemented
86	C₂×#14556553	C₂²	1	2	yes	complemented
87	C₂×C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
88	C₂×#14556550	C₂²	1	2	yes	complemented
89	C₂×#14556548	C₂²	1	2	yes	complemented
90	C₂²×#11924005	C₂²	1	4	yes	complemented
91	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic, complemented
92	C₂²×#41×C₇₃	C₂²	1	2	yes	complemented
93	#550×C₇₃	C₂²	1	16	yes	complemented
94	C₂×#127×C₇₃	C₂²	1	2	yes	complemented
95	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic, complemented
96	C₂×#121×C₇₃	C₂²	1	4	yes	complemented
97	C₂×#121×C₇₃	C₂²	1	2	yes	complemented
98	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
100	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
101	C₂⁴×D₇₃	C₂³	1	4	yes	—
102	C₂⁴×D₇₃	C₂³	1	4	yes	—
103	C₂×#11924027	—	4	8	no	—
104	C₂×#11924027	C₂³	1	16	yes	complemented
105	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
106	C₂²×D₂₉₂	—	4	8	no	—
107	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
108	C₂²×D₂₉₂	C₂³	1	2	yes	—
109	C₂²×D₂₉₂	C₂³	1	2	yes	—
110	C₂²×D₂₉₂	C₂³	1	2	yes	—
111	C₂²×D₂₉₂	C₂³	1	2	yes	—
112	C₂²×D₂₉₂	C₂³	1	4	yes	—
113	C₂²×D₂₉₂	C₂³	1	16	yes	complemented
114	C₂²×C₂²⋊D₇₃	C₂³	1	2	yes	—
115	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
116	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
117	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
118	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
119	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
120	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
121	C₂×D₄×D₇₃	—	4	8	no	—
122	C₂×D₄×D₇₃	—	4	8	no	—
123	C₂×D₄×D₇₃	—	4	8	no	—
124	C₂×D₄×D₇₃	—	4	8	no	—
125	C₂×D₄×D₇₃	—	4	16	no	—
126	C₂×D₄×D₇₃	C₂³	1	16	yes	complemented
127	C₂×D₄×D₇₃	C₂³	1	16	yes	complemented
128	C₂×D₄×D₇₃	C₂³	1	16	yes	complemented
129	C₂×D₄×D₇₃	C₂³	1	32	yes	complemented
130	C₂×D₄×D₇₃	C₂³	1	16	yes	complemented
131	C₂³×Dic₇₃	C₂³	1	4	yes	—
132	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
136	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
137	#14556588	C₂³	1	8	yes	—
138	#14556587	C₂³	1	16	yes	complemented
139	#14556587	C₂³	1	16	yes	complemented
140	#14556587	C₂³	1	16	yes	complemented
141	#14556587	C₂³	1	16	yes	complemented
142	#14556586	C₂³	1	16	yes	complemented
143	#14556584	C₂³	1	16	yes	complemented
144	#14556582	C₂³	1	8	yes	complemented
145	#14556582	C₂³	1	8	yes	complemented
146	#14556580	C₂³	1	8	yes	complemented
147	#14556580	C₂³	1	16	yes	complemented
148	#14556579	C₂³	1	16	yes	complemented
149	#14556578	C₂³	1	8	yes	complemented
150	#14556576	C₂³	1	16	yes	complemented
151	#14556576	C₂³	1	32	yes	complemented
152	#14556575	C₂³	1	32	yes	complemented
153	#14556574	C₂³	1	32	yes	complemented
154	#14556573	C₂³	1	16	yes	complemented
155	#14556573	C₂³	1	32	yes	complemented
156	#14556571	C₂³	1	8	yes	complemented
157	#14556567	C₂³	1	8	yes	complemented
158	#14556566	C₂³	1	8	yes	—
159	#14556566	C₂³	1	16	yes	complemented
160	#14556565	C₂³	1	32	yes	complemented
161	#14556565	C₂³	1	32	yes	complemented
162	#14556565	C₂³	1	16	yes	complemented
163	#14556564	C₂³	1	32	yes	complemented
164	#14556563	C₂³	1	32	yes	complemented
165	#14556563	C₂³	1	32	yes	complemented
166	#14556563	C₂³	1	32	yes	complemented
167	#14556562	C₂³	1	8	yes	—
168	#14556562	C₂³	1	16	yes	complemented
169	#14556562	C₂³	1	32	yes	complemented
170	#14556561	C₂³	1	32	yes	complemented
171	#14556561	C₂³	1	32	yes	complemented
172	#14556559	C₂³	1	32	yes	complemented
173	#14556559	C₂³	1	32	yes	complemented
174	#14556559	C₂³	1	32	yes	complemented
175	#14556559	C₂³	1	32	yes	complemented
176	C₄×Dic₁₄₆	C₂³	1	8	yes	complemented
177	C₄×D₂₉₂	C₂³	1	16	yes	complemented
178	C₄×D₂₉₂	C₂³	1	8	yes	complemented
179	C₄×D₂₉₂	C₂³	1	16	yes	complemented
180	D₄×Dic₇₃	C₂³	1	16	yes	complemented
181	#14556553	C₂³	1	16	yes	complemented
182	C₄×C₂²⋊D₇₃	C₂³	1	16	yes	complemented
183	#14556550	C₂³	1	16	yes	complemented
184	#14556548	C₂³	1	16	yes	complemented
185	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
186	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
187	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
190	C₂×#11924007	C₂³	1	2	yes	—
191	C₂×#11924007	C₂³	1	2	yes	—
192	C₂×#11924007	C₂³	1	2	yes	—
