Subgroups — C₆₇×#60034 #30739285

Order 17152.

2288 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2748	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2703	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2669	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2602	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2589	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2557	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2539	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2516	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2471	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2464	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2456	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2404	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2374	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2366	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2358	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
18	C₄×#121×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
26	C₂×#121×C₆₇	C₂²	1	2	yes	—
27	C₂×#121×C₆₇	C₂²	1	2	yes	—
28	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#120×C₆₇	C₂²	1	2	yes	—
30	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
36	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#400×C₆₇	C₂²	1	2	yes	complemented
41	#399×C₆₇	C₂²	1	2	yes	—
42	#399×C₆₇	C₂²	1	2	yes	—
43	#398×C₆₇	C₂²	1	2	yes	complemented
44	#397×C₆₇	C₂²	1	2	yes	complemented
45	#397×C₆₇	C₂²	1	2	yes	complemented
46	#396×C₆₇	C₂²	1	2	yes	complemented
47	#394×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	2	yes	complemented
49	#393×C₆₇	C₂²	1	2	yes	—
50	#392×C₆₇	C₂²	1	2	yes	—
51	#392×C₆₇	C₂²	1	2	yes	—
52	#392×C₆₇	C₂²	1	2	yes	—
53	#392×C₆₇	C₂²	1	2	yes	—
54	#392×C₆₇	C₂²	1	2	yes	—
55	#392×C₆₇	C₂²	1	2	yes	complemented
56	#391×C₆₇	C₂²	1	2	yes	complemented
57	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#390×C₆₇	C₂²	1	2	yes	—
59	#390×C₆₇	C₂²	1	2	yes	—
60	#390×C₆₇	C₂²	1	2	yes	—
61	#390×C₆₇	C₂²	1	2	yes	—
62	#390×C₆₇	C₂²	1	1	yes	characteristic
63	#390×C₆₇	C₂²	1	2	yes	—
64	#390×C₆₇	C₂²	1	2	yes	complemented
65	#389×C₆₇	C₂²	1	2	yes	complemented
66	#388×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#388×C₆₇	C₂²	1	2	yes	—
70	#388×C₆₇	C₂²	1	2	yes	complemented
71	#388×C₆₇	C₂²	1	2	yes	complemented
72	#388×C₆₇	C₂²	1	2	yes	complemented
73	#388×C₆₇	C₂²	1	2	yes	complemented
74	#388×C₆₇	C₂²	1	2	yes	complemented
75	#387×C₆₇	C₂²	1	2	yes	complemented
76	#387×C₆₇	C₂²	1	2	yes	complemented
77	#387×C₆₇	C₂²	1	2	yes	complemented
78	#387×C₆₇	C₂²	1	2	yes	complemented
79	#386×C₆₇	C₂²	1	2	yes	—
80	#386×C₆₇	C₂²	1	1	yes	characteristic
81	#386×C₆₇	C₂²	1	1	yes	characteristic
82	#386×C₆₇	C₂²	1	2	yes	—
83	#386×C₆₇	C₂²	1	2	yes	—
84	#386×C₆₇	C₂²	1	2	yes	—
85	#386×C₆₇	C₂²	1	1	yes	characteristic
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	1	yes	characteristic
88	#386×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#386×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#386×C₆₇	C₂²	1	2	yes	complemented
92	#386×C₆₇	C₂²	1	2	yes	complemented
93	#385×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	—
96	#381×C₆₇	C₂²	1	1	yes	characteristic
