Subgroups — C₆₇×#36821 #30716072

Order 17152.

1776 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2853	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2789	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2760	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2752	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2751	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2709	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2706	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2700	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2696	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2653	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2607	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2591	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2576	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2477	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2431	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2406	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2333	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2313	C₂	1	1	yes	maximal, characteristic, 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
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
31	#401×C₆₇	C₂²	1	2	yes	—
32	#401×C₆₇	C₂²	1	2	yes	—
33	#400×C₆₇	C₂²	1	2	yes	—
34	#400×C₆₇	C₂²	1	2	yes	—
35	#399×C₆₇	C₂²	1	2	yes	—
36	#398×C₆₇	C₂²	1	2	yes	—
37	#397×C₆₇	C₂²	1	2	yes	—
38	#397×C₆₇	C₂²	1	2	yes	—
39	#397×C₆₇	C₂²	1	2	yes	—
40	#397×C₆₇	C₂²	1	2	yes	—
41	#396×C₆₇	C₂²	1	2	yes	—
42	#395×C₆₇	C₂²	1	2	yes	—
43	#394×C₆₇	C₂²	1	2	yes	—
44	#394×C₆₇	C₂²	1	2	yes	—
45	#394×C₆₇	C₂²	1	2	yes	—
46	#394×C₆₇	C₂²	1	2	yes	—
47	#394×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	2	yes	—
49	#393×C₆₇	C₂²	1	2	yes	—
50	#393×C₆₇	C₂²	1	2	yes	—
51	#393×C₆₇	C₂²	1	2	yes	—
52	#393×C₆₇	C₂²	1	2	yes	—
53	#392×C₆₇	C₂²	1	2	yes	—
54	#392×C₆₇	C₂²	1	2	yes	—
55	#391×C₆₇	C₂²	1	1	yes	characteristic
56	#391×C₆₇	C₂²	1	2	yes	—
57	#391×C₆₇	C₂²	1	2	yes	—
58	#391×C₆₇	C₂²	1	2	yes	—
59	#390×C₆₇	C₂²	1	2	yes	—
60	#390×C₆₇	C₂²	1	2	yes	—
61	#390×C₆₇	C₂²	1	1	yes	characteristic
62	#388×C₆₇	C₂²	1	2	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
65	#388×C₆₇	C₂²	1	2	yes	—
66	#388×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#387×C₆₇	C₂²	1	2	yes	—
70	#387×C₆₇	C₂²	1	2	yes	—
71	#387×C₆₇	C₂²	1	2	yes	—
72	#387×C₆₇	C₂²	1	2	yes	—
73	#387×C₆₇	C₂²	1	2	yes	—
74	#387×C₆₇	C₂²	1	2	yes	—
75	#387×C₆₇	C₂²	1	2	yes	—
76	#387×C₆₇	C₂²	1	2	yes	—
77	#387×C₆₇	C₂²	1	2	yes	—
78	#387×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	1	yes	characteristic
80	#386×C₆₇	C₂²	1	2	yes	—
81	#386×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	2	yes	—
91	#386×C₆₇	C₂²	1	1	yes	characteristic
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#382×C₆₇	C₂²	1	2	yes	—
96	#381×C₆₇	C₂²	1	2	yes	—
97	#381×C₆₇	C₂²	1	2	yes	—
98	#381×C₆₇	C₂²	1	2	yes	—
99	#381×C₆₇	C₂²	1	1	yes	characteristic
100	#380×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