193	C₂×#11924007	C₂³	1	2	yes	—
194	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊Dic₇₃	C₂³	1	4	yes	—
198	C₂×#11924005	C₂³	1	2	yes	—
199	C₂×#11924005	C₂³	1	2	yes	—
200	C₂×#11924005	C₂³	1	4	yes	—
201	C₂×#11924005	C₂³	1	4	yes	—
202	C₂×#11924005	C₂³	1	2	yes	—
203	C₂×#11924005	C₂³	1	2	yes	—
204	C₂×#11924005	C₂³	1	4	yes	—
205	C₂×#11924005	C₂³	1	2	yes	—
206	C₂×#11924005	C₂³	1	4	yes	—
207	C₂×#11924005	C₂³	1	2	yes	—
208	C₂×#11924005	C₂³	1	32	yes	complemented
209	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
210	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
211	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
212	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
213	C₄²×D₇₃	C₂³	1	8	yes	complemented
214	C₂×#41×C₇₃	—	4	8	no	—
215	C₂×#41×C₇₃	C₂³	1	16	yes	complemented
216	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
217	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
218	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
219	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
220	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
221	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
222	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
223	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
224	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
225	#127×C₇₃	C₂³	1	8	yes	complemented
226	#127×C₇₃	C₂³	1	16	yes	complemented
227	#121×C₇₃	C₂³	1	32	yes	complemented
228	#121×C₇₃	C₂³	1	16	yes	complemented
229	C₄×Q₈×C₇₃	C₂³	1	8	yes	complemented
230	C₄×D₄×C₇₃	C₂³	1	16	yes	complemented
231	C₄×D₄×C₇₃	C₂³	1	8	yes	complemented
232	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
235	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
236	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
237	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
239	C₂³×D₇₃	—	2	16	no	—
240	C₂³×D₇₃	—	4	8	no	—
241	C₂³×D₇₃	—	4	8	no	—
242	C₂³×D₇₃	—	4	8	no	—
243	C₂³×D₇₃	—	4	8	no	—
244	C₂³×D₇₃	—	4	8	no	—
245	C₂³×D₇₃	C₂⁴	1	2	yes	—
246	C₂³×D₇₃	C₂⁴	1	4	yes	—
247	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
248	C₂³×D₇₃	C₂⁴	1	16	yes	—
249	C₂³×D₇₃	C₂⁴	1	16	yes	—
250	#11924027	—	4	32	no	—
251	C₂×Dic₁₄₆	—	2	4	no	—
252	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
253	C₂×D₂₉₂	—	2	8	no	—
254	C₂×D₂₉₂	—	2	8	no	—
255	C₂×D₂₉₂	—	2	8	no	—
256	C₂×D₂₉₂	—	2	4	no	—
257	C₂×D₂₉₂	—	4	32	no	—
258	C₂×D₂₉₂	—	4	4	no	—
259	C₂×D₂₉₂	—	4	8	no	—
260	C₂×D₂₉₂	C₂⁴	1	8	yes	—
261	C₂×D₂₉₂	C₂⁴	1	8	yes	—
262	C₂×D₂₉₂	C₂⁴	1	4	yes	—
263	C₂×D₂₉₂	C₂⁴	1	8	yes	—
264	C₂×D₂₉₂	C₂⁴	1	16	yes	—
265	C₂×D₂₉₂	C₂⁴	1	8	yes	—
266	C₂×C₂²⋊D₇₃	—	2	8	no	—
267	C₂×C₂²⋊D₇₃	—	4	8	no	—
268	C₂×C₂²⋊D₇₃	—	4	8	no	—
269	C₂×C₂²⋊D₇₃	—	4	8	no	—
270	C₂×C₂²⋊D₇₃	—	4	8	no	—
271	C₂×C₂²⋊D₇₃	—	4	8	no	—
272	C₂×C₂²⋊D₇₃	—	4	8	no	—
273	C₂×C₂²⋊D₇₃	C₂⁴	1	8	yes	—
274	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
275	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
276	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
277	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
278	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
279	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
280	D₄×D₇₃	—	4	32	no	—
281	D₄×D₇₃	—	4	32	no	—
282	D₄×D₇₃	—	4	32	no	—
283	D₄×D₇₃	—	4	32	no	—
284	D₄×D₇₃	—	4	64	no	—
285	C₂²×Dic₇₃	—	4	8	no	—
286	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
287	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
288	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
289	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
290	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
291	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
292	C₂²×Dic₇₃	C₂⁴	1	16	yes	—
293	C₂×C₄×D₇₃	—	2	4	no	—
294	C₂×C₄×D₇₃	—	2	4	no	—
295	C₂×C₄×D₇₃	—	2	4	no	—
296	C₂×C₄×D₇₃	—	2	8	no	—
297	C₂×C₄×D₇₃	—	4	8	no	—
298	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
299	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
300	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
301	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
302	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
303	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