97	#380×C₆₇	C₂²	1	2	yes	complemented
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
106	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×#41×C₆₇	—	2	4	no	—
109	C₂×#41×C₆₇	—	4	2	no	—
110	C₂×#41×C₆₇	—	4	2	no	—
111	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
119	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
129	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
131	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
132	#127×C₆₇	—	2	4	no	—
133	#124×C₆₇	—	4	2	no	—
134	#123×C₆₇	—	2	8	no	—
135	#123×C₆₇	—	4	4	no	—
136	#123×C₆₇	—	4	4	no	—
137	#121×C₆₇	—	2	8	no	—
138	#121×C₆₇	—	4	4	no	—
139	#121×C₆₇	—	4	2	no	—
140	#120×C₆₇	—	2	4	no	—
141	#120×C₆₇	—	2	8	no	—
142	#120×C₆₇	—	4	2	no	—
143	C₄×D₄×C₆₇	—	4	4	no	—
144	C₄×D₄×C₆₇	—	4	4	no	—
145	C₄×D₄×C₆₇	—	4	4	no	—
146	C₄×D₄×C₆₇	—	4	4	no	—
147	#117×C₆₇	—	4	2	no	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
160	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₆₇	—	4	2	no	—
191	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	2	yes	—
216	C₂⁴×C₆₇	—	2	2	no	—
217	C₂⁴×C₆₇	—	2	4	no	—
218	C₂⁴×C₆₇	—	4	1	no	—
219	C₂⁴×C₆₇	—	4	2	no	—
220	C₂⁴×C₆₇	—	4	1	no	—
221	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
223	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
224	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
226	#41×C₆₇	—	4	16	no	—
227	C₂×Q₈×C₆₇	—	2	2	no	—
228	C₂×Q₈×C₆₇	—	2	2	no	—
229	C₂×Q₈×C₆₇	—	4	1	no	—
230	C₂×D₄×C₆₇	—	2	4	no	—
231	C₂×D₄×C₆₇	—	2	4	no	—
232	C₂×D₄×C₆₇	—	2	4	no	—
233	C₂×D₄×C₆₇	—	2	4	no	—
234	C₂×D₄×C₆₇	—	2	4	no	—
235	C₂×D₄×C₆₇	—	2	2	no	—
236	C₂×D₄×C₆₇	—	2	2	no	—
237	C₂×D₄×C₆₇	—	2	4	no	—
238	C₂×D₄×C₆₇	—	2	4	no	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	2	4	no	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	—	2	2	no	—
244	C₂×D₄×C₆₇	—	4	2	no	—
245	C₂×D₄×C₆₇	—	4	2	no	—
246	C₂×D₄×C₆₇	—	4	2	no	—
247	C₂×D₄×C₆₇	—	4	2	no	—
248	C₂×D₄×C₆₇	—	4	1	no	—
249	C₂×D₄×C₆₇	—	4	1	no	—
250	C₂×D₄×C₆₇	—	4	1	no	—
251	C₂×D₄×C₆₇	—	4	1	no	—
252	C₂×D₄×C₆₇	—	4	1	no	—
253	C₂×D₄×C₆₇	—	4	2	no	—
254	C₂×D₄×C₆₇	—	4	1	no	—
255	C₂×D₄×C₆₇	—	4	2	no	—
256	C₂×D₄×C₆₇	—	4	2	no	—
257	C₂×D₄×C₆₇	—	4	2	no	—
258	C₂×D₄×C₆₇	—	4	2	no	—
259	C₂×D₄×C₆₇	—	4	2	no	—
260	C₂×D₄×C₆₇	—	4	2	no	—
261	C₂×D₄×C₆₇	—	4	1	no	—
262	C₂×D₄×C₆₇	#41	1	4	yes	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	4	no	—
268	C₂²×C₄×C₆₇	—	2	4	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	4	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	4	no	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	4	1	no	—
276	C₂²×C₄×C₆₇	—	4	1	no	—
277	C₂²×C₄×C₆₇	—	4	1	no	—
278	C₂²×C₄×C₆₇	—	4	1	no	—
279	C₂²×C₄×C₆₇	—	4	2	no	—
280	C₂²×C₄×C₆₇	—	4	1	no	—
281	C₂²×C₄×C₆₇	—	4	2	no	—
282	C₂²×C₄×C₆₇	—	4	2	no	—
283	C₂²×C₄×C₆₇	—	4	2	no	—
284	C₂²×C₄×C₆₇	—	4	2	no	—
285	C₂²×C₄×C₆₇	—	4	2	no	—
286	C₂²×C₄×C₆₇	—	4	2	no	—
287	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₆₇	—	2	4	no	—
302	C₄⋊C₄×C₆₇	—	2	4	no	—
303	C₄⋊C₄×C₆₇	—	2	4	no	—
304	C₄⋊C₄×C₆₇	—	2	4	no	—
305	C₄⋊C₄×C₆₇	—	2	4	no	—
306	C₄⋊C₄×C₆₇	—	2	4	no	—
307	C₄⋊C₄×C₆₇	—	4	2	no	—
308	C₄⋊C₄×C₆₇	—	4	1	no	—
309	C₄⋊C₄×C₆₇	—	4	2	no	—
310	C₄⋊C₄×C₆₇	—	4	2	no	—
311	C₄⋊C₄×C₆₇	—	4	2	no	—
312	C₂²⋊C₄×C₆₇	—	2	2	no	—