107	C₂×#41×C₆₇	—	2	4	no	—
108	C₂×#41×C₆₇	—	4	2	no	—
109	C₂×#41×C₆₇	—	4	2	no	—
110	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
126	#127×C₆₇	—	4	2	no	—
127	#124×C₆₇	—	4	2	no	—
128	#123×C₆₇	—	4	2	no	—
129	#123×C₆₇	—	4	4	no	—
130	#123×C₆₇	—	4	2	no	—
131	C₂²⋊Q₈×C₆₇	—	4	4	no	—
132	#121×C₆₇	—	2	4	no	—
133	#117×C₆₇	—	4	2	no	—
134	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
171	C₂×C₄²×C₆₇	—	4	2	no	—
172	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
180	#95×C₆₇	C₂³	1	2	yes	—
181	#95×C₆₇	C₂³	1	2	yes	—
182	#95×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×C₆₇	C₂³	1	2	yes	—
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
208	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
209	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
211	#41×C₆₇	—	4	16	no	—
212	C₂×Q₈×C₆₇	—	2	2	no	—
213	C₂×Q₈×C₆₇	—	2	2	no	—
214	C₂×Q₈×C₆₇	—	4	1	no	—
215	C₂×Q₈×C₆₇	—	4	2	no	—
216	C₂×Q₈×C₆₇	—	4	2	no	—
217	C₂×Q₈×C₆₇	—	4	2	no	—
218	C₂×D₄×C₆₇	—	2	2	no	—
219	C₂×D₄×C₆₇	—	2	2	no	—
220	C₂×D₄×C₆₇	—	2	2	no	—
221	C₂×D₄×C₆₇	—	2	2	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	2	no	—
225	C₂×D₄×C₆₇	—	2	2	no	—
226	C₂×D₄×C₆₇	—	2	2	no	—
227	C₂×D₄×C₆₇	—	4	1	no	—
228	C₂×D₄×C₆₇	—	4	1	no	—
229	C₂×D₄×C₆₇	—	4	1	no	—
230	C₂×D₄×C₆₇	—	4	1	no	—
231	C₂×D₄×C₆₇	—	4	1	no	—
232	C₂×D₄×C₆₇	—	4	2	no	—
233	C₂×D₄×C₆₇	—	4	2	no	—
234	C₂×D₄×C₆₇	—	4	2	no	—
235	C₂×D₄×C₆₇	—	4	2	no	—
236	C₂×D₄×C₆₇	—	4	2	no	—
237	C₂×D₄×C₆₇	—	4	2	no	—
238	C₂×D₄×C₆₇	—	4	2	no	—
239	C₂²×C₄×C₆₇	—	2	2	no	—
240	C₂²×C₄×C₆₇	—	2	2	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	2	4	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	4	2	no	—
247	C₂²×C₄×C₆₇	—	4	2	no	—
248	C₂²×C₄×C₆₇	—	4	2	no	—
249	C₂²×C₄×C₆₇	—	4	1	no	—
250	C₂²×C₄×C₆₇	—	4	1	no	—
251	C₂²×C₄×C₆₇	—	4	1	no	—
252	C₂²×C₄×C₆₇	—	4	1	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	1	no	—
255	C₂²×C₄×C₆₇	—	4	1	no	—
256	C₂²×C₄×C₆₇	—	4	2	no	—
257	C₂²×C₄×C₆₇	—	4	2	no	—
258	C₂²×C₄×C₆₇	#41	1	4	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	4	2	no	—
280	C₄⋊C₄×C₆₇	—	4	2	no	—
281	C₄⋊C₄×C₆₇	—	4	2	no	—
282	C₄⋊C₄×C₆₇	—	4	2	no	—
283	C₄⋊C₄×C₆₇	—	4	2	no	—
284	C₄⋊C₄×C₆₇	—	4	2	no	—
285	C₄⋊C₄×C₆₇	—	4	2	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	4	2	no	—
290	C₂²⋊C₄×C₆₇	—	4	2	no	—
291	C₂²⋊C₄×C₆₇	—	4	2	no	—
292	C₂²⋊C₄×C₆₇	—	4	2	no	—
293	C₂²⋊C₄×C₆₇	—	4	2	no	—
294	C₂²⋊C₄×C₆₇	—	4	2	no	—
295	C₂²⋊C₄×C₆₇	—	4	2	no	—
296	C₂²⋊C₄×C₆₇	—	4	2	no	—
297	C₂²⋊C₄×C₆₇	—	4	2	no	—
298	C₂²⋊C₄×C₆₇	—	4	2	no	—
299	C₂²⋊C₄×C₆₇	—	4	2	no	—
300	C₂²⋊C₄×C₆₇	—	4	2	no	—
301	C₂²⋊C₄×C₆₇	—	4	2	no	—
302	C₂²⋊C₄×C₆₇	—	4	2	no	—
303	C₂²⋊C₄×C₆₇	—	4	2	no	—
304	C₂²⋊C₄×C₆₇	—	4	2	no	—
305	C₂²⋊C₄×C₆₇	—	4	2	no	—
306	C₂²⋊C₄×C₆₇	—	4	1	no	—
307	C₂²⋊C₄×C₆₇	—	4	2	no	—
308	C₂²⋊C₄×C₆₇	—	4	1	no	—
309	C₂²⋊C₄×C₆₇	—	4	2	no	—
310	C₄²×C₆₇	—	4	1	no	—
311	C₄²×C₆₇	—	4	1	no	—
312	C₄²×C₆₇	—	4	2	no	—
313	C₄²×C₆₇	—	4	2	no	—
314	C₄²×C₆₇	—	4	1	no	—
315	C₄²×C₆₇	—	4	1	no	—
316	C₄²×C₆₇	—	4	1	no	—
317	C₄²×C₆₇	—	4	1	no	—