304	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
305	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
306	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
307	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
308	#11924007	C₂⁴	1	8	yes	—
309	#11924007	C₂⁴	1	8	yes	—
310	#11924007	C₂⁴	1	8	yes	—
311	#11924007	C₂⁴	1	8	yes	—
312	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
313	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
314	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
315	C₂²⋊Dic₇₃	C₂⁴	1	16	yes	—
316	#11924005	C₂⁴	1	8	yes	—
317	#11924005	C₂⁴	1	8	yes	—
318	#11924005	C₂⁴	1	16	yes	—
319	#11924005	C₂⁴	1	16	yes	—
320	#11924005	C₂⁴	1	8	yes	—
321	#11924005	C₂⁴	1	8	yes	—
322	#11924005	C₂⁴	1	16	yes	—
323	#11924005	C₂⁴	1	8	yes	—
324	#11924005	C₂⁴	1	16	yes	—
325	#11924005	C₂⁴	1	8	yes	—
326	C₄×Dic₇₃	C₂⁴	1	4	yes	—
327	C₄×Dic₇₃	C₂⁴	1	4	yes	—
328	C₄×Dic₇₃	C₂⁴	1	4	yes	—
329	C₄×Dic₇₃	C₂⁴	1	8	yes	—
330	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
331	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
332	#41×C₇₃	—	4	32	no	—
333	C₂×Q₈×C₇₃	—	2	4	no	—
334	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
335	C₂×D₄×C₇₃	—	2	8	no	—
336	C₂×D₄×C₇₃	—	2	4	no	—
337	C₂×D₄×C₇₃	—	2	8	no	—
338	C₂×D₄×C₇₃	—	4	8	no	—
339	C₂×D₄×C₇₃	—	4	4	no	—
340	C₂×D₄×C₇₃	—	4	8	no	—
341	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
342	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
343	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
344	C₂×D₄×C₇₃	C₂⁴	1	16	yes	—
345	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
346	C₂×D₄×C₇₃	C₂⁴	1	16	yes	—
347	C₂²×C₄×C₇₃	—	2	8	no	—
348	C₂²×C₄×C₇₃	—	4	8	no	—
349	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₇₃	C₂⁴	1	8	yes	—
354	C₂²×C₄×C₇₃	C₂⁴	1	16	yes	—
355	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
358	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
359	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
360	C₂²⋊C₄×C₇₃	C₂⁴	1	8	yes	—
361	C₂²⋊C₄×C₇₃	C₂⁴	1	16	yes	—
362	C₄²×C₇₃	C₂⁴	1	4	yes	—
363	C₄²×C₇₃	C₂⁴	1	8	yes	—
364	C₂³×C₇₃	—	2	4	no	—
365	C₂³×C₇₃	—	2	8	no	—
366	C₂³×C₇₃	—	2	8	no	—
367	C₂³×C₇₃	—	2	4	no	—
368	C₂³×C₇₃	—	2	4	no	—
369	C₂³×C₇₃	—	2	8	no	—
370	C₂³×C₇₃	C₂⁵	1	4	yes	—
371	C₂³×C₇₃	C₂⁵	1	8	yes	—
372	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
373	C₂²×D₇₃	—	2	2	no	—
374	C₂²×D₇₃	—	2	2	no	—
375	C₂²×D₇₃	—	2	4	no	—
376	C₂²×D₇₃	—	2	8	no	—
377	C₂²×D₇₃	—	2	4	no	—
378	C₂²×D₇₃	—	2	8	no	—
379	C₂²×D₇₃	—	2	8	no	—
380	C₂²×D₇₃	—	2	4	no	—
381	C₂²×D₇₃	—	2	32	no	—
382	C₂²×D₇₃	—	4	16	no	—
383	C₂²×D₇₃	—	4	16	no	—
384	C₂²×D₇₃	—	4	16	no	—
385	C₂²×D₇₃	—	4	16	no	—
386	C₂²×D₇₃	—	4	16	no	—
387	C₂²×D₇₃	—	8	32	no	—
388	C₂²×D₇₃	—	8	32	no	—
389	C₂²×D₇₃	H(5,𝔽₂)	1	4	yes	—
390	C₂²×D₇₃	C₂⁵	1	4	yes	—
391	C₂²×D₇₃	C₂⁵	1	8	yes	—
392	C₂²×D₇₃	C₂⁵	1	2	yes	—
393	Q₈×C₇₃	—	2	8	no	—
394	D₄×C₇₃	—	2	16	no	—
395	D₄×C₇₃	—	2	8	no	—
396	D₄×C₇₃	—	2	16	no	—
397	D₄×C₇₃	—	4	16	no	—
398	D₄×C₇₃	—	4	8	no	—
399	D₄×C₇₃	—	4	16	no	—
400	C₂×C₄×C₇₃	—	2	4	no	—
401	C₂×C₄×C₇₃	—	2	4	no	—
402	C₂×C₄×C₇₃	—	2	2	no	—
403	C₂×C₄×C₇₃	—	2	4	no	—
404	C₂×C₄×C₇₃	—	2	16	no	—
405	C₂×C₄×C₇₃	—	4	16	no	—
406	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
407	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
408	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
409	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
410	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
411	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
412	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
413	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
414	C₂²⋊D₇₃	—	2	16	no	—
415	C₂²⋊D₇₃	—	4	16	no	—
416	C₂²⋊D₇₃	—	4	16	no	—
417	C₂²⋊D₇₃	—	4	16	no	—
418	C₂²⋊D₇₃	—	4	16	no	—
419	C₂²⋊D₇₃	—	4	16	no	—
420	C₂²⋊D₇₃	—	4	16	no	—
421	C₂×Dic₇₃	—	2	4	no	—
422	C₂×Dic₇₃	—	2	2	no	—
423	C₂×Dic₇₃	—	2	2	no	—
424	C₂×Dic₇₃	—	2	2	no	—
425	C₂×Dic₇₃	—	2	4	no	—
426	C₂×Dic₇₃	—	2	4	no	—
427	C₂×Dic₇₃	—	4	16	no	—
428	C₂×Dic₇₃	C₂⁵	1	2	yes	—
429	C₂×Dic₇₃	C₂⁵	1	2	yes	—
430	C₂×Dic₇₃	C₂⁵	1	2	yes	—
431	C₂×Dic₇₃	C₂⁵	1	4	yes	—
432	C₂×Dic₇₃	C₂⁵	1	4	yes	—
433	C₂×Dic₇₃	C₂⁵	1	4	yes	—
434	D₂₉₂	—	2	16	no	—
435	D₂₉₂	—	2	16	no	—
436	D₂₉₂	—	2	16	no	—
437	D₂₉₂	—	2	8	no	—