313	C₂²⋊C₄×C₆₇	—	2	4	no	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	2	4	no	—
317	C₂²⋊C₄×C₆₇	—	2	4	no	—
318	C₂²⋊C₄×C₆₇	—	2	4	no	—
319	C₂²⋊C₄×C₆₇	—	2	4	no	—
320	C₂²⋊C₄×C₆₇	—	2	4	no	—
321	C₂²⋊C₄×C₆₇	—	2	4	no	—
322	C₂²⋊C₄×C₆₇	—	2	4	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	—	2	4	no	—
325	C₂²⋊C₄×C₆₇	—	2	4	no	—
326	C₂²⋊C₄×C₆₇	—	2	4	no	—
327	C₂²⋊C₄×C₆₇	—	4	2	no	—
328	C₂²⋊C₄×C₆₇	—	4	2	no	—
329	C₂²⋊C₄×C₆₇	—	4	2	no	—
330	C₂²⋊C₄×C₆₇	—	4	1	no	—
331	C₂²⋊C₄×C₆₇	—	4	1	no	—
332	C₂²⋊C₄×C₆₇	—	4	2	no	—
333	C₂²⋊C₄×C₆₇	—	4	2	no	—
334	C₂²⋊C₄×C₆₇	—	4	2	no	—
335	C₂²⋊C₄×C₆₇	—	4	1	no	—
336	C₂²⋊C₄×C₆₇	—	4	2	no	—
337	C₂²⋊C₄×C₆₇	—	4	2	no	—
338	C₂²⋊C₄×C₆₇	—	4	2	no	—
339	C₂²⋊C₄×C₆₇	—	4	2	no	—
340	C₂²⋊C₄×C₆₇	#41	1	8	yes	complemented
341	C₄²×C₆₇	—	2	2	no	—
342	C₄²×C₆₇	—	2	4	no	—
343	C₄²×C₆₇	—	4	2	no	—
344	C₄²×C₆₇	—	4	2	no	—
345	C₄²×C₆₇	—	4	2	no	—
346	C₄²×C₆₇	—	4	2	no	—
347	C₄²×C₆₇	—	4	2	no	—
348	C₄²×C₆₇	—	4	1	no	—
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	—	2	2	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	—	2	2	no	—
353	C₂³×C₆₇	—	2	2	no	—
354	C₂³×C₆₇	—	2	2	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	2	2	no	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	1	no	—
359	C₂³×C₆₇	—	2	1	no	—
360	C₂³×C₆₇	—	2	1	no	—
361	C₂³×C₆₇	—	2	1	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	2	no	—
364	C₂³×C₆₇	—	2	2	no	—
365	C₂³×C₆₇	—	2	1	no	—
366	C₂³×C₆₇	—	2	2	no	—
367	C₂³×C₆₇	—	2	2	no	—
368	C₂³×C₆₇	—	2	2	no	—
369	C₂³×C₆₇	—	2	2	no	—
370	C₂³×C₆₇	—	2	2	no	—
371	C₂³×C₆₇	—	2	2	no	—
372	C₂³×C₆₇	—	2	2	no	—
373	C₂³×C₆₇	—	2	1	no	—
374	C₂³×C₆₇	—	2	1	no	—
375	C₂³×C₆₇	—	4	4	no	—
376	C₂³×C₆₇	—	4	8	no	—
377	C₂³×C₆₇	—	8	2	no	—
378	C₂³×C₆₇	—	8	4	no	—
379	C₂³×C₆₇	—	8	2	no	—
380	C₂³×C₆₇	C₂×#41	1	2	yes	—
381	C₂³×C₆₇	C₂×#41	1	4	yes	—
382	C₂³×C₆₇	C₂×#41	1	2	yes	—
383	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
384	Q₈×C₆₇	—	4	4	no	—
385	D₄×C₆₇	—	4	4	no	—
386	D₄×C₆₇	—	4	8	no	—
387	D₄×C₆₇	—	4	8	no	—
388	D₄×C₆₇	—	4	8	no	—
389	D₄×C₆₇	—	4	4	no	—
390	D₄×C₆₇	—	4	8	no	—
391	D₄×C₆₇	—	4	4	no	—
392	D₄×C₆₇	—	8	2	no	—
393	D₄×C₆₇	—	8	4	no	—
394	D₄×C₆₇	—	8	4	no	—
395	D₄×C₆₇	—	8	4	no	—
396	C₂×C₄×C₆₇	—	2	8	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	1	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	1	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	2	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	1	no	—
416	C₂×C₄×C₆₇	—	2	2	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	2	2	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	2	no	—
428	C₂×C₄×C₆₇	—	2	2	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	1	no	—
431	C₂×C₄×C₆₇	—	2	1	no	—
432	C₂×C₄×C₆₇	—	2	2	no	—
433	C₂×C₄×C₆₇	—	4	4	no	—
434	C₂×C₄×C₆₇	—	4	4	no	—
435	C₂×C₄×C₆₇	—	4	4	no	—
436	C₂×C₄×C₆₇	—	4	4	no	—
437	C₂×C₄×C₆₇	—	8	4	no	—
438	C₂×C₄×C₆₇	—	8	4	no	—
439	C₂×C₄×C₆₇	—	8	4	no	—
440	C₂×C₄×C₆₇	—	8	2	no	—
441	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
442	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
443	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
444	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
445	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
446	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
447	C₂²×C₆₇	—	2	4	no	—