318	C₂³×C₆₇	—	2	1	no	—
319	C₂³×C₆₇	—	2	1	no	—
320	C₂³×C₆₇	—	2	1	no	—
321	C₂³×C₆₇	—	2	1	no	—
322	C₂³×C₆₇	—	2	2	no	—
323	C₂³×C₆₇	—	2	2	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	1	no	—
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	1	no	—
330	C₂³×C₆₇	—	2	2	no	—
331	C₂³×C₆₇	—	2	1	no	—
332	C₂³×C₆₇	—	2	2	no	—
333	C₂³×C₆₇	—	2	2	no	—
334	C₂³×C₆₇	—	2	2	no	—
335	C₂³×C₆₇	—	2	2	no	—
336	C₂³×C₆₇	—	2	2	no	—
337	C₂³×C₆₇	—	2	2	no	—
338	C₂³×C₆₇	C₂×#41	1	2	yes	—
339	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
340	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
341	Q₈×C₆₇	—	4	4	no	—
342	Q₈×C₆₇	—	8	4	no	—
343	D₄×C₆₇	—	4	4	no	—
344	D₄×C₆₇	—	4	4	no	—
345	D₄×C₆₇	—	4	4	no	—
346	D₄×C₆₇	—	8	2	no	—
347	D₄×C₆₇	—	8	4	no	—
348	D₄×C₆₇	—	8	4	no	—
349	D₄×C₆₇	—	8	4	no	—
350	C₂×C₄×C₆₇	—	2	8	no	—
351	C₂×C₄×C₆₇	—	2	1	no	—
352	C₂×C₄×C₆₇	—	2	1	no	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	1	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	1	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	4	4	no	—
394	C₂×C₄×C₆₇	—	4	4	no	—
395	C₂×C₄×C₆₇	—	4	4	no	—
396	C₂×C₄×C₆₇	—	4	8	no	—
397	C₂×C₄×C₆₇	—	8	2	no	—
398	C₂×C₄×C₆₇	—	8	4	no	—
399	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
400	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
401	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
402	C₂²×C₆₇	—	2	2	no	—
403	C₂²×C₆₇	—	2	2	no	—
404	C₂²×C₆₇	—	2	2	no	—
405	C₂²×C₆₇	—	2	2	no	—
406	C₂²×C₆₇	—	2	4	no	—
407	C₂²×C₆₇	—	4	1	no	—
408	C₂²×C₆₇	—	4	1	no	—
409	C₂²×C₆₇	—	4	2	no	—
410	C₂²×C₆₇	—	4	2	no	—
411	C₂²×C₆₇	—	4	2	no	—
412	C₂²×C₆₇	—	4	2	no	—
413	C₂²×C₆₇	—	4	1	no	—
414	C₂²×C₆₇	—	4	1	no	—
415	C₂²×C₆₇	—	4	2	no	—
416	C₂²×C₆₇	—	4	2	no	—
417	C₂²×C₆₇	—	4	1	no	—
418	C₂²×C₆₇	—	4	2	no	—
419	C₂²×C₆₇	—	4	2	no	—
420	C₂²×C₆₇	—	4	2	no	—
421	C₂²×C₆₇	—	4	2	no	—
422	C₂²×C₆₇	—	4	2	no	—
423	C₂²×C₆₇	—	4	2	no	—
424	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
425	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₆₇	#585	1	2	yes	—
428	C₂²×C₆₇	#585	1	2	yes	—
429	C₄×C₆₇	—	2	2	no	—
430	C₄×C₆₇	—	2	2	no	—
431	C₄×C₆₇	—	2	2	no	—
432	C₄×C₆₇	—	4	2	no	—
433	C₄×C₆₇	—	4	1	no	—
434	C₄×C₆₇	—	4	2	no	—
435	C₄×C₆₇	—	4	2	no	—
436	C₄×C₆₇	—	4	2	no	—
437	C₄×C₆₇	—	4	2	no	—
438	C₄×C₆₇	—	4	2	no	—
439	C₄×C₆₇	—	4	2	no	—
440	C₄×C₆₇	—	4	2	no	—
441	C₄×C₆₇	—	4	2	no	—
442	C₄×C₆₇	—	4	2	no	—
443	C₄×C₆₇	—	4	2	no	—
444	#36821	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
445	C₂×C₆₇	—	4	2	no	—
446	C₂×C₆₇	—	4	2	no	—
447	C₂×C₆₇	—	8	1	no	—
448	C₂×C₆₇	—	8	2	no	—
449	C₂×C₆₇	#3455	1	1	yes	characteristic
450	C₂×C₆₇	#3490	1	1	yes	characteristic
451	C₂×C₆₇	#3510	1	1	yes	characteristic
452	C₂×C₆₇	#3533	1	2	yes	—
453	C₂×C₆₇	#3562	1	2	yes	—
454	#2853	C₂×C₆₇	1	2	yes	complemented
455	#2789	C₂×C₆₇	1	2	yes	complemented
456	#2760	C₂×C₆₇	1	2	yes	complemented
457	#2752	C₂×C₆₇	1	2	yes	complemented
458	#2751	C₂×C₆₇	1	2	yes	complemented
459	#2709	C₂×C₆₇	1	2	yes	complemented
460	#2706	C₂×C₆₇	1	2	yes	complemented
461	#2700	C₂×C₆₇	1	2	yes	complemented