438	D₂₉₂	—	4	8	no	—
439	D₂₉₂	—	4	16	no	—
440	C₄×D₇₃	—	2	8	no	—
441	C₄×D₇₃	—	2	8	no	—
442	C₄×D₇₃	—	2	8	no	—
443	C₄×D₇₃	—	2	16	no	—
444	C₄×D₇₃	—	4	16	no	—
445	Dic₁₄₆	—	2	8	no	—
446	C₂²×C₇₃	—	2	8	no	—
447	C₂²×C₇₃	—	2	4	no	—
448	C₂²×C₇₃	—	2	4	no	—
449	C₂²×C₇₃	—	2	8	no	—
450	C₂²×C₇₃	—	2	8	no	—
451	C₂²×C₇₃	—	2	4	no	—
452	C₂²×C₇₃	—	4	8	no	—
453	C₂²×C₇₃	—	4	16	no	—
454	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
455	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
456	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
457	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
458	C₂×D₇₃	—	2	2	no	—
459	C₂×D₇₃	—	2	2	no	—
460	C₂×D₇₃	—	2	8	no	—
461	C₂×D₇₃	—	2	4	no	—
462	C₂×D₇₃	—	2	8	no	—
463	C₂×D₇₃	—	2	4	no	—
464	C₂×D₇₃	—	2	8	no	—
465	C₂×D₇₃	—	2	4	no	—
466	C₂×D₇₃	—	2	8	no	—
467	C₂×D₇₃	—	4	8	no	—
468	C₂×D₇₃	—	4	16	no	—
469	C₂×D₇₃	—	8	32	no	—
470	C₂×D₇₃	—	8	32	no	—
471	C₂×D₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
472	C₄×C₇₃	—	2	2	no	—
473	C₄×C₇₃	—	2	4	no	—
474	C₄×C₇₃	—	2	4	no	—
475	C₄×C₇₃	—	2	4	no	—
476	C₄×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
477	C₄×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
478	Dic₇₃	—	2	4	no	—
479	Dic₇₃	—	2	4	no	—
480	Dic₇₃	—	2	2	no	—
481	Dic₇₃	—	2	2	no	—
482	Dic₇₃	—	2	2	no	—
483	Dic₇₃	—	2	4	no	—
484	C₂×#3543	—	73	1	no	maximal, Sylow
485	C₂×C₇₃	—	4	4	no	—
486	C₂×C₇₃	—	4	8	no	—
487	C₂×C₇₃	#3543	1	4	yes	complemented
488	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
491	D₇₃	—	2	4	no	—
492	D₇₃	—	4	4	no	—
493	D₇₃	—	4	8	no	—
494	#3543	—	73	32	no	—
495	C₂×#560	—	73	4	no	—
496	C₂×#559	—	73	1	no	—
497	C₂×#550	—	73	1	no	—
498	C₂×#550	D₇₃	1	1	yes	characteristic, complemented
499	C₂×#546	—	73	2	no	—
500	C₂×#546	—	73	2	no	—
501	C₂×D₄²	—	73	2	no	—
502	C₂×D₄²	—	73	2	no	—
503	C₂×D₄²	—	73	1	no	—
504	C₂×#540	—	73	2	no	—
505	C₂×#540	—	73	2	no	—
506	C₂×#535	—	73	2	no	—
507	C₂×#535	—	73	2	no	—
508	C₂×#534	—	73	4	no	—
509	C₂²×#127	—	73	1	no	—
510	C₂×#529	—	73	1	no	—
511	C₂×#529	—	73	1	no	—
512	C₇₃	C₂×#3543	1	1	yes	characteristic, complemented, Sylow
513	C₂²×#41	—	73	2	no	—
514	C₂²×#41	C₂×D₇₃	1	2	yes	complemented
515	C₂³×D₄	—	73	2	no	—
516	C₂³×D₄	—	73	2	no	—
517	C₂³×D₄	—	73	2	no	—
518	C₂³×D₄	—	73	4	no	—
519	C₂³×D₄	—	73	2	no	—
520	C₂³×D₄	—	73	2	no	—
521	#560	—	73	64	no	—
522	#559	—	73	16	no	—
523	#550	—	73	16	no	—
524	#550	C₂×D₇₃	1	16	yes	complemented
525	#546	—	73	32	no	—
526	#546	—	73	32	no	—
527	D₄²	—	73	32	no	—
528	D₄²	—	73	32	no	—
529	D₄²	—	73	16	no	—
530	#540	—	73	32	no	—
531	#540	—	73	32	no	—
532	#535	—	73	32	no	—
533	#535	—	73	32	no	—
534	#534	—	73	64	no	—
535	C₂×#127	—	73	2	no	—
536	C₂×#127	—	73	2	no	—
537	C₂×#127	—	73	2	no	—
538	C₂×#127	—	73	2	no	—
539	C₂×#127	—	73	16	no	—
540	C₂×#127	—	73	1	no	—
541	C₂×#127	C₂×D₇₃	1	1	yes	characteristic, complemented
542	C₂×#127	C₂×D₇₃	1	2	yes	complemented
543	#529	—	73	16	no	—
544	#529	—	73	16	no	—
545	C₂×#126	—	73	2	no	—
546	C₂×#126	—	73	2	no	—
547	C₂×#125	—	73	1	no	—
548	C₂×#125	—	73	1	no	—
549	C₂×#124	—	73	1	no	—
550	C₂×#124	—	73	2	no	—
551	C₂×#124	—	73	1	no	—
552	C₂×#124	—	73	2	no	—
553	C₂×#123	—	73	4	no	—
554	C₂×#123	—	73	2	no	—
555	C₂×#123	—	73	4	no	—
556	C₂×#123	—	73	2	no	—
557	C₂×#123	—	73	4	no	—
558	C₂×#123	—	73	4	no	—
559	C₂×C₂²⋊Q₈	—	73	1	no	—
560	C₂×C₂²⋊Q₈	—	73	1	no	—
561	C₂×#121	—	73	1	no	—
562	C₂×#121	—	73	4	no	—
563	C₂×#121	—	73	4	no	—
564	C₂×#121	—	73	4	no	—
565	C₂×#121	—	73	2	no	—
566	C₂×#121	—	73	4	no	—
567	C₂×#121	—	73	4	no	—
568	C₂×#121	—	73	4	no	—
569	C₂×#121	—	73	2	no	—
570	C₂×#121	—	73	1	no	—
571	C₂×#121	—	73	2	no	—
572	C₂×#121	—	73	4	no	—
573	C₂×#121	C₂×D₇₃	1	4	yes	complemented
574	C₂×#121	C₂×D₇₃	1	2	yes	complemented
575	C₂×#120	—	73	4	no	—
576	C₂×#120	—	73	4	no	—
577	C₂×#120	—	73	4	no	—
578	C₂×#120	—	73	4	no	—
579	C₂×#120	—	73	4	no	—
580	C₂×#120	—	73	4	no	—
581	C₂×C₄×Q₈	—	73	1	no	—
582	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
583	C₂×C₄×D₄	—	73	2	no	—
584	C₂×C₄×D₄	—	73	2	no	—
585	C₂×C₄×D₄	—	73	2	no	—
586	C₂×C₄×D₄	—	73	2	no	—
587	C₂×C₄×D₄	—	73	1	no	—
588	C₂×C₄×D₄	—	73	2	no	—
589	C₂×C₄×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
590	C₂×C₄×D₄	C₂×D₇₃	1	2	yes	complemented
591	C₂×#117	—	73	2	no	—