448	C₂²×C₆₇	—	2	4	no	—
449	C₂²×C₆₇	—	2	4	no	—
450	C₂²×C₆₇	—	2	4	no	—
451	C₂²×C₆₇	—	2	2	no	—
452	C₂²×C₆₇	—	2	2	no	—
453	C₂²×C₆₇	—	2	4	no	—
454	C₂²×C₆₇	—	4	1	no	—
455	C₂²×C₆₇	—	4	1	no	—
456	C₂²×C₆₇	—	4	2	no	—
457	C₂²×C₆₇	—	4	2	no	—
458	C₂²×C₆₇	—	4	2	no	—
459	C₂²×C₆₇	—	4	2	no	—
460	C₂²×C₆₇	—	4	2	no	—
461	C₂²×C₆₇	—	4	1	no	—
462	C₂²×C₆₇	—	4	2	no	—
463	C₂²×C₆₇	—	4	1	no	—
464	C₂²×C₆₇	—	4	2	no	—
465	C₂²×C₆₇	—	4	2	no	—
466	C₂²×C₆₇	—	4	2	no	—
467	C₂²×C₆₇	—	4	1	no	—
468	C₂²×C₆₇	—	4	2	no	—
469	C₂²×C₆₇	—	4	1	no	—
470	C₂²×C₆₇	—	4	2	no	—
471	C₂²×C₆₇	—	4	2	no	—
472	C₂²×C₆₇	—	4	2	no	—
473	C₂²×C₆₇	—	4	2	no	—
474	C₂²×C₆₇	—	4	2	no	—
475	C₂²×C₆₇	—	4	1	no	—
476	C₂²×C₆₇	—	8	8	no	—
477	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
478	C₂²×C₆₇	C₂²×#41	1	2	yes	—
479	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
481	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₄×C₆₇	—	2	4	no	—
483	C₄×C₆₇	—	2	4	no	—
484	C₄×C₆₇	—	2	2	no	—
485	C₄×C₆₇	—	2	2	no	—
486	C₄×C₆₇	—	2	2	no	—
487	C₄×C₆₇	—	2	4	no	—
488	C₄×C₆₇	—	4	2	no	—
489	C₄×C₆₇	—	4	1	no	—
490	C₄×C₆₇	—	4	2	no	—
491	C₄×C₆₇	—	4	2	no	—
492	C₄×C₆₇	—	4	2	no	—
493	C₄×C₆₇	—	4	2	no	—
494	C₄×C₆₇	—	4	2	no	—
495	C₄×C₆₇	—	4	2	no	—
496	#60034	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
497	C₂×C₆₇	—	4	2	no	—
498	C₂×C₆₇	—	4	2	no	—
499	C₂×C₆₇	—	4	4	no	—
500	C₂×C₆₇	—	8	2	no	—
501	C₂×C₆₇	—	8	1	no	—
502	C₂×C₆₇	#3481	1	1	yes	characteristic
503	C₂×C₆₇	#3481	1	2	yes	—
504	C₂×C₆₇	#3490	1	1	yes	characteristic
505	C₂×C₆₇	#3508	1	2	yes	—
506	C₂×C₆₇	#3537	1	1	yes	characteristic
507	#2748	C₂×C₆₇	1	1	yes	characteristic, complemented
508	#2703	C₂×C₆₇	1	2	yes	complemented
509	#2669	C₂×C₆₇	1	1	yes	characteristic, complemented
510	#2602	C₂×C₆₇	1	2	yes	complemented
511	#2589	C₂×C₆₇	1	2	yes	complemented
512	#2557	C₂×C₆₇	1	2	yes	complemented
513	#2539	C₂×C₆₇	1	2	yes	complemented
514	#2516	C₂×C₆₇	1	2	yes	complemented
515	#2471	C₂×C₆₇	1	2	yes	complemented
516	#2464	C₂×C₆₇	1	2	yes	complemented
517	#2456	C₂×C₆₇	1	2	yes	complemented
518	#2431	C₂×C₆₇	1	1	yes	characteristic, complemented
519	#2404	C₂×C₆₇	1	1	yes	characteristic, complemented
520	#2374	C₂×C₆₇	1	2	yes	complemented
521	#2366	C₂×C₆₇	1	1	yes	characteristic, complemented
522	#2358	C₂×C₆₇	1	2	yes	complemented
523	#2358	C₂×C₆₇	1	1	yes	characteristic, complemented
524	C₄×#121	C₂×C₆₇	1	2	yes	complemented
525	#2297	C₂×C₆₇	1	1	yes	characteristic, complemented
526	C₆₇	#60034	1	1	yes	characteristic, direct product factor, Sylow
527	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
528	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
529	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
530	C₂×#123	C₂²×C₆₇	1	2	yes	—
531	C₂×#123	C₂²×C₆₇	1	2	yes	—
532	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
533	C₂×#121	C₂²×C₆₇	1	2	yes	—
534	C₂×#121	C₂²×C₆₇	1	2	yes	—
535	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
536	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
537	C₂×#120	C₂²×C₆₇	1	2	yes	—
538	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
539	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
540	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
541	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