462	#2696	C₂×C₆₇	1	2	yes	complemented
463	#2653	C₂×C₆₇	1	2	yes	complemented
464	#2607	C₂×C₆₇	1	1	yes	characteristic, complemented
465	#2591	C₂×C₆₇	1	1	yes	characteristic, complemented
466	#2576	C₂×C₆₇	1	2	yes	complemented
467	#2477	C₂×C₆₇	1	2	yes	complemented
468	#2431	C₂×C₆₇	1	1	yes	characteristic
469	#2406	C₂×C₆₇	1	1	yes	characteristic, complemented
470	#2333	C₂×C₆₇	1	1	yes	characteristic, complemented
471	#2313	C₂×C₆₇	1	1	yes	characteristic, complemented
472	#2297	C₂×C₆₇	1	1	yes	characteristic, complemented
473	C₆₇	#36821	1	1	yes	characteristic, direct product factor, Sylow
474	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
475	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
476	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
477	C₂×#123	C₂²×C₆₇	1	2	yes	—
478	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
479	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
480	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
481	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
482	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
483	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
484	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
485	#401	C₂²×C₆₇	1	2	yes	—
486	#401	C₂²×C₆₇	1	2	yes	—
487	#400	C₂²×C₆₇	1	2	yes	—
488	#400	C₂²×C₆₇	1	2	yes	—
489	#399	C₂²×C₆₇	1	2	yes	—
490	#398	C₂²×C₆₇	1	2	yes	—
491	#397	C₂²×C₆₇	1	2	yes	—
492	#397	C₂²×C₆₇	1	2	yes	—
493	#397	C₂²×C₆₇	1	2	yes	—
494	#397	C₂²×C₆₇	1	2	yes	—
495	#396	C₂²×C₆₇	1	2	yes	—
496	#395	C₂²×C₆₇	1	2	yes	—
497	#394	C₂²×C₆₇	1	2	yes	—
498	#394	C₂²×C₆₇	1	2	yes	—
499	#394	C₂²×C₆₇	1	2	yes	—
500	#394	C₂²×C₆₇	1	2	yes	—
501	#394	C₂²×C₆₇	1	2	yes	—
502	#394	C₂²×C₆₇	1	2	yes	—
503	#393	C₂²×C₆₇	1	2	yes	—
504	#393	C₂²×C₆₇	1	2	yes	—
505	#393	C₂²×C₆₇	1	2	yes	—
506	#393	C₂²×C₆₇	1	2	yes	—
507	#392	C₂²×C₆₇	1	2	yes	—
508	#392	C₂²×C₆₇	1	2	yes	—
509	#391	C₂²×C₆₇	1	2	yes	—
510	#391	C₂²×C₆₇	1	2	yes	—
511	#391	C₂²×C₆₇	1	1	yes	characteristic
512	#391	C₂²×C₆₇	1	2	yes	—
513	#390	C₂²×C₆₇	1	2	yes	—
514	#390	C₂²×C₆₇	1	1	yes	characteristic
515	#390	C₂²×C₆₇	1	2	yes	—
516	#388	C₂²×C₆₇	1	2	yes	—
517	#388	C₂²×C₆₇	1	2	yes	—
518	#388	C₂²×C₆₇	1	2	yes	—
519	#388	C₂²×C₆₇	1	2	yes	—
520	#388	C₂²×C₆₇	1	2	yes	—
521	#388	C₂²×C₆₇	1	2	yes	—
522	#388	C₂²×C₆₇	1	2	yes	—
523	#387	C₂²×C₆₇	1	2	yes	—
524	#387	C₂²×C₆₇	1	2	yes	—
525	#387	C₂²×C₆₇	1	2	yes	—
526	#387	C₂²×C₆₇	1	2	yes	—
527	#387	C₂²×C₆₇	1	2	yes	—
528	#387	C₂²×C₆₇	1	2	yes	—
529	#387	C₂²×C₆₇	1	2	yes	—
530	#387	C₂²×C₆₇	1	2	yes	—
531	#387	C₂²×C₆₇	1	2	yes	—
532	#387	C₂²×C₆₇	1	2	yes	—
533	#386	C₂²×C₆₇	1	2	yes	—
534	#386	C₂²×C₆₇	1	2	yes	—
535	#386	C₂²×C₆₇	1	2	yes	—
536	#386	C₂²×C₆₇	1	2	yes	—
537	#386	C₂²×C₆₇	1	2	yes	—
538	#386	C₂²×C₆₇	1	2	yes	—
539	#386	C₂²×C₆₇	1	2	yes	—
540	#386	C₂²×C₆₇	1	2	yes	—
541	#386	C₂²×C₆₇	1	1	yes	characteristic
542	#386	C₂²×C₆₇	1	1	yes	characteristic
543	#386	C₂²×C₆₇	1	2	yes	—
544	#386	C₂²×C₆₇	1	2	yes	—
545	#386	C₂²×C₆₇	1	2	yes	—
546	#385	C₂²×C₆₇	1	2	yes	—