592	C₂×#117	—	73	2	no	—
593	C₂²×C₂²⋊C₄	—	73	4	no	—
594	C₂²×C₄²	—	73	1	no	—
595	C₂⁵	—	73	4	no	—
596	C₂⁵	—	73	4	no	—
597	C₂×#41	—	4	8	no	—
598	C₂×#41	—	292	8	no	—
599	C₂×#41	—	73	16	no	—
600	C₂×#41	C₂²×D₇₃	1	16	yes	complemented
601	C₂²×Q₈	—	73	1	no	—
602	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
603	C₂²×D₄	—	292	8	no	—
604	C₂²×D₄	—	292	16	no	—
605	C₂²×D₄	—	292	8	no	—
606	C₂²×D₄	—	292	8	no	—
607	C₂²×D₄	—	292	8	no	—
608	C₂²×D₄	—	292	8	no	—
609	C₂²×D₄	—	73	4	no	—
610	C₂²×D₄	—	73	4	no	—
611	C₂²×D₄	—	73	4	no	—
612	C₂²×D₄	—	73	4	no	—
613	C₂²×D₄	—	73	4	no	—
614	C₂²×D₄	—	73	4	no	—
615	C₂²×D₄	—	73	16	no	—
616	C₂²×D₄	—	73	16	no	—
617	C₂²×D₄	—	73	16	no	—
618	C₂²×D₄	—	73	32	no	—
619	C₂²×D₄	—	73	16	no	—
620	C₂²×D₄	—	73	2	no	—
621	C₂²×D₄	—	73	4	no	—
622	C₂²×D₄	—	73	2	no	—
623	C₂²×D₄	—	73	16	no	—
624	C₂²×D₄	—	73	2	no	—
625	C₂²×D₄	—	73	2	no	—
626	C₂²×D₄	—	73	1	no	—
627	C₂²×D₄	—	73	2	no	—
628	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
629	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
630	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
631	C₂²×D₄	C₂²×D₇₃	1	4	yes	—
632	C₂²×D₄	C₂²×D₇₃	1	4	yes	—
633	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
634	C₂³×C₄	—	73	4	no	—
635	C₂³×C₄	—	73	4	no	—
636	C₂³×C₄	—	73	2	no	—
637	C₂³×C₄	—	73	1	no	—
638	C₂³×C₄	—	73	1	no	—
639	C₂³×C₄	—	73	1	no	—
640	C₂³×C₄	C₂²×D₇₃	1	2	yes	—
641	C₂³×C₄	C₂²×D₇₃	1	4	yes	—
642	#127	—	73	16	no	—
643	#127	—	73	16	no	—
644	#127	—	73	16	no	—
645	#127	—	73	16	no	—
646	#127	—	73	8	no	—
647	#127	C₂²×D₇₃	1	8	yes	complemented
648	#127	C₂²×D₇₃	1	16	yes	complemented
649	#126	—	73	16	no	—
650	#126	—	73	16	no	—
651	#125	—	73	8	no	—
652	#125	—	73	8	no	—
653	#124	—	73	8	no	—
654	#124	—	73	16	no	—
655	#124	—	73	8	no	—
656	#124	—	73	16	no	—
657	#123	—	73	32	no	—
658	#123	—	73	16	no	—
659	#123	—	73	32	no	—
660	#123	—	73	16	no	—
661	#123	—	73	32	no	—
662	#123	—	73	32	no	—
663	C₂²⋊Q₈	—	73	8	no	—
664	C₂²⋊Q₈	—	73	8	no	—
665	#121	—	73	8	no	—
666	#121	—	73	32	no	—
667	#121	—	73	32	no	—
668	#121	—	73	32	no	—
669	#121	—	73	16	no	—
670	#121	—	73	32	no	—
671	#121	—	73	32	no	—
672	#121	—	73	32	no	—
673	#121	—	73	16	no	—
674	#121	—	73	8	no	—
675	#121	—	73	16	no	—
676	#121	—	73	32	no	—
677	#121	C₂²×D₇₃	1	32	yes	complemented
678	#121	C₂²×D₇₃	1	16	yes	complemented
679	#120	—	73	32	no	—
680	#120	—	73	32	no	—
681	#120	—	73	32	no	—
682	#120	—	73	32	no	—
683	#120	—	73	32	no	—
684	#120	—	73	32	no	—
685	C₄×Q₈	—	73	8	no	—
686	C₄×Q₈	C₂²×D₇₃	1	8	yes	complemented
687	C₄×D₄	—	73	16	no	—
688	C₄×D₄	—	73	16	no	—
689	C₄×D₄	—	73	16	no	—
690	C₄×D₄	—	73	16	no	—
691	C₄×D₄	—	73	8	no	—
692	C₄×D₄	—	73	16	no	—
693	C₄×D₄	C₂²×D₇₃	1	8	yes	complemented
694	C₄×D₄	C₂²×D₇₃	1	16	yes	complemented
695	#117	—	73	16	no	—
696	#117	—	73	16	no	—
697	C₂×C₄⋊C₄	—	73	2	no	—
698	C₂×C₄⋊C₄	—	73	2	no	—
699	C₂×C₄⋊C₄	—	73	2	no	—
700	C₂×C₄⋊C₄	—	73	2	no	—
701	C₂×C₄⋊C₄	—	73	1	no	—
702	C₂×C₄⋊C₄	—	73	1	no	—
703	C₂×C₄⋊C₄	—	73	2	no	—
704	C₂×C₄⋊C₄	—	73	2	no	—
705	C₂×C₄⋊C₄	—	73	2	no	—
706	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
709	C₂×C₂²⋊C₄	—	73	2	no	—
710	C₂×C₂²⋊C₄	—	73	2	no	—
711	C₂×C₂²⋊C₄	—	73	2	no	—
712	C₂×C₂²⋊C₄	—	73	4	no	—
713	C₂×C₂²⋊C₄	—	73	2	no	—
714	C₂×C₂²⋊C₄	—	73	2	no	—
715	C₂×C₂²⋊C₄	—	73	4	no	—
716	C₂×C₂²⋊C₄	—	73	4	no	—
717	C₂×C₂²⋊C₄	—	73	32	no	—
718	C₂×C₂²⋊C₄	—	73	2	no	—
719	C₂×C₂²⋊C₄	—	73	2	no	—
720	C₂×C₂²⋊C₄	—	73	2	no	—
721	C₂×C₂²⋊C₄	—	73	2	no	—
722	C₂×C₂²⋊C₄	—	73	4	no	—
723	C₂×C₂²⋊C₄	—	73	4	no	—
724	C₂×C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
726	C₂×C₄²	—	73	1	no	—
727	C₂×C₄²	—	73	1	no	—
728	C₂×C₄²	—	73	2	no	—
729	C₂×C₄²	—	73	1	no	—
730	C₂×C₄²	—	73	8	no	—
731	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
732	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
733	C₂⁴	—	292	8	no	—
734	C₂⁴	—	292	8	no	—
735	C₂⁴	—	292	8	no	—
736	C₂⁴	—	292	8	no	—
737	C₂⁴	—	292	8	no	—
738	C₂⁴	—	73	16	no	—
739	C₂⁴	—	73	16	no	—
740	C₂⁴	—	73	1	no	—
741	C₂⁴	—	73	4	no	—
742	C₂⁴	—	73	2	no	—
743	C₂⁴	—	146	16	no	—
744	C₂⁴	C₂³×D₇₃	1	2	yes	—
745	C₂⁴	C₂³×D₇₃	1	4	yes	—
746	#41	—	4	32	no	—
747	#41	—	292	32	no	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	73	4	no	—
750	C₂×Q₈	—	146	4	no	—
751	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