542	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
543	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
544	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
545	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
546	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
547	#400	C₂²×C₆₇	1	2	yes	complemented
548	#399	C₂²×C₆₇	1	2	yes	—
549	#399	C₂²×C₆₇	1	2	yes	—
550	#398	C₂²×C₆₇	1	2	yes	complemented
551	#397	C₂²×C₆₇	1	2	yes	complemented
552	#397	C₂²×C₆₇	1	2	yes	complemented
553	#396	C₂²×C₆₇	1	2	yes	complemented
554	#394	C₂²×C₆₇	1	2	yes	—
555	#394	C₂²×C₆₇	1	2	yes	complemented
556	#393	C₂²×C₆₇	1	2	yes	—
557	#392	C₂²×C₆₇	1	2	yes	—
558	#392	C₂²×C₆₇	1	2	yes	—
559	#392	C₂²×C₆₇	1	2	yes	—
560	#392	C₂²×C₆₇	1	2	yes	—
561	#392	C₂²×C₆₇	1	2	yes	—
562	#392	C₂²×C₆₇	1	2	yes	complemented
563	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
564	#391	C₂²×C₆₇	1	2	yes	complemented
565	#390	C₂²×C₆₇	1	2	yes	—
566	#390	C₂²×C₆₇	1	1	yes	characteristic
567	#390	C₂²×C₆₇	1	2	yes	—
568	#390	C₂²×C₆₇	1	2	yes	—
569	#390	C₂²×C₆₇	1	2	yes	—
570	#390	C₂²×C₆₇	1	2	yes	—
571	#390	C₂²×C₆₇	1	2	yes	complemented
572	#389	C₂²×C₆₇	1	2	yes	complemented
573	#388	C₂²×C₆₇	1	2	yes	—
574	#388	C₂²×C₆₇	1	2	yes	—
575	#388	C₂²×C₆₇	1	2	yes	—
576	#388	C₂²×C₆₇	1	2	yes	—
577	#388	C₂²×C₆₇	1	2	yes	complemented
578	#388	C₂²×C₆₇	1	2	yes	complemented
579	#388	C₂²×C₆₇	1	2	yes	complemented
580	#388	C₂²×C₆₇	1	2	yes	complemented
581	#388	C₂²×C₆₇	1	2	yes	complemented
582	#387	C₂²×C₆₇	1	2	yes	complemented
583	#387	C₂²×C₆₇	1	2	yes	complemented
584	#387	C₂²×C₆₇	1	2	yes	complemented
585	#387	C₂²×C₆₇	1	2	yes	complemented
586	#386	C₂²×C₆₇	1	1	yes	characteristic
587	#386	C₂²×C₆₇	1	1	yes	characteristic
588	#386	C₂²×C₆₇	1	2	yes	—
589	#386	C₂²×C₆₇	1	2	yes	—
590	#386	C₂²×C₆₇	1	2	yes	—
591	#386	C₂²×C₆₇	1	2	yes	—
592	#386	C₂²×C₆₇	1	1	yes	characteristic
593	#386	C₂²×C₆₇	1	2	yes	—
594	#386	C₂²×C₆₇	1	2	yes	—
595	#386	C₂²×C₆₇	1	1	yes	characteristic
596	#386	C₂²×C₆₇	1	2	yes	complemented
597	#386	C₂²×C₆₇	1	2	yes	complemented
598	#386	C₂²×C₆₇	1	1	yes	characteristic, complemented
599	#386	C₂²×C₆₇	1	1	yes	characteristic, complemented
600	#385	C₂²×C₆₇	1	2	yes	—
601	#385	C₂²×C₆₇	1	2	yes	—
602	#385	C₂²×C₆₇	1	2	yes	—
603	#381	C₂²×C₆₇	1	1	yes	characteristic
604	#380	C₂²×C₆₇	1	2	yes	complemented
605	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
606	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
607	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
608	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
609	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
610	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
611	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
612	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
613	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
614	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
615	C₂×#41	—	2	4	no	—
616	C₂×#41	—	4	2	no	—
617	C₂×#41	—	4	2	no	—
618	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
619	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
620	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
621	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