547	#385	C₂²×C₆₇	1	2	yes	—
548	#385	C₂²×C₆₇	1	2	yes	—
549	#382	C₂²×C₆₇	1	2	yes	—
550	#381	C₂²×C₆₇	1	2	yes	—
551	#381	C₂²×C₆₇	1	2	yes	—
552	#381	C₂²×C₆₇	1	1	yes	characteristic
553	#381	C₂²×C₆₇	1	2	yes	—
554	#380	C₂²×C₆₇	1	2	yes	—
555	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
556	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
557	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
558	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
559	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
560	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
561	C₂×#41	—	2	4	no	—
562	C₂×#41	—	4	2	no	—
563	C₂×#41	—	4	2	no	—
564	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
566	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
571	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
572	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
573	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
577	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
579	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
580	#127	—	4	2	no	—
581	#124	—	4	2	no	—
582	#123	—	4	2	no	—
583	#123	—	4	4	no	—
584	#123	—	4	2	no	—
585	C₂²⋊Q₈	—	4	4	no	—
586	#121	—	2	4	no	—
587	#117	—	4	2	no	—
588	C₂×C₄⋊C₄	—	2	4	no	—
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
625	C₂×C₄²	—	4	2	no	—
626	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
634	#95	C₂³×C₆₇	1	2	yes	—
635	#95	C₂³×C₆₇	1	2	yes	—
636	#95	C₂³×C₆₇	1	2	yes	—
637	#95	C₂³×C₆₇	1	2	yes	—
638	#95	C₂³×C₆₇	1	2	yes	—
639	#95	C₂³×C₆₇	1	2	yes	—
640	#95	C₂³×C₆₇	1	2	yes	—
641	#95	C₂³×C₆₇	1	2	yes	—
642	#95	C₂³×C₆₇	1	2	yes	—
643	#95	C₂³×C₆₇	1	2	yes	—
644	#95	C₂³×C₆₇	1	2	yes	—
645	#95	C₂³×C₆₇	1	2	yes	—
646	#95	C₂³×C₆₇	1	2	yes	—
647	#95	C₂³×C₆₇	1	2	yes	—
648	#95	C₂³×C₆₇	1	2	yes	—
649	#95	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	2	yes	—
651	#95	C₂³×C₆₇	1	2	yes	—
652	#95	C₂³×C₆₇	1	2	yes	—
653	#95	C₂³×C₆₇	1	2	yes	—
654	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	2	yes	—
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	2	yes	—
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	2	yes	—
661	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
662	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
663	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
664	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
665	#41	—	4	16	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	4	1	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×Q₈	—	4	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	4	1	no	—
682	C₂×D₄	—	4	1	no	—
683	C₂×D₄	—	4	1	no	—
684	C₂×D₄	—	4	1	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	4	1	no	—
701	C₂²×C₄	—	4	1	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	1	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	#41×C₆₇	1	4	yes	—
713	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	1	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	1	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₄²	—	4	1	no	—