752	C₂×D₄	—	2	8	no	—
753	C₂×D₄	—	2	4	no	—
754	C₂×D₄	—	2	8	no	—
755	C₂×D₄	—	4	8	no	—
756	C₂×D₄	—	4	4	no	—
757	C₂×D₄	—	4	8	no	—
758	C₂×D₄	—	292	4	no	—
759	C₂×D₄	—	292	8	no	—
760	C₂×D₄	—	292	32	no	—
761	C₂×D₄	—	292	64	no	—
762	C₂×D₄	—	292	32	no	—
763	C₂×D₄	—	292	32	no	—
764	C₂×D₄	—	292	32	no	—
765	C₂×D₄	—	292	32	no	—
766	C₂×D₄	—	292	8	no	—
767	C₂×D₄	—	292	8	no	—
768	C₂×D₄	—	292	8	no	—
769	C₂×D₄	—	292	8	no	—
770	C₂×D₄	—	292	8	no	—
771	C₂×D₄	—	292	8	no	—
772	C₂×D₄	—	73	16	no	—
773	C₂×D₄	—	73	16	no	—
774	C₂×D₄	—	73	16	no	—
775	C₂×D₄	—	73	16	no	—
776	C₂×D₄	—	73	16	no	—
777	C₂×D₄	—	73	16	no	—
778	C₂×D₄	—	73	8	no	—
779	C₂×D₄	—	73	16	no	—
780	C₂×D₄	—	73	8	no	—
781	C₂×D₄	—	73	8	no	—
782	C₂×D₄	—	73	8	no	—
783	C₂×D₄	—	73	4	no	—
784	C₂×D₄	—	73	8	no	—
785	C₂×D₄	—	146	8	no	—
786	C₂×D₄	—	146	8	no	—
787	C₂×D₄	—	146	8	no	—
788	C₂×D₄	—	146	4	no	—
789	C₂×D₄	—	146	8	no	—
790	C₂×D₄	C₂³×D₇₃	1	8	yes	—
791	C₂×D₄	C₂³×D₇₃	1	4	yes	—
792	C₂×D₄	C₂³×D₇₃	1	8	yes	—
793	C₂×D₄	C₂³×D₇₃	1	16	yes	—
794	C₂×D₄	C₂³×D₇₃	1	16	yes	—
795	C₂×D₄	C₂³×D₇₃	1	8	yes	—
796	C₂²×C₄	—	2	8	no	—
797	C₂²×C₄	—	4	8	no	—
798	C₂²×C₄	—	292	8	no	—
799	C₂²×C₄	—	292	8	no	—
800	C₂²×C₄	—	73	16	no	—
801	C₂²×C₄	—	73	16	no	—
802	C₂²×C₄	—	73	1	no	—
803	C₂²×C₄	—	73	1	no	—
804	C₂²×C₄	—	73	1	no	—
805	C₂²×C₄	—	73	2	no	—
806	C₂²×C₄	—	73	2	no	—
807	C₂²×C₄	—	73	2	no	—
808	C₂²×C₄	—	73	4	no	—
809	C₂²×C₄	—	73	4	no	—
810	C₂²×C₄	—	73	4	no	—
811	C₂²×C₄	—	73	8	no	—
812	C₂²×C₄	—	146	4	no	—
813	C₂²×C₄	—	146	4	no	—
814	C₂²×C₄	—	146	4	no	—
815	C₂²×C₄	—	146	8	no	—
816	C₂²×C₄	C₂³×D₇₃	1	8	yes	—
817	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
818	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
819	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
820	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
821	C₂²×C₄	C₂³×D₇₃	1	16	yes	—
822	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
823	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
824	C₄⋊C₄	—	73	8	no	—
825	C₄⋊C₄	—	73	8	no	—
826	C₄⋊C₄	—	73	8	no	—
827	C₄⋊C₄	—	73	8	no	—
828	C₄⋊C₄	—	73	8	no	—
829	C₄⋊C₄	—	73	8	no	—
830	C₄⋊C₄	—	73	4	no	—
831	C₄⋊C₄	—	73	4	no	—
832	C₄⋊C₄	—	73	8	no	—
833	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
834	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
835	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
836	C₂²⋊C₄	—	73	8	no	—
837	C₂²⋊C₄	—	73	8	no	—
838	C₂²⋊C₄	—	73	8	no	—
839	C₂²⋊C₄	—	73	16	no	—
840	C₂²⋊C₄	—	73	8	no	—
841	C₂²⋊C₄	—	73	8	no	—
842	C₂²⋊C₄	—	73	16	no	—
843	C₂²⋊C₄	—	73	16	no	—
844	C₂²⋊C₄	—	73	8	no	—
845	C₂²⋊C₄	—	73	8	no	—
846	C₂²⋊C₄	—	73	8	no	—
847	C₂²⋊C₄	—	73	8	no	—
848	C₂²⋊C₄	—	73	16	no	—
849	C₂²⋊C₄	—	73	16	no	—
850	C₂²⋊C₄	C₂³×D₇₃	1	8	yes	—
851	C₂²⋊C₄	C₂³×D₇₃	1	16	yes	—
852	C₄²	—	73	4	no	—
853	C₄²	—	73	4	no	—
854	C₄²	—	73	4	no	—
855	C₄²	—	73	8	no	—
856	C₄²	C₂³×D₇₃	1	4	yes	—
857	C₄²	C₂³×D₇₃	1	8	yes	—
858	C₂³	—	2	8	no	—
859	C₂³	—	2	4	no	—
860	C₂³	—	2	4	no	—
861	C₂³	—	2	8	no	—
862	C₂³	—	2	8	no	—
863	C₂³	—	2	4	no	—
864	C₂³	—	292	16	no	—
865	C₂³	—	292	16	no	—
866	C₂³	—	292	16	no	—
867	C₂³	—	292	16	no	—
868	C₂³	—	292	16	no	—
869	C₂³	—	584	32	no	—
870	C₂³	—	584	32	no	—
871	C₂³	—	73	4	no	—
872	C₂³	—	73	2	no	—
873	C₂³	—	73	8	no	—
874	C₂³	—	73	4	no	—
875	C₂³	—	146	32	no	—
876	C₂³	—	146	8	no	—
877	C₂³	—	146	4	no	—
878	C₂³	—	146	4	no	—
879	C₂³	—	146	8	no	—
880	C₂³	—	146	4	no	—
881	C₂³	—	146	8	no	—
882	C₂³	—	146	2	no	—
883	C₂³	—	146	2	no	—
884	C₂³	C₂⁴×D₇₃	1	4	yes	—
885	C₂³	C₂⁴×D₇₃	1	8	yes	—
886	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
887	Q₈	—	2	8	no	—
888	Q₈	—	146	8	no	—
889	D₄	—	2	16	no	—
890	D₄	—	2	8	no	—
891	D₄	—	2	16	no	—
892	D₄	—	4	16	no	—
893	D₄	—	4	8	no	—
894	D₄	—	4	16	no	—
895	D₄	—	292	8	no	—
896	D₄	—	292	16	no	—
897	D₄	—	292	16	no	—
898	D₄	—	292	16	no	—
899	D₄	—	292	16	no	—
900	D₄	—	292	16	no	—
901	D₄	—	292	16	no	—
902	D₄	—	292	16	no	—
903	D₄	—	146	16	no	—
904	D₄	—	146	16	no	—
905	D₄	—	146	8	no	—
906	D₄	—	146	16	no	—
907	D₄	—	146	16	no	—
908	C₂×C₄	—	2	4	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	4	no	—
911	C₂×C₄	—	2	4	no	—
912	C₂×C₄	—	2	16	no	—
913	C₂×C₄	—	4	16	no	—
914	C₂×C₄	—	292	16	no	—
915	C₂×C₄	—	292	16	no	—
916	C₂×C₄	—	73	2	no	—
917	C₂×C₄	—	73	2	no	—