622	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
623	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
625	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
626	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
629	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
633	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
635	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
636	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
637	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
638	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
639	#127	—	2	4	no	—
640	#124	—	4	2	no	—
641	#123	—	2	8	no	—
642	#123	—	4	4	no	—
643	#123	—	4	4	no	—
644	#121	—	2	8	no	—
645	#121	—	4	4	no	—
646	#121	—	4	2	no	—
647	#120	—	2	4	no	—
648	#120	—	2	8	no	—
649	#120	—	4	2	no	—
650	C₄×D₄	—	4	4	no	—
651	C₄×D₄	—	4	4	no	—
652	C₄×D₄	—	4	4	no	—
653	C₄×D₄	—	4	4	no	—
654	#117	—	4	2	no	—
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
666	C₂×C₂²⋊C₄	—	4	2	no	—
667	C₂×C₂²⋊C₄	—	4	4	no	—
668	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₄²	—	4	2	no	—
698	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
701	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
702	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
703	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
704	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
706	#95	C₂³×C₆₇	1	2	yes	—
707	#95	C₂³×C₆₇	1	2	yes	—
708	#95	C₂³×C₆₇	1	2	yes	—
709	#95	C₂³×C₆₇	1	2	yes	—
710	#95	C₂³×C₆₇	1	2	yes	—
711	#95	C₂³×C₆₇	1	2	yes	—
712	#95	C₂³×C₆₇	1	2	yes	—
713	#95	C₂³×C₆₇	1	2	yes	—
714	#95	C₂³×C₆₇	1	2	yes	—
715	#95	C₂³×C₆₇	1	2	yes	—
716	#95	C₂³×C₆₇	1	2	yes	—
717	#95	C₂³×C₆₇	1	2	yes	—
718	#95	C₂³×C₆₇	1	2	yes	—
719	#95	C₂³×C₆₇	1	2	yes	—
720	#95	C₂³×C₆₇	1	2	yes	—
721	#95	C₂³×C₆₇	1	2	yes	—
722	#95	C₂³×C₆₇	1	2	yes	—
723	C₂⁴	—	2	2	no	—
724	C₂⁴	—	2	4	no	—
725	C₂⁴	—	4	1	no	—
726	C₂⁴	—	4	2	no	—
727	C₂⁴	—	4	1	no	—
728	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
729	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
730	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
731	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
733	#41	—	4	16	no	—
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	4	1	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	2	4	no	—
748	C₂×D₄	—	2	4	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	1	no	—
756	C₂×D₄	—	4	1	no	—
757	C₂×D₄	—	4	1	no	—
758	C₂×D₄	—	4	1	no	—
759	C₂×D₄	—	4	1	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	—	4	1	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	2	no	—
767	C₂×D₄	—	4	2	no	—
768	C₂×D₄	—	4	1	no	—
769	C₂×D₄	#41×C₆₇	1	4	yes	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	4	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	4	1	no	—
783	C₂²×C₄	—	4	1	no	—
784	C₂²×C₄	—	4	1	no	—
785	C₂²×C₄	—	4	1	no	—
786	C₂²×C₄	—	4	2	no	—
787	C₂²×C₄	—	4	1	no	—
788	C₂²×C₄	—	4	2	no	—
789	C₂²×C₄	—	4	2	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	—	4	2	no	—
792	C₂²×C₄	—	4	2	no	—
793	C₂²×C₄	—	4	2	no	—
794	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
802	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	4	no	—
810	C₄⋊C₄	—	2	4	no	—