765	C₄²	—	4	1	no	—
766	C₄²	—	4	2	no	—
767	C₄²	—	4	1	no	—
768	C₄²	—	4	1	no	—
769	C₄²	—	4	1	no	—
770	C₄²	—	4	1	no	—
771	C₄²	—	4	2	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	C₂×#41×C₆₇	1	2	yes	—
793	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
794	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
795	Q₈	—	4	4	no	—
796	Q₈	—	8	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	4	no	—
800	D₄	—	8	2	no	—
801	D₄	—	8	4	no	—
802	D₄	—	8	4	no	—
803	D₄	—	8	4	no	—
804	C₂×C₄	—	2	8	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	8	2	no	—
852	C₂×C₄	—	8	4	no	—
853	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
854	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
855	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
856	C₂²	—	2	4	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	1	no	—
878	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
879	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
880	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
881	C₂²	#585×C₆₇	1	2	yes	—
882	C₂²	#585×C₆₇	1	2	yes	—
883	C₄	—	2	2	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₂	—	4	2	no	—
899	C₂	—	4	2	no	—
900	C₂	—	8	2	no	—
901	C₂	—	8	1	no	—
902	C₂	C₆₇×#3455	1	1	yes	characteristic
903	C₂	C₆₇×#3490	1	1	yes	characteristic
904	C₂	C₆₇×#3510	1	1	yes	characteristic
905	C₂	C₆₇×#3533	1	2	yes	—
906	C₂	C₆₇×#3562	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2431	C₂
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×#2853	C₂	semidirect
2. C₆₇×#2789	C₂	semidirect
3. C₆₇×#2760	C₂	semidirect
4. C₆₇×#2752	C₂	semidirect
5. C₆₇×#2751	C₂	semidirect
6. C₆₇×#2709	C₂	semidirect
7. C₆₇×#2706	C₂	semidirect
8. C₆₇×#2700	C₂	semidirect
9. C₆₇×#2696	C₂	semidirect
10. C₆₇×#2653	C₂	semidirect
11. C₆₇×#2607	C₂	semidirect
12. C₆₇×#2591	C₂	semidirect
13. C₆₇×#2576	C₂	semidirect
14. C₆₇×#2477	C₂	semidirect
16. C₆₇×#2406	C₂	semidirect
17. C₆₇×#2333	C₂	semidirect
18. C₆₇×#2313	C₂	semidirect
19. C₆₇×#2297	C₂	semidirect
444. #36821	C₆₇	direct (N × H)
454. #2853	C₂×C₆₇	semidirect
455. #2789	C₂×C₆₇	semidirect
456. #2760	C₂×C₆₇	semidirect
457. #2752	C₂×C₆₇	semidirect
458. #2751	C₂×C₆₇	semidirect
459. #2709	C₂×C₆₇	semidirect
460. #2706	C₂×C₆₇	semidirect
461. #2700	C₂×C₆₇	semidirect
462. #2696	C₂×C₆₇	semidirect
463. #2653	C₂×C₆₇	semidirect
464. #2607	C₂×C₆₇	semidirect
465. #2591	C₂×C₆₇	semidirect
466. #2576	C₂×C₆₇	semidirect
467. #2477	C₂×C₆₇	semidirect
469. #2406	C₂×C₆₇	semidirect
470. #2333	C₂×C₆₇	semidirect
471. #2313	C₂×C₆₇	semidirect
472. #2297	C₂×C₆₇	semidirect
473. C₆₇	#36821	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2853	2
C₆₇×#2789	2
C₆₇×#2760	2
C₆₇×#2752	2
C₆₇×#2751	2
C₆₇×#2709	2
C₆₇×#2706	2
C₆₇×#2700	2
C₆₇×#2696	2
C₆₇×#2653	2
C₆₇×#2607	2
C₆₇×#2591	2
C₆₇×#2576	2
C₆₇×#2477	2
C₆₇×#2431	2
C₆₇×#2406	2
C₆₇×#2333	2
C₆₇×#2313	2
C₆₇×#2297	2
#36821	67

Subgroups — C67×#36821 #30716072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#36821 #30716072