918	C₂×C₄	—	73	2	no	—
919	C₂×C₄	—	73	4	no	—
920	C₂×C₄	—	73	4	no	—
921	C₂×C₄	—	73	4	no	—
922	C₂×C₄	—	146	8	no	—
923	C₂×C₄	—	146	4	no	—
924	C₂×C₄	—	146	2	no	—
925	C₂×C₄	—	146	2	no	—
926	C₂×C₄	—	146	4	no	—
927	C₂×C₄	—	146	4	no	—
928	C₂×C₄	—	146	2	no	—
929	C₂×C₄	—	146	8	no	—
930	C₂×C₄	—	146	8	no	—
931	C₂×C₄	—	146	16	no	—
932	C₂×C₄	#14556636	1	4	yes	—
933	C₂×C₄	#14556637	1	4	yes	—
934	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
935	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
936	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
937	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
938	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
939	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
940	C₂²	—	2	8	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	2	4	no	—
943	C₂²	—	2	8	no	—
944	C₂²	—	2	8	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	4	8	no	—
947	C₂²	—	4	16	no	—
948	C₂²	—	292	8	no	—
949	C₂²	—	292	16	no	—
950	C₂²	—	584	32	no	—
951	C₂²	—	584	32	no	—
952	C₂²	—	73	4	no	—
953	C₂²	—	146	8	no	—
954	C₂²	—	146	4	no	—
955	C₂²	—	146	4	no	—
956	C₂²	—	146	8	no	—
957	C₂²	—	146	4	no	—
958	C₂²	—	146	8	no	—
959	C₂²	—	146	2	no	—
960	C₂²	—	146	2	no	—
961	C₂²	—	146	8	no	—
962	C₂²	H(5,𝔽₂)×D₇₃	1	2	yes	—
963	C₂²	C₂×#14556636	1	2	yes	—
964	C₂²	C₂×#14556637	1	2	yes	—
965	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
966	C₄	—	2	4	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	4	no	—
969	C₄	—	2	4	no	—
970	C₄	—	146	4	no	—
971	C₄	—	146	2	no	—
972	C₄	—	146	2	no	—
973	C₄	—	146	4	no	—
974	C₄	—	146	4	no	—
975	C₄	—	146	2	no	—
976	C₄	C₂×#14556636	1	4	yes	—
977	C₄	C₂×#14556637	1	4	yes	—
978	C₂	—	4	4	no	—
979	C₂	—	4	8	no	—
980	C₂	—	292	4	no	—
981	C₂	—	292	8	no	—
982	C₂	—	146	4	no	—
983	C₂	#22624255	1	4	yes	direct product factor
984	C₂	C₂×H(5,𝔽₂)×D₇₃	1	1	yes	characteristic
985	C₂	C₂²×#14556636	1	1	yes	characteristic
986	C₂	C₂²×#14556637	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₃
commutator, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×#550×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
hypercenter	C₂×#550	D₇₃
hypocenter	C₇₃	C₂×#3543
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×#550

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #22624255	C₂	direct (N × H)
2. C₂×#17989325	C₂	semidirect
3. C₂×#17989322	C₂	semidirect
4. C₂×#17989257	C₂	semidirect
5. C₂×#17989232	C₂	semidirect
6. C₂×#17989225	C₂	semidirect
7. C₂×D₄×D₂₉₂	C₂	semidirect
8. C₂×#17989222	C₂	semidirect
9. C₂×#17989221	C₂	semidirect
10. C₂×#17989190	C₂	semidirect
11. C₂×#17989188	C₂	semidirect
12. C₂×#17989151	C₂	semidirect
13. C₂×#17989150	C₂	semidirect
14. C₂×#17989145	C₂	semidirect
15. C₂×#127×D₇₃	C₂	semidirect
16. C₂×#17989124	C₂	semidirect
17. C₂×#17989119	C₂	semidirect
18. C₂×#550×C₇₃	C₂	semidirect
19. C₂²×#11924027	C₂²	semidirect
20. C₂³×D₂₉₂	C₂²	semidirect
21. C₂²×D₄×D₇₃	C₂²	semidirect
22. C₂²×D₄×D₇₃	C₂²	semidirect
23. C₂²×D₄×D₇₃	C₂²	semidirect
24. C₂²×D₄×D₇₃	C₂²	semidirect
25. C₂²×D₄×D₇₃	C₂²	semidirect
26. #17989325	C₂²	semidirect
27. #17989322	C₂²	semidirect
28. #17989257	C₂²	semidirect
29. #17989232	C₂²	semidirect
30. #17989225	C₂²	semidirect
31. D₄×D₂₉₂	C₂²	semidirect
32. #17989222	C₂²	semidirect
33. #17989221	C₂²	semidirect
34. #17989190	C₂²	semidirect
35. #17989188	C₂²	semidirect
36. #17989151	C₂²	semidirect
37. #17989150	C₂²	semidirect
38. #17989145	C₂²	semidirect
40. C₂×#14556587	C₂²	semidirect
41. C₂×#14556587	C₂²	semidirect
42. C₂×#14556587	C₂²	semidirect
43. C₂×#14556587	C₂²	semidirect
44. #127×D₇₃	C₂²	semidirect
45. #17989124	C₂²	semidirect
46. #17989119	C₂²	semidirect
47. C₂×#14556586	C₂²	semidirect
48. C₂×#14556584	C₂²	semidirect
49. C₂×#14556582	C₂²	semidirect
50. C₂×#14556582	C₂²	semidirect
51. C₂×#14556580	C₂²	semidirect
52. C₂×#14556580	C₂²	semidirect
53. C₂×#14556579	C₂²	semidirect
54. C₂×#14556578	C₂²	semidirect
55. C₂×#14556576	C₂²	semidirect
56. C₂×#14556576	C₂²	semidirect
57. C₂×#14556575	C₂²	semidirect
58. C₂×#14556574	C₂²	semidirect
59. C₂×#14556573	C₂²	semidirect
60. C₂×#14556573	C₂²	semidirect
61. C₂×#14556571	C₂²	semidirect
62. C₂×#14556567	C₂²	semidirect
64. C₂×#14556566	C₂²	semidirect