811	C₄⋊C₄	—	2	4	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₄⋊C₄	—	2	4	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	1	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	1	no	—
838	C₂²⋊C₄	—	4	1	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	1	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	—	4	2	no	—
845	C₂²⋊C₄	—	4	2	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₂²⋊C₄	#41×C₆₇	1	8	yes	complemented
848	C₄²	—	2	2	no	—
849	C₄²	—	2	4	no	—
850	C₄²	—	4	2	no	—
851	C₄²	—	4	2	no	—
852	C₄²	—	4	2	no	—
853	C₄²	—	4	2	no	—
854	C₄²	—	4	2	no	—
855	C₄²	—	4	1	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	2	2	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	4	4	no	—
883	C₂³	—	4	8	no	—
884	C₂³	—	8	2	no	—
885	C₂³	—	8	4	no	—
886	C₂³	—	8	2	no	—
887	C₂³	C₂×#41×C₆₇	1	2	yes	—
888	C₂³	C₂×#41×C₆₇	1	4	yes	—
889	C₂³	C₂×#41×C₆₇	1	2	yes	—
890	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
891	Q₈	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	8	no	—
895	D₄	—	4	8	no	—
896	D₄	—	4	8	no	—
897	D₄	—	4	8	no	—
898	D₄	—	4	4	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	4	no	—
901	D₄	—	8	4	no	—
902	D₄	—	8	4	no	—
903	C₂×C₄	—	2	8	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	4	4	no	—
944	C₂×C₄	—	8	4	no	—
945	C₂×C₄	—	8	4	no	—
946	C₂×C₄	—	8	4	no	—
947	C₂×C₄	—	8	2	no	—
948	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
949	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
950	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
951	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
952	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
953	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
954	C₂²	—	2	4	no	—
955	C₂²	—	2	4	no	—
956	C₂²	—	2	4	no	—
957	C₂²	—	2	4	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	4	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	8	8	no	—
984	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
985	C₂²	C₂²×#41×C₆₇	1	2	yes	—
986	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
987	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
988	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
989	C₄	—	2	4	no	—
990	C₄	—	2	4	no	—
991	C₄	—	2	4	no	—
992	C₄	—	2	2	no	—
993	C₄	—	2	2	no	—
994	C₄	—	2	2	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₂	—	4	2	no	—
1004	C₂	—	4	4	no	—
1005	C₂	—	4	2	no	—
1006	C₂	—	8	2	no	—
1007	C₂	—	8	1	no	—
1008	C₂	C₆₇×#3481	1	1	yes	characteristic
1009	C₂	C₆₇×#3481	1	2	yes	—
1010	C₂	C₆₇×#3490	1	1	yes	characteristic
1011	C₂	C₆₇×#3508	1	2	yes	—
1012	C₂	C₆₇×#3537	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2748	C₂	semidirect
2. C₆₇×#2703	C₂	semidirect
3. C₆₇×#2669	C₂	semidirect
4. C₆₇×#2602	C₂	semidirect
5. C₆₇×#2589	C₂	semidirect
6. C₆₇×#2557	C₂	semidirect
7. C₆₇×#2539	C₂	semidirect
8. C₆₇×#2516	C₂	semidirect
9. C₆₇×#2471	C₂	semidirect
10. C₆₇×#2464	C₂	semidirect
11. C₆₇×#2456	C₂	semidirect
12. C₆₇×#2431	C₂	semidirect
13. C₆₇×#2404	C₂	semidirect
14. C₆₇×#2374	C₂	semidirect
15. C₆₇×#2366	C₂	semidirect
16. C₆₇×#2358	C₂	semidirect
17. C₆₇×#2358	C₂	semidirect
18. C₄×#121×C₆₇	C₂	semidirect
19. C₆₇×#2297	C₂	semidirect
22. C₂×#124×C₆₇	C₂²	semidirect
25. C₂×#123×C₆₇	C₂²	semidirect
28. C₂×#121×C₆₇	C₂²	semidirect