65. C₂×#14556565	C₂²	semidirect
66. C₂×#14556565	C₂²	semidirect
67. C₂×#14556565	C₂²	semidirect
68. C₂×#14556564	C₂²	semidirect
69. C₂×#14556563	C₂²	semidirect
70. C₂×#14556563	C₂²	semidirect
71. C₂×#14556563	C₂²	semidirect
73. C₂×#14556562	C₂²	semidirect
74. C₂×#14556562	C₂²	semidirect
75. C₂×#14556561	C₂²	semidirect
76. C₂×#14556561	C₂²	semidirect
77. C₂×#14556559	C₂²	semidirect
78. C₂×#14556559	C₂²	semidirect
79. C₂×#14556559	C₂²	semidirect
80. C₂×#14556559	C₂²	semidirect
81. C₂×C₄×Dic₁₄₆	C₂²	semidirect
82. C₂×C₄×D₂₉₂	C₂²	semidirect
83. C₂×C₄×D₂₉₂	C₂²	semidirect
84. C₂×C₄×D₂₉₂	C₂²	semidirect
85. C₂×D₄×Dic₇₃	C₂²	semidirect
86. C₂×#14556553	C₂²	semidirect
87. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
88. C₂×#14556550	C₂²	semidirect
89. C₂×#14556548	C₂²	semidirect
90. C₂²×#11924005	C₂²	semidirect
91. C₂×C₄²×D₇₃	C₂²	semidirect
92. C₂²×#41×C₇₃	C₂²	semidirect
93. #550×C₇₃	C₂²	semidirect
94. C₂×#127×C₇₃	C₂²	semidirect
95. C₂×#127×C₇₃	C₂²	semidirect
96. C₂×#121×C₇₃	C₂²	semidirect
97. C₂×#121×C₇₃	C₂²	semidirect
98. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
99. C₂×C₄×D₄×C₇₃	C₂²	semidirect
100. C₂×C₄×D₄×C₇₃	C₂²	semidirect
104. C₂×#11924027	C₂³	semidirect
113. C₂²×D₂₉₂	C₂³	semidirect
126. C₂×D₄×D₇₃	C₂³	semidirect
127. C₂×D₄×D₇₃	C₂³	semidirect
128. C₂×D₄×D₇₃	C₂³	semidirect
129. C₂×D₄×D₇₃	C₂³	semidirect
130. C₂×D₄×D₇₃	C₂³	semidirect
138. #14556587	C₂³	semidirect
139. #14556587	C₂³	semidirect
140. #14556587	C₂³	semidirect
141. #14556587	C₂³	semidirect
142. #14556586	C₂³	semidirect
143. #14556584	C₂³	semidirect
144. #14556582	C₂³	semidirect
145. #14556582	C₂³	semidirect
146. #14556580	C₂³	semidirect
147. #14556580	C₂³	semidirect
148. #14556579	C₂³	semidirect
149. #14556578	C₂³	semidirect
150. #14556576	C₂³	semidirect
151. #14556576	C₂³	semidirect
152. #14556575	C₂³	semidirect
153. #14556574	C₂³	semidirect
154. #14556573	C₂³	semidirect
155. #14556573	C₂³	semidirect
156. #14556571	C₂³	semidirect
157. #14556567	C₂³	semidirect
159. #14556566	C₂³	semidirect
160. #14556565	C₂³	semidirect
161. #14556565	C₂³	semidirect
162. #14556565	C₂³	semidirect
163. #14556564	C₂³	semidirect
164. #14556563	C₂³	semidirect
165. #14556563	C₂³	semidirect
166. #14556563	C₂³	semidirect
168. #14556562	C₂³	semidirect
169. #14556562	C₂³	semidirect
170. #14556561	C₂³	semidirect
171. #14556561	C₂³	semidirect
172. #14556559	C₂³	semidirect
173. #14556559	C₂³	semidirect
174. #14556559	C₂³	semidirect
175. #14556559	C₂³	semidirect
176. C₄×Dic₁₄₆	C₂³	semidirect
177. C₄×D₂₉₂	C₂³	semidirect
178. C₄×D₂₉₂	C₂³	semidirect
179. C₄×D₂₉₂	C₂³	semidirect
180. D₄×Dic₇₃	C₂³	semidirect
181. #14556553	C₂³	semidirect
182. C₄×C₂²⋊D₇₃	C₂³	semidirect
183. #14556550	C₂³	semidirect
184. #14556548	C₂³	semidirect
208. C₂×#11924005	C₂³	semidirect
213. C₄²×D₇₃	C₂³	semidirect
215. C₂×#41×C₇₃	C₂³	semidirect
225. #127×C₇₃	C₂³	semidirect
226. #127×C₇₃	C₂³	semidirect
227. #121×C₇₃	C₂³	semidirect
228. #121×C₇₃	C₂³	semidirect
229. C₄×Q₈×C₇₃	C₂³	semidirect
230. C₄×D₄×C₇₃	C₂³	semidirect
231. C₄×D₄×C₇₃	C₂³	semidirect
487. C₂×C₇₃	#3543	semidirect
498. C₂×#550	D₇₃	semidirect
512. C₇₃	C₂×#3543	semidirect
514. C₂²×#41	C₂×D₇₃	semidirect
524. #550	C₂×D₇₃	semidirect
541. C₂×#127	C₂×D₇₃	semidirect
542. C₂×#127	C₂×D₇₃	semidirect
573. C₂×#121	C₂×D₇₃	semidirect
574. C₂×#121	C₂×D₇₃	semidirect
582. C₂×C₄×Q₈	C₂×D₇₃	semidirect
589. C₂×C₄×D₄	C₂×D₇₃	semidirect
590. C₂×C₄×D₄	C₂×D₇₃	semidirect
600. C₂×#41	C₂²×D₇₃	semidirect
647. #127	C₂²×D₇₃	semidirect
648. #127	C₂²×D₇₃	semidirect
677. #121	C₂²×D₇₃	semidirect
678. #121	C₂²×D₇₃	semidirect
686. C₄×Q₈	C₂²×D₇₃	semidirect
693. C₄×D₄	C₂²×D₇₃	semidirect
694. C₄×D₄	C₂²×D₇₃	semidirect
983. C₂	#22624255	direct (N × H)

Maximal subgroups

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

subgroup	index
#22624255	2
C₂×#17989325	2
C₂×#17989322	2
C₂×#17989257	2
C₂×#17989232	2
C₂×#17989225	2
C₂×D₄×D₂₉₂	2
C₂×#17989222	2
C₂×#17989221	2
C₂×#17989190	2
C₂×#17989188	2
C₂×#17989151	2
C₂×#17989150	2
C₂×#17989145	2
C₂×#127×D₇₃	2
C₂×#17989124	2
C₂×#17989119	2
C₂×#550×C₇₃	2
C₂×#3543	73

Subgroups — C2×#22624255 #33993573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22624255 #33993573