35. C₂×C₄×D₄×C₆₇	C₂²	semidirect
36. C₂×#117×C₆₇	C₂²	semidirect
39. C₂²×C₄²×C₆₇	C₂²	semidirect
40. #400×C₆₇	C₂²	semidirect
43. #398×C₆₇	C₂²	semidirect
44. #397×C₆₇	C₂²	semidirect
45. #397×C₆₇	C₂²	semidirect
46. #396×C₆₇	C₂²	semidirect
48. #394×C₆₇	C₂²	semidirect
55. #392×C₆₇	C₂²	semidirect
56. #391×C₆₇	C₂²	semidirect
57. #391×C₆₇	C₂²	semidirect
64. #390×C₆₇	C₂²	semidirect
65. #389×C₆₇	C₂²	semidirect
70. #388×C₆₇	C₂²	semidirect
71. #388×C₆₇	C₂²	semidirect
72. #388×C₆₇	C₂²	semidirect
73. #388×C₆₇	C₂²	semidirect
74. #388×C₆₇	C₂²	semidirect
75. #387×C₆₇	C₂²	semidirect
76. #387×C₆₇	C₂²	semidirect
77. #387×C₆₇	C₂²	semidirect
78. #387×C₆₇	C₂²	semidirect
89. #386×C₆₇	C₂²	semidirect
90. #386×C₆₇	C₂²	semidirect
91. #386×C₆₇	C₂²	semidirect
92. #386×C₆₇	C₂²	semidirect
97. #380×C₆₇	C₂²	semidirect
98. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
99. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
340. C₂²⋊C₄×C₆₇	#41	semidirect
496. #60034	C₆₇	direct (N × H)
507. #2748	C₂×C₆₇	semidirect
508. #2703	C₂×C₆₇	semidirect
509. #2669	C₂×C₆₇	semidirect
510. #2602	C₂×C₆₇	semidirect
511. #2589	C₂×C₆₇	semidirect
512. #2557	C₂×C₆₇	semidirect
513. #2539	C₂×C₆₇	semidirect
514. #2516	C₂×C₆₇	semidirect
515. #2471	C₂×C₆₇	semidirect
516. #2464	C₂×C₆₇	semidirect
517. #2456	C₂×C₆₇	semidirect
518. #2431	C₂×C₆₇	semidirect
519. #2404	C₂×C₆₇	semidirect
520. #2374	C₂×C₆₇	semidirect
521. #2366	C₂×C₆₇	semidirect
522. #2358	C₂×C₆₇	semidirect
523. #2358	C₂×C₆₇	semidirect
524. C₄×#121	C₂×C₆₇	semidirect
525. #2297	C₂×C₆₇	semidirect
526. C₆₇	#60034	direct (N × H)
529. C₂×#124	C₂²×C₆₇	semidirect
532. C₂×#123	C₂²×C₆₇	semidirect
535. C₂×#121	C₂²×C₆₇	semidirect
542. C₂×C₄×D₄	C₂²×C₆₇	semidirect
543. C₂×#117	C₂²×C₆₇	semidirect
546. C₂²×C₄²	C₂²×C₆₇	semidirect
547. #400	C₂²×C₆₇	semidirect
550. #398	C₂²×C₆₇	semidirect
551. #397	C₂²×C₆₇	semidirect
552. #397	C₂²×C₆₇	semidirect
553. #396	C₂²×C₆₇	semidirect
555. #394	C₂²×C₆₇	semidirect
562. #392	C₂²×C₆₇	semidirect
563. #391	C₂²×C₆₇	semidirect
564. #391	C₂²×C₆₇	semidirect
571. #390	C₂²×C₆₇	semidirect
572. #389	C₂²×C₆₇	semidirect
577. #388	C₂²×C₆₇	semidirect
578. #388	C₂²×C₆₇	semidirect
579. #388	C₂²×C₆₇	semidirect
580. #388	C₂²×C₆₇	semidirect
581. #388	C₂²×C₆₇	semidirect
582. #387	C₂²×C₆₇	semidirect
583. #387	C₂²×C₆₇	semidirect
584. #387	C₂²×C₆₇	semidirect
585. #387	C₂²×C₆₇	semidirect
596. #386	C₂²×C₆₇	semidirect
597. #386	C₂²×C₆₇	semidirect
598. #386	C₂²×C₆₇	semidirect
599. #386	C₂²×C₆₇	semidirect
604. #380	C₂²×C₆₇	semidirect
605. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
606. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
611. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
612. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
613. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
847. C₂²⋊C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2748	2
C₆₇×#2703	2
C₆₇×#2669	2
C₆₇×#2602	2
C₆₇×#2589	2
C₆₇×#2557	2
C₆₇×#2539	2
C₆₇×#2516	2
C₆₇×#2471	2
C₆₇×#2464	2
C₆₇×#2456	2
C₆₇×#2431	2
C₆₇×#2404	2
C₆₇×#2374	2
C₆₇×#2366	2
C₆₇×#2358	2
C₄×#121×C₆₇	2
C₆₇×#2297	2
#60034	67

Subgroups — C67×#60034 #30739285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60034 #30739285